lasers: the power and precision of light

Jean-Claude Diels bull Ladan Arissian

LasersLasersLasersThe Power and Precision of Light

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Dateianlage
9783527640058jpg

Jean-Claude Diels and Ladan ArissianLasers

Related Titles

Paschotta REncyclopedia of Laser Physics and Technology2008ISBN 978-3-527-40828-3

Hecht JUnderstanding LasersAn Entry-Level Guide2008ISBN 978-0-470-08890-6

Smith F G King T A Wilkins DOptics and PhotonicsAn Introduction2007ISBN 978-0-470-01784-5

Meschede DOptics Light and LasersThe Practical Approach to Modern Aspectsof Photonics and Laser Physics2007ISBN 978-3-527-40628-9

Quimby R SPhotonics and LasersAn Introduction2006ISBN 978-0-471-71974-8

Jean-Claude Diels and Ladan Arissian

Lasers

The Power and Precision of Light

WILEY-VCH Verlag GmbH amp Co KGaA

The Authors

Prof Jean-Claude DielsUniversity of New MexicoDept of Physics amp Astronomy1919 Lomas BlvdAlbuquerque NM 87131USA

Dr Ladan ArissianUniversity of New MexicoDepartment of Electrical and ComputerEngineeringCenter for High Tech Materials1313 Goddard SEAlbuquerque NM 87106USA

Typesetting le-tex publishing servicesGmbH LeipzigPrinting and Binding Ebner amp SpiegelGmbH UlmCover Design Bluesea Design McLeeseLake Canada

All books published by Wiley-VCH arecarefully produced Nevertheless authorseditors and publisher do not warrant theinformation contained in these booksincluding this book to be free of errorsReaders are advised to keep in mind thatstatements data illustrations proceduraldetails or other items may inadvertently beinaccurate

Library of Congress Card No applied for

British Library Cataloguing-in-PublicationData A catalogue record for this book isavailable from the British Library

Bibliographic information published by theDeutsche NationalbibliothekThe Deutsche Nationalbibliothek lists thispublication in the Deutsche Nationalbib-liografie detailed bibliographic data areavailable on the Internet athttpdnbd-nbde

copy 2011 WILEY-VCH Verlag GmbH amp CoKGaA Boschstr 12 69469 WeinheimGermany

All rights reserved (including those of trans-lation into other languages) No part ofthis book may be reproduced in any formndash by photoprinting microfilm or any oth-er means ndash nor transmitted or translatedinto a machine language without writtenpermission from the publishers Registerednames trademarks etc used in this bookeven when not specifically marked as suchare not to be considered unprotected by law

Printed in the Federal Republic of GermanyPrinted on acid-free paper

ISBN Print 978-3-527-41039-2

ISBN ePDF 978-3-527-64005-8ISBN oBook 978-3-527-64003-4ISBN ePub 978-3-527-64004-1

To my mother Maryam and my daughter VidaLadan Arissian

To my daughter Natacha who taught me that music and lasers canlive in harmony and my wife Marlies for having patiently endured theclickety-clack of a keyboard as evening conversation

Jean-Claude Diels

V

Contents

Preface IXReferences XII

1 A Scenic Route through the Laser 111 The Meaning of raquoLaserlaquo 112 Radiation from an Atom 913 The Anatomy of a Laser 1514 Some Examples of Lasers 2015 Pulsed Lasers 3416 Properties of a Laser Beam 4117 How to Make the Shortest Laser Pulse 4518 Ultrashort Ultraintense Laser Pulses 6119 Ultrashort Ultraprecise Laser Pulses 66110 Ultrashort Ultrasensitive Laser Pulses 69111 The Nonlinear Wizard Juggling with Frequencies 70References 79

2 Laser Coherence at Home 8121 The Laser Printer 8122 The Laser Scanner 8323 The Laser in Data Storage 8724 Miscellaneous Applications 90

3 The Laser in Medicine 9331 Introduction 9332 The Laser in Dentistry 9433 The Laser and Vision 9634 Lasers and the Neural Network 10235 Lasers for the Skin and Cosmetics 10436 Lasers in Surgery 11037 Biostimulation Lasers for Ulcer Treatment 113

VII

38 Lasers in Diagnostics 11339 Ultrafast Peeking 125References 131

4 Lasers in Industry 13341 Laser Machining 13342 Laser CuttingDrilling 13443 Cutting the Forest 13644 Nanostructure with Lasers 137References 140

5 Laser Time Capsule 14151 Introduction 14152 Ultrashort Pulses in Microscopy 14253 Communication 14454 Frequency Combs 149References 158

6 Light in Matter 15961 Attosecond Science 16162 Lasers in Nuclear Physics and Accelerators 17063 Laser Cooling 177References 179

7 High Power Lasers (TazerTeaser) 18171 Filaments 18172 Laser-Induced Lightning 19173 Laser TazerndashTeaser 198References 199

8 Laser Sensors 20381 Passive Sensors 20382 Active Sensors 217References 224

9 Future Perspectives 227References 231

Index 232

Color Plates 237

VIII Contents

Preface

There is no need to convince anyone of the importance of lasers Thegrowth of this technology and its presence in our daily lives cannotbe overemphasized It can be felt as simply as flipping a switch likeusing a laser pointer or a scanner but there are times that its use ismysterious and glorified such as in the case of the laser gun StarWars and laser induced lightning The aim of this book is to provide abetter intuition about this technology and its applications We felt thatknowing about lasers should not be restricted to scientists and engi-neers in the field or to those who are direct users of lasers It can andhas to be shared with everybody We hope this book will inspire thereader to have meaningful dreams about the future of this technologyand its applications and to alleviate confusion and misuse of sciencein public media

We do not believe that science should be boring or be the prerog-ative of strange people with unbrushed hair big glasses and torn t-shirts Science is for everyonersquos benefit When a baby rolls a ball orthrows a stone shehe starts learning mechanics With a simple activ-ity a lot of intuition is established about mass velocity and gravity Thisis why even in a scientific community a common method to under-stand a subject is via mechanical analogies Any physics student hasa tough experience at hisher first exposure to quantum mechanicsonly a carefree baby can easily assimilate new concepts We thoughtthat a way to gain a better understanding about optics and in particu-lar about lasers is to discuss them in an informal way Some detailsare kept some are missed which is the nature of an imperfect work

Who cares about lasers Of course we do because they are at thecenter of our job and lives and we think that others should care aswell Lasers play an important role in the evolution of technology Awheel which is a symbol of the mechanical era served to move ob-jects around and facilitated transportation With mechanical technol-

IX

ogy came another leap in human power and mobility In scientificaspects it helped us understand the mechanics of the universe andplanetary motions in the sky In biology it gave a better picture of themechanics of motion and bone structure Then came the finer tech-nology of electricity enabling the transport of energy through electronsin wires Understanding electricity is not so straightforward and theexperience of an electric shock is not commonly sensed as a knife cut

Having had electricity around for more than a century we havegained some intuition about voltage and current although they arenot as clear concepts as speed and position At the start of the twen-tieth century quantum mechanics appeared and puzzled scientists fora long time It brought with it all new concepts but it was acceptedin the same manner as we have become used to talking to someoneover the phone or meeting a friend on a computer screen rather thanthe traditional face to face interaction We extend our experience andsenses with technology Just like the caveman who lived in bare naturemight not have known all the trees and bushes we may not know allthe scientific reasons and backgrounds of the technologies we have athand

There is a notion that after the mechanic and electric eras it is timefor a photonic era and that the laser is the greatest manifestation ofit The laser is not a stand alone subject it could not have been real-ized without fine machining precision optics and controlled electri-cal power It is a magnifying box for photons not by collecting photonsin one position like a lens but by putting them in phase in a stimu-lation process With the power of a laser we can mimic the sun ina laboratory tame electrons inside molecules and atoms tatoo a bio-logical cell have faster and more precise clocks and eventually guidelightning towards our mean neighborrsquos house

Chapter 1 is a scenic route to the laser It is an overview of the radi-ation of light the properties of the laser the different types of lasersproperties of the beams and of pulses the generation of ultrashortpulses ultra-high intensities and so on We have dropped many de-tails and concepts to make this chapter as short as possible Our puristcolleagues may not appreciate our shortcuts and analogies but thisbook is not intended for them We intentionally omitted naming anyof the great scientists who have contributed to the birth and growth ofthe laser Doing otherwise would have been an unfair selection amongthe tens of thousands of scientists who have been involved in mate-

X Preface

rializing the dream of creating and understanding laser sources andtheir applications

The rest of the book is organized in seven chapters to cover someindustrial medical military and scientific applications of the laserwith many important application having been left out in the interestof brevity The laser has surreptitiously entered so many aspects of ourlives that a comprehensive listing of all its uses may become as bor-ing as reading a dictionary The history of the discovery of the laserand anecdotes about ensuing competition in patent recognition hasalready been published [1ndash5] Instead we present an informal conver-sation about lasers rather than an explanation of their technical andscientific aspects which has been published by others [6]

In view of all the other contributions why did we dare to writethis book Because we thought that our raquocartoonlaquo approach to sci-ence is unique and might reach a different audience than existingtextbooks This book was started as a celebration of the 50th anniver-sary of the discovery of the laser For that occasion we intended tomake an overview of all the applications and how they relate to theexceptional properties of the laser

If you expect to have acquired a textbook please return this bookas fast as possible to the source Physics is very often explained withsimple analogies (which would make a rigorous mind cringe)

No self-respecting science book could be published without exhaus-tive references This is not a self-respecting science book If we had togive credit to all the scientists in the world who have contributed tothe field the content would dwarf the phone directory of New Yorkcity We have purposely omitted citing any names

This book was started on the initiative of Ladan Arissian a poetand physicist as you will clearly sense from the style of various chap-ters She has a broad educational background in various disciplinesof physics (nuclear condensed matter and optical science) In addi-tion to being a research physicist she dreams of being a teacher andstrives to present science in new ways

This book would not have been published if it had not been orna-mented with the name of Professor Jean-Claude Diels who was will-ing to sacrifice his reputation as a serious science writer of raquoultrafastlaser pulse phenomenalaquo [7] He has decades of experience in tweak-ing and building impossible lasers and trying to understand the effectof each optical component on the optical pulse He has never closed

Preface XI

the laser box and refused to reduce it to a rectangle in a diagram Heonly agreed to coauthor this book if he could insert his cartoons in thetext

Our enthusiasm about lasers and their applications is just a minutereflection of the work of men and women in science bearing all thefrustration and obstacles of conducting research We are in debt toall scientists engineers technicians and students whose persistenceand patience have introduced the laser in all fields of science as wellas in our daily lives

Albuquerque March 2011 Jean-Claude DielsLadan Arissian

References

1 Hecht J (2005) Beam The Race toMake the Laser Oxford UniversityPress New York

2 Hecht J (1992) Laser PioneersAcademic Press Boston

3 Taylor N (2000) Laser The Inventorthe Nobel Laureate and the Thirty-Year Patent War Simon amp SchusterNew York

4 Bertolloti M (2005) The Historyof the Laser Institute of PhysicsPublications Bristol Philadelphia

5 Townes CH (1999) How the LaserHappened Adventures of a ScientistOxford University Press New York

6 Hecht J (2008) UnderstandingLasers 3rd edn IEEE press JohnWiley amp Sons

7 Diels JC and Rudolph W (2006)Ultrashort Laser Pulse Phenomena2nd edn Elsevier Boston

XII Preface

1A Scenic Route through the Laser

11 The Meaning of raquoLaserlaquo

raquoLaserlaquo is one of the rare acronyms whose meaning has not beenlost over five decades It stands for Light Amplification by StimulatedEmission Radiation These words are not sufficient to clarify themeaning unless we have a picture associated to each of them inour mind The next few sections will be devoted to unraveling themeaning of each term

111 Light (Photon) is a Wave

The first letter raquoLlaquo tells us that raquolaserlaquo is raquolightlaquo Light is an oldknown entity originating from the sun and the moon Once it wasassociated with fire and thought to be the first essential element Inmodern language we say that light actually consists of photons justas matter is made of atoms Our intuitive picture of atoms is that theycan be nicely classified by their mass in a table ndash the Mendeleev tableAtoms themselves are boxes filled with electrons protons and neu-trons and there is a mass associated with each component

Atoms can combine to make molecules the ultimate componentwe expect to arrive at when grinding to its finest constituent any pieceof material from a live leaf to a piece of paper In a way moleculesand atoms are what we deal with on a daily basis but at such a finescale that it escapes our direct perception Photons are as ubiquitousbut quite different from atoms and their constituents Ubiquitous be-cause they are associated not only with visible light but also with in-visible radiation (infrared and ultraviolet) x-rays gamma rays radiowaves and even the radiation from our electrical network at 50 or60 Hz They are quite different because there is no mass associated to

Lasers The Power and Precision of Light First Edition Ladan Arissian and Jean-Claude Dielscopy 2011 WILEY-VCH Verlag GmbH amp Co KGaA Published 2011 by WILEY-VCH Verlag GmbH ampCo KGaA

1

the photon A wave is associated with the photon which is an oscilla-tion propagating at the speed of light

What is a wave There is always a pattern and motion associated tothe wave the ripples of a stone thrown in a pond or folds of a flagOne can imagine more and more examples that the word raquowavelaquo isapplied to As physicists we would like to pause and clarify some fea-tures of the wave with definitions that can be used to quantify similarobservations If you take a picture from the ripples on the pond yourealize that there are regular patterns that repeat in water and youcan possibly count the number of peaks on the water surface that areseparated by a raquowavelengthlaquo You can also only consider a fixed pointon the surface and monitor its motion as it goes up and down or os-cillates It takes a raquoperiodlaquo for each point on the pond to repeat itsposition The pattern on the wave (for example the peaks) have a cer-tain raquospeedlaquo or raquowave velocitylaquo and the peaks that are created by thewave have an raquoamplitudelaquo It is reasonable to conclude that strongerwaves have bigger amplitudes but there is more to the strength orenergy of a wave as we will see in the following sections

When a wave goes through a medium it does not mean that themedium is necessarily moving with it In the case of a flag waving inthe wind there is a wave that goes through the flag but the fabric it-self is not carried away The wave propagates for huge distances whileeach particle responsible for the wave motion stays at the same aver-age position just inducing the motion of the next particle In mostcases the wave starts from a local oscillation (Figure 11a) and propa-gates radially from there like rings produced by a duck paddling on apond (Figure 11b) In the case of light it is the electric field producedby a charge oscillating up and down that starts off the wave This iscalled dipole emission

The velocity of a wave is a property of the medium in which thewave propagates Sound waves propagate at 343 ms (1125 fts) in dryair at room temperature and faster in denser media The oppositeholds for light waves that usually travel faster in air or vacuum Thereare different types of waves Mechanical waves like spring oscillationsand sound waves are due to mechanical motion of particles The oscil-lation of these waves is along the propagation direction Light waveshowever are electromagnetic waves which originate from the oscilla-tion of charges (electrons for example) This was the first dilemma inearly attempts to interpret light waves what is moving

2 1 A Scenic Route through the Laser

Figure 11 (a) An oscillating electric fieldis created by a pair of charges with a pe-riodically varying distance (oscillatingdipole) This periodically varying field

creates an electromagnetic wave thatpropagates at the speed of light in vacu-um just as a wave is created in (b) by aduck paddling in a pond

Our intuition is shaped by the observation of water waves in apond an oscillating spring or the swing of a pendulum These areall mechanical waves Like sound waves they require a medium theyneed matter to exist Hence was born the notion of the raquoetherlaquo a(fictitious) medium to support the propagation of light waves To-day the raquoetherlaquo has simply given way to vacuum but it does notmean that the understanding of the nature of light has become sim-pler

As will be explained in Section 112 below quantum mechanicstells us that the amplitude of the positivendashnegative charge oscillationis restricted to discrete values Consequently the emitted oscillationalso takes discrete values to which is associated an energy the pho-ton energy hν where ν the frequency of the oscillation and h is calledthe raquoPlanck constantlaquo (see Eq (11) in the next section) It is as if theduckling in Figure 11a had discrete gears to activate his webbed pawsWhat is more puzzling is that the raquoneutrallaquo gear is missing The mini-mum energy state of the quantum harmonic oscillator is not zero but(12)hν This is often referred to as vacuum fluctuation or zero pointenergy The absence of vacuum (the ether concept) has been replacedby an absence of zero energy Since according to Einstein there isan equivalence of matter and energy the two concepts are not so farapart

11 The Meaning of raquoLaserlaquo 3

112 Photon Energy

Quantum mechanics tells us that a photon has dual characteristicsit acts both as a wave (Section 111) and as a particle In a way thephoton is a wave that can be counted This might be a bit hard todigest since our common sense is restricted to our daily experiencewith objects that are not so delicate What do we mean by acting like aparticle They can be counted A photon is like a raquocurrencylaquo and thelight that we experience is like a sum of money we never notice thattiny penny

Let us take a closer look and see why we generally ignore singlephotons A typical red laser pointer has an output power of 3 mW(3 mJs) which consists of individual photons having an energy ofthe order of 3 1019 J This means that every second there are 10 000million million photons shooting out of a pointer If we associate evena penny to each photon in a second we get a sum of money that ismore than the wealth of a country

Just as not all currencies have the same value photons have differ-ent energies Here we need to use the wave aspect of the photon Thefaster a wave oscillates the more energy it possesses

The longest (slower) electromagnetic wave that we encounter in ourdaily life is created by the 50 Hz electrical network covering the globeAs a result the earth radiates making one oscillation over a distanceof 6000 km Radio waves are long too it takes 3 m (33 yd) for a shortwave (FM radio) to make an oscillation For a long wave (AM) it takesabout 300 m (330 yd) to complete one

The visible light that we are used to also oscillates but much fasterThe green visible light consists of photons of 500 nm wavelengthmeaning that over a thickness of a sheet of paper (which is 01 mmor 0004 of an inch) it makes 200 oscillations An x-ray with a wave-length of about 1 nm oscillates 100 000 times over the same lengthIt thus appears that the following connection exists photons that os-cillate faster have a shorter wavelength and more energy Or in thesimplified language of mathematics

E D hν D hcλ

(11)

where raquoElaquo stands for energy raquohlaquo is the physical Planckrsquos constantraquoclaquo is the speed of light raquoνlaquo is the number of oscillations of a pho-


Figure 12 Different objects that radiate electromagnetic waves and the wavelength andelementary energy associated with them Please find a color version of this figure on thecolor plates

ton in a second and raquoλlaquo is the wavelength or the length in which asingle oscillation takes place For the photon associated with visibleradiation the elementary photon energy is too small to use the tradi-tional energy unit of Joule Instead the energy unit used by physicistsis the electronvolt (eV) 1 eV (1602 1019 J) is the energy acquiredby an electron that is accelerated under the potential difference of 1 VInfrared radiation at a wavelength of 124 μm has exactly the energyof 1 eV As shown in Figure 12 our earth due to the electric powernetwork radiates photons of 2067 1013 eV energy

113 Energy and Size

Could raquoSpidermanlaquo really have the strength of a spider scaled upto his size Is a cat that is 100 times more massive than a mouse 100times stronger In biology things will not scale linearly Body massincreases linearly with volume in three dimensions while musclestrength in arms and legs is proportional to cross-sections and there-fore increases only in two dimensions If a human is a million timesmore massive than an ant he is only 10 000 times stronger In a waysmaller animals are stronger relative to their masses Physics scales ina simpler way than biology In a musical instrument higher frequen-cies are generated by shorter strings thus have more energy Somephysicists like to draw a box around the object that they study andthey know that as the box gets smaller they are dealing with higher


Figure 13 Particle and wave in a boxthe longer wavelength fits in the largerbox (a) A shorter wavelength fits in thesmaller box (b) corresponding also to alarger particle energy Electrons (c) orbit-ing around the nucleus are analogous tonested Russian dolls (d) A photon of suf-ficient energy can knock off the electron of

the outer shell as one can easily removethe outer layer of the nested dolls Moreproblematic is the removal of an innershell electron While it would be an unre-solvable raquoChinese puzzlelaquo to remove theinner doll the possibility to eject an in-ner shell electron exists with high energyphotons

and higher energies The speed and energy of the electrons oscillat-ing in an atom are much bigger than the ones traveling in a long wireloop

Using our wave picture and the equation of photon energy (11)we can look more closely at the sizendashenergy relation Consider fittingone full wave into two different size boxes The wave that fits in thesmaller box (Figure 13b) has a shorter wavelength than the one inthe bigger box (Figure 13a) Using the photon energy equation (11)the wave with a smaller wavelength has higher energy It seems thatthe more confined the wave the stronger its elementary energy Thisseems like an oppression force Quantum mechanics tells us that theelectrons around an atom are confined to well defined shells or elec-tron levels like Russian nesting dolls (Figure 13c d) The electronsin bigger shells have less energy and are loosely bound which is whyin most ionization processes the chance of knocking off an electronfrom an outer shell is the highest This order is not as rigid as the or-der of taking out the Russian dolls when dealing with higher energiesphotons it is possible to scoop up the electron from an internal shellleaving the external ones in place (not something you could to withthe Russian dolls)

Looking at the waves in boxes we only concentrated on the con-cepts of size energy and wavelength There are other parallel mani-festations of waves such as in time and frequency This means that


in smaller boxes we are dealing with shorter time scales and fasterfrequencies This is a very important fact for observing phenomenain nature we need the proper time scale to watch an event The speedthat we take our data or snapshots of an event tells us what we canrecord and what we would miss Imagine that we could only under-stand one word per minute It would then be very difficult to get themeaning of sentences in a normal conversation In cinematography24 frames per second is sufficient to capture most daily events butif we want to see faster events like a bullet passing through a targetwe need to take more frames per second and then play it at a normal24 frame per second rate In Figure 12 the time scale of some eventsare shown From this diagram one can see that in order to observeelectron motion in atoms and molecules one should have a camerathat takes picture every femtosecond It is hard to imagine how fast afemtosecond is If one could read the first Harry Potter book with 27million words at the rate of one word per femtosecond the whole bookwould be finished in a few nanosecond Or in other words you couldread Harry Potter a thousand million times in just 1 s An attosecondis to the second as a second is to the age of the Universe (041018 s)Figure 12 illustrates the various sources of radiation that affect ourlives and how they are associated with energy size and time

1131 Light EnergyIn the previous sections we talked about the energy of an individu-

al photon but only in a very sophisticated laboratory can one isolatea single photon What we are exposed to usually consists of a largenumber of these photons One can look at a light source as the wealthof a country and a photon as its currency unit There is no countrywith a total wealth of only one unit of currency For example when wetalk about wealth and debt of the United States of America the num-bers are in trillions and it is quite easy not to mention a cent or twoThat tiny cent which is the unit of currency is like a single photon Itexists but is always lost in the total sum just like a photon in a lightsource

However the analogy between currency and light stumbles at laserlight In our daily lives and economics there is only one way to addnumbers Luckily in science there are more Let us assume not oneduck as in Figure 11b but two paddling in synchronism as if com-peting in synchronized swimming Along certain directions the wave


will add raquoin phaselaquo along other directions they will cancel each otheror raquointerfere destructivelylaquo In the analogy of the coins a large num-ber N of photons of the same frequency will add up to N coins for atotal optical energy of N hν This is how daily white light of incoherentlight adds up In the case of laser light or coherent light N properlypositioned and synchronized photons will produce a beam of N2hνThe reason is simple it is the electric field of the waves that adds upcoherently which means overlapping the oscillations in phase (crestto crest and trough to trough) The total electric field is the sum of theelectric field of each source element However the total intensity of thebeam is proportional to the square of the total field and is thus propor-tional to the square of the number of emitters When the waves arepiled up randomly (incoherently) the phases do not match and onlyintensities are added linearly Incoherent light is a crude summationover waves it just adds the average intensity values and misses thephases This property is being exploited by the US Air Force to createvery high power lasers by adding the beams of an array of fiber lasers

One example of coherence can be found in the stock market Ifwe knew how to add coherently the phase fluctuations of the marketthere would be no limit to our profit It would take a financial wizardto buy stocks in a proper phase (exactly when they are at the lowest)and sell at the highest (peak) Such great wisdom is what fell uponphysicists when they invented the laser they found a way to add thephotons coherently stacking the waves on top of each other with equalphases

How do we explain explain that incoherent raquowhite lightlaquo adds upproportionally to the number of emitters N rather than N2 A similaraddition takes place in daily life at least for some of us Suppose thatafter having celebrated his graduation with numerous drinks yourinebriated friend starts heading for home after hugging his favoritelamp post for the last time The analogy of the photon field is his stepThe total field is represented by the total distance from the lamp postto the end of the last step How far will he have moved away fromhis starting point after N D 100 steps The answer is a distance of10 steps away from the lamp post or

pN ft If he had been sober he

would have moved 100 steps (N) straight towards his destination In-coherent light fields add as incoherently as the steps of the drunkardthe sum of N elementary fields E of random direction adds up to a to-tal field of magnitude

pN E An intensity I proportional to the square


of the field is associated to each field E The total intensity in the in-coherent sum is (

pN )2 I D N I In the case of laser light or coherent

light the elementary fields line up resulting in a total field N E and atotal intensity Itotal D N2 I

12 Radiation from an Atom

So far we have talked about photons as units of light energy thatcan be counted They are not rigid they act and move like waves Nowwe want to know where they come from and how we can make themIn the following sections we learn how to add them properly (coher-ently) in a laser source Photons are electromagnetic waves which aregenerated when charges oscillate It is natural to turn our attention toatoms and molecules where there are as many electrons as the atomicnumber Quantum mechanics tells us that not all the areas aroundthe nucleus have the same chance of having electrons electrons arestacked in shells just like the layers of Russian dolls In the quantummechanics world matter acts like waves which means that it is hardto point at them as they are moving around Electrons move aroundthe atom nucleus in well defined shells There are steps of energy andan electron can absorb a photon to change its energy status from oneshell to another Nothing gets lost in nature if an electron goes froma lower energy shell to a higher energy one it must have absorbedthe energy difference This is reversible if an electron moves from ahigher energy to a lower energy state it must release the energy dif-ference That energy difference can be given entirely to a photon withan energy that satisfies the energy difference

Just like the Brownian motion of particles there is always fluctua-tions and excitements in the universe even in very remote places farfrom all galaxies The electrons are just like children playing on slidesin a playground as illustrated in Figure 14 Here there are also clearenergy levels a lower energy on the ground and a higher energy upthe slide The children here use their muscle energy to go up the slideand they enjoy the release of energy when they slide down This issimilar to what happens around us in all atoms The electrons canpick up energy from photons around us or even from thermal ener-gy to climb the ladder and jump back down That is how photons areabsorbed and created

12 Radiation from an Atom 9

Figure 14 (a) A schematic of energy lev-els of an electron in an atom (b) Childrenriding on slides an analogy of electronsmoving from one energy state to theother We just have to imagine that the

sound momentum and the joy of slidingdown is the released photon energy Inthe absence of coordination this radia-tion is random or raquospontaneouslaquo

The change in energy levels resulting in photon release is called raquora-diationlaquo This random radiation is everywhere and is raquoincoherentlaquoMore than 40 years ahead of the realization of lasers Albert Einsteinformulated two types of radiation raquospontaneouslaquo and raquostimulatedlaquoSpontaneous emission like it sounds is just the release of energyfrom higher to lower states without any coordination just like thechildren in the playground of Figure 14 If the game is converted toa match by adding a referee on the ground giving the raquostartlaquo signalthe motion of the children will be different They will all wait at thetop of the slide and start sliding at the gunshot Here the radiation isstimulated Another example of the comparison between stimulatedand spontaneous emission can be found in shopping Let us considera number of people in the mall who are there with the intention ofbuying clothes and have the money in hand They are all excited justlike our electrons in the upper state ready to emit If there is a nice ad-vertisement or a well dressed person walking by our shoppers followthe signs and buy the same thing as they are being stimulated to Thestimulating advertisement or person puts their intentions in phaseinciting shoppers to walk in the same direction and simultaneouslybuy the same item They are as hypnotized

In the case of the emission from electrons in the excited statesa photon with similar energy difference in the vicinity of the atomcauses the stimulated emission One photon passing by one excitedatom will stimulate the emission of another photon Before the eventthere was one photon and one excited atom After the photon flewby the atom energy has been reduced by the photon energy and two


identical photons are pursuing their course The total energy of atomC radiation is the same before and after the interaction

Having many atoms with electrons in the excited state we need justa few passing by photons to make a cascade of photons with the sameenergy radiating at the same time so well in phase These photons al-so follow the path of the inciting photon and have the same directionThey have the same polarization a concept that will be introduced inthe following section

121 Absorption and Dispersion

An electron can absorb a photon (or multiple photons in a nonlin-ear interaction) and move from one energy level to a higher level itcan also emit a photon and go to a lower level The former is called ab-sorption and the latter is associated to gain The first one is like upgrad-ing living standards by moving to a better house and putting down asum of money the second one is downgrading housing and releas-ing a sum of money for other causes The house price is a fixed valueand transition is only made when the money on the offer letter is pro-vided In the world of quantum mechanics there is no fixed numberand everything is described with probabilities If the light frequencymatches the separation the transition is more probable than when thefrequency is off but still even if the frequency is off the transition inpossible The lines are not so sharp in quantum mechanics and thereis always a shadow around them

As seen in Figure 15 the absorption (which is the opposite of thegain) maximizes for the characteristic frequency raquoν0laquo The absorp-tion is not a delta function and has a characteristic absorption width inwhich the absorption is appreciated Usually the absorption width isthe range of frequencies over which the absorption is above half of itsmaximum value In electromagnetism the permittivity raquolaquo is the resis-tance of the material to the light propagation or how much it permitsthe light to go through It is directly related to the electric susceptibilityraquolaquo which defines how easily the material is polarized by the electricfield

Absorption and index of refraction are two aspects of the complexfunction of light permittivity the former being the imaginary partand the latter the real part They are related mathematically throughKramersndashKroumlnig relations Using these relations the index of refrac-


Figure 15 Absorption and index of re-fraction as a function of frequency ν Theabsorption is maximized for the charac-teristic frequency ν0 Any gain or absorp-tion structure in the medium will effect

the speed of light as seen in the figurethe light slows down for the frequenciesless than the resonance and speeds up forthe frequencies that are greater

tion at a particular frequency can be calculated if the absorption at allfrequencies is known and vice versa1) The physical reason for thismathematical relation is raquocausalitylaquo the fact that the material has aresponse time to the electric field The response comes after applyingthe field The speed of light raquocnlaquo is directly related to the index ofrefraction raquonlaquo No wonder the index of refraction curve in Figure 15is known as the raquodispersionlaquo curve the speed of light is lower for lowfrequencies and higher for frequencies higher than ν0 A pulse cov-ering all frequencies will be negatively chirped with the frequency ofthe optical oscillation decreasing with time

122 Polarization of Light

Polarization of light refers to the direction and path of the electro-magnetic wave as it propagates This property needs to be visualizedin three dimensions As for single photons there is only one path forthe wave a circular path or raquocircular polarizationlaquo A circular polar-ization propagates just like following the grooves of a screw with onedifference most screws are tightened in a clockwise direction Theyhave only one helicity A single photon has an equal chance of hav-ing either choices of helicity Using the image of a screw there are asmany raquoleft threadedlaquo as raquoright threadedlaquo screws A ray of light con-

1) The opposite case which is deriving the absorption from the measurement of theindex of refraction at all frequencies is mathematically possible but rarely practicedin reality


sists of many such photons By combining an equal number of pho-tons with different helicity in phase one can get a linearly polarizedlight A linear polarized light is a wave that oscillates perpendicularto the propagation direction and it can be visualized in two dimen-sions

123 Beam Divergence and Resolution Criterion

Diffraction is a well known phenomenon in optics When a wavepasses through an aperture comparable to its wavelength it gets dis-torted When a bullet gets through a hole comparable to its size itscratches the walls For waves the distortion is imprinted on the pat-tern as can be seen with water waves on a pond hitting a small obsta-cle The reason for this distortion is wave addition or interferenceThe waves are generated at each point of the aperture Looking atthe two selected points at the edge of the aperture and at the cen-ter we can add the wave amplitude coming from these two pointson the observation screen Since a wave completely changes its signat half of its wavelength if the difference in the path from the twobeams is λ2 there will be a shadow on a distant point on whichthe light transmitted by the aperture projected The same differenceis observed as we slide the two chosen points across the openingThey all result in the same path difference on a selected point on thescreen

Diffraction of a beam through an aperture is illustrated in Fig-ure 16 The wave going through a circular opening is distorted Theblack and white stripes of the beam are successive wavefronts spacedby the wavelength Being illuminated by a plane wave all the pointsin the plane of the aperture are in the same phase of the oscillation(represented by the bright segment) As the wave from each point onthe aperture propagates through different paths to the end screeneach one is in a different phase of its oscillation The combination ofall these rays taking into account their interference has an intensitydistribution indicated by the red curve This distribution depends onthe shape and size of the hole that the wave has traversed One caneven follow the gray line that corresponds to the darkness on the rightscreen The blue ray indicates a line corresponding to the first darkring on the screen


Figure 16 (a) Diffraction of a beamthrough an aperture The path differencevaries across the screen showing moreintensities where peaks from waves ofdifferent parts of the opening coincideand darker regions where peaks and valleycoincide on the screen This results in animage (red pattern) of the aperture that isnot so clear (b) It is shown how far twopoints can be from each other in order tobe distinguished In order to resolve two

images the raquoRayleigh criterionlaquo definesthe distance between the two points to besuch that the first minimum ring overlapsthe central maximum of the other image(case II) If the distance between the twopoints is larger (case I) the images arebetter resolved while if the distance issmaller (case III) the resolution is lostPlease find a color version of this figureon the color plates

For a plane wave2) beam incident on a circular aperture as shown inFigure 16 the angular observation of the dark rings on the screen fol-lows the equation D sin(θn ) D nλ where n D 1 2 3 is an integerraquoDlaquo is the size of the hole and θ the angle of minimum brightnessobserved on the screen For the first darkness raquonlaquo is 1

A hole on the wave path is like a source emitting light through itsextension just like anything we want to observe by direct radiationor reflection How close objects can be resolved is a major concernin all imaging techniques from observing the stars to looking at tinyparticles with a microscope The resolution limit in imaging is calledthe Rayleigh criterion which corresponds to having a minimum ofone diffraction pattern overlap the maximum of the other one (II inFigure 16b) If the objects are closer (III in Figure 16b) the two peakswill merge making it difficult to determine whether there are twoobjects It is like having two people talking simultaneously If thereis a small delay between two words coming from the two personswe might have a chance to catch the beginning of a one word and the

2) The plane wave is the simplest of all wave structures in space It is an infinitesinusoidal wave with no transverse structure It is represented as vertical positiveand negative stripes when the beam moves horizontally


ending of the other one and record the two However when they speakwithin fractions of the second it is not easy to distinguish both wordsclearly

In imaging with lenses from two objects the Rayleigh criteri-on requires the distance between the two objects to be greater than06λNA NA stands for numerical aperture For imaging with a lensNA D f D where raquoflaquo is the focal length and raquoDlaquo is the diameter ofthe lens Here the diameter of the lens corresponds to the hole size inthe diffraction image The Rayleigh criterion is a convenient conceptused for any imaging technique from astronomy to microscopy

13 The Anatomy of a Laser

Despite the simplicity of its acronym (Light Amplification byStimulated Emission Radiation) the laser is more than just an opticalamplifier In general it has three main components some raquopumplaquomechanism to excite the radiation in a medium with optical raquogainlaquoand a raquoresonatorlaquo responsible for selecting the laser wavelength Theraquopumplaquo power can be electrical like a battery in a laser diode or itcan be another optical source Its purpose is to excite the radiationThe raquogainlaquo medium can be a solid crystal or gas prepared well tobe excited and emit photons We can use the photons radiated by thegain medium to induce raquostimulated emissionlaquo by sending them backthrough the gain medium provided it is still prepared in its excitedstate by the raquopumplaquo A feedback mechanism is thus needed to returnthe waves in phase to the gain medium This feedback is providedby a resonator usually called the raquolaser cavitylaquo This resonator is notmentioned in the acronym despite its essential role in the generationof laser light There are some high gain pulsed lasers ndash such as thenitrogen laser or some excimer lasers where the resonator is limitedto one or no mirror Because of the high gain raquolasinglaquo occurs throughthe amplification of the spontaneous emission along the axis of thegain medium

131 The Pump

The pump is the power plant for the laser and can take many differ-ent forms It can be a source of incoherent light like in many pulsed

13 The Anatomy of a Laser 15

solid state lasers it can be electrical like in gas discharge lasers or insemiconductor lasers it can be chemical energy which is often thecase in very high power infrared lasers used by the military or it caneven be another laser which is the case for many crystal solid statelasers (the titanium sapphire laser for instance) and dye lasers It isoften the pump that determines how efficient a laser system will beThere is a tremendous range of variation in the raquowall plug efficiencylaquoof laser systems In a Tisapphire laser pumped by an argon laser theargon laser will require over 30 kW of electrical power to finally pro-duce a Tisapphire laser beam of some 100 mW power At the otherextreme are the CO2 laser and semiconductor lasers where the lightoutput power is a sizable fraction of the electrical power input

132 Gain

At the heart of a laser is a medium that has optical gain It consistsof an assembly of atoms or molecules that are in an excited energystate In the analogy of the slides (see Figure 14) there are more chil-dren at the top than at the bottom of the slide As a light pulse contain-ing n photons3) passes through such an excited medium each photonwill induce a certain number of stimulated emissions resulting in anexponential increase of the number of photons with distance (in themedium) This is the reverse of the process of absorption where theatoms are initially in the nonexcited state (raquoground statelaquo) and eachphoton will induce a certain number of upward transitions resultingin an exponential decrease of the number of photons

The higher the little girls stay on top of the slides before jumpingthe more will be up on average This is how a raquopopulation inversionlaquonecessary to achieve gain is created In laser jargon an atom likelyto be a good candidate as laser gain medium is one where the upperlevel of the transition has a long lifetime After each jump the littlechild must quickly move away from the bottom of the slide or therewill be a traffic jam Similarly an essential condition for an efficientlaser gain medium is that the lower energy state of the transition hasa very short lifetime

There is a process described in the next section by which atoms areput in the upper state the raquopumplaquo Given a constant rate of excita-

3) An optical pulse of a given energy in joules4) An optical beam of a given power in jouless or watts


tion into the upper state in a continuous laser n photonss4) pass-ing through that medium will induce a certain number of stimulatedemissions resulting in an exponential increase of the photon flux (orbeam power) with distance

133 The Laser Body (Resonator)

Musical instruments are designed based on the fact that the sizeand geometry of the instrument defines what frequencies can be res-onated in it (Section 113) However it took a long time to apply thisfact and combine it with all other elements to make a laser

The analogy that we want to draw from in this section is that ofan acoustic amplifier between microphone and speaker when the mi-crophone is put too close to the speaker We have all heard the highpitched noise that drowns any other sound when the gain of the ampli-fier is turned up Noise from the speaker enters the microphone getsamplified is blasted from the speaker into the microphone again andso on It is a case of a dog chasing its tail

The same synergy exists between the optical gain medium and theoptical resonator as between the oscillating amplifier and a musicalresonance between microphone and speaker The laser is a similararrangement an optical ndash rather than acoustic ndash amplifier where theoutput (ie the speaker) is fed back to the raquoinputlaquo In the raquoacousticamplifierlaquo the frequency or pitch of the oscillation can be set by anyobject with an acoustic resonance a crystal vase a glass the string ofa guitar a tuning fork a cymbal a drum

The closest analogy to the laser is that sketched in Figure 17awhere the microphone is inserted in a drum It takes the least amountof energy to excite the note for which the drum is tuned The noisefrom the speaker puts the membrane of the drum in vibration result-


Figure 17 (a) An acoustic analogy ofthe laser an amplifier with feedbackThe pitch or wavelength of the soundproduced is determined by the acoustic(mechanical) resonance of the drum Thelaser is also an amplifier with feedbackwhere gain (Section 132) plays the roleof an amplifier A light beam that happensto be perpendicular to the two mirrorson either side of the optical gain mediumis amplified As the light wave makes a

round trip from one mirror to the oth-er and back to the initial point it has toadd upon itself which imposes that theround trip length should contain an inte-ger number of waves The same situationoccurs for the bird taking a bath out of allthe raquonoise waveslaquo that it produces thecontainer is a resonator that will selectthe ones that add up upon themselveshence have an integer number of crestsbetween the walls

ing in a plane compression wave of air propagating between the twofaces of the drum which is picked up by the microphone amplifierand fed back to the drum A similar scenario takes place in the laseras sketched in Figure 17b In the latter case the resonance is provid-ed by the mirrors guiding the light back and forth through the opticalamplifier Some of the sound is lost in going from the microphone tothe amplifier The gain has to be turned up to compensate for theselosses That minimum gain is called the threshold of oscillation orthe lasing threshold in the case of a laser

An integer number of wavelengths has to fit in the raquoboxlaquo definedby the two mirrors of the laser resonator otherwise the crest and thetrough of successive waves will cancel each other A similar situationoccurs when a bird takes a bath in a perfectly rectangular containerNo matter how wild it splashes in the water it will produce standingwaves that fit exactly the length of the box This is a one-dimensionalanalogy ndash we should assume here that the transverse dimension ofthe box is infinite

The role of the mirrors is twofold they provide the wavelength se-lection as well as the directionality of the laser beam If the mirrors


are perfectly plane only the waves that are exactly rigorously orthog-onal to these two planes can provide the raquofeedbacklaquo to the optical am-plifier Only the first few lasers were built with flat mirrors It wassoon realized that curved mirrors made a laser considerably easier toalign a nonperfectly axial beam will still reflect back within a narrowcone but it is no longer the raquoideal resonatorlaquo

The light amplifier and the resonator are not in perfect symbiosisbut thrive for different properties As in acoustics the resonator isthere to provide purity of tone eliminating any wavelength that doesnot fit as an exact integer fraction of the cavity length Thus in a 05 mlong laser cavity there are nλ D 1 000 000 wavelengths of 1 μm in around trip (1 m) At a wavelength of 0999 999 5 μm the round trip cor-responds to 1 000 0005 wavelengths meaning that if the wave startedwith a crest at one mirror it will come back with a trough and whichwill cancel the wave

The most selective resonator will have mirrors of the highest reflec-tivity possible In Figure 17b let us consider one end as a mirror with100 reflectivity and the other mirror with a minor leakage (reflec-tivity 999) A mirror designed for extraction of laser cavity poweris called output coupler If we were to turn off the amplifier and lookat the evolution of stored energy in the resonator we would see thatafter the first trip the light is reduced to 999 of its original value Ina second trip (999 999) D 998 of the energy stays inside Howmany trips does it take for the light to be reduced to half of its energyAfter NRT round trips where 999NRT D 05 only half of the energy isstored in the resonator With a help of a calculator in our example onefinds this number to be 693 round trips In other words it takes 693times the cavity length for the light to be reduced to half and all thewaves must perfectly overlap over this length The effective length ofthe cavity is multiplied by 693 In the example of the 05 m cavity evena wavelength off by 1(693 1 000 000) of a μm will be selected outbecause it will interfere destructively with itself after NRT round trips

While a laser with a good resonator ndash called a raquohigh Qlaquo cavity5)

provides a stringent wavelength selection it does not produce largeoutput power Only a trickle (10) of the power generated inside theresonator leaks out as useful output In order to have large power out

5) The letter Q is used to designate a raquoquality factorlaquo of a resonator ndash it is proportionalto the number NRT of round trips that survive in the cavity


of a laser one would need an end cavity mirror of large transmissionfor instance 50 requiring a gain of at least a factor of 2 per passNot only the wavelength selectivity is compromised by the large out-put coupling but even the collimation of the beam Indeed since thelasing condition is achieved only after one round trip any oblique raythat experiences two traversals of the gain volume will be part of theoutput beam

It seems that lasers are not like a blast of energy as in a bomb butrather a very conservative source of energy Only a small percentageof the stored energy leaks out similarly to the interest trickling out ofa savings bank account

It appears thus that in order to create a laser of high output powerone has to compromise against the main qualities that characterize alaser beam beam collimation and frequency selectivity The solutionto this dilemma is to inject the output of a low power narrow bandand well collimated raquoseedlaquo laser into a high power raquoslave laserlaquo Thisis based on two types of radiation that we have already learnt

We have seen that the stimulated photons are identical and undis-tinguishable from the stimulating photons In general a laser radi-ation is initiated by random spontaneous emission The role of theseed photons is to overpower the spontaneous emission As long asthe seeded coherent radiation exceeds the spontaneous emission inthe slave laser the latter will clone the directionality phase and fre-quency of the seeding radiation This technique is also called raquoinjec-tion lockinglaquo

14 Some Examples of Lasers

141 He-Ne Lasers

One of the first and most manufactured lasers has helium-neon asa gain medium The first continuous He-Ne lasers were a technolog-ical challenge ndash in particular the ones built with a pair of flat mirrorsfor the cavity Since the red He-Ne laser has a very low gain (of the or-der of 01 per pass) the radiation losses should be less than 01 inorder for the laser to operate (or to reach the raquolasing thresholdlaquo) Thetolerances in flatness are incredibly difficult to meet and maintainIn addition the gain of the red He-Ne laser emission line is very small


Figure 18 Short (12 cm) stable He-Nelaser with flat optical elements directlybounded to the fused silica body (cour-tesy of Dr Haisma with permission from

Koninklijke Philips Electronics NV Eind-hoven from [1]) Please find a color ver-sion of this figure on the color plates

it is not sufficient to compensate for the absorption of the best metal-lic mirrors Good dielectric mirrors had to be developed for this laserIn the early 1960s just after the first helium-neon laser was demon-strated Philips Research Laboratories in Eindhoven (NatuurkundigeLaboratorium) took up the challenge to make the perfect laser with aperfect flat resonator The result was a thick wall cylinder of quartzpolished at both ends to better than 002 μm flatness and a paral-lelism of better than 1 arcsec [2] It thus required the development ofpolishing fused silica with extreme flatness and parallelism In ad-dition coating techniques were developed to reach a reflectivity of996 a scattering of 01 and a transmission of 03 Mirrors andthe polished quartz were of such perfect flatness and so polished thatthey formed a vacuum tight seal when put in contact ndash a techniquestill not very often used to this day because of the stringent finish re-quirements There was no alignment possible and no room for errorThe challenge was successfully met leading to the laser sketched inFigure 18 probably the first and last He-Ne laser of its kind

The perfectly cylindrically symmetric laser allowed putting somefundamental questions to test such as the nature of the electric fieldproduced by a laser Is it always a linearly polarized beam and an elec-tric field oscillating along a particular line perpendicular to the beam

14 Some Examples of Lasers 21

The answer was always yes despite the fact that there was no prefer-ential direction for the laser to oscillate

142 Lasers for the Cavemen

Clearly the He-Ne laser was not only a scientific innovation butits construction required high vacuum technology high quality di-electric coatings and mirror polishing to a high degree of flatnessOther lasers due to their high gain andor long wavelength did notpose such a technological challenge For instance the CO2 infraredlaser could have been built centuries ago if only somebody had comeacross the recipe Here the idea came far after the technology wasavailable Many raquokitchenlaquo versions of these lasers have been built andhave probably cost their inventor a hefty electrical shock and a burnedbelly button Lasers are typically more efficient at longer wavelengthInfrared lasers are easier to build and are more efficient than for in-stance ultraviolet lasers One reason is that the mirror technology issimpler the flatness only has to be comparable to the wavelengthwhich is considerably easier at 10 μm (105 m) than at 06 μm An-other reason is that inversion is easier to achieve because there is lesscompetition from spontaneous emission Indeed spontaneous emis-sion rates are higher for more energetic transitions As if the chal-lenge of a higher slide in Figure 14 attracted children ndash a kind ofreverse acrophobia

1421 The CO2 LaserAn example of a continuous CO2 laser is sketched in Figure 19 It is

a tube of pyrex or quartz typically 6ndash10 mm inner diameter and 1ndash2 mlong Ideally a second concentric tube is used for water cooling Anelectric discharge requires a power supply of 15 to 25 kV providing acurrent of 10ndash20 mA (current limiting resistances are essential sincethe discharge has a negative resistance characteristic) A mixture ofcarbon dioxide (CO2) nitrogen (N2) and helium (He) is used typicallyin the ratio 1 W 2 W 10 at a pressure of 10ndash30 torr6) Since CO2 is thelaser medium one may wonder why the other gases are added Infact some gain exists in the discharge even with pure CO2 However

6) 1 torr is 1760 of atmospheric pressure


Figure 19 Typical low pressure CO2 laserThe two windows (BW) can be madeof germanium or salt (transparent tothe wavelength of 10 μm emitted by thelaser) They are at an angle such thatthere are no reflection losses for a beampolarized in the plane of the figure (calledthe Brewster angle) The electrodes can

be small cylinders of nickel The reflec-tivity of a flat plate of germanium (80)is sufficient to achieve lasing action Theother reflector can be a flat metallic mirror(a concave mirror ndash typically 20 m radiusof curvature ndash is generally used)Pleasefind a color version of this figure on thecolor plates

a marvel set of physical coincidences boost up the efficiency of thatlaser when the other gases are present

The CO2 laser is a vibrational laser This means that the photon isemitted when the molecule switches from a higher energy mode ofvibration to a different mode of lower energy The CO2 molecule islinear with the carbon in the middle Specifically the upper state ofthat laser corresponds to the asymmetric motions of oxygen atomswith respect to the central carbon atom To visualize this one can pic-ture an oxygen moving towards the carbon while the oxygen at theother end is moving away from the carbon The lower state is still anexcited state but corresponds to the raquobending modelaquo where the mo-tion is that of a bird flapping its wings with the carbon being thebody and the oxygen at the tips of the wings When the electronsin the discharge collide with a CO2 molecule the latter gets excitedsomewhat preferentially in the asymmetric mode the upper level ofthat laser However the electrons excite the vibration of a nitrogenmolecule much more efficiently Because the quantum vibrational en-ergy of nitrogen is nearly equal to that of the CO2 asymmetric stretch-ing that mode gets preferentially excited Thus excited the CO2 canemit a photon and in the process change to a bending mode or a birdflapping wing mode How does the vibrating molecule come down torest Collisions with a helium atom are very effective in transferringthe bending vibration energy of CO2 into translation energy of the Hewhich is just heat Helium is a very good heat conductor and will be-come cooled by collisions with the wall of the tube Another approach


for eliminating the heat is to replenish the medium quickly in otherwords to increase the flow of gas

The basic design of Figure 19 has evolved over the years to lead tomultikilowatt lasers used for machining The evolution towards high-er power and efficiency has been quite straightforward

One essential part of the efficient operation of a laser is the removalof the molecules in the lower state For each photon created by stimu-lated emission in the beam a CO2 molecule is left in the bending ex-cited state When all the molecules have accumulated into that statethere can be no longer amplification It is thus imperative to removethem There are two methods to remove them physically (high flowraquogas dynamicslaquo lasers) or to cool them more effectively The latter ap-proach involves increasing the (cooling) to surface ratio which is theapproach used in planar waveguide lasers where the cooling surfacesare metallic plates also serving as electrodes The other approach isto increase the energy of the laser for a given size is to increase thenumber of molecules participating in the gain hence to increase thegas density This has led to the atmospheric pressure pulsed CO2 laserwhere a strong electrical discharge is applied transversally across atube containing a mixture of CO2 He and N2 These lasers are gen-erally called TEA lasers (raquotransverse electrical dischargelaquo) This typeof laser produces nanosecond pulses of several joules of energy Highpower ndash several kilowatts ndash CO2 lasers are manufactured for industrialapplications welding cutting surface treatment and so on

1422 The Nitrogen LaserThe nitrogen laser is another example of a laser that was simple

enough to appear in peoplesrsquos kitchen following a recipe publishedin the Scientific American in 1974 [3] Surprisingly in view of the pre-vious discussion in the introductory paragraph of Section 142 aboutthe infrared lasers being easier to produce it is a UV laser operat-ing at 337 nm As stated previously there is more competition fromspontaneous emission at short wavelength Indeed the energy lev-el responsible for lasing in the nitrogen laser empties itself in a fewnanoseconds It is however relatively easy to produce a strong electri-cal discharge transverse to the lasing direction in a shorter time Theenergy storage is electrical a thin sheet of mylar or other dielectricsheet able to withstand very high voltage without breaking down issandwiched between two copper plates to constitute the energy stor-


Figure 110 Sketch of a typical nitrogenlaser Copper foil is taped on both faces ofa thin dielectric (circuit board Kapton orMylar) creating a capacitive transmissionline which is charged via a resistance bya high voltage power supply (right side)The upper copper plates terminate as lineelectrodes in a discharge tube The leftcapacitortransmission line is connect-ed to the right one via inductance of aresistance On the far left the spark gapthat acts as a switch short-circuiting thecapacitor (it can be a needle connected

to the upper plate pointing towards theground plate or a car spark plug) Theshort circuit propagates towards the rightbrings the left electrode to ground poten-tial inducing a discharge across the tubelasting until the complete capacitanceis discharged (about 1 ns) The tube isclosed by two windows or one windowand a mirror Pure nitrogen at 2550 torrpressure is pumped through the tube (aircan also be used but the performancesare reduced) Please find a color versionof this figure on the color plates

age capacitor as sketched in Figure 110 One of the plates is connect-ed to a high voltage (in the order of 1020 kV) and will also constitutethe high voltage electrode of the laser The other electrode is connect-ed to a similar sandwich terminated by a switch called the spark gapto the right of the figure Some lasers have been built using just acar spark plug as a switch Initially the two capacitors are charged tothe same voltage (they are connected by a resistance) As the sparkgap (or spark plug) is fired the short circuit established at that endpropagates towards the left at a speed close to the speed of light and astep function current of the order of a nanosecond in duration travers-es the discharge tube A little venturi pump can be used to flow thenitrogen at a low pressure (2550 torr) through the tube No mirroris needed because of the laser spontaneous emission and very largegain the geometry of the tube is sufficient to have light amplificationby stimulated emission radiation without any mirror Adding a mirrorat one end increases the output energy because the length of the am-plifying medium is doubled This simple technology grew in a smalllaboratory in Goumlttingen and led to one of the largest manufacturers ofnitrogen lasers and excimer lasers These lasers were extremely pop-ular for three decades as a pump for visible dye lasers


143 Semiconductor Lasers

Only two years after the birth of the first laser in 1960 (the rubylaser) IBM GE and the Lincoln labs of MIT simultaneously an-nounced the realization of the semiconductor p-n junction laserThese first diode lasers (also called raquoinjection laserslaquo) were made ofgallium arsenide (GaAs) A semiconductor is characterized by havingtwo energy bands instead of discrete energy levels as is the case foratoms and molecules Photons are emitted by the transition of anelectron from the higher energy band (the conduction band) to thelower energy band (the valence band) The two bands are separated byan energy difference called band gap The laser consists of a small sin-gle crystal with two halves of different physical properties achievedby doping the crystal on either sides with different elements The raquonlaquoregion is doped with impurities labeled raquodonorslaquo (for instance Se)because they tend to produce an excess of electrons giving this partof the crystal metallic like properties The raquoplaquo region is doped withimpurities labeled raquoacceptorslaquo (for instance Zn) which tend to trapelectrons leaving no electron in the conduction band The electricalproperties of such a combination are asymmetric the current willflow easily from the p side to the n side while the junction will showa very high resistance if a positive voltage is applied to the n sideand a negative one to the p side Hence the label raquodiodelaquo for thesedevices

As voltage is applied to the diode positive on the p side negativeon the n side the electrons will cascade down from the high energyconduction band into the valence band at the location of the junctionwhere a population inversion (between the conduction band and thevalence band) is created (Figure 111) provided that the current is suf-ficiently large It is as if the electrons flow down a river encounteringa sudden drop at a waterfall The radiation is thus emitted along a linethat marks the junction between the p doped side and the n dopedside of the semiconductor While having a lot in common with stan-dard lasers a striking peculiarity of semiconductor lasers is their sizeThe p-n junction lasers are minuscule with a size of about 01 mmThe junction thickness itself is of the order of 1 μm The shorter thecavity the less it will select a particular frequency and the lesser its col-limating properties The gain of the junction laser can be very high Itis therefore not necessary to use a reflective coating on the facets of the


Figure 111 Energy band structure of asemiconductor laser The occupation ofelectrons shown by the gray area extendsin the conduction band in the n regionand does not reach the top of the va-lence band in the p region As a field isapplied to the semiconductor the electric

potential adds to the electron energiesresulting in slanted bands (a) The currentof electrons flows down the raquoriverlaquo ofthe conduction band to cascade down tothe valence band at the junction just as awaterfall (b) Please find a color version ofthis figure on the color plates

cube Because the index of the refraction of GaAs is very high (334)the uncoated facets have a reflectivity of 30 which is sufficient forlasing If better performances are needed (single frequency or wave-length better directionality) one may put an antireflection coating onthe facets and place the semiconductor gain medium in a traditionalcavity with mirrors

Another limitation associated with the minuscule size of the p-njunction laser is the optical power that can be extracted With a gainvolume that is in the μm3 range the intensity can reach the dam-age threshold with only a few tens of milliwatt of optical power Theother limitation to the output power is saturation It will be shownin Section 152 on raquosaturationlaquo that the media that have a strongergain and larger spontaneous emission will see a drop in gain at low-er intensities Therefore one would expect that semiconductor lasersdo not have a future in high power applications There is howevera solution to the power limitations brought on by the microscopicemitting cross-section (a narrow line at the junction) of the semicon-ductor lasers a total change in geometry leading to a large emitting


area These are the vertical-cavity surface-emitting lasers (VCSEL) andthe vertical-external-cavity surface-emitting lasers (VECSEL) Insteadof emitting in the plane of a junction these lasers emit along the nor-mal to the plane Instead of being pumped by an electrical currentthey are pumped optically (although electrically pumped devices areunder development) With a large emitting area one can expect toextract more power out of the semiconductor laser for the intensitycorresponds to complete inversion Most often the limiting factor isthe optical pump power available

144 Fiber Lasers

1441 IntroductionThe first few years following the discovery of the ruby laser were

full of surprises After 50 years the ruby laser has nearly fallen intooblivion As early as 1961 another laser was discovered which wasleft largely ignored for the next three decades the fiber laser [4 5]The gain medium was a fiber of barium crown glass doped with theneodymium ion Nd3C This laser did not promise a bright future Cit-ing a review of the laser technology near the end of the first decadeof laser development raquoA number of fiber optics lasers have been con-structed using Nd3C in glass (wavelength 106 μm) as active mediumin glass but these devices have thus far not played a conspicuous rolein the development of laser technologylaquo [6] Fiber lasers have startedtheir comeback since the development of ultralow loss fibers for com-munication in the 1980s Fibers are slowly extending their tentaclesover areas where gas lasers or solid state lasers have been well en-trenched As a commercial ultrashort pulse laser the fiber laser haseven taken a big chunk of the market from the Tisapphire laser It isnow considered to be one of the most promising weapons for the AirForce having replaced the development of chemical lasers

Two main breakthroughs in fiber technology (i) the manufactur-ing of near lossless fibers and (ii) speciality fibers dubbed raquoHoleyfiberslaquo raquophotonic crystal fiberslaquo or raquophotonic band gap fiberslaquo arecontributing to progress in fiber lasers The first is a material tech-nological advance the manufacturing of ultrapure silica which hasenabled the production of silica fibers with such a low loss that afterpropagation through 1 km of fiber 1 W of optical power would on-


ly be attenuated to 096 W7) The second advancement results fromprogress in manufacturing which has made it possible to producefibers where the inner core consists of a complex pattern of hollowand filled structures

1442 Optical FibersAn optical fiber has very much the appearance and size of a hair

In fact after a long haired graduate student had completed a com-plex fiber laser system it became very difficult to disentangle hairfrom fibers Optical fiber in fact exists in nature the hair of polarbears not only provides insulation but conducts the sunlight to theskin A polar bear might even get a suntan under his white coat Theprinciple of light conduction in fibers is total internal reflection assketched in Figure 112a If a light ray is incident on an interface be-tween a medium of a high index of refraction ncore and a lower indexncladding there will be a critical angle of incidence αcr beyond which nolight is transmitted and all light is reflected by the interface (hencethe name raquototal internal reflectionlaquo) The critical angle is given bysin αcr D ncladdingncore An optical fiber consists essentially of a filledspaghetti where the core would be denser than the outer part Thematerial of the core has a higher index of refraction ncore than thatof the surrounding called cladding (ncladding) Rays that are incidenton the interface at an angle larger than αcr ndash or that make an anglewith the axis of the fiber smaller than θ ndash are trapped in the core Ofcourse the light energy will propagate at a different velocity for all therays that zigzag through the fiber core at a different angle This effectis called modal dispersion (the larger the angle the smaller the lightenergy traveling along the fiber) We have seen in Section 123 thata beam of diameter D spreads (diffracts) with a half angle θ D λDIf the diameter of the core is large a large number of rays with dif-ferent angles can be trapped by total internal reflection If the diam-eter of the fiber is reduced the value of λD increases until that an-gle reaches the critical value There is at that point only one ray thatcan be trapped the fiber is said to be single mode for that wavelengthFibers with a larger core diameter are called multimode fibers A singlemode fiber at a given wavelength can be a multimode fiber at a short-

7) The fiber manufacturers express the fiber loss in dBkm where the decibel isdefined as 10 the logarithm in base 10 of the ratio of the transmitted power to theinput power The Corning fiber SMF 28 ULL has a loss of 017 dBkm


Figure 112 (a) Beam incident from thebottom on the interface between twoglasses of different index of refractionncore gt ncladding Rays incident at an an-gle larger than or equal to αcr are totallyreflected without any loss in the mediumof index ncladding (b) Total internal reflec-tion takes place between the core of anoptical fiber and the cladding providedthat the rays make an angle with the axis

of the fiber smaller than the critical valueθ D 90ı αcr The smallest beam diam-eter D that can be trapped is the one forwhich the diffraction angle λD (see Sec-tion 123) corresponds to the critical θ Ifthe core diameter is equal to D the fiberis said to be single mode Please find acolor version of this figure on the colorplates

er wavelength The single mode fiber is to the fiber optics what thefundamental ideal Gaussian beam least diffracting is to free propa-gation

The high quality of single mode fiber optics does not come cheapor easy A fundamental problem is that the glass homogeneity andaccuracy with which the index of refraction can be controlled im-plies a small core size ndash of the order of 10 μm Such a small coresize is incompatible with high optical power since the large intensity(powercore area) will result at best in nonlinear effects (intensity de-pendent index of refraction generation of unwanted wavelengths)at worst in the destruction of the fiber Other related problemsare

Rapid saturation of a fiber laser amplifier Difficulty to effectively couple the fiber to the outside world An

extreme positioning accuracy is required to effectively couple lightfrom a Gaussian beam into a fiber and vice versa


Difficulty in coupling fibers to fiber Difficulty in controlling the polarization along a fiber

The latter point is due to the fact that any motion bending temper-ature change and acoustic disturbance of a single mode fiber affectsthe polarization of the beam that is propagated through the fiber Thedevelopment of fiber lasers and fiber laser amplifiers is intimatelylinked to progress in single mode fiber optics The polarization in-stability and uncontrollability has been solved through the develop-ment of polarization preserving fibers with a slightly different indexof refraction along two orthogonal axes Light linearly polarized alongone of these two axes will conserve its polarization Remarkably so-phisticated instruments have been developed to accurately splice twofibers together (single mode or polarization preserving) with mini-mum loss

A significant breakthrough came when researchers at the Univer-sity of Bath created a new family of single mode fibers by using as apreform8) an array of capillary and rods [7] This new fiber was fabricat-ed by putting together glass tubes of hexagonal cross-section forminga regular pattern with a full rod in the center By pulling and stretch-ing this structure the dimensions of the cross-section were reducedby a factor of 10 000 until the central rod was reduced to a diame-ter of the order of 1 μm the pitch (spacing between holes) reducedto 2 μm and the holes had a diameter of between 02 and 12 μmA considerable number of variations have been made on these struc-ture leading to an equally large number of exotic effects Because ofthe better guidance of the light by the pattern of holes surroundingthe core the raquosingle modelaquo guidance is observed over a wavelengthrange covering the visible to the near infrared [7] The fiber can beengineered to have the light pulse traveling at the same velocity overa broad range of wavelengths [8] which is an important property forthe transmission of ultrashort signals (cf Section 173) Because ofthe high intensity at the core rod a rainbow of new wavelengths canbe generated [8] Other exotic effects are being investigated by insert-ing vapors or gases in the capillaries surrounding the core [9 10]

8) The fiber are typically drawn from a preform consisting in a cylinder of glass Inthis particular case the solid cylinder is replaced by a bundle of tubes of which theinner diameter is progressively reduced in successive stretching steps


1443 Fiber AmplifiersThe fiber laser amplifier is the simplest device of all The core of

the fiber is generally doped with some rare earth (erbium for 155 μmlasers neodymium andor ytterbium for 106 μm fibers to cite only afew) In very early designs the fiber was wrapped around a flashtubeThis practice was totally abandoned with the availability of efficientsemiconductor lasers The pump light from a semiconductor laser iscoupled to a fiber which is coupled directly into the doped fiber witha wavelength division multiplexer (WDM) the fiber equivalent of therailroad switch or beam splitter mirror The limit to the amplifiedpower is set by the cross-section of the core the laser beam cannotbe amplified beyond a certain raquosaturation intensitylaquo (power dividedby cross-section) which is discussed in Section 152 The minusculecross-section of the fiber core sets an upper limit to the power that canbe amplified There has been considerable progress recently in themanufacture of large core fibers with special cladding guiding thepump light such that the amplified power has approached the kWlevel It is anticipated that a very high power device can be realizedby adding the field (ie adding the laser beams as waves in phase) ofseveral of these devices

The semiconductor laser pump pulse loses its energy as it prop-agates down the doped fiber to create a population inversion For agiven pump laser how can one determine the useful (optimal) lengthof fiber to be used given that the IR beams (pump and laser) are in-

Figure 113 Erbium doped fiber glowing in the dark upon excitation by the pump radia-tion at 980 nm Please find a color version of this figure on the color plates


visible and hidden inside the core of the fiber Figure 113 offers ananswer It shows and erbium doped fiber pumped by a 980 nm semi-conductor laser The pump photon excites the erbium to the upperstate of the laser transition as it should to create a population inver-sion for 155 μm However other pump photons excite the erbiumfrom that level to a higher energy one from which green fluorescenceis emitted Hence the green glow can be observed in the dark ema-nating from an erbium doped fiber laser or amplifier

Since there is no limit to the length of a laser amplifier (providedone can continuously add pumped sections) one might wonder howa laser pulse will evolve after a considerable distance Will it evolvetowards a steady state entity like a light bullet speeding through thecore and without any shape distortion We will see that this can in-deed be the case in the study of short pulse propagation in Section 17

1444 Fiber LasersAs we have seen in Section 13 the laser is simply an optical am-

plifier sandwiched between two mirrors The same high reflectivitylow losses and high power mirrors that have been designed for otherlasers do not apply to the fiber the cross-section is too small to makeprecise multiple layer deposition on the fiber end A simple techniqueemployed in the past was to dip the fiber end in mercury but the useof mercury has lost its popularity Another technique still in use ismetallic coating on the fiber end but the intensity at the fiber coremay be sufficient to vaporize the thin film The fiber equivalent of thedielectric mirror is the fiber Bragg grating A dielectric mirror consistsof a stack of transparent materials of different indices of refractionThe material and layer thickness are chosen in such a way that the re-flections produced at each interface add in phase resulting in a nearprefect mirror if a sufficient number of layers is used The fiber Bragggrating consists of periodic changes of the index of refraction over aconsiderably longer distance than the thickness of a dielectric mirrorThe basic principle however is similar the changes of index are en-gineered in such a way that the backscattered radiation adds in phaseA solution that circumvents the need for mirrors is to have the laserliterally as a dog biting its tail splice the input end to the output endto form a ring A short pulse that is let to evolve in this amplifier ina ring configuration looks in vain for the end the ring is in this caseequivalent to the infinitely long amplifier of the previous section In


certain conditions discussed in Section 17 the short pulse will evolveas a light bullet circulating endlessly in the ring Here again the equiv-alent of railroad switch or WDM will come handy in extracting thepulse at every round trip

One of the most successful commercial fiber lasers is the femtosec-ond source of IMRA America which produces a train of pulses of theorder of 100 fs in duration at a repetition rate of 50 MHz This canbe seen as a train of light bullets of only 30 μm in length (c 100 fs)spaced by 6 m

15 Pulsed Lasers

151 The Laser as Energy Storage

A low gain laser requires a very high quality cavity with no morelosses than the gain The laser oscillation starts when the gain perpath exceeds the loss As the light rattles back and forth between thetwo mirrors of the laser cavity the optical power increases just as thelevel of water and the pressure increases when a river is dammed(Figure 114) The power input to the laser eventually comes in equi-librium with the power released through the end mirror just as theriver flow into the lake eventually balances the release at the bottom of

Figure 114 (a) A dam most of the energyis stored in the lake in front of the damOnly a small fraction of the stored waterflows through the release of the dam(b) Optical power is stored between the

two mirrors of a laser cavity The laserbeam issued from this device is actuallythe trickle transmitted by the outputmirror


the dam which increases with the increase in pressure or energy con-tained by the dam In the case of the laser the gain per pass ndash whichinitially exceeded the loss ndash decreases as the power inside the cavityincreases until it exactly balances the losses at the output mirror Thedecrease in gain with power is called gain saturation

152 Saturation

Saturation is a nearly universal phenomenon Unlike the bankerfor whom there is no limit to the number of coins that he can ab-sorb matter has a limited greed There is only so much light that oureye can take Beyond a given intensity we do not see any differencein brightness whether the power is multiplied by 2 or 10 The sameapplies to the temperature of a radiator which results from a balancebetween the power applied to it and the cooling by radiation and con-duction to the surroundings Doubling the power applied to it will notdouble the temperature because the cooling rate to the surroundingswill increase

The process described in the Section 132 assumes that the numberof photons added is small compared to the total population in the up-per state Only a few of the lazy girls on top of the slides (Figure 14)are raquostimulatedlaquo to go down However the total gain which corre-sponds to the release of energy in emitted photons is proportional tothe number of excited atoms which is going to decrease as a resultof the transitions down The girl that has gone down the slide cannotstimulate another transition before she has climbed the ladder again

In the case of a constant rate of excitation into the upper state thestimulated transitions will compete with the pump rate that createsatoms in the upper state and reduce the upper state population andhence the gain The saturation rate is the number of photons per sec-ond that results in a decrease of population difference by a factor of2 Why population difference This might not be an easy concept tograsp The girls down on the ground have a potential to be up theladder and those who are up will be pulled down A good inversionmade by a pump laser brings as many electrons as possible to theupper state If we start with 100 girls up the ladder and none on theground the population difference is 100 Now only if 25 of these girlsgo down on the slide is the population difference reduced to 50 whichis half of initial difference In this example 25 of girls going down

15 Pulsed Lasers 35

corresponds to the saturation rate of the transition At the same timea gain (maybe a trampoline in our example) pumps the electrons tothe upper state

The same applies to an absorber where the atoms are initially inthe lower state There is only so much light that an absorber can takeOnce an atom has been excited by a photon it cannot absorb anoth-er photon before it has relaxed back to its initial absorbing state Themore power in a laser beam that is the more photonssecond are sentto an absorbing medium the lesser the number of atomsmoleculesthat are available to absorb a photon and the medium becomes trans-parent to the light It can also be seen as a gate that gives way underthe pressure of a crowd (in this case of photons) This property is usedquite often in laser technology as a fast gate that gives way to an excessof optical energy

153 Releasing Stored Energy

1531 Q-SwitchingHow do you release the maximum energy that can be stored behind

a dam in the shortest amount of time If the release van of the dam istotally open the water level may never rise In the laser if the outputcoupling mirror has a too large transmission the pumping radiationmay never get the population inversion to the raquothreshold levellaquo thatmakes the laser oscillate In other words there is no dam anymorejust a leveled river

To obtain a maximum flow in a short time the release valve shouldbe closed to let the water level rise to the maximum then suddenlyopened to let the reservoir empty in a giant surge of water In the Q-switching mechanism the van is open but the dam is not eliminatedIn the laser the gain is first accumulated to the maximum value thatthe pump source (a flashlight in the case of a ruby laser a dischargecurrent in the case of a gas laser) can provide In the radiation pic-ture of sliding girls they are all up the ladder to create the maximumpopulation inversion but they cannot go down Then the resonator issuddenly formed allowing the laser oscillation to start at a very fastpace because the gain has reached a high value


Figure 115 (a) A CO2 laser tube is closedat one end by a partially reflecting mirroran uncoated germanium plate or a coat-ed ZnSe plate The other end is sealedwith an enclosure containing the rotatingmirror In position (a) with the rotatingmirror at a nonzero incidence with re-spect to the tube axis the gain developsinside the discharge tube As the rotatingmirror arrives in position (b) the outputmirror and the rotating mirror are paral-lel forming a resonator in which a laser

pulse forms and depletes the gain As themirror pursues its rotation (c) there isno longer a resonator and the gain canrecover until the next position (b) (d)Exploded view of an air turbine used forQ-switching The rotation speed couldreach 60 000 revolutionsmin limitedby the centrifugal expansion of the shaft(courtesy of Koninklijke Philips Electron-ics NV Eindhoven 1970) Please find acolor version of this figure on the colorplates

1532 Mechanical Q-SwitchingIn the early years of the laser the mirror was put physically in and

out of place by placing it in the shaft of a rotating turbine An ex-ample of such a turbine [11] that was used for Q-switching a CO2

laser at Philips Research Laboratories in Eindhoven the Netherlandsis shown in Figure 115 The alignment of the rotating mirror is rathereasy there is only one degree of freedom (around an horizontal axis)since the mirror scans all angles about the vertical axis Such spinningmirrors are particularly convenient for Q-switching lasers with contin-uous gain such as the continuous discharge CO2 laser described inSection 142 During most of the revolution of the shaft the laser cav-ity is not aligned and the gain accumulates For a few seconds of arcduring the revolution the two cavity mirrors come into parallelismand the laser wave builds up from noise extracting all the energy thatwas stored in the gain medium in a pulse that lasts between 10 and

15 Pulsed Lasers 37

100 ns As the mirror continues its spin into the next cycle the gainmedium recovers in preparation for the next pulse after another rev-olution The disadvantages of the rotating mirror are (i) the stringentrequirement of near perfect shaft balancing and (ii) the deafeningnoise (which in the case of the CO2 laser was eliminated by operatingin vacuum) Therefore while this method of creating raquogiant pulseslaquohad some popularity in the late 1960s it was abandoned in favor ofeither electronic Q-switching or passive Q-switching

1533 Electronic Q-SwitchingInstead of moving the mirror successively out- (to prevent laser

emission in order for the gain to evolve to its maximum value) andin-position (to suddenly dump all the stored energy in a giant laserpulse) it is easier to place an ultrafast obturator in front of the mirrorwhich opens at the time that the gain has reached its peak value Thistechnique was conceived and demonstrated in the early days of theruby laser [12] The principle involves the manipulation of the laserpolarization discussed in Section 122

A linear polarization can be rotated or changed to elliptical or circu-lar by propagating the light in a medium which has a different prop-agation velocity along two directions at ˙45ı from the polarizationdirection (raquobirefringent mediumlaquo or raquowaveplatelaquo) After some prop-agation distance the components of the electric field oscillation alongthese two directions will no longer be in phase resulting in ellipti-cal polarization Or they may have opposite phase resulting in linearpolarization again but rotated by 90ı There also exist componentsthat selectively deflect a particular polarization direction (polarizingbeam splitters) or transmit only one direction of polarization (polariz-ers)

The birefringence property can be created by application of an elec-tric field since the material structure and electronic response couldvary from one direction to the other The key to optical switching isthe Kerr effect which is a change of the wave velocity (or index of re-fraction9)) of a material under application of an electric field The orig-inal implementation involved a liquid Todayrsquos Q-switch elements arenonlinear crystals called Pockels cells These elements are based on the

9) The index of refraction is the fraction of the speed of light in vacuum that a lightwave can take inside the medium


Figure 116 (a) The gain of the laser is ac-tivated (a flashlamp is fired in the case ofthe ruby or NdYAG laser) A high voltage(HV) is applied to the Kerr cell K suchthat the polarization of the beam issuedfrom the amplifier is rotated 90ı and re-jected by the polarizing beam splitter P

The combination of Kerr cell and polarizeressentially eliminates the end mirror fromthe cavity (b) After a time such that thegain has reached its maximum value thevoltage on the Kerr cell is shorted the endmirror is part of the cavity and the laseroscillation can develop with full gain

electro-optic by which the index of refraction of a beam is changed up-on application of an electric field This change is different along differ-ent axes of the crystal It results in a linear polarization being distortedin elliptical or circular polarization Under application of a sufficientelectric field the polarization of the beam can be rotated by 90ı Araquoswitchlaquo consisting of a Kerr cell (or a Pockels cell) combined witha polarizing beam splitter is inserted in the cavity as in Figure 116A voltage is applied to the Pockels cell rotating the polarization by90ı such as to eject any light that would be generated in the cavity asthe laser medium (amplifier) is being activated (Figure 116b) After atime such that the maximum population inversion ndash that is the max-imum gain of the laser element ndash has been reached the high voltage(HV) on the Kerr cell is shorted suddenly the laser cavity is closedand a raquogiant pulselaquo develops (Figure 116b)

1534 Passive Q-SwitchingThe advantage of electronic Q-switching is that the timing of the

laser emission is well controlled which is important when severallaser systems have to be synchronized The disadvantage is that thepulse to pulse reproducibility is not ideal A preferred technique whensynchronization is not an issue is to let the laser itself decide the op-portune moment to open its cavity This is done by replacing the elec-tronic switch of Figure 116 by a raquosaturable absorberlaquo Saturation is aubiquitous phenomenon There is only so much light that an absorbercan take Once an atom has been excited by a photon it cannot absorbanother photon before it has relaxed back to its initial absorbing state

15 Pulsed Lasers 39

As shown in Section 152 the more power in a laser beam that is themore photonssecond are sent to an absorbing medium the smallerthe number of atomsmolecules that are available to absorb a photonand the medium becomes transparent to the light

One can think of a saturable absorber as a closed gate of a footballstadium After the game the crowd presses on to exit The pressurebuilds up at the gate as more and more people squeeze against itas the light level increases inside a cavity trying to make the absorbertransparent Finally the gate gives way the saturable absorber opensand scores of people are ejected through the opening

The saturable absorber can be a dye a crystal a color glass (RG-8 fil-ters of Schott glass for example in the case of ruby lasers) which is to-tally opaque to the laser light Inserted in the cavity it prevents lasingsince the amplifier does not raquoseelaquo the end mirror When the amplifieris fired there is so much radiation from the spontaneous emissionthat after a certain dose the absorber raquocannot take it anymorelaquo andbleaches (becomes transparent) This simple technique provides themost reliable operation with the shortest pulses but with a timing thatcannot be controlled

One can compare the raquosaturable absorberlaquo and raquoelectronic switch-inglaquo to taking money from a bank account In the saturable absorbercase the money is taken when it reaches a certain value in the elec-tronic method it is withdrawn at equal time intervals As a result onehas certain values but may not be necessary timed equally and the oth-er is timed but may not have the same value In cavity dumping thewhole bank account is emptied and then closed for the new build up

1535 Cavity DumpingIn our analogies of the dam the previous Q-switch techniques

amounted to close the dam let the water level rise to the maximumbefore opening the valves to maximum Once the Kerr or Pockels cellis opened the laser oscillation develops as fast as the raquonet gainlaquo (gainminus transmission through the output mirror) allows If the out-put mirror has a very high reflectivity the optical pulse will developfast but the power will remain trapped in the cavity If the outputmirror has high transmission more output will be released but theoscillation will develop more slowly The solution to maximize the ex-traction of energy from the laser and from the dam is to let the waterlevel rise to its highest level and blow up the dam as in Figure 117


Figure 117 (a) A dam is filled slowly tocapacity ideally by closing all water re-lease The energy stored by the dam canbe released in a minimum amount oftime by blowing up the dam (b) Similarlyin a laser cavity with totally reflecting mir-rors the optical power increases swiftly

with time (c) To release the energy storedin that cavity in the shortest amount oftime one of the cavity mirrors is raquore-movedlaquo in a time short compared withthe time it takes light to make a completeround trip in the cavity Please find a colorversion of this figure on the color plates

This technique is called cavity dumping because all the energy storedbetween the mirrors is extracted in a pulse that will have exactly thelength of the cavity Instead of raquoblowing uplaquo the output mirror it iseliminated electronically In Figure 116 the output mirror is chosento have maximum reflectivity As soon as the power in the cavity hasreached its maximum value a pulse is applied to the electronic switchto release all the energy via the polarizing beam splitter The switchingtime has to be short compared to the cavity round trip time of lighthence it must typically have a rise time shorter than 1 ns

16 Properties of a Laser Beam

161 Directionality

A simple and useful characteristic of a laser beam is its direction-ality it propagates with minimal diffraction Most light sources willexpand through space which is generally a desired feature Houselight is made to illuminate a whole room without sharp exposuresAs we move towards virtual words and replace material with dataand images our interest in using light as an appliance increases wecan replace a knife or a ruler with a laser beam In Section 1753and in Chapter 7 we will learn about a new medium created by laser

16 Properties of a Laser Beam 41

Figure 118 (a) A well collimated outputof a laser Rigorously speaking such aperfect collimation can only take placefor beams of infinitely large diameterIn general the diameter of a laser beamwill increase from the smallest value (thewaist) as in (b) The diameter of the waistdefines the angle θ of the divergenceThe situation of (a) applies to a laser withflat mirrors where the light rays are thestrings spanned between the two mir-

rors Curved mirrors lead to the situationof (b) the raquoringslaquo are twisted with re-spect to each other The envelope of therays (that are perpendicular to the surfaceof the mirror) draw an hyperboloid whichcan often be seen with a laser beam in adusty environment If the curvature of themirrors is equal the minimum diameterraquoDlaquo ndash the waist ndash is at the midpoint ofthe cavity Please find a color version ofthis figure on the color plates

light that has a unique properties and even less divergence than laserbeams

When we compare a flash lamp with a laser pointer we notice thatthe laser seems to have a well collimated output (Figure 118a) whilethe output of the flash lamp expands quickly in the space Why can alaser beam can be collimated better than the light of a flashlamp

The resonator is the main body of the laser (Section 133) and itdefines the size of the beam In that body laser engineers use variouscomponents to adjust the wavelength amplitude or in the case ofpulsed lasers the length and shape of the pulse One can look at theraquoresonatorlaquo as the cooking pot of the laser where you can spice thebeam as desired Often the population inversion required for laseraction is confined to a small volume which imposes to design theresonator with the smallest beam size (waist) at the location of thegain medium From the waist the beam diverges as in Figure 118b


with a half angle θ

θ D 06λD

(12)

where raquoλlaquo is the laser wavelength and raquoDlaquo the minimum beamsize or beam waist Mirrors or lenses are generally used to recolli-mate the diverging beam Another way to quantify the spreading ofa laser beam with distance is the Rayleigh length ( 23D2λ) whichis the length over which the beam diameter has increased from D to14D Clearly the smaller the wavelength the smaller the divergenceangle

The simple Equation 12 tells us basically what can and cannot beachieved with a laser beam Given the diameter D of a laser beam ittells us how large the spot will be at a large distance For instancein the early years of the laser (1962) a pulsed Ruby laser was sent tothe moon The beam was expanded to fill the 48 inch diameter of thetelescope at MIT Lincoln Observatory Only a few photons were ableto return back to earth but that was sufficient to measure the timetravel of the pulse and measuring the distance from the earth to themoon With λ D 6943 nm and D 1 m θ 04 μrad which atthe distance earthndashmoon of 300 000 km meant a 100 m radius circleIf one had replaced the ruby laser with a pulsed flash lamp the size ofthe beam on moon would have been much bigger than the moon andthere would be no chance for a single photon to make it to the moon

The Equation 12 tells us also how small a waist can be achieved byfocusing a large diameter beam For instance the military dream offocusing an infrared laser (λ 3 μm) at 10 km distance to a spot sizeof only 1 cm imposes that the radius of the focusing lens or mirror be18 m The focal size is directly related to the intensity of the light thatcan be concentrated as will be seen in the next section

162 Intensity

Focusing light is akin to placing a jet nozzle on a water hose tosqueeze a large flow into an intense jet We all know how to start abrush fire with the lens of reading glasses (at least those of us wholive in country where the sun shines) Large glasses may not be thefashion but they are sure more efficient in starting a fire The pow-er of the sun radiation that is captured over 1 m2 area is an intensity


corresponding to 1 kWm2 or 01 Wcm2 If we can make an imageof the sun of 1 mm diameter with a lens we reach and intensity of100 kWcm2 which is above the threshold to start a fire

In fine applications like dealing with nanostructures and surgery(Chapter 3 and Section 44) it is not only the limited resource of ener-gy that makes us use focusing elements but also the fine control overthe material How finely can we focus a light Is there any special propertyspecific to the lasers in that matter

The major advantage of laser light over other electronic and ther-mal light sources is its coherence This is partly due to the differencein the nature of radiation as discussed in Section 12 In stimulatedradiation all excited electrons follow the stimulated photon the ra-diation happens at the same time and the same direction Temporalcoherence or coherence in time refers to radiation that is in phase intime This is not enough to have a coherent source just like it is notenough if chorus members all sing at the same time each one at theirown home Somehow we need to have all these voices together to havecoherent music This is where size of the source plays its role For alarge source even if all the points of the source emit photons at thesame time there will be a delay between the photons due to the ex-tension of the source Knowing that waves change sign completely injust half a wavelength distance we prefer to have sources as small aspossible referred to as the point source Having the same phase acrossthe source size is coherence in space or spatial coherence

A laser can produce a collimated beam that is coherent over itscross-section and that will focus on a minimum size spot (Fig-ure 119a) The reverse is an ideal point source (Figure 119b) whereall the emitted photons across the source are in phase With a properlens one can make a collimated beam A different situation emergeswith a filament from an incandescent lamp as shown in Figure 119cEvery point of the filament emits photons of different phases Therays issued from the filament are like spears put in a trash can allpointing in different directions

Given a collimated laser beam as in Figure 119a Eq (12) tellsus the minimum spot size that we can achieve with a lens If forinstance we use a lens of diameter D D 1 cm and focal distancef D 10 cm to focus a laser beam θ D R f D 01 and the spot

diameter is D D 06λθ 6 μm for 1 μm wavelength radiation


Figure 119 (a) The illustration of coher-ence at source is given by comparing apoint source with an extended one like aflash lamp filament If all rays come froma tiny (compared to the light wavelength)source they all generate waves ( photons)with the same oscillation phase With ide-al lenses and mirrors one can generatea parallel beam to infinity (b) The sameapplies in reverse if a beam is parallelit can be focused to one spot (c) Sincewe do not live in an ideal word all theseterms are relative such that as the source

get more extended the collimation is lessIf the source emission is not spatially co-herent the radiation is like having spearsout of a trash can that are all in differentdirections An extended filament evenif emits light at the same time will notgenerate a well collimated beam and willnot be able to merge to a focal point Thesmallest beam at the focus correspondsto imaging the filament Please find acolor version of this figure on the colorplates

17 How to Make the Shortest Laser Pulse

The methods of raquoQ-switchinglaquo and raquocavity dumpinglaquo produce en-ergetic laser pulses but not the shortest possible The shortest pulsethat can be generated by the methods outlined in the previous sectionscorrespond to the time travel in the length of the laser Since this pack-et of energy propagates at the speed of light of c D 299 792 458 ms orapproximately 3 108 ms the pulse dumped from a 1 m long cavitywill pass through an object in a time of 1(3 108) D 3 109 s D3 ns This is not a short time by the standard of raquoultrashort pulseslaquoachieved two to three decades after the invention of the laser

17 How to Make the Shortest Laser Pulse 45

In Q switching and cavity dumping the cavity is like a bucket or adam that is filled with water and then drained partially or fully in ashort time An ultrashort pulse in comparison is like a high wavecompressing all the water of a dam like a light bullet rather thana filling material In the language of athletics Q-switching and cavitydumping are analogous to walking through the laser cavity and a shortpulse is like a raquojavelin long jumplaquo that covers the whole length in asudden high jump

It may come as a surprise that the conformation of the laser pro-ducing extremely short pulses is as simple as the elementary devicesketched in Figure 17b Yet each element of the cavity has to have itsproperty accurately selected in order to develop the shortest pulse pos-sible Before going into the mechanism of pulse generation itself letus first get into the dissection of a short pulse of light how continuouswaves can add up to create a short pulse

171 The Nature of a Pulse

How do we construct a pulse in a mathematical language We haveseen that the nature of laser light is an electric field oscillating at afrequency characteristic of the color of the beam A pulse is made of acombination of waves of different frequencies that add constructivelyat one point and destructively at other points We will call t D 0 theinstant at which the waves that constitute the pulse add at their crestAn example is illustrated in Figure 120 were five waves of increasingfrequency are added on top of each other The sum of these waves isshown with a thick red line At the common crest (t D 0) the sumof the electric field of all these waves adds up to 5 the field of asingle wave which implies that the intensity is 25 that of a singlewave There is no violation of energy conservation because after afew optical cycles the fields add up to nearly zero

Using our picture of radiation (Section 12) of girls on the slideshaving many modes is like having different sets of slides that vary inheight The radiation (sliding) can be in phase if all the girls start at thesame time but eventually since the slides are different the landingtime overlap is zero


172 The Mode-Locked Laser and the Train of Pulses

In order to get shorter pulses one has to manipulate the waves in-side the laser resonator itself Let us return to the analogy of the duck-ling paddling in a rectangular box of Figure 17c It produces a seriesof waves that have different wavelengths with the condition that allthese wavelengths are a submultiple of the box length All these wave-lengths that fit into the ducklingrsquos pond are called modes of the pond(or laser cavity) If the duck were a real genius he could perhaps pad-dle in such a way that all the waves were generated raquoin phaselaquo as inFigure 120 creating a giant crest that would probably swallow himup This is however the secret of ultrashort pulse generation in alaser creating as many frequencies as possible equally spaced andadding them in phase

This process of putting the modes in phase is called raquomode-lockinglaquo In the music world this is as if many harmonics (10 000to 1 000 000) of a note would be resonating together The resultingpulse will propagate back and forth in the resonator with a raquosplashlaquoat the cavity end (the output mirror) creating a train of pulses at aregular interval which is the cavity round trip time tRT D 2nLcwhere L is the cavity length and cn the speed of light in the mediumof index of refraction n that constitutes the laser

We have seen in Section 1131 that there is a frequency of oscilla-tion of the light field ν associated with a wavelength λ ν D c(nλ)The wavelengths λ1 D 2LN λ2 D 2L(N C 1) λ3 D 2L(N C 2) are spaced in frequency by Δν D c(2Ln) The longer the laser cavi-ty L the smaller the spacing between these wavelengths or raquomodeslaquo

Figure 120 Five waves are added on top of each other such that at a given time all thecrests coincide Please find a color version of this figure on the color plates


of the cavity and generally the easier it will be to create short pulsesThis remains true to the limit of an infinitely long cavity as is thecase when a short pulse is generated directly by propagation throughan amplifying optical fiber It also flows from the discussion of thepreceding section that the shortest pulses require the broadest spanin frequencies or the largest number of modes For example in aTisapphire laser the spacing between modes is typically 100 MHzand the number of modes that constitute the pulse can be as high asone million

These million modes cover a frequency range of a hundred millionMHz or a wavelength range of more than 100 nm over which notonly the gain but the speed of light varies Indeed while the speed oflight in vacuum c is a universal constant the index of refraction n is aproperty of the matter and varies across the spectrum This propertyof the medium is called dispersion and plays an essential role in thecreation (and destruction) of ultrashort laser pulses

If each wave that constitutes a pulse propagates at a different ve-locity cn(λ) what will be the speed of the wave packet or pulse (wewill assume that there is still a pulse ndash we will show in the next sec-tion how it will be modified) A pulse is the sum of groups of wavesthe speed of the group of wavelengths (group velocity) differs from thespeed at a particular wavelength This can be visualized as a group ofpeople walking on a street there is a collective speed for the group Itcan be shown that the pulse travels at a velocity vg (the subscript raquoglaquofor raquogrouplaquo) that is generally slower than the velocity of the wave atthe average wavelength

Thus we see that a short pulse rattling back and forth in a mode-locked laser hits the end mirror at regular time intervals t D 2Lvgeven though the wave velocity is not a constant across the range ofthe wavelength that is contained in the pulse The output of the laserwill consist in a train of pulses equally spaced like a pendulum tick-ing at a rate of 1 tRT This is more than an analogy as we will seethat the mode-locked laser is used as an accurate timefrequency stan-dard

It remains now to be seen how the mode-locked laser can contin-uously produce a string of ultrashort identical pulses despite the factthat the waves all have different velocities This is the topic of the nextsection


173 The Mechanism of Pulse Compression by Propagation

To understand how short pulses can be generated we refer to Sec-tion 171 where it was shown that a pulse of light consists of a super-position of propagating waves that have a common crest propagatingat a velocity called raquogroup velocitylaquo The broader the range of frequen-cies involved the shorter the pulse There are two mechanisms inthe production of ultrashort pulses in a laser a mechanism ndash dubbedraquononlinearlaquo because the speed of light depends on the pulse intensityby which the range of frequencies is extended and another one calledraquodispersionlaquo by which all the waves are synchronized to crest at thesame point

In the case of a laser the waves that raquofit in the boxlaquo are equal-ly spaced in frequency (that frequency spacing is the inverse of theround trip time of the laser cavity) In general when such a pulsepropagates back and forth between two mirrors it will broaden intime The reason is that there is a slight difference in velocity betweenthe high frequency waves (short wavelength) and low frequency waves(long wavelength) that constitute the raquowave packetlaquo This wavelengthdependence of the velocity is called dispersion and applies to waterwaves as well How then can ultrashort pulses be generated in pres-ence of this ever present dispersion The answer is in a nonlinearphenomenon by which the wave velocity is linked to the intensityof the wave (Kerr effect) The speed of light is highest in vacuumc D 299 792 458 ms As it propagates through matter it is sloweddown by the interaction with atoms and molecules resulting in a ve-locity v D cn where n is the index of refraction The electric fieldof the laser light (we will assume here that light is linearly polarizedwith its electric field oscillating in a direction perpendicular to the di-rection of propagation) tends to orient the molecules resulting in ahigher interaction with the light field and therefore a larger n and aslower wave velocity

Thus as the pulse intensity is ramped up the wave decelerateswhich implies that the optical cycles will stretch in time or in otherwords the frequency decreases with time The reverse occurs at thepulse tail Near the peak of the pulse the frequency sweeps from lowto high this is called raquoupchirplaquo (Figure 121a) This is the importantfirst step in pulse compression the sweep in frequency such that the


Figure 121 (a) Generation of new opti-cal frequencies by propagation of a pulsein a medium where the wave velocity in-creases with intensity The optical signalof increasing intensity is shown as havinga stepwise increase on its leading edge(the time axis points to the left for a bet-ter visualization of a pulse propagating tothe right) The different intensities prop-agate at velocities v1 v2 v3 and v4 withv4 lt v3 lt v2 lt v1 As a result thepulse optical frequencies decrease withtime along the pulse (or the wavelengthsincrease along the pulse) after somepropagation distance (b) Through the

process shown in (a) one has generatedan raquoupchirpedlaquo pulse that is a pulse ofwhich the optical frequency increases withtime This is exactly what the little bird atthe bottom of the picture is singing Thispulse is now sent through a medium withnegative dispersion (ie a medium inwhich the higher frequencies (blue) prop-agate faster than the lower frequencies(red)) As a result the tail of the pulsecatches up with the pulse leading edgeresulting in pulse compression Pleasefind a color version of this figure on thecolor plates

lower frequencies are pushed ahead of the pulse and the higher fre-quencies are pushed towards the trailing edge

As we saw in Section 171 many frequencies are needed to makea pulse Now the next question is how to stack those frequencies inphase to make a short pulse The trick to continuously compress thepulse is to select a laser cavity configuration such that the lower fre-quencies propagate more slowly than the higher frequencies10) whichimplies that the leading edge moves towards the peak and the trailingedge also recedes towards the peak Hence the pulse is compressedas sketched in Figure 121b It is the task of laser engineers to use op-tical components such as mirrors and prisms to modify the speed oflight as a desired function of frequency

10) This is called a cavity with negative dispersion


174 The Real Thing From Splashing Dyes to Crystal Lasersto Semiconductor Lasers

1741 Milestones and Stumbling Blocks in Femtosecond LaserDevelopment

From the nanosecond Q-switched and cavity dumped pulse thepath to ultrashort pulse generation has not been straight but full ofstumbling blocks the last one being the attosecond barrier Histori-cally the field of ultrashort pulses has grown with dye lasers It hasbeen a remarkable circular evolution as successive mechanisms werediscovered which led to new designs apparently repeating a mucholder one The dye laser was chosen because of its high gain (up to afactor of 2 gain with continuous pumping and a factor 3 with pulsedpumping could be achieved through the 100 μm thick dye jet) An-other advantage is that it is a visible laser which in addition to thebeautiful palette of colors that it provides (Figure 122) implies rel-


Figure 122 A ring dye laser The dye jet isseen in the middle of the picture pumpedby the bright blue beam of an argon ionlaser The mirror in the foreground focus-es the argon leaser beam at a tiny spotin the dye jet This gain spot is at the fo-

cus of two curved mirrors which direct acollimated beam in the other part of thecavity The red intracavity beam of the dyelaser can be seen on the picture Pleasefind a color version of this figure on thecolor plates

ative ease of alignment because of the visible fluorescence11) of thegain medium The high gain made it possible to implement succes-sive lossy mechanisms of pulse formation and compression inside thelaser cavity The first one that came to mind was saturable absorptionwith an organic dye as saturable absorber contained in a thin liquidjet similar to the jet contained the solution of the gain medium Theorganic dye ndash Rhodamine 6G being the most popular gain medium ndashwas dissolved in ethylene glycol and forced at high pressure througha thin (100 μm typically) stainless steel nozzle The pump laser beam(argon ion laser of up to 20 W power) was focused into and nearlytotally absorbed by that flowing sheet of liquid It is because the fo-cal volume was replenished at very high speed that such high powerdensity could be injected into that gain medium It should be notedthat in this configuration the dye laser could handle higher powerdensity than any other medium Such properties explain why the dye

11) Radiation that is due to pumping with a different wavelength usually a shorterpump wavelength


laser has been one of the most popular sources for spectroscopy andshort pulse generation for at least two decades One can wonder whyit seems to have vanished in the twenty-first century Several factorscontributed to its demise First was the inconvenience of having tohandle a noisy pump system and high pressure liquids Not only didthe laser produce a colorful display of colors but most often the op-erator was covered from head to toe with red orange green colorsthanks to the occasional bursting of a high pressure hose Second wasthe chemical hazard While Rhodamine 6G was used as food color-ing in the early 1960s it was soon discovered to be carcinogenic asmost other organic dyes A little known fact is that the viscous solventethylene glycol which is commonly used in car radiators is listed as ahazardous liquid when heated its vapor can cause permanent braindamage

As mentioned above the first continuously mode-locked laser hada saturable jet and a gain jet in the same cavity as sketched in Fig-ure 123a [13] The pulse duration was 06 ps Then a frantic compe-tition started with subsequent publications citing a pulse reductionby a small percentage due to a new physical approach of configu-ration Improved saturation absorption was achieved by what waslater dubbed raquocolliding pulse mode-lockinglaquo the implementation issketched in Figure 123b [14] The principle is that when two travelingwaves raquocollidelaquo head on they create a standing wave where the crestand trough of each wave add up at one position Water waves willdouble in amplitude Light waves will double in electric field ampli-tude at the crests but quadruple in intensity which implies increasedsaturation Two traveling colliding waves can be created by reflectinga wave against a wall ndash in the case of optics by reflecting a pulse ona mirror The first raquocolliding pulse mode-lockinglaquo used a saturableabsorber flowing against an end-cavity mirror [14] and resulted in thegeneration of 03 ps pulses A prism in these first configurations wasused as in a spectrometer to select the wavelength at which the sat-urable absorber can operate As we have seen the shorter the pulsethe larger the range of wavelengths that constitute the pulse andtherefore wavelength selection by a prism is contradictory to makinga short pulse The next increment in a shorter pulse was obtainedby eliminating the bandwidth limitation of the prism and using acavity mirror that uniformly reflects only the wavelengths over whichthe saturable absorber functions This simplest cavity shown in Fig-


Figure 123 Successive configurationsof mode-locked dye lasers G is the gainjet ndash most commonly Rhodamine 6G ndashand S is the saturable absorber ndash mostcommonly diethyloxadicarbocyanine io-dide The configuration (a) of the early1970s [13] gave way to (b) a raquocollidingpulse mode locked cavitylaquo [14] A sim-pler cavity in (c) used all dyes mixed in

one jet and mirrors with square spectralbandwidth [15 16] In (d) with the raquocol-liding pulselaquo mode-locking implementedin a ring cavity the prism is reinstatedbut at the center of curvature of a mir-ror [17] In (e) a four prism sequence isintroduced in the ring to produce negativedispersion [18] Please find a color versionof this figure on the color plates

ure 123c [15 19] produced pulses of 120 fs duration It was realizedthat the thickness of the saturable absorber dye jet was setting alimitation on the length of the optical pulse The next improvementthat brought down the pulse width to 90 fs was a thinner saturableabsorber dye jet and the same colliding pulse mechanism as in Fig-ure 123b but implemented by a cavity with a ring geometry [20] The90 fs shortened to 65 fs [21] after a group at Rochester reported 70 fsout of the configuration of Figure 123c pumped synchronously by amode-locked argon laser [16] As time seems to proceed backwardsthe edge mirror was eliminated the prism was reintroduced but lo-cated at the center of curvature of a mirror so that the wavelengthselection it introduced was greatly reduced (Figure 123d) That con-figuration which is identical to that of Figure 123a except for thering geometry of Figure 123d generated pulses of 55 fs duration [17]


The innovation was to compress the pulses inside the laser cavity byadjusting the amount of glass (translating the prism)

The mechanism is exactly that of raquosoliton compressionlaquo men-tioned earlier in Section 173 In this particular case the dispersionof the prism is positive compensating a downchirp caused by satura-tion of the dye (as the absorber dye saturates its index of refractiondecreases which causes a downchirp) The soliton approach took adifferent twist with the introduction of a four prism sequence tocreate negative dispersion (Figure 123d) and a positive self-phasemodulation12) in the solvent of a jet that in this case was no longeracrobatically thin The balance of the Kerr effect and prism dispersionled to a pulse duration of 27 fs [18] which was the basis of the designof the solid state lasers that followed such as the Tisapphire laser

As the 1970s and 1980s were the decades of the dye laser the 1990ssaw the start of two decades of the ultrafast Tisapphire laser Pulsedurations of less than 12 fs in the early 1990s [22 23] evolved to pulsesof less than 5 fs (only two optical cycles) in 2001 [24] This is the limitof what can be achieved directly out of a laser The next era is in theattosecond range

What made the Tisapphire laser more successful than the dyelaser The gain is lower and the beam is barely visible The outputpower of a laser is not determined by the gain but by the satura-tion intensity A high gain implies a low saturation intensity whichexplains that the mode-locked dye lasers had only an output pow-er typically in the mW range The Tisapphire laser has a thousandtimes lower fluorescence much smaller gain but a thousand timeslarger saturation intensity Output powers of the order of 1 W can beroutinely obtained from the Tisapphire laser The wavelength in thenear infrared is barely visible The configuration is similar to that ofthe dye laser as shown in Figure 124 The control of dispersion ofthis laser is made with a prism sequence the first one of which isseen on the left of the picture In subsequent lasers the function ofnegative dispersion is achieved with special coatings of mirrors The

12) Self-phase modulation is a changeof phase or speed of light across thepulse due to the Kerr effect This isa self-induced phenomena becausethe medium response varies withthe intensity of the pulse A positive

self-phase modulation results in afrequency sweep across the pulsehaving lower frequencies at the frontand higher frequencies at the tail ofthe pulse


Figure 124 A Tisapphire laser The Tisapphire crystal is pumped through one ofthe two curved mirrors projecting the gain spot into the cavity by a frequency doubledvanadate mirror Please find a color version of this figure on the color plates

mode-locked Tisapphire lasers used for ultrashort pulse generationhave a pulse duration that can be as short as 8 fs Since the speed oflight is approximately 03 μmfs this represents a light bullet of only24 μm of three optical cycles at the wavelength of 08 μm

It is not certain however that the Tisapphire laser has a brightfuture Its biggest shortcoming is the cost of acquisition and opera-tion It requires a semiconductor pumped vanadate laser operatingat 1064 nm which is frequency doubled (see Section 111) to 532 nmto pump the Tisapphire This chain of lasers is not only expensivein acquisition but also inefficient The future most likely belongs tosemiconductor lasers with high wall-plug efficiency which are slowlyapproaching pulse durations comparable to those of the Tisapphirelaser


175 Water Waves and Laser Pulses

1751 From Water to Lasers The SolitonThe equation that describes the compression mechanism of the

previous section is famous in physics and in mathematics it is theraquononlinear Schroumldinger equationlaquo It has been used to describe theevolution of a pulse in a cavity leading to a steady state solution whichis a stable pulse of well defined shape energy and duration propa-gating back and forth in that laser cavity The nonlinear Schroumldingerequation in space is also used to describe the spatial profile of abeam that collapses and creates its own waveguide in a nonlinearmedium (which can be any medium including air as will be seenin a subsequent chapter) The soliton is one steady state solutionof the nonlinear Schroumldinger equation The phenomenon was dis-covered long before the mathematical equation even existed by theengineer and shipbuilder John Scott Russell (1808ndash1882) [25] whonamed it raquothe wave of translationlaquo In 1834 he was riding by theGrand Union Canal at Hermiston Glasgow and observed that whena canal boat stopped its bow wave continued onward as a well de-fined elevation of the water at constant speed It was only in the1960s that the name raquosolitonlaquo was coined when the phenomenonwas rediscovered by the American physicist Martin Kruskal De-tails of the early history of the soliton can be found in a book byRobin K Bullough [26] The soliton took up so much importance inall areas of physics and laser optics that a recreation of the obser-vation of John Russell was organized for the 150th anniversary ofhis observation Figure 125 shows a picture of a re-creation of thatevent

1752 From Laser to Water The raquoFreak WavelaquoIt is a water problem (the goal of John Russell was to design the best

dimensioned canal for navigation) that led to the discovery of solitonswhich brought a revolution in the field of lasers and fiber communi-cations Most recently the same raquononlinear Schroumldinger equationlaquothat became an essential tool to understand the propagation of ultra-short optical pulses came under renewed interest to solve a puzzlingproblem for oceanographers It was the biggest mystery of the seasLarge ships disappeared over centuries without leaving any tracksThis led to the creation of myths of sea monsters and then that of raquogi-


Figure 125 Recreation of the soliton in 1984 ndash soliton home page Heriot Watt Uni-versity (Reprinted by permission from Macmillan Publisher Ltd Nature 376 (1995)373)

ant waveslaquo These stories were dismissed as seamenrsquos tales until twowell documented events in 1995

The first was an automated recording at the Norwegian Oil plat-form Draupner-E which indicated in the New Year night a singlewave of 26 m height The second was on 11 September of the sameyear when the luxury liner Queen Elizabeth 2 on its way to New Yorkwas hit by a giant wave (report of Ronald Warwick Captain of theQueen Elizabeth 2 interviewed on the BBC Radio 2 on 14 November2002) All oceanographic models so far predicted a statistical distri-bution of waves not exceeding 7 m while the freak waves recordedreached more than 30 m

The wave equations used were similar to the linear wave propa-gation in optics including a frequency dependent wave velocity Thebreakthrough came when the same nonlinear term as in optics wasintroduced an intensity (in this case height) dependent wave veloci-ty One can justify this behavior by arguing that the higher the wavethe less its velocity would be affected by friction with the deeper waterUnlike the case of lasers where there is a deterministic controlled dis-tribution of waves the random distribution of water waves in a storm


Figure 126 Huge waves are common near the 100-fathom curve on the Bay of BiscayPublished in the 1993 Fall issue of Marinerrsquos Weather Log

have only a very small but still existing probability to be in the condi-tion of raquopulse compressionlaquo defined in Section 173 hence the freakoccurrence of the raquogiant wavelaquo

There is a more scientific name than just raquoroguelaquo or raquofreaklaquo forlarge events that have a nonzero probability of occurring The proba-bility distribution ndash that is the probability that a wave of size h occurshas a characteristic heavy tailed raquoL-shapelaquo In stark contrast to Gaus-sian probability where the probability of being in the mean (middle)value is the most likely events much larger than the mean occur withsignificant probability

1753 Back from Water to Lasers Freak ColorsThe raquorare but significantlaquo statistic [27] had stirred some excitement

among mathematicians and physicists who started to search for sim-ilar statistical events in other areas [28] Once again theoretical find-ings of water waves found their analogy in laser physics This time itis not raquofreak waveslaquo but raquofreak colorslaquo as shown in Figure 127

One of the key characteristics of laser light is the ability to form anearly perfectly uniform collimated beam (see Section 161) Drivingyour car at night with the best large laser headlight you would be ableto uniformly illuminate a wide road at 1000 km distance This would


Figure 127 (a) The annular display seenon a door 25 m away from the intenseshort pulse laser source The beam hascollapsed into a single filament whichhas produced these concentric colorfulcones (b) A filament produced in glassThe color spectrum is displayed horizon-tally (from long wavelength to the left to

short wavelengths to the right) and theangle the individual rays make with thehorizontal is the vertical axis The intensebeam propagates along an horizontalaxis (shown in black) The directions ofthe rays is indicated for different colorsPlease find a color version of this figureon the color plates

Figure 128 Formation of a raquofilamentlaquo ora self-guided intense beam in air A laserbeam is propagating from left to rightwith an intensity versus radius sketchedat the extreme left Given a sufficientlyhigh intensity the index of refraction willincrease proportionally to the intensity asindicated by the dashed curve This spa-

tial dependence of the index of refractionresults in a lensing effect The wavefrontswill curve and the rays perpendicularto the wavefronts will bend towards theaxis A waveguide is formed by the beamitself similar to the fiber sketched in Fig-ure 112 Please find a color version ofthis figure on the color plates

work only if our earth were flat and if there were no distortion dueto atmospheric turbulence However that ideal headlight would nolonger give you good uniform illumination if you were to try to in-crease the optical power beyond reasonable limits At powers exceed-ing 10 GW (10 GW or 10 000 MW) the hitherto uniform beam willcollapse into tiny light needles or raquofilamentslaquo (Chapter 7 Section 71)Of course this can only be observed for very short times generatingsuch high power your car battery would run empty in less than a μs


The physical origin of such collapse is the same intensity depen-dent wave velocity that was exploited in Section 173 to generate ul-trashort pulses However here at these intensities it is the index ofrefraction (Kerr effect) of air that becomes intensity dependent cre-ating a lensing effect where the intensity is the highest as sketchedin Figure 128 The beam is focused by that self-induced lens untilit reaches a very small diameter it creates its own waveguide guid-ing light in a similar manner as a fiber (Figure 112) The spatialshape (intensity versus radius) of these filaments is also governed bythe raquononlinear Schroumldinger equationlaquo another contribution from wa-ter science to the laser optics field These filaments are raquosolitons inspacelaquo as opposed to the raquosolitons in timelaquo presented in the previoussection However a dashing display of colors is associated with thesefilaments as shown in Figure 127 Beauty however does not comewith Gaussian statistics It was recently suggested that the widest dis-play of colors is related to the freak wave statistics For instance theappearance of the violetndashblue in Figure 127 is characterized by thesame raquoL-shapedlaquo statistics as the freak oceanic waves [29]

18 Ultrashort Ultraintense Laser Pulses

When dealing with pulses one must consider the extension of pulsein time One joule per second output of a continuous laser with spotsize of 1 cm2 gives the intensity of 1 Wcm2 For a pulsed laser out-put of 1 J and 10 fs long and the same size the intensity is 1014 or100 million million Watt per square centimeter Short pulses are usedwhenever extreme high intensity is needed at the expense of the ex-posure time

181 Definition of raquoIntenselaquo

The perception of what is an raquointenselaquo laser pulse varies over an im-mense range For the medical user a beam that burns the skin can bequalified as intense and this requires no more than 10 or 100 Wcm2A chemist will consider high the intensity that will break a chemicalbond which can be in the range of MWcm2 to GWcm2 The mostpower hungry are the physicists At the lower end of the scale the

18 Ultrashort Ultraintense Laser Pulses 61

atom physicist will only get excited if the field of the laser13) reaches asufficient value in one oscillation to extract an orbiting electron fromthe atom (Figure 129a) and pull it back at the next half cycle of thefield (Figure 129b) The disturbed electron comes back to the atomwith a vengeance producing a burst of x-rays of incredible short du-ration in the attosecond range (Figure 129c) One attosecond 1000times shorter than the femtosecond is in the same ratio to the sec-ond as the age of the universe is to the second (1018) The intensitiesto reach electron extraction ndash return to the atom ndash are now in the ter-awatt (1012) to petawatt (1015 Wcm2) range To move away from theabstraction of these numbers let us try to get a feeling for what theseintensities mean by considering the pressure of light The photon hasno mass but it acts like a solid particle having a momentum hνcWhen bouncing off a surface such as a mirror it induces a recoil mo-mentum Mv D 2hνc where v is the velocity given the mirror ofmass M A beam with a flux of N photons(cm2 s) has an intensity I(in Wattscm2) and exerts a pressure of N2hνc D 2Ic on the mir-ror Sunlight has an intensity of 01Wcm2 The pressure that sunlightexerts on the 1 cm2 area of the reflecting raquolight milllaquo shown in Fig-ure 129d is equivalent to one millionth of a 1 mg flea distributed overa cm2 area Definitely not sufficient to make a light mill spin14) At theintensity level of 1016 Wcm2 used in attosecond pulse generation theradiation pressure is 1000 higher than the pressure at the deepestpoint of the ocean (Figure 129e)

As impressive as these intensities may seem there is another breedof physicists that looks upon them with disdain At sufficiently highintensities electrons can be accelerated during a half optical cycle torelativistic velocities that is velocities close to the speed of light Asone tries to accelerate an electron more by increasing the light fieldthe mass of the electron increases (to reach infinity at the speed oflight) For the relativist plasma physicist high intensity means above1018 Wcm2 for 1 μm radiation That intensity corresponds to an op-

13) Remembering that laser light is anelectric field that oscillates in time

14) One may wonder what makes a lightmill spin Each of the four planes ofthe light mill has a black face and amirror face The radiation pressureacts on the reflecting surface Onemay notice that the irradiated mill

turns as if the light was pushing theblack surface This is because theblack surface absorbs the photon andheats the surface which partiallyvaporizes It is the recoil from themolecules escaping the black surfacethat makes the light mill spin


Figure 129 The electric field of a pulsenear the peak of a cycle is sufficientlyhigh to eject an electron from its orbit (a)The electron is accelerated away from theatom then decelerated to a halt the nexthalf cycle as the light electric field revers-es sign (b) During the next quarter cycleof the light pulse the electron is acceler-ated back towards the atom Numerouscomplex physical phenomena can occurduring that recollision one of them be-

ing the emission of an extremely short(typically 100 as) burst of x-ray radiation(d) The pressure of sunlight or a He-Nelaser is not sufficient to make the raquolightmilllaquo (or raquoCrookes radiometerlaquo) spinHowever the radiation pressure at inten-sities used to create attosecond pulses is10 000 times larger than that at the bot-tom of the ocean (e) Please find a colorversion of this figure on the color plates

tical field strength that accelerates the electron to a speed at which theelectron mass has increased by 50

There is a group of physicists even greedier for power the parti-cle physicist For him an intense laser field E is such that for in-stance an electron would be accelerated over a wavelength λc to anenergy eE λc 2mc2 where m is the mass of the electron (or anoth-er particle) mc2 is according to Einstein the energy equivalent to aparticle of mass m at rest As will be seen in Section 62 λc is thewavelength associated with the accelerated electron or the raquoComptonwavelengthlaquo


A back of the envelope calculation shows that the correspondinglaser intensity is above 1023 Wcm2 The concentration of energyis such that the creation of matter ndash a pair of electronndashpositrons ndashwill emerge from vacuum A plethora of other effects are expectedat such intensity levels which are totally beyond the scope of thisoverview

One question to answer however is whether such intensities be-long to science fiction or real research Numerous countries havenational facilities in the PW (1015 W) range The peak power of thenext generation laser that is contemplated is above the raquoexawattlaquo (or1018 W) range Such a laser is no longer at the scale of a nationallaboratory but requires resources at the scale of a continent TheEuropean Community has started such a project the raquoExtreme LightInfrastructurelaquo or ELI Extreme is even an understatement when try-ing to describe the highest intensities contemplated in this projectTo get another appreciation of the meaning of high intensity let usembark on a thought exercise of what is required to keep a beamcollimated despite the diffraction effect mentioned in Section 161In air at atmospheric pressure it has been established that a pow-er of at least 3 GW peak power is required to create a self-inducedof waveguide as described in the previous section The power re-quired is inversely proportional to the density of air since the in-tensity dependent increase of index or refraction is proportional tothe number air molecules that create the nonlinear index Could afilament be produced in the mesosphere (approximately 100 km alti-tude) for instance to guide a reentry vehicle The density of air thereis 1016 moleculescm3 or 10 000 less than the 1020 moleculescm3 atsea level The power required to create a light filament is then of theorder of 10 000 GW or 10 TW In deep space the density of moleculesdrops down to N D 105cm3 and the power required to create a fil-ament is then 1023 W At this level of intensity we are out of classicalphysics Quantum field theory tells us of the existence of self-focusingraquoby vacuum polarizationlaquo and raquobirefringence of vacuumlaquo in shortvacuum itself will cause the beam to self-focus at a power level of 10231024 W For these powers vacuum itself is a nonlinear medi-um since it will absorb the light energy through creation of matterThere will also be nonlinear phase changes all effects that are acces-sible in the range of power and intensities are contemplated by theELI project


182 How Ultraintense Pulses are Generated

We have described a laser source as an optical amplifier sandwichedbetween two mirrors The shortest pulses are produced in a laserwhere a short pulse rattles back and forth in a laser cavity hittingthe end mirror at regular time intervals (Section 17) These mode-locked lasers are the source of the shortest optical pulses that can begenerated (a couple of optical cycles) but the energypulse is gener-ally small at most a few nanojoules Amplifiers are required to boostthe energy of one or a few pulses from the train of pulses emitted bythe laser As in the case of the laser the amplification process is lim-ited by saturation of the gain medium The pulse to be amplified hasto be sent through several amplifier stages of increasing diameter sothat the intensity of the amplified pulse remains below the saturationintensity of the gain medium The energy required to keep the mediaamplifying (maintain a population inversion) increases with the diam-eter of the gain medium (Figure 130) It is like threading a growingelephant through tubes of which the diameter and strength have toincrease with the growing elephant size The problem can be solvedby stretching the ultrashort pulse so that its intensity is reduced bythe stretching ratio and it can be amplified to considerably higher en-ergies before its intensity reaches saturation or damage levels

Figure 130 (a) Any amplifier stage hasto be matched to the size of the amplifiedpulse For a given amplifier diameter thesaturation limits the maximum pulse en-ergy that can be extracted as the diameterof the tube limits the size of the elephantthat can pass through it (b) Instead of in-

creasing the diameter of the tube why notstretch the elephant to make him passthrough a narrower tube and give him theoriginal proportion after amplificationPlease find a color version of this figureon the color plates


Figure 131 Chirped pulse amplificationAn ultrashort pulse is sent through astretcher which can be constructed withdiscrete elements (gratings prism) or bea piece of glass or a fiber The differentfrequency components of the pulse aredelayed with respect to each other re-sulting in chirp and pulse stretching The10 000 to 100 000 times pulse stretching

ratio allows considerable amplification be-fore the damage limit to the componentsof the amplifier is reached The action ofthe stretcher is reversed in the amplifierresulting in the creation of an extremelyintense ultrashort pulse Please find acolor version of this figure on the colorplates

The mechanism of stretching is dispersion a mechanism that wasdiscussed in Section 173 Figure 121 In a medium with dispersion(gratings prisms glass) different frequency components of the pulsespectrum propagate at different velocities resulting in pulse stretch-ing This mechanism is linear and reversible as the sign of the dis-persion is changed raquoChirped pulse amplificationlaquo (CPA) [30] refersto an amplifier system where an ultrashort pulse is stretched by fourto five orders of magnitude sent through several stages of amplifica-tion before being compressed back to the original pulse width Thesuccessive components as sketched in Figure 131 are stretcher (lin-ear) amplifier and compressor In femtosecond high energy systemsthe peak intensity reached are so high that the compressor has to beput in a vacuum chamber Indeed as will be seen in more detail inSection 71 the air itself is a nonlinear medium at these extremelyhigh intensities

19 Ultrashort Ultraprecise Laser Pulses

In the previous sections we introduced ultrafast events which atfirst sight would have little relevance with the time scales associatedwith our daily life By a bizarre twist of nature it is the fastest eventthat ends up providing the most accurate time measurements for long


duration events Let us take for instance the rotation of the earthabout its axis Because of the huge mass involved one would expectthe length of the day to be a perfect clock for long term events yearscenturies and millennia The rotation of the earth is not constant thetides cause a small friction that slows down the earth rotation Para-doxically motions of electrons in an atom which are on the femtosec-ond scale provide a more accurate clock than astronomical events Aquartz clock ticking at kHz has a considerably longer range accura-cy than grandmarsquos pendulum clock ticking at a second rate Atomicclocks however ticking at petahertz (1015) considerably outperformthe quartz clock in long term accuracy Atomic clocks are not onlyused as a time standard but also as a distance standard Here alsoaccuracy and stability are provided by microscopic standards ratherthan by large objects The meter was initially defined at the time ofthe French revolution as being 1100 of the decimal degree on theequator (or 140 000 of the circumference of the earth) This definitionhas been replaced by a smaller object a block of quartz a meter longstored at constant pressure and temperature in Paris However eventhat object does not have the long range stability of the wavelengthof the cesium clock Presently the length standard is defined throughthe time standard (the period of oscillation of the Cs clock in the fsrange) multiplied by the speed of light in vacuum (defined as a fixednumber c D 299 792 458 ms)

While accuracy may come as a surprise it should be obvious thatthe shortest clock period will provide the most sensitivity or resolutionin time measurement since the measurement is performed with finertick marks A seemingly impossible challenge is to count time whenthe time interval between clock ticks is only a couple of fs a milliontimes faster than standard electronics can resolve This is where thelaser made a remarkable revolution which was recognized by the No-bel Prize in Physics in 2005 It refers to a property of the mode-lockedlaser that has puzzled researchers for some time [31] The sketch ofFigure 132 will help explain the dilemma We have seen that lasersused for generating ultrashort pulses by mode-locking have gain overa very broad range of wavelengths Therefore if they are not mode-locked (see Section 172) they can be operated over a broad range ofwavelengths As we tune that wavelength we can record the roundtrip rate of that cavity on a frequency counter Since the speed of lightin the components of the cavity is a function of the wavelength we

19 Ultrashort Ultraprecise Laser Pulses 67

Figure 132 On the left the output ofa tunable laser (such as a dye laser or aTisapphire laser) is sent to a detectorconnected to a frequency counter Thelatter records the repetition rate (roundtrip rate) of the laser as a function ofwavelength The repetition rate variesacross the spectrum The transformation

of the laser from a continuously tunableinto a mode-locked laser is equivalent tosending the laser to an orthodontist Asthe output of the laser is sent to a spec-trometer and thereafter to the frequencycounter the same number (repetition rateof 101 884 130 Hz) is observed across thespectrum

will record a curve as shown in Figure 132a What is measured is theseparation between the optical frequencies or modes that can be pro-duced by this laser These optical frequencies form a frequency combof which the spacing between teeth is not constant If by a strike ofmagic we make the same laser produce ultrashort pulses we can per-form a similar experiment consisting in measuring the pulse rateafter selecting a particular wavelength region We find that the repeti-tion rate is constant over the spectrum The frequency comb producedby the laser in mode-locked operation has a constant spacing betweenteeth [32] Mode-locking the laser is like sending the laser to the or-thodontist it corrects the tooth spacing The mechanism by which theteeth spacing is raquocorrectedlaquo is rather complex [31] and is related to thesoliton operation discussed in Section 173 Having a perfect comb infrequency has important consequences in metrology It means firstthat this comb can be used to measure frequency differences just asa metric ruler is used to measure distances It also implies that in thetime domain the pulse train that is issued from the mode-locked lasercan be represented by a single frequency wave (labeled the raquocarrierlaquo)that is sampled at regular intervals (which correspond to the roundtrip time of the laser cavity) as shown in the top part of Figure 133In frequency the mode-locked laser can be represented by a combof equally spaced teeth as shown in the bottom part of Figure 133


Figure 133 The mode-locked pulse trainin the time domain (top) is shown as awave at a single carrier frequency modu-lated by and envelope The correspondingcomb of optical frequencies is represent-ed on the bottom (a) A general casewhere the envelope spacing is not an in-

teger number of optical cycles (b) Theenvelope spacing is an integer number oflight periods and in addition the carrierto envelope phase is zero Please find acolor version of this figure on the colorplates

For each pulse the phase of the carrier at the peak of the envelope iscalled the carrier to envelope phase (CEP) In Figure 133a the spac-ing between envelopes is not an integer number of optical cycles ofthe carrier and therefore varies from pulse to pulse The frequencyat which this CEP varies (the ratio of CEP for two successive pulsesto the pulse spacing) is called the carrier to frequency offset (CEO)The situation represented in Figure 133b is that where the envelopespacing is an integer number of light periods Thus the time betweenthe pulses is defined with the precision and accuracy of the light pe-riod (typically 25 fs) and is of the order of a nanosecond and thuscan be electronically counted If the carrier frequency is linked to thatof an atomic clock one has created a time standard of femtosecondprecision In the frequency domain one tooth of the comb has beendefined with absolute accuracy The spacing between teeth is also de-fined with the same accuracy since it is being forced to be an integernumber of light periods (forcing the CEO to be zero) The frequen-cy comb is then a frequency ruler of utmost accuracy and precisionwhich is particulary useful in astronomy

110 Ultrashort Ultrasensitive Laser Pulses

The near perfection of the laser output itself makes it very sensitiveto any perturbation As an example if we consider only the propaga-tion of the frequency comb of zero CEO shown in Figure 133b the

110 Ultrashort Ultrasensitive Laser Pulses 69

velocity of the pulse envelope will generally be different from that ofthe carrier As a result the CEP will change a change that can be ex-ploited to monitor the properties of the medium traversed Highestsensitivity can be achieved if this change in CEP is exploited insidethe laser itself as will be analyzed in more detail in Chapter 8 Oth-er properties of ultrashort laser pulse that can be exploited to senseproperties of the traversed media are the possibilities of high pow-er pulses to project high intensities at distance through filaments (asdiscussed above in Section 8) and create other wavelengths throughthe nonlinear process to be described in Section 111 that followsMethods to exploit filaments for remote sensing will be the topic ofChapter 7

111 The Nonlinear Wizard Juggling with Frequencies

1111 Stacking up Photons

The nonlinear wizard is not a scary cross-sighted scientist but in-stead a jewel a small crystal The generation of harmonics is commonwith electronic amplifiers If a pure note is given by the amplifier andwe turn up the volume the sound will be distorted When a wave is nolonger a pure sinusoidal wave that means it contains higher frequen-cies ndash the harmonics The first of these harmonics is the raquosecond har-moniclaquo that is an electromagnetic oscillation as twice the frequencyof the light or half the wavelength

For instance the invisible IR NdYAG laser or the vanadate laserat 1064 nm can be made to generate in a crystal a second harmonic


at the green wavelength of 532 nm This has become the most com-mon source of green light used in green laser pointers in powerful(up to 20 W) continuous lasers to pump Tisapphire lasers or for rockconcerts

There are some stringent conditions to be met by the crystal to gen-erate efficiently the second harmonic The first condition is a lack ofsymmetry the crystal structure should not have a center of symme-try The second condition is called raquophase matchinglaquo The generatingwave (called the raquofundamental wavelaquo) will create its second harmonicat any point of the crystal The fundamental propagates at the velocityof the wave vw1 D cn1 where n1 is the index of refraction of the crys-tal for the fundamental wavelength along the direction of propagationand polarization of the fundamental Figure 134 illustrates three cas-es of second harmonic generation in a crystal with a raquosnapshotlaquo ofthe waves passing through the crystal at a certain instant The waveF is the fundamental wave the same in all three cases In all threecases a second harmonic is generated at the entrance plane A andpropagates through the crystal at a velocity vw2 D cn2 where n2 isthe index of refraction of the crystal for the shorter second harmonicwavelength along the direction of propagation and polarization of thesecond harmonic Case (a) corresponds to the case where the crystalis phase matched that is n2 D n1 and the second harmonic andthe fundamental propagate at the same velocity in the crystal Con-sequently the second harmonic generated in the plane B SHB is inphase with the second harmonic generated in A that has propagatedto B The two signals add in phase to create a larger second harmonicfield SH Case (b) shows the more general case when the crystal is notphase matched n2 curren n1 and the second harmonic SHA generated atthe entrance plane A of the crystal having propagated to a plane Bmay destructively interfere with the second harmonic SHB created atthe plane B The resulting second harmonic field SH is zero In thecase of phase matching (a) the second harmonic generation can thenbe very efficient up to 80 of the fundamental light can be convert-ed into the second harmonic However one cannot always find in acrystal an orientation for which n2 D n1 In that case there is anoth-er possibility to generate a second harmonic efficiently by using theproperty that the crystal has no center of symmetry In (c) the secondharmonic generated at the entrance plane A and propagated to planeB is SHA as in case (b) However by reversing the crystal orientation

111 The Nonlinear Wizard Juggling with Frequencies 71

Figure 134 Simplified sketch to illustratethe second harmonic generation in a non-linear crystal F is the fundamental wavesent through the crystal In (a) the crystalis phase matched the second harmonicgenerated at the entrance plane A prop-agates to the plane B (SHA) and addsconstructively with the second harmonicproduced by the fundamental at plane B(SHB to form a large second harmon-ic field SH) In (b) case of a nonphasematched crystal the second harmonicSHA is out of phase with the second har-monic produced by the fundamental at

plane B (SHB the two fields cancel out toform a zero second harmonic SH) (c) isthe case of a periodically poled crystalWith the optic axis oriented as shown bythe arrows the propagation and secondharmonic generation from plane A to Bare the same as in case (b) In case (c)the optic axis is reversed after plane Band the second harmonic generated in Bis reversed as compared to cases (a)and (b) Consequently the two fields SHAand SHB add in phase to create a largesecond harmonic SH Please find a colorversion of this figure on the color plates

at plane B the phase of the second harmonic generated at that planeSHB is also reversed and therefore adds in phase with SHA The crys-tal where the optical axis is flipped periodically is called a periodicallypoled crystal This technique is called quasi-phase matching and isused most often with lithium niobate crystals which have a very highnonlinearity and good transparency The acronym PPLN is quite oftenused to designate these crystals The nonlinearity is the highest alongan optic axis of the crystal the z-axis Poling is achieved by applyingthin electrodes (1040 μm wide depending on the length of the in-dividual domain desired) on the faces perpendicular to that axis Theraquopolinglaquo or orientation of the axis is made by applying a very highelectric field at high temperature on these electrodes

Nonlinear optics can easily be described through the photon pic-ture Two photons of the fundamental radiation are converted intoone photon of the second harmonic of twice the photon energy underthe influence of the crystal The two generating photons do not needto be of the same frequency if one photon has the energy hν1 and the


other the energy hν2 they can combine in the crystal to form the sumfrequency photon of energy hν3 D hν1 C hν2 As almost everything isreversible with laser light there is also a process of difference frequencygeneration where two light beams at optical frequencies ν3 and ν2 aresent into a crystal to generate a wave at frequency ν1 D ν3 ν2 Asin the case of the second harmonic generation the process has to bephase matched to be efficient all three waves have to propagate at thesame velocity

Two photons of equal frequency or wavelength can add up in sec-ond harmonic generation or raquofrequency doublinglaquo or they can sub-tract from each other resulting in zero frequency generation or opticalrectification In that case a field of zero frequency which is a contin-uous field is applied to the crystal The reverse of that operation isthe electro-optic effect which was introduced in Section 1533 bywhich the sum of a zero-frequency photon (continuous electric field)and an optical photon at frequency ν1 is made to result in an opti-cal photon still at frequency ν1 with slightly different phase andorpolarization

1112 Parametric Generation and Amplification

In the previous section a higher frequency photon was created byadding two lower energy ones Two photons are lost from the funda-mental beam in order to create a single photon of higher energy Inthe reverse process if starting with a higher energy photon of ener-gy hν3 there is gain for radiation at the frequency νs lt ν3 This iscalled parametric gain and is fundamentally different from stimulatedemission gain In the presence of a beam of frequency νs the raquopumplaquophoton of energy hνp gives birth to two photons respectively of ener-gy hνs (the raquosignal photonlaquo) and hν i (the raquoidler photonlaquo) such thathν3 D hνs C hνi (Figure 135) As in the case of gain with popu-lation inversion the photon hνs is undistinguishable from the otherphotons of the beam at frequency νs Despite the similarity paramet-ric gain is fundamentally different from gain produced by a popula-tion inversion as sketched in Figure 135 In this case we consider asquare pulse pump (in time) that is the pump beam is turned on for avery short time then turned off The propagation of a weak pulse in amedium with population inversion is similar to a skier going downhill(Figure 135a) The signal pulse extracts more and more energy from


Figure 135 Comparison of gain throughpopulation inversion and parametric gain(a) In the case of gain through populationinversion the signal pulse extracts more

and more energy from the medium as itgrows (b) In the case of parametric gainthe signal pulse only gains energy as longas the pump is present

the medium as it grows because the gain has a lifetime of the orderof microseconds in the case of crystal host lasers such as TisapphireNdYAG YbYAG etc which is a very long time in the laser worldFor a parametric gain however (Figure 135b) the signal pulse at νs

only gains energy as long as the pump (the bear at νp) is present Withparametric gain there is no background noise from fluorescence asthere is with a population inversion gain medium

11121 Optical Parametric Oscillators and Optical Parametric GeneratorsAs we have seen in Section 133 a laser is an amplifier with the

feedback of some mirrors which can be arranged in a linear configu-ration or a ring cavity An optical parametric oscillator is very similarto a laser with gain The main difference is that the gain medium isa crystal and that the pump radiation has to be provided by a laserThe main use of the optical parametric oscillator is to be a source oflaser radiation in the infrared since it provides photons of lower en-ergy than the pump photons At each round trip through the cavity ofthe beam at frequency νs pump photons of energy hνp are replaced


Figure 136 (a) An optical parametric oscillator in a ring cavity (b) An optical paramet-ric generator (c) A seeded optical parametric generator Please find a color version ofthis figure on the color plates

by two photons of energy hνs and hν i The photon of energy hνs iscalled the signal photon and adds up coherently (that is in phase) tothe beam of wavelength λs D cνs In general the cavity will onlybe resonant for the signal wavelength as sketched in Figure 136aThere would be too many constraints if both the idler and signal wereresonant with the cavity Indeed the idler frequency would be simul-taneously fixed by two conditions that in general may conflict to bethe difference of the pump and signal frequencies and at the sametime a mode of the cavity

We have seen in the case of a nitrogen laser (see Section 1422)that a mirrorless laser can operate if the gain is sufficiently high thefluorescence is amplified along the longest dimension of the gain vol-ume In the case of the pumped nonlinear crystal there is no fluo-rescence to be amplified Yet with sufficient excitation a crystal usedfor optical parametric oscillation may produce a rainbow of colors asillustrated in Figure 136b Complementary colors for which the sumof the optical frequencies equal that of the pump are generated at an-gles such that all three waves remain in phase throughout the crystalThis is called an optical parametric generator (OPG) Since there is nofluorescence to be amplified what is the radiation that is being am-plified We have seen that vacuum itself is filled by a sea of photons(cf Section 111) It is this vacuum photon or zero-point energy thatseeds the optical parametric generator In the typical arrangement ofFigure 136 the pump radiation will be green laser light near 500 nmThe signal will be in a range of 7001100 nm and the idler at the com-plementary wavelength so that the sum of photon energies (idler andsignal) equals the pump energy

There is a remarkable application to the OPG that of being a sourceof light that has its own intensity calibration The intensity of the vacu-um radiation is known from theory The gain along a path of amplified


radiation can be measured by sending seed radiation along that samepath and measuring the ratio of amplified to initial intensity (Fig-ure 136c) The amplified seed radiation is seen as a bright spot withinthe ring of optical generation of the same color in Figure 136c Abso-lute calibration of a light source by such an arrangement has beendemonstrated with high power pump lasers [33] If miniaturized andimplemented with efficient compact lasers it can become a valuabletool for spacecrafts and satellites in need of detector and source cali-bration that is not dependent on lamp standards that are susceptibleto aging

1113 Too Many Photons to Swallow Multiphoton Absorption

The phenomena described in the previous sections have a remark-able property no energy is lost from the light waves The materialacts as a catalyst exchange two or more photons for a higher en-ergy photon In harmonic generation the crystal is a generous so-cial worker definitely not a capitalist he does not keep any energyfor himself The sum of the product of the photon energies by theirnumber is conserved in harmonic generation We have seen in Sec-tions 132 and 152 that an atommolecule with energy levels sep-arated by the photon energy will absorb the photon The total ener-gy of the radiation-matter system is conserved but energy has beentransferred from the beam to the matter In another situation a medi-um that is transparent to low intensity radiation may become absorb-ing for high intensity light if there are some energy levels at twicethe photon energy The mechanism of multiphoton absorption is im-portant for depositing energy inside a transparent medium Indeedwhen focusing an intense pulse inside a material the intensity in-creases along the beam to reach a maximum at the focus Likewisethe absorption will increase to a maximum at the focus In the case ofa two-photon absorber the beam absorption or the number of pairsof photons absorbed is proportional to the square of the intensity ofthe laser radiation For n-photon absorption the attenuation is propor-tional to the nth power of the exciting beam intensity Radiation maybe emitted by fluorescence following multiphoton absorption This ra-diation is quite different from the harmonic generation discussed inSection 1111 Harmonic generation of intense radiation at the wave-length λ0 is instantaneous and at a wavelength that is an exact sub-


multiple of the fundamental λn D λ0n Fluorescence following mul-tiphoton absorption is not instantaneous [34] and the radiation thatfollows the excitation at a wavelength λF lt λ0n lasts for a raquofluores-cence lifetimelaquo in the range of ns to ms Applications of multiphotonabsorption are discussed in Chapter 5

Ultrashort pulses can typically eject an electron from an atom ina processus called multiphoton ionization This phenomenon has animpact on filamentation (negative lensing due to the electron plas-ma ndash see Section 1753) attosecond pulse generation (see Chapter 6)and plasma shutter

11131 Plasma Shutter ndash How It Leads to a Better Understandingof Absorption

The plasma shutter deserves a few lines of introduction as one ofthe oldest and simplest applications of multiphoton ionization It isgenerally used in combination with a TEA laser (see Section 1421)The MW peak power of that CO2 laser is focused in air (or any othergas) creating a plasma of electrons by multiphoton ionization Theseelectrons are accelerated by the field of the laser to an energy suffi-cient to ionize all the other surrounding molecules a process calledcascade ionization The latter cascade ionization results in a total ion-ization of the focal volume or creation of a raquoplasmalaquo of electrons andions as dense as the atmosphere Within this volume the air has be-come a perfect conductor and has all the properties of a metal includ-ing the reflectivity of a metallic surface The air that was initially trans-parent to the CO2 laser pulse has suddenly become totally opaque andreflecting and therefore the pulse emerging from the focal spot hasits tail abruptly cut By creating pulses with an abrupt (picosecond) cutoff the plasma shutter has been an early tool for subnanosecond pulseshaping [35] The experiment performed with such a plasma shuttersketched in Figure 137 leads to an understanding of absorption as aninterference In Figure 137a a powerful beam of a CO2 laser is sentthrough an absorbing cell of sufficient length so that the completenanosecond pulse is absorbed and the detector placed at the end ofthe tube does not observe any signal

The phenomenon of absorption can be understood in the followingway The photons that are absorbed excite molecular dipoles at the fre-quency of the light We have seen that an oscillating dipole is a sourceof radiation (see Figure 11 at the beginning of this chapter) which


Figure 137 Absorption can be interpretedas being due to the incoming light ex-citing dipoles that radiate with oppositephase In (a) A CO2 laser pulse15) is sentthrough a resonant absorber (typicallyheated CO2) The excited molecules emita wave that destructively interferes withthe incoming wave resulting in a nullsignal on the detector In (b) a plasma iscreated in air which abruptly cuts the tailof the ns pulse There is no more incom-

ing wave to destructively interfere with theradiation from the excited molecules Anintense pulse is observed on the detectorwhich has a duration determined by thetime that the excited molecules remain inphase That time is related to the collisiontime between an excited molecule and anyother atom or molecule in the cell Pleasefind a color version of this figure on thecolor plates

is emitted at the same frequency as the exciting radiation but exact-ly 180ı out of phase Waves that are out of phase tend to cancel eachother If a number of dipoles equal to the number of photons in the in-coming pulse are reradiated out of phase the incoming pulse is com-pletely destructively interfered The plasma shutter can provide a dra-matic demonstration of this effect In Figure 137b the plasma abrupt-ly cuts the tail of the strong CO2 laser pulse near the peak of its inten-sity All the dipoles that were excited by the slowly rising pulse contin-ue to reradiate but since there is no more incoming wave to cancelthe detector will be blinded by an intense pulse This pulse will last aslong as these dipoles have not lost their relative phase by collision Thetime it takes for dipoles to dephase by collision is inversely proportion-al to the pressure and of the order of ns torr (depending on the partic-ular molecules involved) For instance at 20 torr pressure the pulsecreated in this manner would have a duration of the order of 50 psr

15) In the figure the source is labeledas a TEA laser In general thebandwidth of this laser is too largecompared to that of the absorberwhich is a low pressure heated CO2cell Some raquotrickslaquo are needed in the

actual experiment to make the sourcea narrow line such as injecting itwith another laser or inserting alow pressure CO2 laser in the sameresonator


References

1 Haisma J and Spierings GACM(2002) Contact bonding historicalreview in a broader scope and com-parative outlook Mater Sci EngRep 37 1ndash60

2 Haisma J (1962) Construction andproperties of short stable gas laserPhD Thesis Rijksuniversiteit teUtrecht Utrecht the Netherlands

3 Strong CL (1974) The amateurscientist Sci Am 230 122ndash127

4 Snitzer E and Osterberg H (1961)Observed dielectric waveguidemodes in the visible spectrumJ Opt Soc Am 51 499ndash505

5 Snitzer E (1961) Optical Maseraction of Nd3C in barium crownglass Phys Rev Lett 7 444ndash448

6 Heard HG (1968) Laser Parame-ter Measurements Handbook JohnWiley amp Sons Inc New York

7 Knight JC Birks TA RussellPSJ and Atkin DM (1996) All-silica single-mode optical fiber withphotonic crystal cladding Opt Lett21 1547ndash1549

8 Kumar VVRK George AKReeves WH Knight JC RussellPSJ Omenetto F and TaylorAJ (2002) Extruded soft glass pho-tonic crystal fiber for ultrabroadsupercontinuum generation OptExpress 10 1520ndash1525

9 Bhagwat AR and Gaeta AL(2008) Nonlinear optics in hollow-core photonic bandgap fibers OptExpress 16 5036ndash5047

10 Slepkov AD Bhagwat ARVenkataraman V Londero Pand Gaeta AL (2008) Generationof large alkali vapor densities insidebare hollow-core photonic band-gap fibers Opt Express 16 18976ndash18983

11 Trum HMGJ and Diels JC(1970) Quiet turbine for high speed

optical applications J Phys E SciInstrum 3 564

12 McClung FJ and Hellwarth RW(1962) Giant optical pulsationsfrom ruby J Appl Phys 33 828ndash829

13 Ippen EP Shank CV andDienes A (1972) Passive mode-locking of the CW dye laser ApplPhys Lett 21 348ndash350

14 Ruddock IS and Bradley DJ(1976) Bandwidth-limited sub-picosecond pulse generation inmode-locked CW dye lasers ApplPhys Lett 29 296

15 Diels JC and Sallaba H (1980)Black magic with red dyes J OptSoc Am 70 629

16 Mourou GA and II TS (1982)Generation of pulses shorter than70 fs with a synchronously pumpedCW dye laser Opt Comm 41 47ndash49

17 Dietel W Fontaine JJ and DielsJC (1983) Intracavity pulse com-pression with glass a new methodof generating pulses shorter than60 femtoseconds Opt Lett 8 4ndash6

18 Valdmanis JA Fork RL andGordon JP (1985) Generationof optical pulses as short as 27 fsdirectly from a laser balancing self-phase modulation group velocitydispersion saturable absorptionand saturable gain Opt Lett 10131ndash133

19 Diels JC Stryland EWV andBenedict G (1978) Generation andmeasurements of pulses of 02 psecduration Opt Comm 25 93

20 Fork RL and Shank CV (1981)Generation of optical pulses short-er than 01 ps by colliding pulsemode-locking Appl Phys Lett 38671

21 Shank CV (1982) Progress in ul-trashort optical pulse generation


Paper WE3 presented at the XIIthInt Quantum Electron Conf

22 Asaki MT Huang CP GarveyD Zhou J Kapteyn H andMurnane MM (1993) Generationof 11 fs pulses from a self-mode-locked Tisapphire laser Opt Lett18 977ndash979

23 Stingl A Spielmann C KrauszF and Szipoumlcs R (1994) Gen-eration of 11 fs pulses from aTisapphire laser without the use ofprisms Opt Lett 19 204ndash406

24 Ell R Morgner U KaumlrtnerFX Fujimoto JG Ippen EPScheuer V Angelow G TschudiT Lederer MJ Boiko A andLuther-Davis B (2001) Generationof 5-fs pulses and octave-spanningspectra directly from a Tisapphirelaser Opt Lett 26 373ndash375

25 Russell JS (1844) Report onwaves in Report of the fourteenthmeeting of the British Association forthe Advancement of Science Yorkpp 311ndash390 plates XLVIIndashLVII

26 Bullough RK (1988) The waveraquopar excellencelaquo the solitary pro-gressive great wave of equilibriumof the fluid ndash an early history ofthe solitary wave in Solitons (edM Lakshmanan) Springer Seriesin Nonlinear Dynamics pp 150ndash281

27 Coles S (2001) An Introductionto Statistical Modeling of ExtremeValues Springer-Verlag London

28 Solli DR Ropers C Koonath Pand Jalali B (2007) Optical roguewaves Nature 450 1054

29 Kasparian J Beacutejot P Wolf JPand Dudley JM (2008) Opticalrogue wave statistics in laser fila-mentation Opt Express 17 12070ndash12075

30 Maine P Strickland D Bado PPessot M and Mourou G (1988)Generation of ultrahigh peak powerpulses by chirped pulse amplifica-tion IEEE J Quantum ElectronQE-24 398ndash403

31 Arissian L and Diels JC (2009)Investigation of carrier to envelopephase and repetition rate ndash finger-prints of mode-locked laser cavitiesJ Phys B At Mol Opt Phys 42183001

32 Jones RJ and Diels JC (2001)Stabilization of femtosecond lasersfor optical frequency metrology anddirect optical to radio frequencysynthesis Phys Rev Lett 86 3288ndash3291

33 Migdall A Datla R SergienkoA Orszak JS and Shih YH(1998) Measuring absolute infraredspectral radiance with correlatedvisible photons technique verifica-tion and measurement uncertaintyAppl Opt 37 3455ndash3463

34 Rudolph W and Diels JC (1986)Femtosecond time resolved fluores-cence Picosecond Phenomena V (edAE Siegman) Springer-VerlagBerlin pp 71ndash74

35 Yablonovitch E (1974) Self-phasemodulation and short pulse gener-ation from laser-breakdown plas-mas Phys Rev A 10 1888ndash1895


2Laser Coherence at Home

What is in the laser that makes it play a part in the raquolaser printer andscannerlaquo raquolaser pointerlaquo and raquoDVD burnerslaquo16) Knowing the prop-erties of lasers as discussed in the previous chapter we can apply themanywhere that suits our purpose just like a cook who knows where toput a particular spice It can be compared to the properties of a spin-ning wheel to transfer motion at low energy cost exploited in toys andcars printers and so on One of the main properties of a laser used inthe technologies mentioned above is its raquodivergencelaquo (Section 123)The laser light unlike other sources can be well directed in a smallspot Moreover its energy can be tuned and used to change materialas in DVD burners

21 The Laser Printer

Printing has come a long way from carving on a stone to the masspublication of today The goal is to print data as fast as possible withthe highest fidelity at the lowest cost for the enjoyment of the few ofus that still favor reading from paper rather than staring at a screen

Todayrsquos printer technology stands on the shoulders of advances inmechanics chemistry electronics and optics In early photographyprinting the main role was given to the optical lenses that projectedthe image of the negative on a paper sensitive to light from therethe proper chemical reaction and development of photography de-fined the quality of the image Laser printers on the other hand arebased on xerography (or electrophotography) which is a dry photo-copying technique The process consists of three steps as outlined be-low (1) charge initialization (2) exposure and (3) development

16) DVD is one of these acronyms for which the meaning has been forgotten by mostIt stands for digital video disc


81

In the first step (charge initialization) a cylindrical roll called thedrum is uniformly charged In some designs the cylindrical drum isreplaced by oval or triangular belts The initialization platform con-sists of two materials one conductor and the other photosensitiveInitially amorphous selenium was used as a photosensitive materi-al but this is now being replaced in favor of organic materials In atypical laser printer drums are made of a doped silicon diode sand-wich structure with a hydrogen doped silicon light chargeable layera charge leakage layer (boron nitride) and a surface layer of dopedsilicon

In the exposure step the data is recorded on the drum by neutraliz-ing or changing the sign of charges This is done by turning the laseron and off (which is being scanned across the drum in laser printers)or a light emitting diode (LED) array projected onto the drum In thecase of lasers and LEDs the image recorded on the drum is a positiveimage which means that the charges on the drum are neutralized orchange sign with the illumination that carries the data For copy ma-chines based on the exposure from the original paper the image onthe drum is a negative one The drum is not exposed where there areletters

In the last step (development) with the proper bias for positive andnegative imaging of the previous step charged toners will find theirproper place on the drum and sit on the digital raquooneslaquo The recordingis based on electrostatic attraction of opposite charges This image isthen transferred onto a piece of paper and run over a heated drumwhere the toner is melted onto the paper This process is repeated forother toner colors in the case of a color printer

The mechanism of the laser printer is shown in Figure 21 In thisfigure the drum is uniformly negatively charged before the exposureThe laser has its role in the second part to transfer the informationon the drum Here is where we remind ourselves of properties of thelaser that justify its use it has a small spot size that can propagate withless diffraction so as to maintain its size With a proper lens and steer-ing mirror the laser spot size on the corner of the drum is the sameas that in the middle Here mechanical stability and reproducibilityare essential especially when various toner colors are used We wantto make sure that the laser hits the same spot for the various tonersadded This is where we know that we would not have a laser printerif our technology in machinery were limited to carriage designs

82 2 Laser Coherence at Home

Figure 21 Schematic of a laser printerThe computer digital data of the imageis transferred to brightness and darknessof the laser Then the laser is steered witha mirror and a lens to discharge the neg-ative charge of the drum where there isbrightness (ones) Based on the electro-

static charge attraction negative tonerswill ride on the discharged points of thedrum The toner is picked up by paperand the image is transferred for a partic-ular toner color (picture from Wikipedia)Please find a color version of this figureon the color plates

Another common type of printer is the inkjet printer which does notinvolve optical imaging or electrostatic attraction the liquid dropletsare pressed on the paper to print the image

From the palette of laser properties such as ultrashort pulse multi-color wavelength selectivity we can see that laser printers ignore mostof the many potentials of the laser focusing on just one property thedirectionality

22 The Laser Scanner

A scanner works like a camera An object is illuminated and the re-flected beam is recorded by a photosensitive material Whenever thereis illumination one can use laser light The technology of charged-coupled devices (CCD) converts optical signals to electronic signalsthat can be digitized and saved in a data file or used directly as analog

22 The Laser Scanner 83

Figure 22 Principle of laser scanningbased on triangulation The object andimage are fixed in space and only the laserlight is steered across the sample Re-

flection from front and back faces andcorners of the object end up on differ-ent spots on a CCD Please find a colorversion of this figure on the color plates

signals to drive the printing mechanism Using a laser in the scanningprocess enables 3D scanning

There are two main classes of 3D scanners one based on raquotriangu-lationlaquo and the other on raquotime of flight measurementlaquo In triangula-tion the point of observation is illuminated with a laser beam (colli-mation is again the important property of the laser that is exploited)The reflected beams from various surfaces are imaged with a lens ona CCD Reflection from different depths are transferred to differentpositions on a CCD as shown in Figure 22 The technique is calledtriangulation because the laser source object and the image make atriangle in which one point in the triangle (the object) is unknownThe beam is scanned across the object to collect the full image Thequality of this imaging technique depends on the laser beam sizelens quality CCD pixel size stability in laser scan across the objectand the stability of the object itself This technique takes advantageof our knowledge of geometrical optics and ability to follow the raysfrom various layers and corners to the imaging screen

In time of flight measurement a light pulse is sent to an object andthe total travel time is measured Light travels with a known speedthat depends on the medium it propagates in This application of thelaser is similar to a radar Light detection and ranging (LIDAR) is atechnique based on time of flight measurement of laser pulses in a


military context it is often referred to as laser detection and ranging orLADAR Here we can use our knowledge of pulses and make the firstlegitimate comparison between a laser scanner and a radar based onthe pulse length The laser pulse can be engineered in much short-er lengths so as to have a better resolution Laser scanners are usedat various wavelengths from environment scan with green pulses theunderwater scan of coral reef in the wavelength range of 430460 nmto minefield scans of a half inch resolution In museums and at histor-ical sites one can see the noninvasive application of 3D laser scannersto discover artwork hidden under mold Here the time taken for alaser pulse to make a trip to the sample and back to the origin whichis travel of twice the distance gives the distance as t v2 where raquovlaquois the speed of light in the medium and raquotlaquo is the travel time So theaccuracy of a time of flight 3D laser scanner depends on how precise-ly we can measure the time 33 ps resolution in time measurementcorresponds to 1 mm

Scientists used time of flight measurement of 10 Hz laser pulses at1064 nm to record the variation of snow depth on the surface of Marsin a Martian year The Mars Orbiter Laser Altimeter or MOLA was aninstrument launched on a spacecraft in 1996 From 400 km altitudeabove the surface of Mars the difference between the center of massand the surface was measured over a Martian year The same ideaof time of flight measurement is applied on a totally different scaleto image the eye For the latter application purely optical techniqueshave to be used since the raquotime of flightlaquo has to be measured withconsiderably better temporal resolution than electronics means canafford These techniques will be presented in Section 39

One can combine the short pulse capability of the laser with thewavelength resolution in an interferometer to achieve subwavelengthresolutions This is a more subtle application of the laser and will bediscussed in Chapter 8 Unlike the above-mentioned techniques thatshoot laser pulses like a bullet in this method the inner structurewhich is the wavelength of the laser is used A crude estimation of thedistance is made by overlapping (timing) of a sample and a referencepulse A finer inner structure overlap is done with adding the twopulses in phase and out of phase (half a wavelength apart)


221 The Laser Barcode Reader

The barcode is an optical representation of data Originally devel-oped to label railroad cars with blue and yellow stripes todayrsquos bar-codes are mostly noticed for their use in labeling supermarket prod-ucts Most barcodes consist of black and white stripes of differentthicknesses that correspond to numbers Barcodes were also realizedin 2D but in most cases coloring is not a parameter in the pattern thathas to be recognized

Various ways of imaging barcodes converge towards the single goalimaging the reflected light from the barcode

Pen type readers In this method the barcode is illuminated with anarrow light source in the tip of a pen The reflected light from thepen is recorded with a photodiode To record the entire barcodethe light source is scanned with a steady strike over the barcode

Laser barcode scanner This is the same as the pen type reader onlythe light source is replaced by a laser source Because of thedirectionality (Section 161) of laser light the barcode no longerneeds to be in close proximity to the barcode

CCD barcode scanner The reflected light from the barcode whichin this case is more scattered is recorded with an array of tinylight sensors in the head of the barcode reader

Camera barcode reader The camera based barcode reader takes theimage of a bar code The snapshot is then analyzed usingsophisticated image processing techniques

The application of lasers in barcode reading does not use any specialproperty of this form of light The only benefit of using lasers is betterillumination and detection of the reflected light due to the laser direc-tionality The main credit for this technology goes to signal detectionand computer programming After the scan the optical modulationof the reflected light is transferred (electronically) to numbers thatidentify the product The data is assigned to a particular product bya computer program using the data base The price of the product ispulled out of the data base and the inventory is updated as the productis purchased


23 The Laser in Data Storage

The demand for recording visual and vocal data has existed since theearly days of television The oldest patents of optical storage goes backto John Logie Baird the inventor of modern TV He presented a sys-tem in which the storage consisted of a transparent film of modulateddarkness The information retrieval involved the focused radiation of alamp illuminating the black and white storage medium and the mod-ulated transmitted light being recorded by a detector The first opticalstorage had a very small bandwidth of 20 kHz and was only able torecord 15 min of a TV program with a quality that was not even suf-ficient at the time Until 1983 the main device for storing data wasthrough magnetic storage devices

The invention of semiconductor lasers made cheap by mass pro-duction digital coding and error correction contributed to makingthe first compact discs (CD) available for audio data in 1982 Therace in making higher capacity optical data storage has since beenunabated The CD uses gallium aluminum arsenide (GaAlAs) semi-conductor lasers at 780 nm for storing and recovering data The nextimprovement in data density came with the digital video disc (DVD) in1995 which used basically the same principle but shorter wavelengthlasers for reducing the size of the raquobitlaquo The latter lasers are alu-minum gallium indium phosphide (Aly Gax In1xy P) diodes (wave-length 650 nm) The storage capacity of the DVD is not sufficient tosatisfy the demands of high definition digital television The violetlaser came to the rescue The gallium indium nitride (GaInN) laserscame to light in 1990 and are a key element in the high-density opticaldata storage in raquoBlu-raylaquo disks and HDVDs (high definition digitalvideo disc)

Lasers play an important role in optical data storage as more andmore characteristics of the laser light are included in adding dimen-sions to the data storage Lasers are used both for reading and writ-ing (burning) on the optical storage medium The laser intensity forreading is around 5 mW and for writing on the storage medium theintensity can go up to 400 mW In writing a laser light is focused onthe surface and a permanent mark as a bit of information raquo1laquo or raquo0laquois recorded Depending on the material used for the storage the in-

23 The Laser in Data Storage 87

Figure 23 (a) Laser portion of a CDDVDreaderwriter The lens focusing thebeams onto the disk is in the centerof (a) On the left of the lens is the drivescrew for translating the focal point alongthe radius of the disc (b) The raquobottompartlaquo is shown magnified The 780 nmlaser is for CD readwrite and the 650 nmlaser for DVD readwrite The two beams

are combined via a beam splitter thattransmits the 780 nm beam and reflects650 nm Next one can distinguish thecollimating lens followed by a 45ı mirrorsending the beam towards the focusinglens seen in (a) The remarkable com-pact device includes temperature controlelectronics

formation can be reversible and rewritten The first thing to consideris the size of the spot allocated to a bit of data or the size of the fo-cused laser beam The physical size of the bit is of the order of thelaser wavelength with a depth ranging from one-quarter to one-sixthof the wavelength

The marking on the storage associated with the data recorded iscalled a pit It is important to maintain the laser spot over the spiralpath (groove) while recording and reading the data Two electrical ser-vo loops control the motion of the laser across the groove and main-tain its distance to the layer In some cases the laser head needs to bemaintained as close as 30 nm to the storage screen Note that the focuscan be at different depths of the storage media In the case of audioCDs the data is recorded at the bottom of the disc through a trans-parent media A DVD is written in the middle of the disc through atransparent media and Blu-ray discs have data recorded very close tothe top layer

The density of data storage is defined by the Rayleigh criterion (Sec-tion 123) that specifies the limit of how close two resolvable spots canbe The spot size itself is a function of the imaging lens and the lightwavelength There is a limit on how tight light can be focused with a


lens In air the highest numerical aperture17) raquoNAlaquo is 1 In a materialwith index of refraction raquonlaquo the numerical aperture is NAn whichmakes tighter focus feasible The closest two data points can get is06λNA

One can estimate the density of data storage on a single layer bydividing the useful area by the size taken by a spot

density D 18

area06 λ

NA

2 (21)

Considering a DVD system operating with 650 nm light and the DVDhaving a useful area of 927 cm2 (inner and outer recording radii of 23and 59 mm) the Rayleigh criterion prediction leads to 2 GB capacityDue to improvement in digital signal theory and practice the realizedcapacity is 47 GB which is more than a factor of 2 higher than pre-dicted The Blu-ray DVD employs a higher numerical aperture and ashorter wavelength to achieve an even higher capacity (21) When da-ta is only recorded on a single surface of the storage the volume usedfor recording is 1 of the total volume of the disc

A dramatic increase in data storage capacity did not occur throughchanges in wavelength or numerical aperture but by multilayer writ-ing and information multiplexing For a three-dimensional recordingone can use recording and reading of data at various distances fromthe surface hence one can access layers at different depths inside thestorage volume In order to have more precision on layer access andsmaller spot size nonlinear effects (Section 111) are used In 2008researchers recorded 200 layers of data using two photon absorptionwith 5 GB capacity in each Two photon absorption is a nonlinear ef-fect very sensitive to light intensity so that material transformationtakes place only at the tight focal spot rather than along the path to thefocus Note that the typical thickness of a DVD substrate is 12 mm

There is more to laser light than just its intensity and spatial con-finement in the focus A fourth dimension in data recording is lightpolarization (Section 122) When the pattern generated by varioustypes of polarization can be sorted out in the reflected beam one canrecord more than a bit at one spatial location More dimensions to thedata storage arise from adding frequencies and the spatial phase of

17) NA is the sine of the half angle by which the spot sees the lens times the index ofrefraction For imaging with a lens in air the numerical aperture is approximatelyD2 f where raquoflaquo is the focal length and raquoDlaquo is the diameter of the lens


the laser light that creates the pattern and detect those qualities in thereturn beam We can thus make a more delicate usage of the laser asif we could see and detect an x-ray and a blood test of a person accord-ing to its appearance and be able to follow the pattern associated withthese inner structures and metabolism This is called multiplexingwhere various parameters of the light are detected in the fingerprintsleft as the data

24 Miscellaneous Applications

241 Laser Level

The laser appears as a virtual ruler to draw a straight line overa large distance Mass production of semiconductor lasers have re-duced their price to the point that one can find various affordable lasersources widely used in construction and home applications Laser il-lumination can be in two and three dimension with various colorsThe idea behind using the laser is very simple light travels along astraight line and the bundle of rays that make up a laser beam staysconfined that is laser light travels with least divergence A line canbe well defined within the size of the laser beam so that everyone canhang frames at home in a straight line without the need for stringsand rulers

242 Laser Pointers

Laser pointers are used as a tool for communication in speech-es and presentations The laser light is shined on a screen and re-flected light from the surface is observed by the audience We usu-ally do not see the beam path on the way to its target unless thereis a scattering material on the way The colors used for this pointercan vary from originally red (633 nm from helium-neon) deep red(650670 nm from the diode laser) the green laser (532 nm) the yel-low orange laser (5935) up to the blue violet laser at 405 nm

The main reason for using laser sources as pointers is the smallbeam size over long distance or directionality (Section 161) Thebrightness of the spot seen by the audience is a function of the laseroutput power scattering of the surface and the chromatic responseof the human eye


Figure 24 The laser pointer makes raquowar historylaquo A soldier points on a target with alaser pointer In a scenario if the defender has a cat with raquocatrsquos eyelaquo or any mirror todeflect the laser the bomber would be mislead and aim at his own comrade

2421 The Laser Pointer as the Ultimate WeaponThe brightness of a laser is not only used to emphasize a part of

a technical presentation but has also been used to emphasize a tar-get for a smart bomb A propaganda video of the British illustratedthe role of a laser in marking an Argentine antiaircraft gun during theMalvinas island (some call it Falkland islands) war The video was a bitshaky bullets were heard whistling near the ears of the cameramanand the infantry soldier holding a NdYAG laser and trying to keep itpointed as steadily as possible on a not-so-distant antiaircraft batteryThanks to the brightness of the laser spot a pilot could release hisraquosmart bomblaquo from a safe distance The smart bomb could guide it-self onto the marked target After all the infantry man is dispensablebut not the pilot Maybe the course of history may have been changedif the farmers that populated the bare Malvinas islands had raised catsinstead of sheep The catrsquos eye is a good retro-reflector and would haveguided the not-so-smart bomb to the laser instead of the antiaircraftgun

24 Miscellaneous Applications 91

3The Laser in Medicine

31 Introduction

raquoMagiclaquo is portrayed in most cartoons with a magician brandishinga stick uttering some mumbo jumbo resulting in a flash of light Theflash of light coming out of Harry Potterrsquos wand results in healing ordeath We do have some preconception that there is healing power inlight Does it originate from biblical and other religious stories Or itis triggered by observation of the majestic power of light in lightningfire and even the sun

One can trace back the use of light for healing to 1500 BC when theGreeks suggested that exposure to light was essential for the restora-tion of health Indian medical literature dating to 1500 BC describesa treatment combining herbs with natural sunlight to treat nonpig-mented skin areas Buddhist literature from about 200 AD and tenthcentury Chinese documents make similar references

A well documented application of light to healing which was re-warded with a Nobel prize is red light therapy applied to the treatmentof smallpox and tuberculosis Niels Ryberg Finsen suffered from anillness now called Pickrsquos disease which is characterized by progres-sive thickening of the connective tissue of certain membranes in theliver the heart and the spleen Having a great interest in the heal-ing power of the sun he conducted studies both in the laboratory andthorough clinical experiments adopting a procedure very similar tothe one used today to find applications of lasers in medicine The factthat he did not know the details of the lightndashtissue interaction in thelaboratory did not prevent him from using light in clinical applica-tions He devised the treatment of smallpox in red light (1893) and thetreatment of lupus (1895) and was recognized with the Nobel prize in1903 In beautiful but simple experiments Finsen demonstrated thatrays from the sun or from an electric arc may have a stimulating effect


93

on tissues If the irradiation is too strong however it may give rise totissue damage It is the same fine line that medical applications oflasers need to walk on

Light therapy or phototherapy (classically referred to as heliothera-py) is the application of light for various therapies such as skin sleepdisorder and some psychiatric disorders Other holistic applicationsof light therapy are more involved in metaphysics and are beyond thescope of this book

Lasers not only provide various coherent color sources but alsowith their unique capability of focusing and high peak pulsed oper-ation will materialize the use of light as a sharp cutting knife thatcan be switched on and off with femtosecond speed In its high powerapplication it can act like a virtual knife (with submicron blade) thatdoes not need sterilization Beyond simply cutting some laser radia-tion can induce coagulation which is a complicated process of formingblood clots hence reducing bleeding Laser ablation can be used to re-move materials from skin or teeth or cutting in depth by moving thefocal point Selective absorption is used to blast a kidney stone or forhair removal Low laser light level dosages are used for wound healingand raquocold laser therapylaquo

Technological advances in various branches of laser optics havestimulated growth in the medical field This is the case for imagingand light transfer New understanding of light and progress in mea-suring its phase and frequency leads to high resolution tomography(optical coherent tomography) applied to biological tissues fluores-cence labeling and cell manipulation (optical tweezers) Surgical laserendoscopy is made possible through light transfer in optical fibers

32 The Laser in Dentistry

Few of us may remember the mechanical dentistrsquos drill a grind-ing bit making a chilling noise as it churns it way slowly through thetooth rotating at a speed of only 3000 rpm These monstrous drillbits were slowly replaced in the late 1960s and early 1970s by airturbine driven miniature bits spinning at rotation speeds of the or-der of 400 000 rpm Not everybody however enjoys the shrill highpitch sound of the spinning tungsten carbide bit speeding throughthe tooth So why not use an intense continuous or pulsed laser beam

94 3 The Laser in Medicine

to blast away decaying tooth material and make a clean hole in prepa-ration for the filling material The prospect of having teeth sculptedin total silence and painlessly is quite appealing

raquoDental laserslaquo ndash the type of lasers used in dentistry ndash can be ap-plied as low level lasers (Section 37) for oral surgery (Section 36) aswell as for periodontal treatment The laser beam is attractive in den-tistry because of its cleanliness bacteria cannot ride on the laser beamas they can on hand scalers Compared to ultrasonic devices the laserbeam produces less stress on the patient since it does not induce vibra-tion or high pitch sound It may reduce bleeding (coagulation effect)and remove the need for local analgesia

Lasers can be manufactured in various wavelengths time dura-tions and energies There are a large number of raquoknobslaquo or parame-ters that can be used as control of laserndashtissue interaction The oppor-tunities are multiple provided that the details of the interaction canbe better understood The complexity of the study of the dynamics ofa single molecule interacting with a laser will be alluded to in Chap-ter 6 The road is long for a fundamental scientist to gain a completethorough understanding of the phenomena We have to be thankfulto engineers medical doctors and dentists for taking a more practicalroute exploiting a technology right after its scientific birth

Some of the lasers that are used in dentistry are neodymium-dopedyittriumndashaluminumndashgarnet (NdYAG) at 1064 μm and carbondioxide (CO2) at 106 μm for soft tissue and erbium-dopedyittriumndashaluminumndashgarnet (ErYAG) at 294 μm for hard tissue The CO2 laserradiation is highly absorbed at the surface Diode lasers at shorterwavelengths of 655 810 and 980 nm are also used for calculus de-tection and bacterial decontamination NdYAG lasers are used inperiodontics for their excellent soft tissue ablation Applying to theroot surface or to the alveolus18) results in carbonization and thermaldamage

White teeth means good reflective properties for visible light andvery poor penetration and heating For this reason a red laser such

18) The part of the jaw from which the teeth arise

32 The Laser in Dentistry 95

as the Alexandrite (750 nm) is reflected by the tooth but absorbed bythe calculus which can thus be selectively removed Dental enameland dentin are comprised of hydroxylapatite also called hydroxyap-atite (HA)19) which is strongly absorbed by the 294 μm wavelength ofthe ErbiumYAG (ErYAG) laser This wavelength is also strongly ab-sorbed by water which means that the ErbiumYAG laser is often ap-plied to biological tissues The ErYAG laser is a crystal laser pumpedeither by flashlamps as was the early ruby laser or by semiconductorlasers The possible operations are either raquofree runninglaquo (the sim-plest ndash no intracavity element and an emission consisting of randomstreams of pulses following flashlamp excitation) or Q-switched Thefree-running operation generates long (hundreds of microseconds)pulses the Q-switched operation short (tens of nanoseconds) puls-es Recent research showed better results when Q-switched ErYAGpulse radiation is used with a substantial increase in bond strengthafter filling the cavity The shorter more intense pulses can create asmoother smaller cavity for very precise microsurgery [1]

Lasers can also be used for implant maintenance for its bacterialdecontamination effect that will reduce the peri-implant inflamma-tion of the surrounding soft tissue responsible for the breakdown ofthe implant Lasers are used for plaque removal as well Instead ofscraping the tooth surface with metal pieces low level laser light isused to remove plaque One may surmise that the heat generated bythe laser will slow down the bacteria growth as well

The purpose of this short overview is not to judge and comparetechniques but to pinpoint the properties of laser light matter interac-tion that are exploited The take home message for comparing dentallasers with ultrasonic and manual scales is that the energy can bedeposited in a very short time the local heat generated can be highand concentrated and light matter interaction can select various tis-sue bonding and materials

33 The Laser and Vision

It is not a surprise that when dealing with laser safety the first thingthat comes to mind is the eye The eye is a very sensitive organ which

19) A form of calcium apatite with the formula Ca5(PO4)3(OH)


also has a lens that can focus the beam and increase its intensity ona retina by orders of magnitude Horror stories abound about unfor-tunate encounters between laser beams and eyes On the other handfrom the midinfrared to the deep ultraviolet dozens of lasers havebeen used in ophthalmology for diagnosis and treatments of the eyeThe most popular applications are excimer lasers for refractive surgeryfemtosecond laser for making corneal flap in refractive surgery greenand yellow lasers for retinal photo-coagulation for diabetic treatmentand IR laser iridotomy for glaucoma treatment How can the worst en-emy of the eye be its savior at the same time Let us first review thehazards posed by laser beams before focusing on their benefits inophthalmology

331 Lasers and Sight Loss

Most laser related accidents have occurred in research laboratorieswhich is not too surprising since the construction of a laser involvesexposed high voltage lines unprotected beams and unknown outputpower levels How could the first He-Ne laser be aligned if there wasno alignment He-Ne laser available It is a sort of chicken and eggstory what appeared first the chicken or the egg Autocollimators ex-isted in the early 1960s which could be used to position a mirror per-pendicular to an optical-axis with sufficient accuracy However suchinstruments required an aperture of several centimeters ndash it was notpossible for instance to align the large autocollimator beam throughthe narrow tube (mm diameter) of the He-Ne laser In the 1960s asenior researcher had an original solution by using his own eye as au-tocollimator He first adjusted the end mirror beyond the laser tubeto center the reflection of his pupil He then put the second mirrorin place looked through the-axis of the tube for an increase in fluo-rescence as the second mirror came close to parallelism and jumpedskillfully away as the laser beam was produced He still maintained a2020 vision over the several decades that followed while disturbinga brief exposure to a He-Ne laser beam of 1 mW is not harmful Thisis of course not a recommended procedure alignment lasers and de-tectors as well as light viewers at various wavelengths are on hand fora laser engineer

The eye is a sensitive detector of visible radiation (a very sensitiveone at night) It saturates easily it is impossible to estimate the di-

33 The Laser and Vision 97

ameter of a visible laser beam impinging on a piece of white papereven if the laser power is only 1 mW The reason is that the eye (likeany other detector) cannot distinguish any level of intensity beyonda certain value corresponding to the saturation intensity of the eyeat that particular wavelength Since the intensity distribution of mostlasers is bell shaped the eye will generally see a uniform illumina-tion at its saturation intensity over a diameter much larger than thereal one (defined as the full width at half the peak intensity) The in-direct illumination of the impact of a visible laser on paper or on awall is still of a considerably smaller intensity than if the beam weredirected straight into the eye It is not surprising therefore that tem-porary blinding results from having a direct hit from a laser pointerat night when the pupil is dilated at its widest opening It is a veryunpleasant experience for pilots in the landing phase who have beenthe object of bad jokes from idle kids There have been various reportsof laser pointer misuse around the world many of them resulting ina big fine and jail sentence for the blameworthy It was mostly target-ed on a pilot eye police officer or even in the football stadium by awild football fan To handle this problem some governments imposedrestrictions on laser pointer import In only 6 years there were 2800incidents of laser light directed to aircrafts within the United StatesFDA regulation is that pointers are limited to 5 mW output power inthe visible wavelength range from 400710 nm There are also limitsfor any invisible wavelengths and for short pulses

If the laser pointer and He-Ne laser beam of only a few mW powercan be a nuisance the 20 W Argon ion lasers used in open air concertscan be a serious hazard The raquocoolestlaquo acoustic effects are to have arock concert in a deep valley and for an unforgettable light show scanthe surrounding flanks of the valley with green and blue beams of theargon laser This application of lasers referred to as audience scanningor crowd scanning is based on a hope that no one in the audience will beexposed for a long time at a wrong spot as the special effect is createdThe unfortunate resident of the surrounding houses who opens hiswindow to express his displeasure at the noise may lose his sight fromthe passage of the laser beam The laser hazard would increase withusage of short pulse lasers since higher peak power is encapsulatedin a pulse

The high power visible lasers at least come with a warning theirbrightness This is no longer the case for infrared lasers The wave-


length of the titanium sapphire laser 800 nm is at the limit of theeye sensitivity Therefore the beam appears as a harmless pale redspot on ones shirt which turns to bright red when the tissue is setablaze This type of hazard increases with the wavelength A numberof researchers building the first CO2 laser as described in Figure 19were taken by surprise by the ease of alignment of the end mirror ofthis high powerhigh gain laser resulting in a burned shirt and bellybutton and a bruised ego

Perhaps the most harmful lasers emit around the wavelength of1 μm for which the eye cornea lens and liquid are totally transparentStrict adherence to safety rules without being cautious has sometimesnot been sufficient to prevent serious injury For example a researcherof a US national laboratory was wearing prescribed goggles to protectfrom the radiation of a NdYAG laser at 106 μm A stray reflectionof the 100 W laser melted the plastic goggle material and burned hisretina An infrared exposure of the eye although it might be painlessand un-noticed may result in a 100 ıC temperature increase and boil-ing of the retina resulting in a permanent blind spot while the sameexposure with visible light would lead to 10ı heating and damage tophotoreceptor cells in the retina

There are various criteria for classifying a laser output power wave-length and peak intensity It is trivial to relate the risk associated to alaser with its power just like the way the danger to the electrical pow-er is categorized Holding the wires coming out of a home battery issafe but holding the wires coming out of an electrical wall plug is notIt might not be so trivial to consider the wavelength and the pulselength As we saw in Chapter 1 the energy stored in the cavity canleak out continuously or in pulses (sometimes very short pulses) Weneed to know the material (here tissue) response to the laser light tounderstand the damage mechanism There are two types of damagemechanism thermal damage and photochemical damage

Laser radiation can deposit a lot of heat on the material a depo-sition of energy that depends on the laser pulse length The abruptheat that is impinged at the focus will transfer through the materialUsing lasers material scientists and mechanical engineers are facedwith orders of magnitude of time scale of material response that leadto completely different structure (Chapter 4) Short pulses induce fastheating of a tissue which can be a good thing because it reduces the


exposure time At the same time one should consider the shock wavecreated by rapid and local temperature increase

Another concern is the light wavelength and resonance effectsAny material is made of molecules and structures that have differentresponses to the wavelengths For example microwave wavelengthexcites the vibration resonance in water molecules and has a differ-ent effect on plastic and glass containers Visible light is absorbedby melanin pigments behind the photoreceptors Also the eye isequipped with a raquoblink reflexlaquo for visible light At shorter wavelengthsof less than 400 nm (violet) into the ultraviolet the light is absorbed inthe lens and cornea and it takes less power to create a photochemicaldamage The hazards associated with short wavelength irradiation ofthe eye are discussed in Section 3321 that follows Near infraredlasers induce thermal damage on the retina The frontal part of theeye will absorb longer wavelengths mid infrared to long infrared (theCO2 laser for instance)

332 Lasers to the Rescue of the Eye

The human eye is different from other organs in light scatteringFor the vision window of 400760 nm it is an almost transparentmedium without significant scattering The ocular media display clar-ity beyond the visual range up to 1400 nm The response of the corneaand lens are different and depend on the size and consistency of thecells and the spacing between molecules One advantage of the eyeover other organs is its small scattering coefficient Despite the haz-ards posed by laser light one has attempted to find applications oflaser light in ophthalmology just as antipoison can be made out of apoison

3321 Choice of WavelengthA big concern is of course the risk laser radiation poses to the eye

It seems that arbitrary boundaries have been set for the wavelength al-lowed in ophthalmology For instance the FDA has banned the use oflasers at wavelengths between 230 and 350 nm This wavelength rangeis considered carcinogenic Why would such a wavelength range bemore harmful than shorter or longer wavelengths The argument isthat at wavelengths shorter than 230 nm the penetration depth of thelight is even small compared with the size of a cell Before it reaches


its nucleus the cell has been destroyed by the radiation At 230 nmthe penetration depth being of the order of the cell size the radiationmight perturb the nucleus of the cells and modify their reproduc-tive properties before destroying them This argument is used in therange of 230350 nm At wavelengths longer than 350 nm the photonenergy is considered to be too weak to affect the cell properties

Lasers with emission wavelengths that are absorbed in the eyesrsquoscornea and lens are generally labeled raquoeye-safelaquo The reason is thatbecause of the absorption no significant radiation can reach the reti-na This criterium applies to wavelengths below 350 nm and above1400 nm It should not be taken as literally as one company did whichin a Science report (2003) advertised a laser producing raquoeye-safe puls-es of 1 J 100 fs at 250 nmlaquo Such a pulse would blast its way throughmost of the eye structure and probably what is behind too

3322 Shaping the CorneaAt the two extremes of the spectrum shorter than 230 nm or longer

than 3 μm laser radiation penetrates less than 1 μm at these wave-lengths20) The whole radiation energy is absorbed in the corneal tis-sue Therefore a pulse of the proper energy will blast away (raquoablatelaquo) aminuscule thickness of the cornea Since the latter accounts for a bigportion of the focusing property of the eye shaping the cornea cancorrect astigmatism or imperfection of the imaging properties of theeye While various lasers are being researched for this type of ablationincluding the ErYAG laser at 294 μm [3] the ultraviolet excimer kryp-ton fluoride laser has been mostly used The procedure is called laserassisted in situ keratomileusis The surgeon uses a mechanical oscil-lating blade called a microkeratome to cut a flap 100200 μm thick inthe cornea Thereafter the inside of the cornea is reshaped with theablating laser After the procedure the cornea with its restored flapheals In the healing process stresses may modify the shape of thecornea resulting in new aberrations

Always in search of the latest most sophisticated laser applicationophthalmologists are now replacing the cutting blade by tightly fo-cused ultrashort pulses As will be seen in Section 44 interaction withmatter of these ultrashort pulses is different to the standard heatingvaporizing and burning effect seen with longer pulses It is the high

20) The absorption coefficient of water is 10 000 cm1 at a wavelength of 3 μm [2]


Figure 31 (a) The LASIK operation pro-cedure (b) Wavefront LASIK which notonly looks at correcting the focal pointon the retina but also follows the whole

wavefront of the eye as seen and collectedon the retina Please find a color versionof this figure on the color plates

field of the femtosecond laser pulse that ionizes the molecules subse-quently dissociating in some cases creating some raquobubbleslaquo makingit easier to separate the flap cut by the laser

In a standard LASIK procedure (Figure 31) the eyersquos ability to focuslight rays is measured and a 3D map is created by wavefront technol-ogy to map the irregularities in the way that eye processes images (seeSection 393) Information contained in the map guides the laser incustomizing the treatment to reshape the eyersquos corneal surface so thatthese irregularities can be corrected Wavefront technology is ground-breaking because it has the potential to improve not only how muchone can see in terms of visual acuity measured by the standard 2020eye chart but also how well one can see in terms of contrast sensitiv-ity and fine detail

34 Lasers and the Neural Network

Nerve cells form a complex network in the human body To under-stand the correlation between electrical function and morphology andto monitor spike activity from ordered networks in culture there isa need for network simplification through surgical intervention Mi-crosurgical intervention at the cellular level is a remarkable demon-stration of the precision of laser beams [4] Burn patterns that aremuch smaller than the focal spot can be created with nitrogen lasers


Figure 32 (a) Patterns created in whiteblood cells by focusing under microscopethe nanosecond pulses from a nitrogenlaser at 357 nm (b) Irradiation by 120 ns

shots of the nitrogen laser at the locationof the arrow (c) 30 s after irradiation tran-section is observed (courtesy of GuentherGross University of North Texas)

at 337 nm For example Figure 32a shows happy and not-so-happyfaces engraved by a low power nitrogen laser on blood white cellsThe reason that such small size features can be drawn is that the in-tensity threshold above which damage occurs is very sharply definedTherefore if the pulse energy is accurately controlled only the top ofthe intensity distribution of the beam is sufficient to create a markOf course the goal of laser microsurgery is not to force microorgan-isms to smile at you The capability of the nitrogen laser to performprecise microsurgical manipulations on neuronal andor glial cellsand thereby modifysimplify complex networks is illustrated in Fig-ure 32b c In Figure 32b the arrow indicates the location where thecell is irradiated with 120 shots of the nitrogen laser with an ener-gy of approximately 15 μJμm2 which is far below the threshold fornonlinear processes Shortly after irradiation pinching of the cell isobserved at that site Figure 32c shows that complete transection hasbeen achieved 30 s after irradiation

34 Lasers and the Neural Network 103

35 Lasers for the Skin and Cosmetics

The skin is the largest organ in the human body measuring 2 m2

and weighing 5 kg It is made of two distinct layers the outer epider-mis and inner dermis Below the dermis lies a subcutaneous layercomposed of proteins and adipose tissue (fat) not part of the skinitself Figure 33 schematically shows the layered structure of theskin The epidermis is made of four to five layers together measuringabout 100 μm They are made of keratinocytes cells which producefibrous protein keratin and compose 90 of the epidermis Deeperlayers are made of younger cells which gradually travel outwardstransforming into a hard protective layer along the way Scatteredbetween the keratinocytes are melanocytes which are the cells pro-ducing the pigment melanin responsible for the skin color whichis important from the point of view of the laser Groupings of thesecells are called melanosomes whose main function is the protectionof keratinocytes from UV light (protection originally intended againstsunlight) All people have a roughly equal number of melanocytesbut they produce different amounts of melanin Its distribution canalso vary (eg forming freckles patches and age spots) hence differ-ent skin colors A much thicker dermis (1 mm) unlike the epidermisis richly supplied with blood and nerves Most of the dermis about75 is made of two proteins collagen and elastin which provideskin strength and elasticity There are many structures in the dermistiny loops of blood vessels with an important role in regulation ofbody temperature glands receptors for various stimuli and hair fol-licles Hairs protruding from hair follicles are made of keratin whilemelanin gives them color The heavy presence of blood provides yetanother important pigment hemoglobin which is by contrast ex-tremely scarce in the epidermis

How will each one of these components react to photon energiesof various wavelengths to pulsed or continuous light One can sepa-rate each structure and study its interaction in an experimental setupa biological research program in itself (the study of laserndashtissue in-teraction with multiphoton microscopy Section 111) It is howeverdifficult in the real world to separate other effects such as scatteringin the tissues and thermal effects Here again the laser with its mul-ticolor and various energy and pulse characteristics opens challengesand opportunities for lightndashtissue interaction


Figure 33 (a) The skin has a layeredstructure of epidermis and dermis withmany small structures embedded (b) Ab-sorption spectra of the skin main ab-sorbers water (blue) melanin (brown)

and hemoglobin (red) Also shown arewavelengths of some important dermato-logical lasersPlease find a color version ofthis figure on the color plates

The absorption of light in biological tissues is mainly through wa-ter molecules (in the infrared) proteins (in the UV) and pigments (inthe visible region of the spectrum) As light propagates in the medi-um photons are absorbed or scattered leaving less photons for fur-ther interaction This can be expressed as an exponential decay withthe BeerndashLambert law The intensity of the light at depth raquozlaquo for thewavelength raquoλlaquo is I(z λ) D I0eαtotal(λ)z where αtotal is the total at-tenuation coefficient of the tissue including scattering (αs) and ab-sorption (αa) αtotal D αs C αa Both the scattering and absorptioncoefficients are wavelength dependent with the scattering coefficientαs 1(λ4) for a given tissue and the absorption coefficient depen-dent on the particular substance Water strongly absorbs above 2 μmwith the strongest peak at 3 μm Proteins have a peak absorption inthe UV (280 nm) leaving pigments dominating in the visible and NIR(4002000 nm) regions of the spectrum Figure 33b shows the ab-sorption coefficient for water and for the two main absorber pigmentsmelanin and hemoglobin Melanin varies among individuals with dif-ferent skin types For Caucasians at NdYAG wavelength it is approxi-mately αa D 01 cm1

The absorption process could lead to various phenomena based onthe energy deposited on the skin and on the pulse length For energiesin the range of 1 Jcm2 to 100 Jcm2 a crude classification of events isas follows

35 Lasers for the Skin and Cosmetics 105

Photochemical for 1000 s pulses Thermal for millisecond pulses Photoablation21) for microsecond and shorter pulses Plasma-induced ablation22) Photodisruption23) for picosecond and femtosecond pulses

The local temperature increase is a function of the pulse length aswell For the same energy deposited on the skin as the pulse getsshorter the local temperature increases Usually the temperature dif-ference is kept under 100ı C A thermal shock induced by the temper-ature gradient must also be taken into consideration

Lasers are used for skin therapy and cosmetics because of their finefocal spot selective interaction and because they cause less bleed-ing and contamination Excimer lasers diode lasers CO2 lasers andNdYAG lasers with different pulse lengths and wavelengths are usedThe argon laser24) successfully treats telangiectasias [5] and venouslakes [6] Telangiectasias are small dilated blood vessels near the sur-face of the skin or mucous membranes measuring between 05 and1 mm in diameter Venous lakes (BeanndashWalsh) of the lips are blood-filled dome-shaped lesions their treatment often requires surgeryDeep capillary or cavernous hemangiomas and those of the oral cavitymay be best managed using the NdYAG laser Tattoos can be removedby the carbon dioxide (CO2) laser although some scarring of the over-lying skin usually occurs A list of laser applications for the skin are

21) When matter is exposed to focusedexcimer light pulses of less than230 nm wavelength (for instancethe argon fluoride laser at 193 nm)the pulse energy is absorbed in athin layer of materials typicallyless than 01 μm thick due toan extremely large absorptioncoefficient at that wavelengthThe high peak power of anexcimer light pulse when absorbedinto this tiny volume results instrong electronic bond breakingin the material The resultantmolecular fragments expand ina plasma plume that carries anythermal energy away from thework piece As a result there

is little or no damage to thematerial surrounding the producedfeature

22) Where local pressure from thegenerated plasma results in materialremoval

23) When exposed to very short andfocused laser pulses the interactionregion is reduced to less than 1 μmand the energy deposited in thetissue is confined to the focal regionThis results in material separation orphotodisruption with minimal effecton the surroundings

24) Most applications that use an argonion laser at 514 nm are shifting to themore efficient neodyniumvanadatelaser frequency doubled to 532 nm


Photodynamic therapy (PDT) using excimer lasers Photodynamictherapy (PDT) is a treatment that uses a drug called aphotosensitizer or photosensitizing agent and a particular type oflight When photosensitizers are exposed to a specific wavelengthof light they produce a form of oxygen that kills nearby cells Eachphotosensitizer is activated by light of a specific wavelength Thiswavelength determines how far the light can travel into the bodyThus doctors use specific photosensitizers and wavelengths oflight to treat different areas of the body with PDT The majorconcerns are phototoxicity induced by photosensitizers and theirlimited penetrationThe xenon fluoride excimer laser emits wavelengths from theultraviolet-blue spectrum (308 nm) and selectively targets lesionsAdvantages offered by the excimer lasers have been exploited totreat psoriasis vitiligo and several other skin diseases Earlierhigh fluences gave excellent results but with a high level of sideeffects Lower fluences are now being used to avoid side effectsNumerous studies have confirmed the efficacy of and tolerance toexcimer lasers

Actinic keratoses (AK) treatment Actinic keratosis refers toprecancerous scaly patches on the skin caused by chronic sunexposure A midinfrared laser (for instance the thulium (Tm) fiberlaser with a 1927 nm wavelength) is used to precisely remove theactinic keratoses and the affected skin underneath Localanesthesia is often used to make the procedure more comfortableSome pigment loss and scarring may result from laser therapy

Basal cell carcinoma (BCC) treatment Skin cancer is divided intotwo major groups nonmelanoma and melanoma Basal cellcarcinoma is a type of nonmelanoma skin cancer and is the mostcommon form of cancer in the United States According to theAmerican Cancer Society 75 of all skin cancers are basal cellcarcinomas Basal cell carcinoma starts in the top layer of the skincalled the epidermis It grows slowly and is painless A new skingrowth that bleeds easily or does not heal well may suggest basalcell carcinoma The majority of these cancers occur on areas ofskin that are regularly exposed to sunlight or other ultravioletradiation When treated with an infrared laser the skin outer layerand variable amounts of deeper skin are removed Carbon dioxide(CO2) at 106 μm or erbium YAG (155 μm) lasers are often used


Lasers give the doctor good control over the depth of tissueremoved and are sometimes used as a secondary therapy whenother techniques are unsuccessful

Squamous cell carcinoma (SCC) treatment Squamous cellcarcinoma (SCC) is a form of cancer of the carcinoma type thatmay occur in many different organs including the skin lipsmouth esophagus urinary bladder prostate lungs vagina andcervix Localized squamous cell carcinoma of the skin is a curabledisease CO2 lasers are helpful in the management of selectedsquamous cell carcinoma in situ They are the preferred treatmentwhen a bleeding diathesis is present since bleeding is unusualwhen this laser is used

Psoriasis treatment Psoriasis is a common skin condition where theskin develops areas that become thickly covered with silveryscales It is a common problem and millions of people in theUnited States have psoriasis The course of psoriasis is quitevariable but in most sufferers it is a chronic problem thatcontinues for years The presence of psoriasis can cause emotionaldistress Psoriasis is considered a skin disease but really it is theresult of a disordered immune system The xenon chlorideexcimer laser with wavelength of 308 nm (Ultraviolet) targets thepsoriasis effectively The short pulses (nanoseconds) can befocused on areas such as the scalp knee and elbow whereremoval of psoriasis by other means is more difficult

Vitiligo treatment Vitiligo is a skin condition where there is loss ofpigment (color) from areas of skin resulting in irregular whitepatches that feel like normal skin The laser treatment involvesusing also a xenon chloride excimer laser sometimes called anXTRAC system The light is guided and focused on the areaaffected by vitiligo with a special fiber optic device A series oftreatments can often lead to dramatic repigmentation of the skin

Acne laser treatment Laser treatment of acne is now an establishedtherapy With its direct action on the sebaceous glands it givessuperior results It has to a great extent overcome the drawbacksof traditional therapies Many kinds of lasers giving variableresults are now in use The 1450 nm diode laser gives the bestresults Optimum results are obtained when laser treatment iscombined with other therapies


Laser treatments for other skin lesions Other skin lesions such aswarts nevi rhinophyma seborrheic keratoses and ulcers aresome of the vast number of skin lesions where laser treatment is aviable option In the majority of cases high-power short-pulsedCO2 lasers are used For rhinophyma the CO2 laser withanesthesia gives precise tissue removal For severe rhinophymaprior excision may be necessary before laser treatment Epidermalnevi therapy was difficult to treat before the advent of CO2 lasersSurgery was difficult due to the size and configuration of thelesions and left ugly scars The pulsed CO2 laser gives arguablythe best results CO2 lasers have been very effective in clearingthick and large seborrheic keratoses although there is somescarring Scarring is much less with pulsed lasers

351 Laser Hair Removal

Hair removal is one of the most popular medical application oflasers Laser hair removal is based on preferred absorption in the en-dogenous chromophore melanin which is mainly found in the hairshaft compared to other parts in the tissue For light wavelengths be-tween 700 and 1000 nm the absorption coefficient of melanin is closeto two orders of magnitude higher than water and oxyhemoglobin Inthis window of wavelength when the laser is directed at the skin lightis primarily absorbed in the hair shaft melanin Heat is generated anddiffuses to the surrounding follicular epithelium

The laser discrimination in hair removal treatment borders onracism It is relatively easy to treat in the winter a hairy Caucasianliving in Alaska if he has black hair Any visible laser will do thereis considerably more absorption by black hair than by white-bleachedskin The same individual will feel like being interrogated in Guan-tanamo if he undergoes the same treatment after spending a sum-mer month on the beaches of Florida the laser will have a hard timedistinguishing between hairs or the dark sun cooked skin More prob-lematic even is the treatment of a Norwegian blonde sun tanned onthe Riviera a visible laser will selectively burn the skin rather than thefair hair Ruby lasers (643 nm) were used initially because they werethe most raquopickylaquo in their choice of skin color Less color sensitivity isexpected at longer wavelengths where the beam penetrates deeper in


the skin Therefore the ruby laser has been successively replaced bythe Alexandrite (750 nm) diode lasers (810 nm) and the NdYAG laser(1064 nm) each advertised as being more raquoskin color blindlaquo

The typical pulse width of the laser is 5100 ms which is longerthan the thermal relaxation time of the epidermis and comparable tothat of the follicle This pulse width range can effectively damage thefollicle However the epidermis also contains some melanin and mustbe protected There is a fine line to be walked in terms of pulse dura-tion Longer pulse durations allow the skin to heat up more slowly andare safer for darker skin tones Alternatively shorter pulse durationscan be more effective for treating fine and light colored hair

The spot size of the laser beam is a few millimeters The smaller thespot size the less radiation sent to the skin When applying the laserfor hair removal the beam is usually not aimed at a particular hair andthe laser beam is scanned across the skin There is an optimum spotsize that reaches the threshold for damaging follicles without thermaldamage to the skin Even so the distance from the lens to the skinis very critical the laser should be focused on the root of the hairbeyond the surface of the skin or a certain burn will result Sincehair is a living cell it goes through stages anagen is the active growthphase catagen is the regression phase and telogen is a resting phaseOne expects that the best time for hair removal is in the early phasessince the hair is only held in its tube and would fall soon anyway inthe last phase The response of the hair to the laser light varies indifferent stages The removal is not permanent How long the effectsof the treatment will last depends on the phase in which it is appliedComplete or partial reduction of hair is a clinical application of pulsedlaser beams

36 Lasers in Surgery

One can give the biggest applause to the invention of fiber opticsfor making it possible to transfer the light into deep tissues With-out the fiber laser all the medical applications of the laser would havebeen limited to the surface although a slight improvement of pene-tration depth can be achieved through multiphoton interaction (111)For example a fiber optic cable can be inserted through an endoscope


(a thin lighted tube used to look at tissues inside the body) into thelungs or esophagus to treat cancer in these organs

It seems that raquosurgerylaquo is getting further away from its originalLatin meaning of raquohand worklaquo Surgeons are introducing finer me-chanical and optical tools to the surgery and the laser is indeed one ofthem Lasers can be used for ablation of hard material such as teethand bones Short pulses are preferred for these type of operations be-cause the peak intensity that can be applied is much higher and in-duces less damage on surroundings (thermal damage) For examplewith 150 fs pulses of 775 nm of 1 kHz repetition rate a very precisecutting of mouse bones has been observed

Soft tissue removal can be controlled within a precise depth withlasers this can be used for skin cancer and tumors and for woundhealing caused by surgery or cancer treatment Lasers can be used forwelding veins or in a medical term coagulation The coagulation (clot-ting) of tissue uses a coagulation laser that produces light in the vis-ible green wavelength which is selectively absorbed by hemoglobinthe pigment in red blood cells in order to seal off bleeding blood ves-sels Studies have shown that ulcers can be successfully treated byCO2 and NdYAG lasers These treatments also improve the healingprocess

361 Blasting Kidney Stones or Laser Lithotripsy

Laser application to the body parallels its application in industry(Section 42) it can be used for scratching the skin welding veins andblowing up kidney stones The technique aimed at breaking stonesis laser lithotripsy which is a surgical procedure to remove stonesfrom urinary tracts such as the kidneys the ureter the bladder orthe urethra A urologist inserts a scope into the urinary tract to locatethe stone A laser fiber is inserted through the working channel of thescope and laser radiation is directly beamed into the stone The fiberdiameter is of the order of few 100 μm The stone is disintegrated andthe remaining pieces are washed out of the urinary tract

The study of the destruction of urinary calculi in vitro started withthe early days of the ruby laser (Section 142) The 694 nm light wasfocused through quartz rods shaped to allow delivery of the laser en-ergy through an endoscope The stones vaporized into steam becauseof the excess heat generated in this process Staining the stones blue

36 Lasers in Surgery 111

and black enhanced the absorption Different calculi had different re-sponses some stones apatetic and struvite broke easily and oxalateswith more difficulty

Later it was realized that creating shock waves with laser pulsescould be even more efficient than removal of the stone through heatgeneration A Q-switched ruby laser with 20 ns pulse duration cangenerate 20 kbar stress waves As a result of this study both peakpressure and pulse duration were considered as factors for treatingurinary calculi

A systematic search for the best laser and proper wavelength wasinitiated to tackle this problem Continuous wave (CW) carbon diox-ide lasers mainly drilled holes in the stones without inducing shockwaves and breaking them It was hard to pass CO2 lasers in fibersand the generated heat was too high Moreover the aim was not todesign patterns on the stones with drilling holes but to break themContinuous wave NdYAG lasers with a high energy level of (50 J s1)had only thermal action on the stones and damaged the fibers Thesame NdYAG laser operating in the pulsed mode (1 J pulses 15 nslong) in full power had no measurable thermal effect and resulted infragmentation of stones for 30 min of operation The problem at thetime was the energy transfer through the fiber which is why the studywas pursued with tunable dye lasers

Tuneable flashlamp pumped dye lasers with a variety of dyes wereused to emit light at 445 504 and 577 nm Different fiber diametersand pulse width were used to find the optimum parameters for stonefragmentation One should not be surprised to see the rise of frag-mentation threshold with the increase of fiber diameter (less inten-sity) or increase of pulse duration (less intensity) The 445 nm lighthad the strongest impact on the stone but the 504 nm wavelengthwas selected due to the differential absorption of the stone over theureter The 504 nm wavelength is not well absorbed by hemoglobinand therefore tissue but is well absorbed by yellow pigment of manycalculi

Why should a short pulse work better There is an opportunity ofplasma formation at the focal spot of the laser the plasma expandsand contracts hence creates a shock wave This optico-acoustic effectresults in high pressures of 1000 bar From there it is all mechanicalshock wave forces fracture on the stone through natural fault lines


The residual fragments may be either retrieved with stone grabbingforceps or may be left to pass

37 Biostimulation Lasers for Ulcer Treatment

Biostimulation lasers also called low level laser therapy (LLLT) coldlasers soft lasers or laser acupuncture devices are used to stimulatehealing in the tissues The laser usually emits in a narrow band in therange of 6001000 bar Low density laser irradiation was introducedas a noninvasive therapeutic modality for acceleration of wounds forthe treatment of chronic ulcers due to poor microcirculation It ap-pears that low intensity laser enhances metabolic pathways by dif-ferent mechanisms These include activation of previously partiallyinactivated enzymes mainly ATPases induction of reactive oxygenspecies stimulation of Ca2C influx and mitosis rate augmented for-mation of messenger RNA and protein secretion At the cellular lev-el enhancement of cell proliferation and mobility of fibroblasts25) andkeratinocytes were frequently noted after laser irradiation and play amajor role in wound healing There is evidence that low level laserapplication also improves the skin circulation There are reports onlow intensity light radiation for the reduction of dermal necrosis afterx-radiation Low level laser application can also treat ulcers resultingfrom radiotherapy

For this low level laser application a continuous wave 30 mW He-Ne laser was used Unlike many other applications of lasers that re-quired tight focus and a small spot the beam was expanded to covera large area The intensity of the light was of the order of only a fewmWcm2 for an extended period to achieve a total dosage of tens ofJcm2

38 Lasers in Diagnostics

Lasers are used in clinical diagnostics and biological studies Look-ing at the shape of the wave in space or the wavefront as it propagatesand reflects from a surface is one example of diagnostics The very

25) A fibroblast is a type of cell that synthesizes the extracellular matrix and collagen

37 Biostimulation Lasers for Ulcer Treatment 113

intuitive picture of a wave that is generated by disturbing a quiet pondwith throwing a stone is quite familiar The generated waves start niceand circular but as they are diffracted and reflected from leaves andstones on the pond their shape is deformed Measuring the changein the wave front gives information about a reflective object with sub-wavelength accuracy The wavefront across the beam is the spatial fin-gerprint of the light

Nowadays thousands of dentists are getting help from a devicecalled raquoDiagnodentlaquo which shines new light on easy-to-miss cavitiesThe hand-held instrument uses a red laser to penetrate the outer layerof the teeth By measuring the way light reflects back Diagnodentdetects signs of decay in a reassuringly gentle manner

381 Detection of a Single Virus in a Nanostructure with Laser Light

As mentioned previously there is another fingerprint aspect of thelight its frequency A continuous laser will have a well defined singlefrequency due to a stiff and high quality laser cavity resonator A mul-ticolor mode-locked laser (Section 171 and Chapter 5) will provide afrequency comb with sharp teeth Light interaction with material canchange this frequency due to excitation and reemission In most cas-es at the end of the photon interaction process a photon is ejectedwith less energy and the difference is consumed to induce excitationin vibration rotation or electronic excitation

Raman spectroscopy is a technique that involves the measurementof a change in a single frequency light (near infrared visible nearultraviolet) by an amount corresponding to the rotation or vibrationof a molecule An intense laser is sent through the material to be ana-lyzed (the wavelength of that laser does not have to match any require-ment other than being able to be transmitted through the medium) Aspectrometer is used to detect light reemitted at a wavelength close tothe laser wavelength What is measured is the wavelength shift of thereemitted radiation Since each molecule has a unique level structureone can use this change in frequency (energy) to define the unknownmolecule Although the Raman technique involves laser light the In-dian scientist Sir CV Raman ndash who received the Nobel Prize of 1930and has his name imprinted on this phenomenon ndash made this obser-vation by using as a source sunlight passing through a narrow bandfilter


The process defined above is generally called raquospontaneous Ramanscatteringlaquo and is not a very efficient process Only one out of a mil-lion photons will experience Raman scattering and also there aremany modes in rotation and vibration For a typical molecule likea protein there are many atoms and as a result a large number ofconnections between atoms (bonds) can be excited The use of lasersin this application chooses to selectively excite a particular bond ina molecule Both the selectivity and efficiency of Raman scatteringare considerably enhanced in impulsive stimulated Raman scatteringmade possible by the control of light signals with femtosecond preci-sion The basic principle is to repeatedly excite the particular bond tobe analyzed at its resonance frequency The analogy is that of a bridgewhich is stepped upon at exactly a natural frequency of resonance ofthe mechanical structure Each step is a light impulse (which has tobe much shorter in time than the vibration period of resonance ofthe bond) The bridge will start oscillating with a large amplitude ifthe time interval between steps is equal to the period of vibration of abeam of the bridge With light the time interval has to be in the hun-dred femtosecond range since molecular bonds vibrate in the THzrange Various pulse shapers have been devised which can for in-stance create a train of regularly spaced femtosecond pulses out of asingle pulse As in spontaneous Raman scattering a single frequencylaser is sent through the material along the same path as the pulsetrain and the frequency shift (between the laser frequency and that ofthe vibration) is measured

Having tunable laser sources in hand either the shifted or the in-coming beam can be set close to a particular charge transition Forexample in a biomolecule such as hemoglobin by tuning the laserto energy associated to charge-transfer of the iron the resulting spec-trum shows the shift in spectrum only due to stretching and bendingof the iron group This way there is less complexity in the spectrumbut the researcher must have a smart guess and know what hesheis looking for The technique of selecting a particular bond throughresonance is called resonance Raman spectroscopy

From spontaneous to stimulated Raman scattering one has a hugesensitivity enhancement but this is not yet sufficient to detect a sin-gle virus Nanotechnology comes to the rescue to provide a furtherenhancement in sensitivity by 100 million It is well known that anelectric field can be enhanced at the tip of a sharp needle This is the

38 Lasers in Diagnostics 115

reason that all metallic parts of high voltage installation are shapedas much as possible as spheres The same applies to the electric fieldof light At the molecular level nanowires can act like antennas andenhance the laser field or the detection signal Silver nanorods with adensity of 13 nradmm2 with angle of 72 ˙ 4ı are arranged normal toa silver film The thin silver film is on a glass slide and the thicknessof the nanorods are 10 000 times finer than a human hair The physicsis a little more complex than the static electric field enhancement atthe time of a needle because the light field oscillates at such a highfrequency The field is said to be enhanced by surface plasmons whichare optical frequency oscillation of electron gas in a surface Surface en-hanced Raman scattering (SERS) has been around since 1974 A prop-er design in size and spacing and material of the nanostructures en-hances the signal so that even a single virus can be detected A typi-cal experiment uses a fiber-optic coupled infrared 785 nm diode laserwith power in the range of 1015 mWm The virus sample needed fordetection is only 0510 μl volume

382 Optical Tweezers

Have you ever been caught in a crowd trying to scape from a tinyopening When everyone is pushing hard towards the door and youexperience all forces in different directions and cannot predict whatwill be the result of it all That is what happens to a tiny particle withincident light As we saw seen in Chapter 1 (112) each photon hasan energy proportional to its frequency that scales with Planckrsquos con-stant (hν) Mechanics is the most intuitive branch of physics many ofits concepts are realized in life with running collisions turning andjumping If you have the privilege to have a chance of hitting a realball on the wall rather than an imaginary one in a computer gameyou have had the chance of having a feeling about how energy is con-verted to momentum In a collision momentum is transferred basedon Newtonrsquos law the total momentum is conserved before and afterthe accident In the game of pool the fast running raquocue balllaquo has theenergy of 12mv 2 where raquomlaquo is the mass and raquovlaquo is the velocity ofthe ball In the nine-ball game after the first hit of the cue ball thetotal system of the nine ball has the same initial energy and the nine-ball system as a whole still moves in the same direction as of the cueball with the total energy of 12(9m)v 02 The value of v 0 is calculated


from the conservation of linear momentum mv D (9m)v 0 which isa mathematical statement that the momentum of the cue ball beforehitting the balls at rest is the same as the momentum of cue ball plusthe other eight balls after the collision

The above example is for objects with mass but anything that car-ries energy has also momentum the photon being one object withoutmass but with momentum The pressure exerted by a light beam iscalled raquoradiation pressurelaquo Due to the gravity of the earth a grain ofsalt with a mass of 585105 g exerts pressure on a flat surface equalto 6 kgms2 or 6 Pa which is million times more than the pressureof sun radiation on earth As discussed in Section 18 a tightly fo-cused laser beam can reach intensities of 1016 Wcm2 which is 1000times more than the pressure at the deepest part of the ocean Is this acontradiction This huge difference is just an illustration of the hugedifference in orders of magnitude of intensities that can be achievedwith light concentrating photons in time and space The laser lightcan be focused tightly and on the tight focal spots the photons are or-ganized to move parallel to each others and all the photons can beorganized to hit the surface for a very short time As we had tamedthe power of horses we can take advantage of this force by manipu-lating the light profile and intensity Although the radiation pressurewas known in the nineteenth century it only had a noticeable effect inastronomy where no friction opposes the motion of interstellar dustand light intensities and distances are huge

With the mass production of laser sources it is easy to buy a simplekit to manipulate and trap individual cells and particles The sameeffect of radiation can be used for optical cooling of atoms as dis-cussed in Section 63 As we see in Chapter 6 in a tight laser focalspot molecules tear apart and high energy electrons can be used fornuclear reaction Clearly optical parameters such as wavelength in-tensity and intensity gradient have to be tailored to manipulate smallparticles without inducing optical damage We can put pressure on abook and by pressing it to the wall the forces are balanced in such away that the book stays still on the wall and gravity is compensatedHowever if we try to do the same on a ripe berry and try to hold it ona wall by putting some pressure the berry might get deformed andjust leave a mark on the wall

With optical trapping we can manipulate particles remotely with-out any mechanical tweezers to hold or push things around using


the transverse variation of laser intensity as shown in Figure 34 Afocused beam of 1 W exerts only a force of 10 μnN on a particle thesize of a wavelength This seems a minuscule force but if the parti-cle reflects all the light back on itself for a small mass (for example1011 g) the acceleration received by the change of light momentum(acceleration) Fm is of the order of 105 g where raquoglaquo is the accelera-tion of gravity on earth This is a huge acceleration that can be tamedfor watching the dynamics One of the important studies that can bedone with this controlled dynamics is watching the motion of a singlemotor molecule such as kinesin Kinesin is a motor protein that (inmost cases) walks towards the raquopluslaquo end of a microtubule26) The mo-tion of these motors appears to have a role in cell division or mitosisThese motors are necessary for separation of chromosomes into thedaughter cells during cell division With optical tweezers the detailedmotion of this motor protein with a stepping motion of only 10 nmper step on the submicron tube is resolved

The control is based on the light pressure or radiation pressure Herewe can think of photons as balls on a pool table (although we knowthat light photons do not carry mass) A cue ball hits the arrangementon the table and balls move in all directions on a pool table Lookingcarefully at the ensemble of balls moving in various directions werealize that the net momentum of the ensemble motion is in the di-rection of the cue ball This is the same for a particle sitting on a beamof light that has a higher index of refraction than the surroundingsPhotons hit the ball in the entire region of the illumination As a resultthere is a net force towards the center of the beam where the intensi-ty is higher This force is both in the transverse direction and in thedirection of propagation The transverse component is called the gra-dient force and the component along the propagation is the scatteringforce [7] As shown in Figure 34 one can follow the path of the lightbeam as it goes through a sphere The bending through the sphereis due to the change of speed of light (change of index) between thesphere and surroundings The force on the particle is in the directionof change of the beam path27) In this figure only the propagation oftwo beams is shown The inclusion of all rays results in a net push

26) Microtubules are polymers and one of the active matter components ofcytoskeleton

27) The force in mechanics is F D Δmv where mv is the momentum So that forceis in the direction of the difference of the momentum


Figure 34 (a) The effect of the light pres-sure on small objects A incident beamwith a spatial intensity gradient creates anonuniform push to a particle and steersit towards the center (high intensity) partof the beam in the transverse direction(gradient force) In the longitudinal direc-tion the beam pushes the particle alongthe propagation axis This is a scatter-ing force from reflected photons thatbounce back from the surface Transmit-ted light also transfers some momentum

for a gradient intensity profile we can fol-low this force as normal to the beam raybending in the sphere The thickness ofthe line representing each ray is an indi-cation of the intensity of that portion oflight (b) With proper adjustment of thelight intensity radiation pressure can beused to make a levitation trap If the forcedue to radiation pressure cancels theweight of the particle a stable suspensionis achieved Please find a color version ofthis figure on the color plates

along the laser propagation axis and towards the center If the indexof refraction of the particle is less than the surroundings the particlewill be pushed away from the center and along the propagation axis

Instead of a single beam illumination from the left as shown inFigure 34a a second beam can be sent from the right If the two focalspots (from left and right) are made to overlap the neutral particleis trapped in the common focus of the two beams The two identicalbeams focusing from opposite sides have equal forces that cancel eachother The net force (F1 F2) exerted on the particle is zero but thesurface force stretches the particle by (F1 C F2)2 and this force canbe up to several hundred piconewton [8] This technique is attractivefor stretching single cells or a long molecule and is known as opticalstretching (OS)

An optical lattice is formed with multiple beams to make a sort-ing sieve based on intensity and phase of the beams This applicationof lasers is more used in basic research studies as discussed in Sec-tion 63


Radiation has similar effect on smaller particles like atoms andmolecules Here we cannot use the simple picture of bending rayssince we are dealing with absorption and emission in units of photonsas seen in Section 12 The photon incident on an atom or moleculemight be on resonance with one of its intrinsic levels separation Thelow intensity absorption or raquolinearlaquo absorption has a probability re-lated to the ratio of the size of the particle (atom or molecule) to thatof the photon Since the characteristic size of the photon is its wave-length it should not come as a surprise that the absorption proba-bility varies as the square of the wavelength it being higher for thelower wavelengths The collision of light and matter at this micro-scopic level is not instantaneous and the lifetime of the upper statemust be included The photon ball that hits the atom is going to agooey-sticky level and will stay on that upper state for a time that isaveraged to the raquospontaneous emission lifetimelaquo then it is emitted Itis just like hitting the jelly ball with a photon the momentum trans-fer and the resulting pressure are different in this case For an en-semble of atoms the saturation needs to be included Considering asimple two level structure and a single electron the electron is ei-ther in the lower state or the upper one In the fully saturated casethe population in the upper state is f D 12 The scattering force tothe atom resonant with the light is Fscat D h f λ t where raquoflaquo is thepopulation in the upper state and raquotlaquo is the spontaneous emissionlifetime

The scattering force is not negligible when dealing with atomicbeams As a result of this force when incident on a sodium beamat room temperature at saturation intensity the atomic beam is di-verted to a circle of radius of 40 cm This force accelerates the atomsmoving in the same direction as the light and slows down those mov-ing in opposite direction It can be exploited to design an atomic beamvelocity selector or an isotope selector [9]

The force on atoms in the transverse direction is more complicatedbecause it depends on the polarizability of the atom or the strengthof slushing the electrons back and forth28)

28) The classical formula for the gradient force on a neutral atom is 12αrE 2 whereα is the polarizability The polarizability changes sign at resonance just like thegradient force reverse sign when the index of particles relative to their surroundingchanges sign


Carefully matching all these forces one can balance out the gravi-ty and keep the particle suspended with light pressure Many exper-iments and devices have been designed by exploiting the radiationpressure A Levitation trap is achieved when the weight of a particleis balanced with the scattering force Hollow glass spheres that areused as small fusion targets are levitated with laser beams An opti-cal tweezers trap may be realized with a single strongly focused laserbeam Changing the position of the lens moves the focal spot and thetrapped particle accordingly In high quality optical microresonators thetuning of the wavelength changes the radiation pressure forces whichin turn influence the resonance of the resonator A minute change inforce or a evolution of the force on a particle can be measured precise-ly by tuning laser intensity

383 Monitoring Blood Velocities

3831 The Doppler EffectThe Doppler effect is not unique to light but is simply a manifes-

tation of how a moving observer perceives a wave ndash any wave To il-lustrate this point we return to our ducklings paddling in a windypool Figure 35 is a space (in the direction of propagation of thewave) ndashtime representation of the water wave The z axis (towardsthe right) shows the distance (an axis normal to the wave) and thetime axis indicates the position of the nonmoving duckling on the farleft at z D 0 The raquoverticallaquo axis is the position of the up-and-downmotion of the object on the wave The dash-dotted line t D zvw

Figure 35 Illustration of the Dopplershift (A) No Doppler shift for the duck-ling that is at rest and goes up and downat the frequency of the wave (B) Red shift(lower frequency) for the duckling mov-

ing in the direction of the wave (C) and(D) Blue shift (higher frequency) for theduckling moving with a velocity oppositeto the wave


indicates the propagation of the wave (the wave propagation is alsoindicated by the thin dotted lines parallel to the dash-dotted line)The duckling at rest goes up and down at the true frequency of thewave νw (A) The center duckling is paddling in the same directionas the wave at a velocity vsurfing nearly raquosurfinglaquo and experiences theDoppler down-shifted frequency νsurfing D νw (1 vsurfingvw ) alongthe line B in Figure 35 The third duckling is quacking flying andpaddling full steam ahead at a velocity vCD against the wave (lines Cand D) He is clearly bouncing up and down at a much higher fre-quency νCD D νw (1 C vCDvw )

3832 Doppler AnemometryThese expressions for Doppler shift apply also to light The only

difference is that the speed of the wave is the speed of light c whichis considerably higher than the motion of any object in our commonworld Therefore measuring a relative change of the optical frequencyof vc where v is the velocity of a moving car animal particle gasto be determined is a nearly impossible task However the frequen-cy of the light ν 1014 Hz is also a gigantic number29) Thereforethe product νvc which is the Doppler shift is a frequency easily ac-cessible with standard electronics To measure directly that frequencywe are blessed by the fact that a light detector measures an intensityrather than an electric field Therefore if we mix into a detector theoriginal signal with an electric field oscillating as cos(2πν t) at a fre-quency ν with the Doppler shifted signal cos[2π(ν C νvc)t] at thefrequency ν C νvc the intensity seen by the electronic detector isproportional to fcos(2πν t) C cos[2π(ν C νvc)t]g2 which is a signaloscillating at the difference frequency (the Doppler frequency νvc)The mixing is easily realized in the arrangement of Figure 36a Thebeam from the laser is split into a reference beam and an interro-gating one The reflection of the latter by a moving object is Dopplershifted and mixed on a detector by the reflection of a fixed object Notethat the detector sees a Doppler shift of 2νvc the moving object seesthe incoming light shifted by νvc and raquoreemitslaquo the light with an-other shift of νvc The moving object and the reference are generallynot mirrors but objects that backscatter the light in all directions with

29) One should probably use an adjective derived from tera (1012) since raquogiganticlaquo isderived from raquogigalaquo (only 109)


Figure 36 Various implementations oflaser Doppler anemometry (a) the beamfrom a laser is split into a reference armdirected to a fixed (diffuse) reflector anda probe beam directed to the movingobject The backscattered reference andbackscattered Doppler mix in the detec-tor D giving rise to an AC signal at theDoppler shift frequency (b) A reference(weak) beam and a strong probe cross at

an angle in a flowing liquid The Dopplershifted scattered light mixes with thereference in the detector D A is an aper-ture L a lens (c) Blood anemometry Thelaser is delivered via a fiber in the arteryPart of the backscattered radiation of themoving and fixed particles is recoveredby the fiber sent via the tap DC to thedetector D

random phase It is thus a sum of N (where N is a very large number)elementary Doppler contributions of random phase that contributesto the detected signal We have seen in Section 1131 that such a sumis not zero but an electric field of

pN the elementary contribution

(photons adding incoherently rather than coherently) An interpreta-tion of the signal recorded by the detector ndash which is equivalent to theDoppler picture ndash in Figure 36a is that the signals from the referenceand interrogating arms add successively in and out of phase as theobject is moved

Doppler anemometry is also used to measure flow velocities of gas-es and liquid Two different configurations are shown in Figure 36band c In Figure 36b a very weak reference is set to intersect at anincidence normal to the flow of a liquid a more intense probe beamBecause the particles in the liquid have a velocity component alongthe probe beam the scattered light is Doppler shifted Components ofthe scattered light along the weak probe beam create a beat signal onthe detector with a frequency proportional to the flow velocity

The configuration of Figure 36c has been used since the 1970s tomonitor the flow of blood [10] This arrangement is simpler than theprevious ones as there is no raquoreference armlaquo A fiber is introducedinto the artery to be tested The backscattered radiation is collected in


the same fiber and raquotapedlaquo by a coupler DC into the detector Sinceboth moving particles and the fixed walls of the artery contribute to thebackscattering the detector sees a beat note at the difference frequen-cies between all particles at rest and in motion The interpretationof that broad spectrum is not straightforward One chooses the high-est frequency as representative of the Doppler shift corresponding tothe blood velocity In some cases a separate fiber is used to collectthe backscattered light The difficulty of the Doppler blood anemom-etry is the short penetration depth of light The wavelength range thathas the best transmission for biological substances is between 11 and125 μm

Blood anemometry plays a crucial role in the latest method of imag-ing through optical scanning tomography as will be described in Sec-tion 392 to follow


39 Ultrafast Peeking

In the previous section we saw what the laser can do to the eye andfor the eye Here we discover that the laser can be a kind of eye forus making it possible to achieve three-dimensional pictures with un-precedented resolution The inspiration behind this technique comesfrom the radar applied to ultrashort laser pulse technology

391 Time Domain Reflectometry

A striking example of the influence of the radar is in the imagingof the eye The radar is an important invention of the early 1940ssince it contributed ultimately to the defeat of the German LuftwaffeAs sketched in Figure 37a the principle is simple A pulse of elec-tromagnetic radiation at a frequency of a few GHz scans the sky Thepulse is short by GHz standards a few optical cycles will constitutea nanosecond pulse As it encounters a reflecting object such as anairplane a weak reflection retraces to path of the interrogating beam

39 Ultrafast Peeking 125

The time it took for the pulse to propagate from the radar site to theplane and back to the radar site is measured The resolution is typical-ly a meter (a 3 ns pulse has a spatial extension of 3 ns c D 1 m) Theprinciple of the raquooptical radarlaquo is the same as sketched in Figure 37bbut the scale quite different An ultrashort pulse from a mode-lockedlaser (see Section 172) is beamed towards the eye where it encoun-ters a considerable number of reflecting interfaces As in the case ofthe classical radar it is the time it takes for the light pulse to prop-agate to an interface and back to the laser (or to a suitable detector)that is measured in order to determine the exact location of the inter-face For a pulse duration of 30 fs the resolution is 30 fs c D 10 μmThe analogy stops here there is no electronic light detector that canresolve an event in the femtosecond scale It was soon realized thatlight pulses themselves would have to be used to provide a temporalresolution of a fs [11 12] The laser beam is split in two one pulse issent to the target (the eye) the other to a reference mirror Both reflec-tions (from the eye and from the mirror) are sent to a raquoblack boxlaquo thatmakes the product of the two beams a product that is only nonzero ifthe two pulses overlap that is if the reference mirror is at the samedistance as the interface (Figure 37b) The simplest raquoblack boxlaquo usedfirst consisted of a raquononlinear crystallaquo If two laser pulses of sufficientintensity are sent simultaneously to a crystal they will create radiationat the optical frequency equal to the sum of the frequencies of the twopulses In the case of Figure 37b the two pulses have the same opticalfrequency and the light that is generated in the crystal is at twice thatfrequency of the half wavelength (usually UV) Thus by scanning theposition of the reference mirror M the detector D will record UV ra-diation each time the position of M corresponds to an interface Therewas only one flaw to this scenario the raquononlinear detectionlaquo requiredlight of high intensity at a wavelength (red light at 620 nm in the ini-tial experiments [13]) that penetrates into the eye which is not a veryappealing prospect for the patient

392 Optical Coherence Tomography (OCT)

The solution to the high power requirement of the nonlinear detec-tion is to use linear detection combined with property of laser lightto be raquocoherentlaquo and to make interferences [14] No raquoblack boxlaquo isneeded anymore in Figure 37b As the mirror M is scanned back and


Figure 37 (a) The radar emitter sendsa few cycles of electromagnetic waves ina nanosecond pulse towards a target inthe sky The distance to the target is de-termined from the measurement of thetime it took the pulse to make the raquoroundtriplaquo (b) The same technique applied tothe measurement of the eye It is now afs pulse from a mode-locked laser that issent to reflect off the various interfaces

within the eye The pulse length (pulseduration c) is shorter than even thethickness of the epithelium (membranein front of the cornea) The time of flightmeasurement is performed as a pure op-tical coincidence method the raquoblack boxlaquoonly detects a signal if the raquoreferencelaquoand raquosignallaquo (from the eye) pulses ar-rive at the same time Please find a colorversion of this figure on the color plates

forth over a few μm if an interface of the eye is located at the samedistance as the average position of the vibrating reference mirror thebeam from the eye and from the reference will interfere successivelyconstructively (maximum signal on D) or destructively (minimum sig-nal on D) creating an alternating signal on D If there is no reflectinginterface in the eye at the depth corresponding to the average posi-tion of the reference mirror there will be only a constant backgrounddetected on D A schematic representation of OCT as it applies to theimaging of the retina is shown in Figure 38a There is no need forthe source to be an ultrashort pulse as long as it is a source with thesame raquoincoherencelaquo as an ultrashort pulse The light from the sourceis sent through fibers via a 5050 fiber splitter to a reference and a sig-nal arm At the end of the signal arm a collimating lens followed byan xndashy scanning mechanism an optical system to bring the scannedbeams into focus onto the retina At the end of the reference arm amirror oscillates back and forth with an amplitude equal to the co-herence length of the source At each half cycle of the mirror motionthe backscattered light from a layer from the eye makes a successionof constructivedestructive interferences with the pulse reflected fromthe reference arm The range over which the interference occurs is ap-


Figure 38 (a) Typical set-up for opticalcoherent tomography The source is ei-ther an ultrashort (femtosecond) pulselaser or a low coherence semiconductorsource coupled to a fiber which is dividedinto two arms at the beam splitter BS Ascanning retroreflector AS at the end ofthe reference arm returns a signal backtowards the beam splitter BS The oth-er fiber arm is collimated by the lens Lgiven a transverse scanning (in x and y)by the scanner TS before being sent to

the eye by a set of lenses L The backscat-tered radiation from the eye is mixedwith the reference signal in the detec-tor D (b) Since information obtained byscanning is equivalent to a spectrum theretroreflector of the reference delay canbe left fixed and a single shot spectrumrecorded by a CCD is substituted to thescanning information G is a grating toproduce the spectrum Please find a colorversion of this figure on the color plates

proximately the length of the pulse (if ultrashort pulses are used as asource) or equivalently the coherence length of the radiation (if whitelight or a light emitting diode or a laser diode of low coherence areused as a source)


Figure 39 Successive steps of tomo-graphic reconstruction (a) The objectunder investigation (b) One-dimensionalscanning (c) Scanning from four different

directions (d) The planes that define theobject Please find a color version of thisfigure on the color plates

While the resolution of the depth can be of the order of a few μmthe transverse resolution is much coarser An innovative techniquehas been found to restore to the transverse direction the exquisite lon-gitudinal (depth) resolution provided by time domain reflectometryThe technique consists of adding angular scanning to the transversescanning To realize the power of this method called tomographic re-construction let us consider the problem of visualizing a membraneorganized in a sphere of 25 nm diameter (Figure 39a) A longitudi-nal scan is performed first with a transverse resolution of 10 nm anda depth resolution of 02 nm The result is four larger returns cor-responding to the four interfaces normal to the beam (Figure 39b)Next a longitudinal scan is performed from another angle Then an-other one The result of four illuminations is shown in Figure 39cAfter a sufficient number of angles of illumination the object is de-fined by an envelope of tangents to the object (Figure 39d) Eventhough the transverse resolution was 10 nm the final transverse re-construction after angular scanning is 02 nm

There is more information that can be extracted from the set-up ofFigure 38a The scattering from moving blood cells in the retina willbe Doppler shifted This Doppler shift will result in a phase shift ofthe interference recorded on Detector D which can be determined byrecording the signals in phase and in quadrature with the motion ofthe reference mirror [15]

Speed in data acquisition is essential in capturing images raquoin vivolaquoAn interesting improvement on the system of Figure 38a is sketchedin Figure 38b The scanning of the reference arm is eliminated In-


stead a spectrum is recorded on a CCD of the correlation betweenthe reference and backscattered signals [16] It can be demonstratedthat the spectrum recorded on the CCD contains the same informa-tion as the correlation between the reference and signal that was ob-tained by scanning in Figure 38a but without the need for scanningThe Doppler information itself is also carried by the spectrum Thearrangement of Figure 38b enables a larger speed of data acquisitionbecause the spectrum can be acquired in a single shot rather than themechanical reference mirror scanning of Figure 38a

The spatial resolution is limited to a few optical waves dependingon the pulse length or the coherence length of the source One mightwonder whether this is the ultimate resolution possible As will be pre-sented in Chapter 5 the laser itself has a precision that can beat thewavelength limit What is contemplated in the section on intracavi-ty phase interferometry is a futuristic extension of Figure 38 wherethe laser cavity instead of being the black box at the top left cornerof the figures extends and includes the reference mirror and the ob-ject under investigation As the Doppler effect provides a frequencyΔνD proportional to a flow velocity v scaled by the light frequency ν(ΔνD D ν(vc)) the intracavity phase interferometry provides a fre-quency ΔνIPI proportional to a position or elongation (ΔL) scaled bythe light frequency (ΔνIPI D ν(ΔLL))

393 Wavefront Sensing

Lasers have helped considerably in quantitatively analyzing theaberration to be corrected We have seen that the laser light is a coher-ent wave characterized by a wavefront which is the surface normalto the rays The plane wavefront of a collimated laser beam shouldbe transformed into a spherical one by reflection or transmissionthrough a perfect lens The ShackndashHartman sensor is an instrumentthat measures the shape of the laser beam wavefront surface andcan therefore analyze the exact transformation brought by the eyewhich is information that can be used to predict the exact ablationto be brought to the cornea The HartmanndashShack sensor consists ofan array of microscopic lenses (typically 200 μm side) focused ontoa CCD array A collimated plane wave creates a two-dimensional dotpattern of equally spaced dots The departure from that equally spaced


pattern can be used to determine the exact shape of the wavefront asit differs from a perfect plane wave

References

1 Jelinkovaacute H Dostaacutelovaacute T NemecM Koranda P Miyagi M ShiKIYW and Matsuura Y (2007)Free-running and Q-switchedErYAG laser dental cavity and com-posite resin restoration Laser PhysLett doi101002lapl200710062

2 Boulnois JL (1986) Lasers MedSci 1 47ndash66

3 Jelinkovaacute H Pasta J Nemec MSulk J and Koranda P (2008)Near- and midinfrared laser radi-ation interaction with eye tissueAppl Phys A doi101007s00339-008-4618-8

4 Gross G Lucas JH and Hig-gins ML (1983) Laser microbeamsurgery ultrastructural changes as-sociated with neurite transection inculture J Neurosci 3 1779ndash1993

5 Achauer BM and Kam VMV(1987) Argon laser treatment oftelangiectasia of the face and neck5 yearsrsquo experience Lasers SurgMed 7 495ndash498

6 Neuman RA and Knobler RM(1990) Venous lakes (BeanndashWalsh)of the lipsndashtreatment experiencewith the argon laser and 18 monthsfollow-up Clin Exp Dermatol 15115ndash118

7 Ashkin A (1997) Optical trap-ping and manipulation ofneutral particles using lasersProc Natl Acad Sci USA 944853ndash4860

8 Guck J Ananthakrishnan RMoon TJ Cunningham CC andKas J (2000) Optical deformabilityof soft biological dielectrics PhysRev Lett 84 5451ndash5454

9 Diels JC (1976) Efficient selectiveoptical excitation for isotope sep-

aration using short laser pulsesPhys Rev A 13 1520ndash1526

10 Tenland T (1982) On Laser Dopplerflowmetry methods and microvas-cular applications PhD ThesisLinkoumlping University Departmentof Biomedical Engineering S-58185 Linkoumlping

11 Diels JC and Fontaine JJ (1983)Imaging with short optical pulsesOpt Laser Engin 4 145ndash162

12 Diels JC Fontaine JJ andRudolph W (1987) Ultrafast diag-nostics Rev Phys Appl 22 1605ndash1611

13 Diels JC Rudolph W andFontaine JJ (1987) Optical radarusing femtosecond light pulses inProc Ernst Abbe Conf Jena 1987EAC Friedrich Schiller UniversitaumltJena Jena Germany vol EAC

14 Huang D Duker JS FujimotoJG Lumbroso B Schuman JSand Weinreb RN (2010) Imag-ing the Eye from Front to Back withRTVue Fourier-Domain Optical Co-herence Tomography Slack IncBoston

15 Yazdanfar S Rollins AM andIzatt JA (2000) Imaging and ve-locimetry of the human retinalcirculation with color doppler op-tical coherence tomography OptLett 25 1448ndash1450

16 Leitgeb RA Schmetterer LDrexler W Fercher AF Za-wadzki RJ and BajraszewskiT (2003) Real-time assessment ofretinal blood flow with ultrafast ac-quisition by color doppler Fourierdomain optical coherence tomogra-phy Opt Express 11 3116ndash3121


4Lasers in Industry

41 Laser Machining

Lasers have come to cover a huge palette of macroscopic and micro-scopic applications Under macroscopic one implies welding cuttingmarking surface treatment and so on Microscopic applications in-clude micromachining microdrilling microassembly and precisionmarking The first applications to see the light of day were on sheetmetals Other applications followed as it became clear that the laserprovides a good return despite a relatively large investment

411 Marking

The laser offers the cowboy a more sophisticated tool than the red-glowing iron to mark the cows of his herd Other objects than cowsneed marking such as serial numbers on metallic parts or bar codeson any commercial product Contrary to the glowing iron stamp ofthe ranch laser marking is not limited to soft tissue The laser beamcan be used to mark any surface such as metal plastic ceramic glassor wood of any surface state There is also little thermal load on theobject to be marked (especially compared to the hot iron stamp) Thewriting speed can reach several ms Using computer controlled de-flectors the marking does not require the fabrication of masks orstamps It can be done on the surface or inside transparent materialsFigure 41a shows the marking of what was the raquoCenter for AppliedQuantum Electronicslaquo at the University of Texas Denton in 1987The marking was made with a Q-switched Ndglass laser focused in-side the plastic block

A particular type of marking is engraving Surface material is re-moved with a focused high power laser such as a CO2 laser The ad-vantages of using a laser is the absence of tool bit wear no raquodead


133

Figure 41 (a) Initials of the Center for Applied Quantum Electronics written with aNdglass laser focused in a block of plexiglas (a farewell present to one of the authorsin 1986) (b) Wood engraving made by the CO2 laser

timelaquo if the tool bit has to be replaced a better spatial resolution andthe possibility of creating complex patterns even three-dimensionalTypical commercial instruments use a CO2 laser of 10100 W such aspresented in Section 1421 and achieve a resolution of the order of10 linesmm An example is shown in Figure 41b

42 Laser CuttingDrilling

Lasers have become the preferred tool for sheet metal and foils Alaser vaporizes and melts the foil or sheet without applying any de-forming force on it As the plane to be sliced is moved transverse tothe focused beam the molten or vaporized matter is blown away witha neutral gas The precision of the cut varies with the mode of irra-diation which is a parameter that can vary in huge proportions Thecontinuous laser typically provides cuts with a precision of 100 μmPulsed lasers can provide a precision of 10 μm The mechanism bywhich the material is ablated is thermal in the range of pulse dura-tion from continuous to picosecond The mechanism of femtosecondpulse ablation is nonthermal the atoms are ionized by multiphotonabsorption and the strong repulsive forces of positive ions make themolecules fly apart (raquoCoulomb explosionlaquo) Femtosecond lasers have

134 4 Lasers in Industry

not taken a sizable portion of the market for industrial applicationsand will not be discussed more in this context

For thermal ablation the laser pulse should be long enough to sig-nificantly heat the sample The coupling of the laser onto the materialmay be increased at the tail of the pulse due to the preheating of thepulse leading edge There are a number of parameters to be consid-ered to optimize the process pulse length pulse shape pulse repe-tition rate and velocity of the material Solid state lasers pumped bysemiconductor lasers are widely used Two oppositing solutions arebeing implemented to address the problem of heat dissipation facedby high power lasers High power fiber lasers have a narrow diameterand the heat can be extracted radially The other extreme is the thindisk laser where the gain crystal having the shape of a penny effi-cient heat removal is achieved over the large area A pulse durationfrom 2001000 ns and a repetition rate from 10100 kHz providesflexibility to optimize the laser cut Laser cuttingdrilling is particular-ly attractive for highly brittle materials such as ceramics and semicon-ductors which are difficult to machine by other techniques

421 Laser Welding

As opposed to electrical arc welding the melting of material re-quired for welding is not limited to conducting metals Welding ofmetals use typically pulse durations between 100 μs and 20 ms andwelding velocities of the order of mmin Power densities of up to1 MWcm2 are required for metals and of the order of 10 000 Wcm2

for plastics These techniques also allow the bounding of very dissim-ilar materials (junctions of polymermetal elastic plastics with rigidones and so on)

422 Lasers to the Rescue of Cultural Treasures

Lasers are increasingly used to clean buildings and statues and arereplacing more destructive techniques such as sand blasting A partic-ularly challenging cleaning operation has been the cleaning of reliefsof the Acropolis of Athens blackened by pollution The laser prop-erty mainly exploited is the absorption by the pollution of selectedwavelengths The wavelengths selected for this operation were thatof the Q-switched NdYAG laser at 1064 nm and its third harmon-

42 Laser CuttingDrilling 135

ic at 355 nm Accurate intensity control was required to remove thepollution without damaging the structure At 1064 nm the damagethreshold for the black crust covering the relief is about 08 Jcm2while damage to the marble will occur above 35 Jcm2 Irradiation be-tween these two values ensures self-limiting removal of the encrusta-tion without damage to the marble A 20ndash30 proportion of third har-monic radiation prevents a discoloration and yellowish tinting of themarble that otherwise occurs when only infrared radiation is used [1]

Lasers have also been applied to the even more delicate task ofpainting restoration Here again it is the wavelength selectivity thatis exploited in eliminating degraded contaminated varnish from thesurface of painted works of art That varnish absorbs strongly in theUV (at wavelengths less than 300 nm) At the wavelength of the kryp-ton fluoride laser (248 nm) only a thin superficial layer is absorbedmost of the time leaving a 10 μm thick layer of intact clear varnishto protect the painting when the removal is made with nanosecondpulses In the cases where the varnish layer is too thin or absent (wallpaintings or Asian art) the nanosecond excimer laser is not the idealtool for restoration This is the case where femtosecond laser puls-es are considered because the interaction is through multiphotonexcitation rather than thermal excitation Comparative studies havebeen made of the etching rate of various varnishes with femtosecondand nanosecond pulses [2] Femtosecond pulses at 800 nm requiredhigh energy densities (gt 2 Jcm2) and produced melting and cracksFemtosecond pulses at 248 nm had the lowest etching rate per pulse(which is desirable) of 05 μmpulse at 200 mJcm2 irradiation Thefemtosecond etching rates increase more smoothly with increased en-ergy density than with nanosecond pulses of the same wavelengthwhich implies a better resolution and control

43 Cutting the Forest

A saw a planing tool a scraper are all wood cutting tools takingaway chips of material until the final shape is achieved They are nei-ther delicate nor discriminating and one can feel that they must hurtthe wood cells as badly as the occasional finger they snap off Thesetools leave crushed and broken wood cells The tree will occasionallyget its revenge by putting a hard node in front of the tool sometimes


defeating the tool One thought early enough to use the CO2 laser asan alternate cutting tool The advantages are that no sawdust is creat-ed complicated profiles can easily be cut no reaction force is exertedon the workpiece and there is no tool wear Unfortunately the CO2

laser did not bring a great improvement of surface quality The effectis akin to using a torch to cut wood The CO2 laser is a beam of heatand it leaves behind burned surfaces and unpleasant smells The ef-fect of high power continuous shorter wavelength lasers (NdYAGlaser at 1064 nm or the argon ion laser at 514 nm) is similar burningis the sensation left on the wood (as well as on the human skin) Isthis finally an area where the laser does not find its place The proverbraquowhere there is a will there is a waylaquo may apply or more appropriatelyraquowhere there are $$$ there is a waylaquo We have already mentioned inthe case of eye ablation for LASIK that ultrashort (femtosecond) laserpulses interacted with tissues in a nonthermal manner The same ap-plies to wood cutting except that it takes more energy to cut a woodenboard than to remove a layer of a few μm depth from a cornea Testshave been performed with a large femtosecond laseramplifier sys-tem [3] (over several million times more energy per pulse than thelaser used in ophthalmology) Figure 42a shows the layer of planedmaple wood surface after a conventional planing It is to be noticedthat the cells are crushed and broken This is to be contrasted by thefemtosecond laser cut which leaves a remarkably smooth and cleancut as shown in Figure 42b The cells are left undamaged and an ex-cellent surface quality can even be seen under 10 000 magnification(Figure 42c)

44 Nanostructure with Lasers

Some readers might still remember those days of writing andrewriting homework with pencil and eraser Now with computers onhand it is an easy task to use the raquoback spacelaquo and rewrite again andagain without any trace of previous words It is hard to extend thisability from the virtual world to the real one how to fix a broken piece(or mend a broken heart) or undo a scratch is still challenging Focus-ing laser light as we saw in Section 41 can create localized damageIn free space the focal spot of the laser is limited by the wavelengthand it can be reduced to 1n of the wavelength in a material with

44 Nanostructure with Lasers 137

Figure 42 (a) Cut through maple wood with standard (planing) tool (b) Cross-sectionof oak wood cut by an intense fs laser (c) Maple wood cut by an intense fs laser mag-nified 10 000 (courtesy of See Leang Chin Laval University Quebec [3])

index of refraction raquonlaquo Although wavelength seems to be the limit-ing factor structures that are two orders of magnitude smaller thanthe wavelength are created by focused laser light One can use laserlight to create well defined structures (waveguides) on the materialThe structure generated on the material enhances the transmissionof the light This can be understood as the material choosing as itswar strategy the line of least resistance to the incoming beam

An example realized with the output of a commercial laser is shownin Figure 43 The 50 fs output of a TiSapphire laser at 100 kHz repe-tition rate is focused on a fused silica substrate with lenses of 045 and065 numerical aperture (NA) [5] The energy is deposited in a smallvolume and plasma is generated For a certain pulse energy between200 and 1000 nJ a clean pattern is generated with linearly polarizedlight The lines shown in Figure 43 are separated by λ2n where raquoλlaquois the wavelength of the light in vacuum and raquonlaquo is the index of re-fraction of fused silica (about 145 for 800 nm light) Figure 43a bpresent different cross-sections of the pattern taken with an atom-ic force microscope (AFM) The thickness of each line was carefullymeasured with a scanning electron microscope (SEM) to be less than10 nm The structure can extend tens of microns inside the sampleand can be scanned as well across the sample by moving the focusedlight The direction of light propagation raquoklaquo is set to the raquozlaquo-axis ofthe coordinates the direction of scan raquoslaquo is along the raquoylaquo-axis and thelight (linear) polarization direction is along the raquoxlaquo-axis The struc-ture goes as deep as tens of microns in the sample Note that light is


Figure 43 Atomic force microscope im-age of a laser modified region (a) Cross-section of nanostructure formation in theX Z plane shows the depth of the struc-ture (b) Cross-section of the structure on

the top surface (X Y ) plane shows the pe-riodicity of the planes formed perpendicu-lar to the light polarization and spaced byλ(2n) (courtesy of Ravi Bhardwaj [5])

Figure 44 Schematic showing the localfield enhancement outside a nanoplasmaK denotes the direction of propagationof the laser beam and E the electric field

EE and EP are the local fields found at theequator and poles of the sphere respec-tively for an overall field E (courtesy ofRavi Bhardwaj [5])

absorbed as the structures are formed due to the nonlinear process(Section 111)30) identified earlier as stimulated Raman scattering [4]

So far it was all about experimental focusing conditions The excit-ing part is that as the linear light polarization is rotated in the X Yplane the structures are modified to have planes perpendicular to thenew light polarization axis It is not an instantaneous effect takinga few hundred shots for the structure to be rewritten It is a smartguess to think that no such structure would be formed with circular

30) About 50 of the light is absorbed for 200 nJ input pulse energy


polarization This guess is indeed correct as confirmed in the labora-tory

How and why are these structures formed The plasma generatedby the laser light forms a bobble as shown in Figure 44 The fielddistribution is not uniform around the bobble because the symmetryis broken with light polarization31) The plasma density generated isless that the critical density 0 lt 1 in Figure 44 The field in theequator EE is larger than the fields at poles EP At half the criticalpower the field at the equator is about twice the field at the polesThis may seem not a large difference but in a nonlinear multiphotoninteraction it leads to a structure grown perpendicular to the fieldpolarization and along the equator of the initial bobble [5]

References

1 Frantzikinaki K Panou A Vasil-iadis C Papakonstantinou EPouli P Ditsu T Zafiropulos Vand Fotakis C (2007) The cleaningof the Parthenon west frieze aninnovative laser methodology inProc 10th International Congress onthe Deterioration and Conservation ofStone ICMOS Sweden

2 Pouli P Paun IA Bounos GGeorgiou S and Fotyakis C(2008) The potential of UV fen-tosecond laser ablation for varnishremoval in the restoration of paint-ed works of art Appl Surf Sci 2546875ndash6879

3 Naderi N Lagaceacute S and ChinSL (1999) Preliminary investiga-tions of ultrafast intense laser wood

processing Forest Prod J 49 72ndash76

4 Brueck SRJ and Ehrlich DJ(1982) Some applications of pi-cosecond optical range gatingstimulated surface-plasma-wavescattering and growth of a periodicstructure in laser-photodepositedmetal films Phys Rev Lett 481678ndash1682

5 Bhardwaj VR Simova E RajeevPP Hnatovsky C Taylor RSRayner DM and Corkum PB(2006) Optically produced arrays ofplanar nanostructures inside fusedsilica Phys Rev Lett 96 057404

6 Jackson JD (1975) Classical Elec-trodynamics McGraw-Hill NewYork

31) The field distribution is calculated by satisfying the boundary conditions [6]


5Laser Time Capsule

51 Introduction

Perhaps the most spectacular performances of the laser in terms ofraquoprecisionlaquo are in the time and frequency domain In Section 17 weintroduced the basic nature of an ultrashort pulse methods of pulsecompression as well as ultrashort pulse generation through raquomode-lockinglaquo A first part of this chapter contains a brief overview of someapplications related to ultrashort pulses themselves The impact of thelaser pulse is here mostly in the time domain and is related to ultra-fast dynamics of laserndashmatter interaction Digital communication isstill limited in speed by electronics and the frequency of the wavesthat carry the information Purely optical communication with fem-tosecond pulses has the potential to bring the communication speedfrom GHz to the tens of THz There are numerous applications of ul-trashort pulses that require particularly high power in order to reachoptical electric field strength exceeding the intraatomic fields Theseapplications will be left for Chapter 6 that follows

The last part of the present chapter is dedicated to applications in-trinsic to the continuous train of pulse generated by a mode-lockedlaser The emphasis is then on frequency the spectrum of the contin-uous train of pulses is a comb of frequency teeth which is reachingan accuracy and precision unequalled in any other field The applica-tions range from fundamental physics (are the physical constants ofnature really constants with no drift whatsoever) to astronomy andto numerous aspects of metrology


141

52 Ultrashort Pulses in Microscopy

Progress in biology chemistry and physics have been intimately re-lated to the ability of visualizing ever smaller objects Microscopy hascaused a revolution in many aspects of science from physics to biol-ogy manufacturing electronics and the medical field The laser andnonlinear optics have brought more than incremental improvementsleading for instance to 3D imaging of the eye by optical coherencetomography as we saw in Section 392 Microscopy is as its nameindicates limited to μm appropriate for bacteria and cells but notviruses or nanostructures The wavelength has long been a resolutionbarrier to optical imaging New techniques are emerging to image ob-jects with electromagnetic waves on a different scale As objects be-come smaller the dynamics become faster as well A technique to im-prove the resolution in imaging is nonlinear fluorescence microscopy

The exciting photons produce transitions to a band of excited statesin a fluorescing molecule The excitation decays to the bottom of thatband from where there is a transition to the ground state with emis-sion of the fluorescent photon In conventional fluorescence spec-troscopy the fluorescence signal is proportional to the irradiating lightintensity As illustrated in Figure 51a the fluorescence will be nearlyuniform over the focal volume In the case of two-photon fluorescencefor instance the excitation is proportional to the square of the excitingradiation as we saw in Section 1113 Therefore the excitation (andthe resulting fluorescence) is confined to a smaller portion of focalvolume Hence the spatial resolution is increased Another advantageis the improved penetration depth In the case of multiphoton exci-tation the attenuation of the irradiation beam starts only in the partof the focal volume where there is substantial multiphoton excitationIn the case of single photon fluorescence as in Figure 51a the lightis attenuated as soon as it enters the sample For a large density offluorescing molecules the emission at the focal spot can even be lessintense than at the entrance of the medium [1]

In a laser scanning microscope either the laser focus is scannedacross the sample or the sample is scanned while the laser focus isstationary The reconstruction of high resolution three-dimensionalimages is possible Nonlinear microscopy is not limited to n-photonfluorescence Third harmonic microscopy has also been demonstrat-ed Here also an ultrashort pulse is focused by a microscope objec-

142 5 Laser Time Capsule

Figure 51 (a) Conventional fluorescence(single photon) microscopy If the fluo-rescing material is uniformly distributedin the sample the entire spectral volumewill emit fluorescence radiation (b) In the

case of two-photon fluorescence the flu-orescence is confined to the center of thefocal volume Please find a color versionof this figure on the color plates

tive through the sample Some third harmonic (see Section 1111)of that radiation is generated collected by another microscope objec-tive and separated with filters from the fundamental radiation Theadvantages highlighted in Figure 51 still apply As compared to con-ventional microscopy that probes the linear absorption or the linearrefractive index the contrast in nonlinear microscopy is based on thenonlinear properties of individual molecules Harmonic generation isvery sensitive to structural changes like symmetry breaks in crystalslocal field environments and dopand concentration in solids Nonlin-ear microscopy through harmonic generation is a type of raquocoherentmicroscopylaquo the harmonic that is generated is a coherent pulse sim-ilar to the pulse that was sent to generate the harmonic As a resultthe phase and polarization of the generated signals are prescribed bythe same parameters of the exciting radiation but also by the geo-metric distribution of radiating molecules their symmetry and theirphysical properties Incoherent microscopy instead involves the gen-eration of signals with random phases which are generally emittedrandomly in all directions The various multiphoton absorption tech-niques are included in this category where the signal that is producedis incoherent fluorescence

The resolution of a microscope in particular an ultrashort opticalmicroscope can be defined in terms of many different criteria Theeffective three-dimensional size of the interaction volume is one ofthese This interaction volume is determined by the focusing proper-ties of the microscope (its numerical aperture NA) the wavelengthof the excitation light and also the order of the nonlinearity of theinteraction

52 Ultrashort Pulses in Microscopy 143

Figure 52 (a) Third harmonic generat-ed picture of sections of a live neuron(courtesy of httpwwwweizmannacilhomefeyaronindexhtm 2 March2011) (b) Two-photon fluorescence ofhorse chestnut bark From httpwww

uni-muensterdePhysikAPFallnichForschenNichtlineareMikroskopiehtmlJune 2011 (c) A picture of the horsechestnut Please find a color version ofthis figure on the color plates

Two examples of nonlinear microscopy are reproduced in Fig-ure 52 Sections of a live neuron are shown in Figure 52a as anexample of third harmonic generation microscopy Two bright nucle-uli are visible inside the dark nucleus sections of a live neuron Twobright nucleuli are visible inside the dark nucleus The example oftwo-photon excited fluorescence is that of cut through horse chestnutbark The latter naturally contains aesculin which is a fluorescent dyeof the coumarin family which naturally occurs in horse chestnut Thelatter typically fluoresces blue light when excited by UV radiationThe image (Figure 52b) clearly displays the cell structure and thedistribution of aesculin within the cells when exiting the bark cellsby two-photon absorption of 100 fs pulses from a TitaniumSapphirelaser at 780 nm

53 Communication

531 Introduction

A straight line of sight communication is definitely older than thelaser Once upon a time children did not ask for a walkie-talkie forChristmas but were happy to improvise with an old tin can as a mi-crophone a tin can as receiver and a string spanned between the twocans as the communication medium It is all wave communicationfrom the spoken words to the vibration of the air exciting the bottom


of the tin can communicating its vibration to the stretched stringThe sound travels as a longitudinal wave to the bottom of the receiv-er can which communicates its vibration as a sound wave propagat-ing in air It did not take long after the discovery of the laser beforethe string was replaced by an He-Ne laser beam The electro-optic ef-fect mentioned in Section 1533 by which an electric field appliedto a crystal changes its index of refraction is used to replace the tincan A microphone transforms the sound wave into voltage whichis amplified and applied to the electro-optic crystal The laser beamsent through the crystal carries a phase modulation proportional tothe sound wave At the reception the wave can be demodulated forinstance by beating with another oscillator (another laser) in a simi-lar manner to radio wave transmission Unfortunately one could onlyfind disadvantages with respect to radio wave communication Somespy agency however found that the laser be could be used as meansto eavesdrop remotely on conversations using the Doppler effect dis-cussed in Section 3831 A laser is beamed on the window of an of-fice which vibrates with the sound waves of the conversations insideThe vibrations Doppler shift the beam which is backscattered by thewindow collected and mixed with the original beam in a detectorjust as in Figure 36a The signal from the detector directly carriesthe sound perceived by the window Here again it is not the best ormost discrete means of spying The East Germans had more successlistening to the Bundestag conversation from the top of the St Marien-Krankenhaus in Berlin with microwaves Does this mean the end ofthe line for lasers in communication As we have entered the digitalage the properties of ultrashort laser pulse gives them a clear edge inultrafast communication

532 Soliton Communication

In digital communication each alphameric character is represent-ed by a string of pulses We will assume raquoreturn to zerolaquo communica-tion where the signal returns to zero between each pulse The raquosoli-tonlaquo as discussed in Sections 173 and 1751 maintains its shapeover long distances as an equilibrium is set between a nonlinear in-dex of refraction (intensity dependent) and the dispersion of a fiberThe stability of the soliton makes it attractive for communication oververy long distances for instance across oceans Here the emphasis is

53 Communication 145

more on reliability stability and fidelity of the information than onspeed Because of the long distances involved pulses of the order ofps are generally used

533 Multiplexing

There is an unavoidable disconnect of three orders of magnitudebetween the minimum pulse duration that electronic circuits can pro-vide and the shortest optical pulses that can be generated With 10 fsoptical pulses the raquoclock ratelaquo of a communication system could be100 THz How could this extreme speed be exploited while the elec-tronically supplied information is only at 10 GHz The solution is inmultiplexing or putting all signals in parallel Two approaches arepossible wavelength multiplexing and time multiplexing

5331 Wavelength MultiplexingIn wavelength multiplexing the electronic signals ndash represented by

a succession of raquo0laquo and raquo1laquo ndash that come from difference sources areeach used to modulate a beam at a different wavelength (Figure 53)All these different channels are sent simultaneously into a fiber At thereceiver end the various wavelengths are separated again (raquodemulti-plexinglaquo) and sent to detectors which will restitute the same electronicsignal at each of the original channels

Figure 53 The principle of wavelengthmultiplexing Several words (pulsestrings) from various sources modu-late a difference color channel in a fiberFilters (resonators) are used at the detec-

tion to separate the different wavelengthhence restituting the individuality of eachchannel Please find a color version of thisfigure on the color plates


The number of channels is limited by the number of wavelengthsthat can be inserted in the bandwidth of the gain medium For a givenbandwidth of the gain medium the number of channels is equal tothat bandwidth divided by the bandwidth required by a single signalpulse The faster the clock rate (which is the frequency of the signalif every signal was a raquo1laquo) the shorter the individual pulse needs tobe the broader its bandwidth and the lesser the number of chan-nels available It is clearly impossible to take advantage of the shortestpulse that the broad bandwidth of the gain medium has to offer

5332 Time MultiplexingTo illustrate how time multiplexing can operate let us consider a

clock signal at 12 GHz At that frequency a 12 bit word covers a timeinterval of 1 ns A typical mode-locked laser will generate pulses short-er than 80 fs It is thus possible to squeeze a 12 bit word within a timespan of 1 ps The clock rate with fs pulses can be 1000 times fasterthan with electronics The 80 fs pulse corresponds to a bandwidth of6 THz considerably larger than the bandwidth of any electronic in-strument This very large bandwidth can be exploited if each 12 bitword from up to 1000 independent channels is compressed into astring of 12 fs pulses spanning 1 ps and if all these compressed chan-nels are put back to back in an optical beam sent from an emitterto a receiver The string of pulses that is beamed towards a receivercontains in 1 ns the first word of all the 1000 electronic channels assketched in Figure 54 raquoTime demultiplexinglaquo at the reception con-sists in separating each of the successive ps signals and expanding thelt 1000 12 bit fs words in similar electronic words at a 12 GHz clockrate and addressing them to the appropriate channel

There are interesting methods of optics that make time multiplex-ing possible [2] Optical signals behave in time just as optical beams inspace An optical system (in space) with lenses can make a magnified(as in a microscope) or reduced real image of an object Similarly anoptical system (temporal) can make an expanded time sequence or acompressed time sequence of a time dependent signal This is calledthe space time analogy [3] The broadening of a beam as it propagatesthrough air (diffraction ndash see Section 123) is the equivalent of thebroadening of a pulse as it propagates through a fiber The action ofa lens is to modify the profile of the wavefront in space The timeequivalent is phase modulation such as occurs in the Kerr effect (Sec-


Figure 54 Principle of time multiplexing(a) each 12 bit electronic word from dif-ferent channel covers approximately 1 nsOptical methods exist to compress thisword 1000 times so that it covers only

1 ps Therefore up to 1000 channels canbe put back to back and transmitted Atthe reception side the reverse processhas to occur (b) pulse representation ofthe same

tion 173) There are numerous electronic and optical means to im-part a large phase modulation in time (the equivalent of a microscopeobjective)

The time multiplexing scenario sketched in Figure 54 has the spaceanalogy shown in Figure 55 A short focal distance lens placed faraway from the object will produce a real image which is reduced insize and inverted The real image of the successive channels will be


Figure 55 Space equivalent of time multiplexing

displaced respectively to each other if the objectndashlens distance is in-cremented a little from one channel to the next At the reception thereduced real images are magnified to their original size by a similarlens system with the focal point of each lens close to the real image tobe magnified In the time picture the long propagation distances arereplaced by temporal dispersion The hardware producing the largesttemporal dispersion is a grating The temporal equivalent of the lensis a phase modulator

An alternative method to transform a single fs pulse into a string of12 bit string of pulses covering 1 ps is the raquopulse shaperlaquo of raquofrequen-cy synthesizerlaquo discussed in the next section

54 Frequency Combs

Any string instrument violin guitar or piano emits some sort offrequency comb Playing one of these musical instrument amountsto broadcasting a well defined combination of acoustic frequenciescontrolling the relative amplitude ndash and even to a certain extent thephase ndash of all these emitters We have seen in Section 19 that themode-locked laser emits a comb of optical frequencies with rigourous-ly equal spacing With the mode-locked laser we have moved from the20+ strings of the sitar to 10 000 000 sharp frequency (optical) notesThe difference as the book title indicates is in the raquoprecision of lightlaquoas well as the very high frequency of optical waves Would it be pos-sible to raquoplay the pianolaquo with all the keys represented by this vastamount of notes and extract a wonderful melody Accurate control

54 Frequency Combs 149

and measurement of such an extraordinary large raster of frequencieshas been achieved as will be detailed in Section 543

Methods of generating extended frequency combs and how theycan be locked to time frequency standards are presented in Sec-tion 541 Applications of such accurate combs are in fundamentalphysics astronomy (Section 542) and metrology (Section 544)

541 Creating Extended Frequency Combs

Up to the era of the laser the meter was defined by a block of quartzin the raquobureau des poids et mesureslaquo ndash the French equivalent of NIST(National Institute of Standards) ndash kept at standard temperature andpressure The raquometer sticklaquo had a length of 1 m with 1000 graduationmarks spaced by 1 mm With the frequency comb the raquotick markslaquoare the wavelength As we saw in Section 19 when the carrier to en-velope offset (CEO) is set to zero an integer number of wavelengths(larger than 1 million) defines the raquocoarselaquo tick marks (distance be-tween successive pulses)

The meter definition was replaced in favor of a wavelength stan-dard the meter in the new SI system is defined as 1 650 76373 wave-lengths of the orange-red emission line of the krypton-86 atom invacuum An equivalent definition is that the meter is the lengthof the path traveled by light in vacuum during a time interval of1299 792 458 of a second Other visible emission lines have com-parable accuracy and stability such as a hyperfine component of aniodine transition near 532 nm or the He-Ne laser new 339 μm stabi-lized by a CH4 cell or an Ytterbium ion transition at a frequency of688 358 979 309 312 Hz ˙ 6 Hz

One method to have an absolute calibrated frequency comb is tolock one tooth of the comb to a calibrated atomic emission line andto lock the repetition rate to a RF standard such as a rubidium or ce-sium clock as sketched in Figure 56a The 9 631 770 Hz ground statehyperfine transition in cesium-133 is the internationally recognizeddefinition for the second The disadvantage of this method is that theerror in determining another optical frequency N teeth away is NΔ f where Δ f is the error bar on the radio frequency

A more accurate method sketched in Figure 56b is to stabilize twomodes of the comb to a pair of atomic emission lines for instance thecesium D1 line at 335 THz (895 nm) and the fourth harmonic of a


Figure 56 Stabilization methods of afrequency comb (a) Control the repetitionrate by locking one tooth of the comb toa calibrated line at ν1 and the spacingbetween two modes to a RF atomic clock(b) Lock two modes of the comb to two

reference lines at ν1 and ν2 (c) Lock onmode of the comb to an optical referenceνR and measurestabilize independent-ly the carrier to envelope offset (raquoself-referencing techniquelaquo)

CH4-stabilized 339 μm He-Ne laser [4] The disadvantage is complex-ity since it requires two optical standards

A third method (Figure 56c) that requires only a single opticalstandard is to lock a tooth of the comb to an optical standard andmeasurestabilize the CEO through a raquoself-referencinglaquo technique


That self-referencing technique is sketched in Figure 56c It requiresa train so short that the pulse spectrum is broad enough to includeone mode νN at the low frequency side and a mode of double thatfrequency ν2N at the high frequency side However if the pulse traindoes not start at zero frequency but at the CEO f0 the double of thelow frequency mode is 2νN which differs from the mode frequen-cy ν2N precisely by the CEO frequency f0 Having thus determinedthe CEO frequency f 0 a single optical standard at νR suffices to com-pletely and accurately characterize the frequency comb The difficultyin this last method is that it requires extremely short pulses of the or-der of 5 fs Such pulses have been generated by Tisapphire lasers [5]A method has been devised to extend the frequency combs throughnonlinear effects by simply propagating them through specially man-ufactured fibers The rigorous mode spacing of the original combis preserved if the pulses launched into the fiber have a duration ofless than 100 fs The fiber used include raquomicrostructured fiberslaquo [6]tapered fibers [7] and so-called raquohighly nonlinear dispersion shifted(HNLF) fiberslaquo [8]

542 Femtosecond Pulse Trains to Probe Our Universe

The frequency comb truly illustrates the precision of light withgood optical standards any optical frequency can be measured withthis ruler in frequency with an accuracy better than one part in 1017One might wonder whether there is any use anywhere for such an ac-curacy The answer is somewhere in the fundamentals of our under-standing of our world and of basic physics There are a lot of physicalparameters in our physics world believed to be immutable such as theelectron charge the dielectric constant of vacuum Planckrsquos constantand the speed of light But are they Physics is not about believing ornot believing whether these constants are real but about observingfacts It is not possible to go back in time to measure all these quanti-ties and verify that they had the same value However there is a raquomag-ic numberlaquo a dimensionless combination of these sacred quantitiesthat could be probed in the past This number the raquofine structureconstant αlaquo is the ratio of the square of the electron charge to theproduct of Planckrsquos constant h by the speed of light and twice the di-electric constant of vacuum 0 There are countless physical meaningsfor α We will cite only one the ratio of the energy it takes to force two


repulsing electrons to come from infinity to a small distance d of eachother divided by the energy hν D hcλ of the photon of wavelengthλ D 2πd The fine structure constant is responsible for the relativefrequencies of emission and absorption lines of elements Given a hy-pothetical value of α theorists can calculate emission and absorptionspectra These spectra are compared with the spectra of the light fromvery distant quasars that has been absorbed by gas clouds The redDoppler shift of these spectra provides information on how far in thepast the matter that is probed is situated (up to 138 Gyr the age ofthe Universe) and the relative position of the spectral lines providescompared to the calculation the value of the fine structure constantat that time [9] The results indicate a smaller fine structure constantsome 10 billion years ago of 0999 995 the present value Other mea-surements indicate a 45 108 relative change 2 billion years ago Ifthere was a constant drift of the fine structure constant it would bebetween a 1016 and 1018 fractional change per year Present stabi-lized frequency combs are zooming in onto this level of accuracy andmeasurements of a drift of the fine structure constant may emerge inthe near future

543 The Giant Keyboard

5431 Pulse ShapingBefore discussing the manipulation of the individual tooth of a

comb let us see whether a particular signal in time can be createdthrough manipulation of the spectrum of an ultrashort pulse Produc-ing a controllable signal in time by manipulating a set of frequenciesis a technique that has started before the notion of the raquofrequencycomblaquo We saw in Figure 120 in Section 171 that any optical pulseis made of a combination of various pure frequencies The shorter thepulse the larger the range of optical frequencies that are containedin it Starting from an ultrashort pulse one uses any device that de-composes the pulses in its individual frequency components and ma-nipulates each of them changing its amplitude andor phase Thecontrollable signal in time or raquosynthesized waveformlaquo is obtained byrecombining the individual notes the reverse process that split thepulses in its frequency components This pulse shaper [10 11] is assketched in Figure 57 There are two essential elements one that cre-ates a display of the light frequency (or wavelength) versus space and


the other that manipulates the spectral components that have thusbeen separated A simple device to display the wavelength is a prismIt is a common occurrence to observe the display of colors when thelight from the sun is decomposed by a prism However the separa-tion of the difference wavelengths or optical frequencies provided bya prism is not sufficient to clearly separate the different spectral com-ponents of a pulse The next best separator is a grating essentiallya reflecting block of metal in which fine parallel grooves have beentraced separated by a little more than a wavelength A grating is whatwas used in the first raquopulse shaperslaquo as sketched in Figure 57a Thefrequency components of successive pulses from the laser are spreadin the plane of the figure A raquomasklaquo that provides either differenceopacity at different points (amplitude mask) or different index of re-fraction (phase mask) is used to modify the spectrum of the pulseThe individual components of the spectrum are recombined with a

Figure 57 (a) A standard pulse shaperA first grating displays the spectrum ofeach pulse of a pulse train onto a pro-grammable mask The mask manipulatesthe spectral components in amplitudeand phase The transformed spectralcomponents are brought back together bya second grating Each pulse of the origi-

nal train has given birth to a sequence ofpulses controlled by the mask (b) Com-bination of a VIPA and a grating to isolateevery single tooth of a frequency comb(courtesy of Scott Diddams [12]) Pleasefind a color version of this figure on thecolor plates


second grating exactly the reverse process that had spatially sepa-rated the frequency components of the original pulse with the firstgrating raquoProgrammable maskslaquo can be purchased which are raquoliquidcrystalslaquo between arrays of electrodes on which voltages are applied tochange either the index of refraction or the polarization of the trans-mitted light When placed between polarizers the change in polar-ization becomes a change in intensity of the transmitted light Withproper programming of the mask any pulse shape can be generatedby this technique provided that it is longer than the original pulse Forinstance if the mask consists of a series of equally spaced dark linesthe spectrum transmitted will be a series of spikes equally spaced infrequency or a raquomini-frequency comblaquo We saw in Section 19 that aseries of equally spaced frequencies (in phase) make up a pulse trainof repetition rate equal to the frequency spacing of the teeth of thecomb As sketched in Figure 57a an appropriately applied patternof electric signals ndash for instance the digital word mentioned in Sec-tion 53 can be imprinted on a time sequence of femtosecond puls-es

5432 Comb ManipulationThe grating provides a linear display of the frequencies which can

be played upon like a piano keyboard to create the desired beat intime However the grating is not sufficient to separate each of the1 000 000 teeth of the frequency comb generated by a fs mode-lockedlaser One has to make use of a second dimension as the organ key-board is made of a series of piano-like keyboards That type of op-tical instrument with a huge (in terms of the number of keys) key-board has been realized with the combination of a grating and a planeparallel glass plate with appropriate reflection coatings The device issketched in Figure 57b The combination of a cylindrical lens anda thin ( 100 μm) plate of glass is called a virtually imaged phasedarray or VIPA [13] VIPA has the advantage over diffraction gratingsthat it separates the various wavelengths (or optical frequencies) 10ndash20 times more effectively than a typical grating The right-hand sideof the glass plate is coated to have a reflectivity of 95 The left-hand side is totally reflecting except for a small totally transmittedwindow in which the beam is launched through a cylindrical lensAs with the grating different wavelengths are transmitted at differentangles and are collimated by a lens onto a grating The disposition of


Figure 58 VIPA

the various frequency components of the frequency comb [12 14] issketched in Figure 58a Along the vertical axis (y) the successive dotsare the impact of the individual modes (separated by νr) on the CCDas they are separated by the VIPA Like any FabryndashPeacuterot resonatorVIPA can only provide information over a certain range Δνfsr D N νrThe point A0 in Figure 58a corresponds to a tooth of the comb offrequency ν0 Successive teeth of the comb will be represented atA1 A2 A N1 However the tooth corresponding to the frequen-cies ν0 C mΔνfsr with m D 1 2 would again be at position A0in the absence of grating The deflection of the grating has as effectto shift on the CCD spots corresponding to increasing frequency tothe left so that the frequency ν0 C Δνfsr falls on B0 distinguishablefrom A0

One application of the VIPA sketched in Figure 57b is to provide araquokeyboardlaquo of a huge number of raquonoteslaquo such that when inserted inthe shaper of Figure 57a every tooth of the comb can be accessed

Another application is simple spectroscopy A portion of the VIPAdisplay of a frequency comb is shown in Figure 58b A cell contain-


ing iodine has been inserted in the path of the beam to generate thedisplay of Figure 58c The missing dots indicate absorption at thefrequency corresponding to the missing tooth This is not differentfrom conventional spectroscopy except for the extreme frequency res-olution since this raquospectrometerlaquo is capable of resolving differencesin frequency at the electronic level rather than the optical level Thisspectroscopy also has extreme accuracy if the frequency comb hasbeen locked to a frequency standard

544 Reaching Beyond the Wavelength

The applications presented in this chapter pertained to the utmostaccuracy in time that can be achieved with lasers Being a length stan-dard through the wavelength one should expect that laser beams canbe exploited to measure displacement and lengths The applicationsin metrology are so numerous that a separate chapter will be devotedto them

The near perfection of the laser output itself makes it very sensitiveto any perturbation As an example if we consider only the propaga-tion of the frequency comb of zero CEO shown in Figure 133b thevelocity of pulse envelope will generally be different from that of thecarrier As a result the CEP will change a change that can be exploitedto monitor the properties of the medium traversed These propertiescan be influenced by magnetic and electric fields the linear motionof the transparent medium traversed rotation and so on Hence thelarge number of sensing applications which in general involve thepropagation of the laser through some device that will convert thequantity to be measured in a phase or amplitude change of the light(Chapter 8)

Highest sensitivity can be achieved if this change in CEP is exploit-ed inside the laser itself as will be analyzed in more detail in Sec-tion 822 These sensing applications are local that is the object tobe measured has to be in the proximity of the laser The possibili-ty offered by high power pulses to project high intensities at distancethrough filaments leads to a new type of remote sensing Propagationof these high power beams is discussed in Section 71 The specific ap-plication to remote sensing will be the object of Section 715


References

1 Zipfel WR Williams RM andWebb WW (2003) Nonlinear mag-ic multiphoton microscopy in thebiosciences Nat Biotechnol 211369ndash1377

2 Diels JC (2005) Method andapparatus for femtosecond com-munication United States Provi-sional Patent Application DocketNb1863049US1 UNM-676

3 Kolner BH and Nazarathy M(1989) Temporal imaging with atime lens Opt Lett 14 630ndash632

4 Udem T Reichert J HolzwarthR and Haumlnsch T (1999) Absoluteoptical frequency measurement ofthe cesium D1 line with a mode-locked laser Phys Rev Lett 823568ndash3571


6 Ranka JK Windeler RS andStentz AJ (2000) Visible con-tinuum generation in air-silicamicrostructure optical fibers withanomalous dispersion at 800 nmOpt Lett 25 25ndash27

7 Birks TA Wadsworth WJ andRussel PS (2000) Supercontinu-um generation in tapered fibersOpt Lett 25 1415ndash1417

8 Nicholson JW Yan MF WiskP Fleming J DiMarcello FMonberg E Yablon A JorgensenC and Veng T (2003) All-fiberoctave-spanning supercontinuumOpt Lett 28 643ndash645

9 Webb JK Murphy MT Flam-baum VV Dzuba VA BarrowJD Churchill CW ProchaskaJX and Wolfe AM (2001) Fur-ther evidence for cosmologicalevolution of the fine structure con-stant Phys Rev Lett 87 091301

10 Weiner AM Heritage JP andKirschner EM (1988) High reso-lution femtosecond pulse shapingJ Opt Soc Am B 5 1563ndash1572

11 Weiner AM (2000) Femtosecondpulse shaping using spatial lightmodulators Rev Sci Instrum 711929ndash1960

12 Diddams SA and Hollberg L(2007) Molecular fingerprintingwith the resolved modes of a fem-tosecond laser frequency combNature 445 627ndash630

13 Shirasaki M (1996) Large angulardispersion by a virtually imagedphased array and its application toa wavelength demultiplexer OptLett 21 366ndash368

14 Xiao S McKinney J and Wein-er A (2004) Photonic microwavearbitrary waveform generation us-ing a virtually imaged phased-array(VIPA) direct space-to-time pulseshaper Photon Technol Lett 161936ndash1938


6Light in Matter

The interaction of light and matter is sensed through seasonalchanges the heating of a pond by sunlight and the growth of plantleaves The energy of the photons is transferred to molecules in airand water and the transfer of energy manifests itself in increase ofparticles velocity and therefore heat The transfer of energy is likeadding hot water to cold water high energy water molecules collidewith slower ones (low energy) and after a while an equilibrium isreached In the case of heating with sunlight the transfer of energy isthrough absorption Since photons have no mass they do not collidelike water molecules When a molecule absorbs a photon the excessenergy leads to a higher vibration state or an increase in linear velocityThe excess energy is then distributed among other molecules

The mutual interaction of light and matter goes beyond warming apond of water In a low-energy phenomenon such as the photoelectriceffect a photon of energy matching the work function of a conductorexpels a free electron that would be measured as a current Histor-ically the knowledge of a discrete energy gap helped us to discoverthat photons individually have discrete energy (Section 112) A fin-er interaction such as photosynthesis has kept biologists physicistsand chemists busy for a long time Sunlight is the fuel for the mag-ical green engine that synthesizes simple molecules such as carbondioxide into more complicated ones like sugar that store energy

Can we imitate a plant Is there a way to monitor and control chem-ical reactions Molecules are formed and dissociated The formationand dissociation of molecules are through chemical bonds whereelectrons play a key role The atomic-molecular and optical (AMO)physics studies matterndashmatter and lightndashmatter interaction in atomsand molecules with the aim to extend it to larger biological moleculesLaser light can induce a reaction and also monitor it (ie a change inthe molecular system such as bond stretching is imprinted on an op-


159

tical pulse) As we have seen in Chapter 5 coherent waves as smallas a few cycles have been generated in laser cavities There is a dou-ble advantage of using short pulse lasers time resolution and highintensity

As the time resolution reaches the femtosecond scale we are ableto watch and control the electronic motion that takes place withinmolecules How do we take a picture of these fast electronic eventsWhat carries the information for these fast motions The laser pulsethat is used as the time stamp perturbs the system in a way that ei-ther itself or other photons or even electrons carry the informationin their phase frequency or in the case of electrons in their velocitydistribution In this chapter we are more focused on the interroga-tion of electrons and generated photons or the energy deposited bythe intense light In Section 82 we look instead at the imprint on theoptical pulse itself

The coherent interaction of light with atoms and molecules led usto control and measure of motions in an attoseconds32) time scaleIt takes 24 as for electrons in the hydrogen atom to make a full or-bit around the nucleus Interaction of short laser pulses with atomsand molecules leads to another class of photon emission As a re-sult attosecond pulses are generated which are not due solely tolaser designs such as described in Chapter 1 The coherent rideof the electrons and excitation of atoms and molecules with lightmust be carefully considered The coherence of light is transferredto an electron that interacts coherently with matter thereby gener-ating short light pulses that cannot be created in optical cavitiesHere matter (electrons) acts like a frequency multiplier for the ini-tial photon This interaction can also be viewed as collision betweenparticles In a high laser field an electron is carried away from itsparent with the laser field This electron is accelerated with the fieldand can achieve extreme energies The collision of those high energyelectrons with the atoms serves various fields of study Attosecondpulses are photons generated as a result of this recombination whileother products are high and low energy electrons For a heavy nucle-us and at higher intensities laser-induced nuclear reactions mightoccur

32) 1 as is 1018 s In the physics community when a time less than a femtosecond isresolved the class of attosecond phenomena has started

160 6 Light in Matter

The precise timing of light pulses is exploited to watch chemical re-actions and electron dynamics in atoms and molecules Laser pulsesare also used to orient molecules in space In Section 382 the pho-tonrsquos force is applied to confine and move particles in defined direc-tions Laser pulses can slush the electrons inside a molecule Elec-trons are not necessarily uniformly distributed and neither is the pho-ton wave (see polarization 122) The relative orientation of the elec-tron orbital33) with respect to the light polarization leads to a torquethat would align the electron orbital (and as a result the molecules)with respect to the field

In this chapter (Section 62) we see how the coherent interactionof light and matter results in surfing electrons on a light wave Withprecise engineering of the wave the accelerated electron can be usedfor new light generation particle acceleration and laser-induced nu-clear reaction Lasers are used in nuclear fusion since laser pulsescan be added coherently to create the intensity needed for initiating areaction confined in time and space Laser cooling is an unexpectedapplication of lasers in contrast to most applications of lasers whichare in energy deposition and heating For laser cooling with a properchoice of energy level and light frequencies the emitted photon ener-gy exceeds that of the absorbed photon hence a net loss of energy forthe material which is then cooled [1]

This chapter discusses using laser properties as completely as pos-sible simultaneously exploiting the energy the coherence and thefrequency structure Although these applications do not have the visi-bility of the supermarket scanner they make a tremendous contribu-tion to our control and understanding of the universe

61 Attosecond Science

While most of all the laser properties studied in Chapter 1 revolvedaround the photons it was barely mentioned that these photons aregenerated from electron absorption in gain media Driving electronswith applied fields had been practiced for a century in electronic cir-

33) An electron orbital is defined as the distribution of electrons (halo of electrons)around the atom nucleus It is obtained by solving the Schroumldinger equation ofmotion for the probability presence of the electron The orbitals of atoms arenamed s p d and for molecules σ π

61 Attosecond Science 161

cuits and machinery Since laser light is an oscillation of the electricfield the same driving can be performed with laser fields The opticalfield is definitely more precise than the voltage difference imposedby a capacitor since we can engineer pulses in time and space withvarious frequency components and spatial distribution

A neutral atom can be decomposed to its loosest electron and therest (positively charges) of the atom which includes the nucleus andthe remaining electrons This electron is attached to the remainingatom and molecule due to Coulomb attraction and stuck in a poten-tial well The electron sits in this well like a birdie in its nest Theionization potential of an atom is the energy required to hold the loos-est electron to the positive nucleus or the energy needed to release itIt is the wormrsquos energy that has to be fed to the little bird to give it thestrength to escape from the nest It is higher for the ionized atom be-cause the charged particle holds the remaining electrons more tightlyIn the presence of a high electric field (such as caused by an intenselaser pulse) the potential well is distorted It is similar to the nestbeing tilted by a high wind Fortunately the classical birdie will notfall out of the nest being kept still by the rim of the nest In quan-tum mechanics however there is a chance for the little bird to fall outof the tree by passing through the barrier of the nest ndash this is calledtunneling For the electron there is also a chance (probability) for anelectron to pass through the barrier of the deformed well through atunneling process This probability increases with the laser field Aswe will see in Section 8115 light itself can also raquotunnellaquo through abarrier

611 The Three Step Model

The linearly polarized laser field displaces the electron and takes itto a journey on its shoulder speeds it up and like a slingshot (seeFigure 61a) throws the electron back It is amazing that a simpleintuitive picture for this event [2 3] named the three step model canexplain the basics of this phenomena In this model a complicatedatom or molecule is simplified to an electron and the nucleus At restthe electron oscillates around the nucleus and in the view of the out-side word is stuck deep down a potential well (see Figure 61b) Thelaser electric field distorts this potential by its force raquoeElaquo and addsthe term raquoeE rlaquo to the total energy of the system The position raquorlaquo


Figure 61 (a) A laser pulse takes the elec-tron and accelerates it just like a slingshottaking a stone For the light photon of800 nm the electron wavelength after thisacceleration is only between 10 to 03 Aring(b) The electron in an atom or moleculeis held in a potential well by Coulomb at-traction to the positive nucleus Althoughin quantum mechanics contrary to clas-sical physics a particle has a chance topass a barrier beyond its energy the prob-ability of this event is negligible whenthe particle is at rest (c) With the high

electric field of the laser the atom is ion-ized and the electron oscillates with thelaser field The three curves on the rightside represent three different moments ofionization which will lead to different ac-celeration and ultimate speed of electronThe trajectory of the electrons with ap-plied laser field is calculated by classicalphysics (d) The ejected electron travelswith the laser field and may return andrecombine with its parent ion Please finda color version of this figure on the colorplates

is the distance of the electron distribution from the center of nucle-us The light electric field opposes ndash hence reduces ndash the attractiveforce between electron and the remaining atom In other words theCoulomb potential is distorted (see Figure 61d) and an electron has ahigh chance of leaving the atom and tunneling through (step 1)

The electron now is called a free electron As it moves away fromthe center the attractive force between electron and remaining atominversely proportional to the square of the distance (ie 1 r2) isreduced but the electron is not completely raquofreelaquo it is forced to followthe laser field Since a wave changes sign after half a light period fora linearly polarized light the same field that pulled the electron away


is going to push it back The electronrsquos journey with the light pulse isstep 2 of the process

For the returning electron step 3 or recombination takes place Notethat just as with a slingshot with a stone the electron can acquire alot of energy ranging from 1 to 103 eV in a noble gas atom with an IRlaser field This high energy electron generates a high energy photonor creates electronndashelectron collision

This model is simple enough to be understood by anyone withsome basic knowledge of field charge and classical motion of par-ticles However deep down the simple picture shelters many inter-esting details about lightndashmatter interaction In step 1 the process ofionization can be multiphoton tunneling or above barrier Here againa theory that was not initially made to apply to a laser field and wassupposed to explain the ionization through a strong continuous (DC)field [4] is stretched to predict the probability and mechanism of theionization phenomena with alternating high laser fields at frequen-cies of 1014 Hz

6111 Step 1 Ionization or TunnelingThere are two distinct mechanisms by which the electron can es-

cape the atom or molecule By absorbing several high energy photonsthe electron can pop out of its well like the chick can escape from thenest after swallowing a few high energy pills This mechanism relatesmore to the particle nature of light At the other extreme when theperiod of the light is long (low photon energy) the potential is slow-ly distorted to let the electron escape by tunnel effect as the slowpersistent wind tilts the nest to reduce the barrier holding back thebird Tunneling dominates over photoionization (multiphoton) whenthe light electric field raquoElaquo is large relative to the depth of the well ofthe ionization potential raquoIplaquo and applied for a long time (large lightperiod T D 1ν) It is therefore not surprising that a raquoKeldysh pa-rameterlaquo [4] proportional to ν

pIpE has been defined to mark the

vague transition between tunneling and multiphoton ionization Val-ues of less than 1 for this parameter correspond to large fields andlow frequencies of light with respect to the depth of the well Con-sidering the tunnel image in space (Figure 61b) low values of theKeldysh parameter correspond to slow and deep distortion of the wellso that the electron can tunnel out and the ionization is called raquotun-nel ionizationlaquo If the electric field of the light changes rapidly (high


Figure 62 A means to monitor the ion-ization in high field is by measurement ofthe ejected electron momentum in threedimensions The electron momentum isrepresented in atomic units where 1 cor-responds to the velocity of the electron ina hydrogen atom The x-axis correspondsto the direction of propagation and they-axis to the light polarization The 3D

image is projected in two dimensions inthe measuring apparatus of velocity mapimaging (a) Multiphoton image of theelectrons from argon with 400 nms linear-ly polarized laser light (b) Tunnel ioniza-tion image of the electrons produced inargon with 800 nm linearly polarized laserlight

optical frequency) the electron bounces back and forth in the well asif it is ionizing in a vertical channel The angular distributions of theejected electrons are different as seen by direct electron momentumimaging from argon with 400 and 800 nm lasers of linear polarization(Figure 62) showing a clear transition between multiphoton and tun-neling The rings seen on the picture are raquoabove threshold ionizationlaquo(ATI) [5] rings These are due to the electrons that are above the barrierbut still close to the ion and can absorb more photons that are neededto overcome the barrier Photons have well defined energy and sincethere is no way to absorb half a photon these rings are well separatedby the light photon energy The separation of the rings is related to thephoton energy of light which is naturersquos way to provide a calibrationfor the image

6112 Step 2 The Path of the Ejected ElectronThe ejected electron follows the laser field by the classical force

raquoeElaquo just as the stone travels with the elastic on the slingshot Thelaser light changes its sign at each half period implying that the elec-tron that was carried away is forced to come back During the traveltime the electron is accelerated and ends up with a final velocity that


is a function of the moment of ionization (Figure 61c) The path andfinal velocity of the electron are strongly dependent on the moment ofionization Because the amplitude of a linearly polarized electric fieldoscillates the probability of ionization is not the same at all timesIn most cases the ionization occurs at the peak field The electronthat ejects before the peak value has no chance to return back by thetime the field changes sign the electron is already too far from theion Electrons ejected at and after the peak each have a different pathThe ones leaving closest to the peak have a larger travel path thanthose ejected closer to the sign reversal point of the field short andlong trajectory For a near-infrared laser at field strength of 109 Vcmthe total excursion of the electron reaches several tens of angstromswhich is beyond the size of the molecule Under the influence of thealternating field E cos(2πν t) of linearly polarized light an electronundergoes a periodic motion with its velocity changing at each peri-od 1ν To this periodically changing velocity or raquoquiver motionlaquo isassociated the kinetic energy Up D (e2E2)[4m (2πν)2] This energyis known as pondermotive potential For a single carrier frequency laserthe maximum energy that the electron can acquire is 32Up34)

6113 Step 3 RecollisionThe last step is recollision for the electrons who can make it back

to the ion35) The returned electron can have a range of energies anddifferent accumulated propagation phases (because of different travelpaths) The result of the collision also varies (i) Elastic backscatter-ing of the electron results in emission of highly energetic electrons(ii) An electron may recombine with the ground state and emit a highenergy photon The photon generation is known as raquohigh harmonicgenerationlaquo (HHG) The highest energy photon has the maximum32Up pondermotive energy plus the energy of the ionization poten-tial Ip (iii) It may knock off another electron from inner shell andcause a double ionization (raquononsequential double ionizationlaquo) (iv) In-elastic collision and transfer of energy to bound electrons

34) This is enhanced by using a chirpedpulse laser

35) That is for linear or slightly ellipticalpolarization since in circularlypolarized light the field changes itsoscillation direction continuously sothat the ejected electron never has a

chance to return back In this casethe ejected electron always receivesan acceleration perpendicular to itslinear motion It is interesting thatwith a change of polarization we cansimply avoid recollision


As poets and painters may see and present the event of raquoa sunsetlaquoin their own individual way scientists from various background havetheir own interpretation For a collision physicist with memories ofneutron and ion collision in targets high field ionization is a minia-ture accelerator (see Section 62) An electron is accelerated by thelaser field to high velocities and upon return it is all collision physicsThis includes elastic collisions or the billiard ball bounce of the elec-tron against the ion and inelastic collisions with transfer of energy to aphoton or an electron A scientist with a quantum optics backgroundmay see it as an interference of the electron wave floating on the laserfield with a remaining wave inside the ion Above threshold ioniza-tion of the electrons and high harmonic generation of photons withdiscrete energy difference is the result of this interference The trav-eling electron is coherent with the remaining electron In quantummechanics language part of the wavefunction has left the atom andpart of it is still inside waiting for the return of the passenger Thesuperposition of the wavefunction of the traveling electron with thatof the bond electron results in dipole oscillation a charge oscillationthat results in photon emission

The details of these processes and mathematical description ofthese events can be found in review papers [6 7] and referencestherein

612 Application of Attosecond Science

In the evolution of science there are efforts that may result in asingle isolated paper over a lifetime and there are times that the pickhits the oil well and there follows a nonstop gush of scientific dis-coveries Attosecond science is one of these miraculous oil wells Toname a few scientific applications we will look at molecular alignmentwith short pulses analyze the ionization process image molecular or-bitals drive currents inside atoms and watch the evolution of chemi-cal bonds

6121 Molecular AlignmentLaser pulses rotate polarized molecules The strength of this force

depends on the shape of the electronic-orbital in molecules and itspositioning with respect to the laser field As a result of this interac-tion the laser field pulls the electron orbital into its plane of polar-


Figure 63 (a) Tunneling with high laserfield The ejected electron from the tun-nel carries the information about theorbital that it left (b) Recording of themomentum distribution of aligned andanti-aligned molecules is used to producea normalized image of the electron or-bital The image recorded of low energytunneled electrons with the highest elec-tronic orbital calculated for nitrogen andoxygen is in agreement with the imageof direct electrons [9] (c) A schematic ofa COLTRIM to synchronously record themomentum of the ejected electrons andions The source is the gas jet that moves

up in the picture to meet with the laser(the red light from the left) at its focalspot After the reaction the charged prod-ucts are guided to their proper recordingdevice The high voltage bias separatesthe ions from electrons The magnetic coilon the COLTRIMS overpowers the earthmagnetic field and extends the travel timeof electrons COLTRIMS are made of vari-ous chambers to separate the interactionand detection procedures (courtesy ofAndre Staudte and Moritz Meckel) Pleasefind a color version of this figure on thecolor plates

ization Quantum mechanics suggest that the rotational energy lev-els are discrete Having discrete energy levels results in a rotation ofthe molecule with a characteristic revival time36) The revival can beseen as a common period of a series of pendulums with proportion-al lengths There is a common multiple among the periods at whichthe pendulums comes back to the same spot In a simple diatomicmolecule like N2 the electronic orbital is pulled towards the laser field

For a long enough pulse around 100 fs of 800 nm light the molec-ular orientation comes to alignment with the laser field This push

36) For example nitrogen has 84 and oxygen has 116 ps as revival time


towards the field starts the pendulum of rotation The sample comesback to the same orientation after 84 ps from the raquopromptlaquo alignmentwith the laser field This is a necessary tool for studying light matterinteraction because the alignment and orientation of a molecule is setwith a laser pulse and can be studied with a probe laser in the absenceof any perturbing field so called field free alignment

6122 Watching the Ionization from a MoleculeCountless research programs have been devoted to the understand-

ing of the dynamics of chemical reactions and the inner structure ofmolecules and atoms In one example the detailed process of ioniza-tion from an HCl molecule was investigated It was shown that inhigh field ionization the probability of removing an electron from thehydrogen side is higher than at the chlorine pole of the molecule Hav-ing a highly polarized HCl atom that is mostly shown as HCCl theresult of the experiment was unexpected [8]

The challenge is to expand these observations to larger moleculesto understand the dynamics of charge transfers and chemical reac-tions Another experiment [9] was to image the electron orbitals inoxygen and nitrogen by measuring the distribution of momentum ofthe ejected electrons (step 1) Cold target recoil ion momentum spec-troscopy (COLTRIMS) is a device to monitor lightndashmatter interactionby recording the time and position (therefore the momentum) of ionsand electrons generated in the high intensity laser focal spot

6123 Molecular BreathingThe information about the molecule is carried away in the pho-

ton(s) of high harmonic generation as well as in the recolliding elec-tron Simultaneous imaging of the geometric and electronic structureof a molecule as it undergoes a chemical reaction can be recorded bymonitoring the photons (high harmonic generation) generated fromrecombination of the electron to its parent ion (step 3)

Since the electronic orbital is strongly affected by the separationbetween the molecules a temporal shift of less than an attosecondof high harmonic generation is documented between stretched andcompressed geometry of diatomic molecule Bromine [10]


62 Lasers in Nuclear Physics and Accelerators

As we saw in Section 121 any matter in physics has some ener-gy characteristics If the matter is excited at energies matching a levelstructure the resonance is induced The resonance can be sharp as inatomic structures or broad and vague as in the solids in Chapter 4 Inthis section we consider very high intensities of tightly focused lightFor the applications considered in this section the synchronizationof events essential in the case of attosecond generation takes a back-stage role in favor of maximizing the energy deposition

The unique coherence property of the laser results in a well colli-mated beam and high quality focus The photons have temporal andspatial coherence and as they are brought together they constructivelyinterfere which is why a high intensity spot is created A typical Q-switched NdYAG laser produces pulses of 10 MW intensity in 10 nsA bright flash of white light with a loud raquoBANGlaquo is produced by fo-cusing this pulse in air This effect is called raquoavalanche breakdownlaquo atthe laser intensity of the order of 1 TWcm2 reached at the focus a fewlone electrons are accelerated by the field of the pulse to a sufficientenergy to ionize molecules of air creating electrons that are in turn al-so accelerated etc Much higher intensities are achieved with ultra-short pulses It is shocking that a commercial (amplified) Tisapphireof a few tens of femtosecond duration and millijoule energy once fo-cused to a 30 μm spot creates intensities that exceed those at the sunrsquossurface (about 1015 Wcm2) The sun is right there in the laboratorybut there should be no worry that the building might melt down thehigh intensity is confined geometrically and in time Surprisingly theultrashort pulse is much more discrete than its nanosecond counter-part The reason is that there is not enough time in less than 1 ps forthe avalanche process Nevertheless the multiphoton ionization doesmake itself heard and seen Instead of the bright flash of white lightand the very loud noise the focused millijoule pulse produces only alittle crackle a small streak of purple light and some colors that canbe seen on a screen These are indications for the experimentalist thatthe laser operates with short pulses and high energy

The race to get higher intensity lasers is not just to set a record itis also for cracking up higher energy processes Some of the physicalprocesses with their associated intensity are listed in Figure 64 Heli-um is ionized at laser intensities of the order of 31014 Wcm2 When


Figure 64 Selected events occurring at high laser intensity This graph is just for pre-sentation and the threshold values for the events are not exact

the first electron is removed from an atom the balance between pos-itive and negative components is lost The positive charges havinggained a majority pull the electrons tighter and it takes more effortto ionize more In a sense atoms are not like gamblers who are moredrawn into games after losing a sum of money with a hope to winIf an atom loses an electron it will hold to the remaining ones muchtighter Higher laser fields are necessary to tilt the Coulomb poten-tial (Figure 61) in order to release another electron Stripping all theelectrons of neon occurs at 1017 Wcm2 For a heavier atom like argonremoving all 10 electron requires intensities of 1018 Wcm2 Between1018 and 1019 Wcm2 photon-induced nuclear reactions are possi-ble The production of the first elementary particle the pion takesplace around 1021 Wcm2 At a very high intensity of 1028 Wcm2 elec-tronndashpositron pair or pair production (Figure 65) from the vacuum ispossible

Of the photonuclear effects nuclear fission or laser-induced fissionwas observed from uranium at the VULCAN laser facility in 1999 Theuranium nucleus has the shape of the rugby ball For the uranium iso-tope 238 the short-range attractive nuclear force balances the repul-sion of 92 protons to give the nucleus its prolate deformation For sucha big molecule the excess of energy from a photon or incident neutronresults in vibration or rotation of the nucleus The vibration results

62 Lasers in Nuclear Physics and Accelerators 171

in an increase of average distance between nucleons The short-range(attractive) nuclear force is strongly dependent on the average distancebetween nucleons while the (repulsive) balancing Coulomb force isless affected by the increased average distance Once the balance isbroken it is hard to keep the nucleons together two main fragmentsand a few evaporated neutrons and gamma rays are generated A per-son walking with free hands will keep hisher balance but one car-rying parcels with every tooth and finger like a Christmas tree willtip over and drop hisher loose companions Fission of uranium pro-duces fragments with mass numbers about 95 and 140 correspondingto the neutron magic numbers of 50 and 82 The way to monitor thefission is normally by detecting characteristic gamma rays emitted bythis process

In nuclear industry both fast and slow neutrons are used to inducefission Other nuclear probes like protons electrons deuterons alphaparticles heavy ions electrons muons and gamma rays also ignitethe fission With terawatt (1012) and petawatt (1015) lasers on hand alight source can be used alongside (or perhaps replace) an acceleratorfor nuclear studies Accelerators are limited by electric breakdown atfields of about 20 MVm when electrons are torn from the atom in theacceleratorrsquos support structure A 100 J energy in a picosecond pulseusing a parabolic mirror is focused to a few μm2 regions In this smallarea an intensity of 1020 W per square centimeter is reached Electricfields of the order of 1011 Vcm are generated along with a huge alter-nating magnetic field close to 109 Gs which is only 1000 times smallerthan the magnetic field of a typical black hole In Section 61 we sawhow a laser pulse tears the atom and accelerate electrons In the late1970s it was noticed [11] that highly accelerated electrons could begenerated by focusing light into a plasma medium

As seen in Section 61 light pulses create high energy electronsIn a low density target the motion of the electrons is mainly due tothe laser field In a dense material however a laser pulse sets up ahigh electrostatic wave within a plasma by displacing the negativelycharged electrons with respect to the heavier positive charges Thisdisplacement creates an accelerating field in which electrons oscillateat speeds close to the speed of light Electron energies of over 200 MeVcan be created in this way

In a target with high atomic number Z the accelerated electronsslow down and emit high energy photons as gamma radiation The


Figure 65 (a) Bremsstrahlung radia-tion or braking radiation of an electronThe electron trajectory is affected by thepositive charge of the nucleus This en-ergy loss due to the deceleration of theelectron is transferred to a photon in thex-ray and gamma ray range (b) Comp-ton scattering the high energy photonis deflected by collision with electrons inmatter The photon energy is reduced (itswavelength is increased) and the energy

difference is given to the electron (c) Pairproduction when a light photon has highenough energy to produce an electronand a positron pair (D 2 511 keV)a photon can be annihilated and be re-placed by matter The excess energy isgiven as kinetic energy to the electron andpositron going in opposite direction toconserve the momentum Please find acolor version of this figure on the colorplates

process of this gamma radiation is called raquobraking radiationlaquo or in itsoriginal German raquoBremsstrahlunglaquo In Figure 65a an electron is de-celerated and deflected in the vicinity of a charged particle In physicsthe law of conservation of energy is a hint to solve most problemsThe difference in the energy of the electron goes to a high energy pho-ton radiation which fits in the x-ray or gamma range x-ray tubes arebased on the Bremsstrahlung phenomenon where electrons accelerat-ed through an applied voltage hit a high atomic number sample andthe deceleration of these electrons leads to continuous x-ray spectraThe Bremsstrahlung process applies to deceleration of any chargedparticle that has an energy larger than its rest mass (E D mc2) Sincethe electron is lighter than ions and protons this phenomena is most-ly applied to electrons

There are three major phenomena of lightndashmatter interactionwhich are recognized by their characteristic energy the photoelectriceffect Compton scattering and pair production Low energy photonsaround the visible wavelength (electron volt) are in resonance withenergy gaps of metals In the photoelectric effect the discreteness ofphoton energy was observed by recording the current of the electronsthat jumped through the energy gap If the energy gap or the workfunction is discrete so must be the photon energy

In Compton scattering the x-ray or gamma ray photon scatters froman electron The photon needs to have an energy comparable with


the rest energy of the electron that is around 511 keV When theenergy of the photon and electron are comparable the particle natureof the light shows up in this interaction as if a collision is taking placebetween balls on a pool table (not exactly the same because collisionson a pool table are elastic) As a result of transferring its energy tothe electron at rest the electron receives this recoil energy the photonenergy is reduced and the light wavelength is changed from λ to λ0

λ0 λ D hmc

(1 cos (θ )) (61)

The light is deflected to an angle θ after this collision The larger thedeflection angle the more energy is transferred to the electron Whenlight acts as a particle the particle acts like a wave too The right-handside of the equation has raquomlaquo as the mass of the electron and hmc hasthe dimension of the wavelength which is why it is called the Comptonwavelength of the electron37) This electron can be further acceleratedwith the laser field

When the photon energy is high enough to host a positron and anelectron (note that the photon has no charge so it can only be trans-formed to species of zero total charge) it can annihilate and give birthto matter (a positron and an electron) following the conservation ofmass and energy E D mc2 The threshold of the formation of elec-tronndashpositron pairs is at a laser intensity of 1028 Wcm2 It is excitingto realize that matter can be produced out of laser light focused into asmall focal spot It suggests a vision of the universe formation out ofa tiny focal spot on the order of the light wavelength

What is the limit in the highest achievable intensity with laserpulses As the energy of the laser goes up it ionizes the materialand damages objects upon illumination The critical quantum elec-trodynamics QED field of Es D m2c3ebdquo D 132 V 1016 Vcm [12]represents a field value at which the photon is annihilated and an elec-tronndashpositron pair is created in vacuum As mentioned in Section 18this critical field is such that it accelerates an electron over the dis-tance equal to the Compton wavelength λc to the energy at rest ofthe electron mc2 It is thus defined by the relation eEsλc D 2mc2 Atthis field one expects to see the photons transferred to matter so there

37) The Compton wavelength of the electron is 243 1012 m


could be no light with higher fields38) It was a heated debate and aparadox to consider fields of that strength The simulation shows thatwhen using multiple pulses the threshold for such a reaction is re-duced to fields 100 times smaller Optical intensities of the order of5 1025 Wcm2 (corresponding to 001Es) are sought in projects of ex-treme light infrastructure ELI and x-ray free-electron lasers XFEL Aslaser fields accelerate electrons (Section 61) up to relativistic veloci-ties the accelerated particles emit hard photons that in turn producea new electronndashpositron pair This pair production with lasers was ob-served before the turn of the century in SLAC [13]

If a laser can be strong enough to burn any material and create anelectronndashpositron pair in vacuum how could it ever exist in a cavityWhat is the gain medium for such a source The answer is based onwhat we have learned about laser coherence used in achieving a tightfocal spot (Section 162) stretching and compressing a pulse in time(Section 182) and the coherence of a pulse train (Chapter 5) Thelaser beam can be expanded to tens of centimeters and at the pointof interaction reduced to micron size The size change from 5 cm di-ameter to a micron focal spot results in 50 000 times enhancement ofthe intensity Pulses can be stretched in time about 10 000 times andeven more For a given energy that stretching means reducing thepeak power by the same factor To avoid most damage to optical com-ponents the instantaneous field has to be kept lower than a thresholdStretching the pulse in time is a convenient way to keep the compo-nents of a laser system safe The last tool at hand is to use multiplelasers and synchronize their oscillation to acquire a coherent super-position of pulses a difficult task since each laser has its own worldThe laser cavity size pump laser intensity and a fly flapping its wingswould affect the phase of the laser oscillation under the envelope andso will be the superposition of the pulses

Petawatt lasers are the class of lasers that is able to deliver powersof 1015 W in short bursts of optical pulses39) One example of this class

38) Theoreticians now consider fieldshigher than this value Withfurther developments on QED theKlein paradox is resolved and theelectromagnetic Lagrangian is validat arbitrary field strength

39) To keep things in perspective thetotal average (gas electricity etc)power consumption of the UnitedStates in 2005 was about 3 TW(334 1012 W)


Figure 66 (a) A picture of the HERCULES Laser from the FOCUS project of the Univer-sity of Michigan (courtesy of Anatoly Maksimchuk) (b) The four-grating compressor toreduce the pulse to 30 fs (courtesy of V Yanovsky)

of lasers is the HERCULES petawatt laser at the University of Michi-gan which reaches 1023 Wcm2 by focusing about 15 J of 30 fs pulsesto a diffraction limited focal spot of one micron A picture of this sys-tem is shown in Figure 66a The four bursts of purple light are fromthe flash lamp pumped Nd-YAG rods The pump laser has two stagesof amplification The frequency-doubled output of the first stage (thegreen light in Figure 66a) is used for pumping the 25 cm diameterTisapphire amplifier while the unconverted infrared light is inject-ed into the second stage of the pump laser for further amplificationThe frequency-doubled output of the second stage is used for pump-ing of the booster (5 cm diameter) amplifier of the HERCULES laserThe pump laser has a quasi-flat-top beam profile that was achieved at01 Hz repetition rate

The HERCULES laser design (Figure 66a) is based on chirped-pulse amplification with removal of the amplified spontaneous emis-sion (ASE) noise after the first amplifier Special care has been givennot to amplify unwanted spontaneous radiation of the laser (Sec-tion 12) instead of the stimulated radiation Two cross-polarizers areused to reduce the radiation from amplified spontaneous emission(ASE) to a background of less than 1011 of the laser power The out-put pulse of the 12 fs pulse of the laser is preamplified in the two-passpreamplifier to the microjoule energy level The clean microjoule en-ergy pulse is stretched to about 05 ns by the stretcher based on a mod-ified mirror-in-grating design The whole laser is designed to be fifth-order dispersion-limited over 104 nm bandwidth The high-energyregenerative amplifier and cryogenically cooled four-pass amplifier


bring the pulse energy to an energy level of one joule with nearlydiffraction-limited beam quality Two sequential two-pass-Tisapphireamplifiers of 25 cm and 5 cm beam diameter respectively raise theoutput energy to a value approaching 20 J The booster two-passamplifier uses an 11-cm-diameter Tisapphire crystal (red light in Fig-ure 66a) In order to suppress parasitic oscillations the side surface ofthe crystal is covered with a thin layer of index-matching thermoplas-tic coating doped with organic dye absorbing at 800 nm The compres-sor design to reduce the pulse width to 30 fs is shown in Figure 66b

63 Laser Cooling

May be one of the most surprising applications of the laser is lasercooling Most of the applications that we have considered so far de-posit the energy of the laser in a structure or material (Chapter 4) forablation and modification in a cell (Chapter 3) or to impinge uponan atom or a molecule (Section 61) No matter what the scale of theinteraction the energy of the photon resulted in heating or accelerat-ing particles Here we look at a peculiar application of lasers in cool-ing materials which can be extended into solids This application isbased on radiation pressure (Section 382) of light This refrigerationof matter can be applied in vacuum and can thus operate in space

The momentum kick that an atom receives from a photon is quitesmall and a typical velocity change is of the order of 1 cms Howev-er by exciting a strong atomic transition it is possible to scatter morethan 107 photonss The gain linewidth for an interaction is not a deltafunction (Section 121) The strength of the interaction is reduced asthe frequency is detuned from its resonance value Having atoms inmotion (for a temperature raquoTlaquo and an atom with mass raquomlaquo moving inthree dimensions kT D 32mv 2) each one sees the light at a slight-ly different frequency due to a Doppler shift40) When the laser lightis tuned to be lower than the atomic resonance the atoms movingagainst the laser light see the frequency of the light closer to the res-onance value and have stronger interaction than those moving alongthe direction of the laser light The particles in the laser beam experi-ence a scattering force (Section 382) along the propagation direction

40) The Doppler shift is ΔνDoppler D vc νlaser where raquovlaquo is the velocity of the atomraquoclaquo is the speed of light and νlaser is the frequency of laser light

63 Laser Cooling 177

Figure 67 The scattering rate profile as afunction of frequency detuning ω ω0where ω0 is the resonance frequency andω is the light frequency An atom mov-ing upstream with respect to the laserfield sees the light frequency upshiftedby ν C ΔνDoppler and the one moving

downstream sees the frequency downshifted ν ΔνDoppler When the laserlight is tuned below the resonance theatom moving against the laser field hashigher interaction with light and receivesa kick (scattering force) opposite to itspropagation direction

of light Therefore the atoms moving upstream from the laser fieldwill receive a kick against their direction of motion The slowed downatoms experience cooling

The laser cooling process needs to be extended to atoms movingin opposite direction with a counter propagating laser beam Six laserbeams confine the motion of the atom in three-dimensional spaceThe cooling solely based on the radiation pressure of light can reducethe target temperature to 100 μK Indeed when one uses Dopplercooling there is a residual motion of the atoms that one cannot getrid of Whenever an atom absorbs or reemits a photon it acquiresan additional momentum in a random direction even if the Dopplercooling is improved the atoms will keep moving a little

In a magneto-optical trap laser cooling is combined with a slowmodification of a magnetic trap The potential well is modified witha magnetic field so that the higher energy atoms with larger valuesof dipole moment can leave the well and the cooler ones stay insideWith this evaporative cooling method temperatures of micro Kelvinare attained


References

1 Sheik-Bahae M and Seletskiy D(2009) Laser cooling in dense atom-ic media Nat Photonics 3 680ndash681

2 Lewenstein M Balcou PIvanov MY LrsquoHuiliier A andCorkum PB (1994) Theory ofhigh-harmonic generation by low-frequency laser fields Phys Rev A49 2117ndash2132

3 Corkum PB (1993) Plasma per-spective on strong-field multipho-ton ionization Phys Rev Lett 711994

4 Keldysh LV (1965) Ionization inthe field of a strong electromag-netic wave Sov Phys JET 20(5)1307ndash1314

5 Agostini P Fabre F Mainfray GPetite G and Rahman NK (1979)Freendashfree transitions following six-photon ionization of xenon atomsPhys Rev Lett 42 1127ndash1130

6 Krausz F and Brabec T (2009) At-tosecond physics Rev Mod Phys81 163ndash234

7 Brabec T and Krausz F (2000)Intense few-cycle laser fields Fron-tiers of nonlinear optics Rev ModPhys 72 545ndash591

8 Akagi H Otobe T Staudte AShiner A Turner F Doumlrner RVilleneuve DM and CorkumPB (2009) Laser tunnel ioniza-

tion from multiple orbitals in HClScience 325 1364ndash1367

9 Meckel M Comtois C ZeidlerD Staudte A Pepin HCBHKieffer JC Doumlrner R VilleneuveDM and Corkum PB (2008)Laser-induced electron tunnelingand diffraction Science 13 1478ndash1482

10 Woumlrner NJ Bertrand J Kar-tashov DV Corkum PB andVilleneuve DM (2010) Followinga chemical reaction using high-harmonic interferometry Nature466 604ndash607

11 Tajima T and Dawson JM (1979)Laser electron accelerator PhysRev Lett 43 267ndash270

12 Fedotov AM Narozhny NBMourou G and Korn G (2010)Limitations on the attainable inten-sity of high power lasers Phys RevLett 105 080402

13 Burke DL Horton-SmithRCFG Spencer JE BerridgeDWSC Bugg WM ShmakovK Weidemann AW Bula CMcDonald KT Prebys EJ Bam-ber C Boege SJ Koffas TKotseroglou T Melissinos ACMeyerhofer DD Reis DA andRagg W (1997) Positron produc-tion in multiphoton light-by-lightscattering Phys Rev Lett 79 1626ndash1629


7High Power Lasers (TazerTeaser)

As we saw in Chapter 1 raquohigh powerlaquo is a different concept for peo-ple of different disciplines In this chapter we look at what is perceivedas high power for common mortals lasers that can inflict some dam-age at a distance and are not bigger than what is commonly found inuniversity research laboratories These have a whole range of applica-tions from remote sensing to lightning protection to military applica-tions and even raquocrowd controllaquo

71 Filaments

A raquofilamentlaquo is the name given to a high intensity submillimeterfeature in a broader beam of infrared [1] or UV [2] radiation as itwas seen to drill a minuscule hole on any target such as a mirror ormetal put in its path Filaments are sometimes confused with brightlight created from breakdown in air which is just dense plasma (seeSection 62) One of the main features of a filament that can be usedfor its definition is that its size is confined to a small dimension overa long distance As we saw in Section 161 even though a laser isreferred to as having the best collimated beam it diverges reaching14 its size over the Rayleigh distance A filament is a light beam thatretains its size for distances much longer than the Rayleigh length Acomplex combination of plasma effect on radiation phase front andpolarization is the source for this feature Upon observation of fila-ments researchers became excited about its promising application toguide light and transport optical energy over long distances Howev-er they got more than they bargained for another puzzle of nature toscratch their heads about


181

711 The Filament Fighting for Its Existence

We saw in Chapter 1 Section 1753 that a laser beam of sufficientintensity can create its own waveguide even in air The mere existenceof filaments as self-guided beams has been the object of controversysince shortly after the invention of the laser a controversy that contin-ues to this day

In the good times of the Cold War there was a hot debate between aRussian and American scientist The Russian scientist [3 4] explainedfilamentation as a balance between a nonlinear lensing effect (nonlin-ear index of refraction increasing proportionally to the intensity) andan index of refraction decreasing proportionally to the square of theintensity As we saw in Section 1753) the former effect would causethe beam to focus to a point but the latter effect would take over closeto the focus and maintain a stable beam (or filament) radius His em-inent US colleague countered that filaments do not exist but are justan illusion created by the fact that as the intensity increases alonga pulse the self-focus recedes towards the source [5] To explain thispoint of view a pulse has been divided in slices of increasing intensityin Figure 71b As the pulse intensity increases along the leading edgeof the pulse it will start to focus reaching a focal point at the extremeright of the picture The next slice of the pulse being of higher inten-sity will focus at a shorter distance The fourth slice corresponding tothe peak intensity will focus at the shortest distance There is thus aspot of highest intensity that travels along the center of the beam giv-ing the illusion of a filament In transparent solids such as glass thatintensity spike is sufficient to shatter the material leaving a string ofbeads of broken glass inside the optical component which has theappearance of filaments This explanation of the damage caused insolids by pulses of nanosecond duration is generally accepted That isnot to say that the Russian theory was incorrect

Somewhere in the middle between the Cold War warriors a Frenchscientist proved the existence of filaments creating visible self-induced waveguides with a continuous laser beam [6] The mate-rial used was a suspension of minuscule (4 nm diameter) spheresin a transparent liquid The nanospheres were either plastic (latex)spheres in water of oil droplets maintained in a stable configura-tion in a mixture of soap alcohol and water (microemulsion) If thenanoparticles have an index of refraction higher than the liquid it

182 7 High Power Lasers (TazerTeaser)

Figure 71 Comparison of the mov-ing focus model and true self-inducedwaveguide For the moving focus suc-cessive slices in intensity reach a focusat a different point along the beam axisgiving the illusion of a filament True self-waveguiding is observed in suspensionsof nanospheres which tend to aggregatein the most intense part of the beam (on

the axis in the case of the figure) As theparticles accumulate on the axis theyincrease the average index of refractionof the suspension and create a lens TheBrownian motion counteracts this effectby dispersing the nanoparticles Pleasefind a color version of this figure on thecolor plates

can be shown that they will migrate towards the center of the beam(see Section 382) Since they have a higher index than the liquid thehigher concentration will result in an overall higher index of refrac-tion near the beam axis which creates a lens or an optical waveguideas in Section 144 The distribution of the nanoparticles inside theliquid will reach an equilibrium because the aggregation force of thelight is countered by the Brownian motion that wants to disperse thespheres

Scientists do not seem to have paid much attention to that Frenchdemonstration which has been widely forgotten by the filamentationresearchers The controversy has continued to grow between propo-nents of some version of the moving focus [7 8] and champions of theself-induced waveguide [9 10] How could such a seemingly simpleproblem have gone unresolved for such a long time In the case offemtosecond pulses visualizing an ultrashort ndash 40 fs for instance ndashlight pulse spread transverselly over several cm transform itself intoa minuscule light bullet is not trivial The initial light pulse is likean ultrathin pancake 20 000 μm diameter by 12 μm thickness Howcould the best cook imagine squeezing such a pancake into a 50 μmdiameter spaghetti There is no reason to expect that the edges of the

71 Filaments 183

pancake will move towards the axis of the beam and reach the centralpart at the same time Not only does that happen sometimes but it hasbeen observed that the bullet-in-spaghetti is squeezed to be narrowerthan the original thickness of the pancake Through the filamentationprocess a pulse that was only 40 fs in duration was transformed in-to a 6 fs pulse [11] The ability to compress high energy pulses hasbecome one important application of filaments As we saw in Sec-tion 61 these ultrashort intense pulses are mainly used in researchto create even shorter (attosecond) pulses There are however less ex-otic applications for these filaments as we shall see in the remainderof this chapter

712 Various Types of Filaments

We saw in the previous section that a moving focus can have the ap-pearance of a filament and that a femtosecond pulse can give rise to afilament where the energy stays confined near the beam axis Nearlyall filament research in the world (up to 2011) has concentrated onfilaments created by ultrashort pulses from a Tisapphire laser Oneexception is the continuous radiation filament [6] discussed in the pre-vious section Another exception is the UV filament at 266 nm whichinvolves pulses of 1000 longer duration and energy [12]

Let us quickly review how a filament is generated in air The index ofrefraction (Kerr effect) of air is intensity dependent creating a lensingeffect where the intensity is the highest as is sketched in Figure 128The beam is focused by that self-induced lens reducing in size andat the same time increasing its intensity on axis until reaching a verysmall diameter There is a minimum diameter at which the intensityon axis becomes high enough to ionize the air creating a cloud of


electrons of density decreasing from the center (beam axis) outwardsElectrons are known to have a negative contribution to the index ofrefraction This implies that they create a negative lens compensatingthe self-focusing effect The two opposing effects are the stabilizingeffects that make a filament possible

One might wonder why ultrashort pulses are generally used to cre-ate a filament Could an arbitrary long pulse of sufficient intensitybe used The high intensity electric field of a pulse accelerates theelectrons at each cycle The average velocity of the electron cloud ofthe plasma increases with successive light periods This is called plas-ma heating In a gas the temperature is determined by the averagevelocity of the molecules It is the average velocity of electrons thatcharacterize the temperature of a plasma After some time electronsmay reach such a velocity that their kinetic energy exceeds the min-imum needed to ionize a molecule These electrons upon collisionwith a molecule will ionize it creating another electron which willin turn be accelerated and so on This is called an avalanche processand ultimately leads to a complete ionization of the gas The timeneeded to reach the avalanche is inversely proportional to the inten-sity and to the wavelength For the UV filament the intensity is 100times less than at 800 nm and the wavelength squared 10 times lessTherefore a UV filament can exist with a 1000 times longer pulse du-ration than that of the 800 nm filament and thus carry a much largerenergy This realization led to the generation of filaments with longUV pulses using a Q-switched laser as a source rather than a mode-locked laser [12]

The demonstration of filamentation in the UV is shown in Fig-ure 72 The UV pulse is generated from a Q-switched near infrared(1064 nm) NdYAG laser which is twice frequency doubled to a wave-length of 266 nm This intense UV beam (nearly 1 Jns) is focused ina 3 m long vacuum tube The focused beam is then launched in theatmosphere Since no solid state or liquid can withstand the focusedpower of the UV source a supersonic flow of air is used as a barrierbetween vacuum and atmosphere (Figure 72a) This raquoaerodynamicwindowlaquo consists of a narrow nozzle followed by a specially profiledexpansion chamber The shape of that expansion chamber is calculat-ed in such a way as to achieve the pressure distribution shown in thefigure The color coding for the pressure inside the expansion cham-ber shows a range from 0 to 760 torr (mm of Hg) 5 to 10 cm following

71 Filaments 185

Figure 72 UV Filament (a) A 2 cm di-ameter high power laser beam at 266 nmis focused through a 3 m long vacuumtube The focal spot is located 1 to 2 cmin front of the aperture of an aerodynamicwindow where a supersonic flow of airserves as seal between vacuum and at-mosphere The various colors inside theexpansion chamber of the aerodynamicwindow indicate the local pressure (fromdark blue 0 torr to red 700760 torr) Toattenuate the beam without any distor-tion a 15 cm diameter mirror at grazing(89ı) incidence first reduced the filament

intensity by a factor of 10 million Furtherattenuation can thereafter be made bysimple absorbing gray filters (raquoneutraldensity filterslaquo) (b) At low intensity thebeam diverges after the focus coveringthe entire aperture of the CCD at 1 mdistance (c) At high intensity the beamdiameter remains constant at 300 μm ofthe 4 m propagation distance available inthe laboratory (d) Profile of the filament(cross-section through (c)) and theoreti-cal curve (dashed line) Please find a colorversion of this figure on the color plates

the nozzle there is vacuum in the inside bend (dark blue) and atmo-spheric pressure at the outside curve (red) A 3 mm diameter hole orslot is made for passage of from the region of minimum pressure tothe atmospheric pressure side It should be noted that the transitionfrom low pressure (200 torr light blue) to atmospheric pressure (red)takes places over a distance of only a few mm The aerodynamic win-dow is operated continuously by a compressor providing a pressureof 8 kgcm2 with a flow of 150 dm3s This somewhat complicated ar-rangement has the advantage to prove unequivocally that when a fil-ament is observed it is unequivocally the result of a balance betweenself-focusing and defocusing Indeed a moving focus cannot takeplace since the beam is focused in vacuum to a point before the inter-face vacuumndashair At a distance L from the window varying from 0 to4 m the beam or the filament is linearly attenuated before being ob-served with a CCD The linear attenuator consist first in a large mirrorat grazing incidence (89ı) followed by neutral density filters Becauseof the grazing incidence the high intensity of the filament is spreadover a relatively large area (150 mm 06 mm) thereby preventing


laser damage that would otherwise occur At a distance L of more than1 m and at low power the beam covers completely the viewing area ofthe CCD as shown in Figure 72b At maximum power the pattern onthe CCD is a round spot of 300 μm diameter at any distance between 0and 4 m (longest distance available in the laboratory) [12] (Figure 72c)

713 Remote Sensing with Filaments

Filaments ionize molecules of oxygen and nitrogen creating posi-tive ions and electrons The positive ions of oxygen and nitrogen fluo-resce It is that fluorescence that is at the origin of the Aurora Borealwith the oxygen ion fluorescing in the green (5577 nm) and the red(630 and 636 nm) and nitrogen in the UV (337 nm) and blue (39154283 and 4709 nm) These colors do not have the spectacular appealof the Aurora Boreal and go unnoticed except for researchers attempt-ing to analyze and visualize the filaments A considerably more spec-tacular radiation of the filaments is what is called the conical emis-sion The name is inspired from the fact that this emission makes asmall angle with the axis of the filament The relation between spec-trum and angle is shown in Figure 127 of Section 1753 This narrowcone of light is an ideal white light source for spectroscopy The exactmechanisms giving rise to this display of colors is still the object ofheated debate

Researchers have not waited to understand the phenomenon beforeapplying it and it is fair to say that excitement over filaments startedwith a simple experiment of remote sensing of the atmosphere [1314] A filamenting laser was beamed to the sky and the spectrum of thelight backscattered was recorded as a function of time The principleis the same as in Figure 37a except that there is no airplane scatter-ing back the light but dust water droplets and other particles in theatmosphere Another difference is that not only the round trip timefrom the laser to the particle and back is recorded but also the fullspectrum of the radiation For a given time delay (that translates intoa given altitude) the spectrum shows absorption lines characteristicsof the pollutants encountered in the light path The three-dimensionalset of data (backscattered intensity versus distance and wavelength) issufficient to determine the composition of the atmosphere along thedirection of the laser beam Adding two dimensions ndash by scanning thedirection of the laser beam ndash can lead to a complete volumetric map-

71 Filaments 187

ping of the atmosphere This first application of filamentation wasable to detect backscattering from an altitude of 13 km which led nu-merous readers to the wrong conclusion that stable filaments couldpropagate over such a distance It is the white light (conical emission)beamed by the first few meters of propagation of the filaments thatwas backscattered by clouds and particles and recorded by gated pho-ton counting technique after a delay of up to 43 μs (the delay corre-sponding to a distance of 13 km)

714 Remote Sensing by THz Spectroscopy

The white light produced by a high power filamenting beam hasan astounding wide spectrum ranging from UV to mid-IR More sur-prising even is the generation by filaments of radiation of THz fre-quency41) (in the range of 130 THz) corresponding to a wavelengthrange of 10300 μm This wavelength range is extremely interestingfor spectroscopy and imaging

THz radiation traverses porcelain and leather and is absorbed bywater Spectroscopy in the THz range can identify molecules for in-stance through their rotation and vibration spectrum The large watervapor absorption of THz radiation makes this type of radiation uselessfor remote sensing Filaments exhibit a remarkable ability to generatepulsed THz waves through an optical nonlinear process A filamentcan thus be used as a remote source of THz radiation Techniques arebeing developed by which another filament can be used for remotedetection The dream is to exploit the range of filaments to transportat a large distance a source and detector of THz The distance betweenthe remote source and detector can be optimized to enable imagingand spectroscopy with best resolution and sensitivity

715 The Filament Competing with Sniffing Dogs

The remarkable sniffing sensitivity of dogs have has made themvaluable auxiliary of law enforcement personal in the detection ofexplosives The limitation is distance the nose has to come withinraquosniffing distancelaquo to the suspect object Instead of relying on a raquodogshieldlaquo for protection from material liable to explode it would be de-

41) 1 THz D 1012 Hz


Figure 73 Is there an alternative to thesniffing dog to detect some suspicioussubstance on a suitcase It would benice to be able to shoot a filament on thesuitcase collect the light emitted by theplasma plume created by the filamentwith a parabolic mirror and send it to

a spectrometer With 800 nm filamentssuch an experiment has been performedand can identify the material from whichthe suitcase is made42) The spectrumshown has been taken in this fashion for apolystyrene target (from [15])

sirable to have remote optical detection of dangerous substances Fil-aments offer this possibility because they are able to project a highintensity at hundreds of meter distances

When a filament hits a target it vaporizes and ionizes some ofthe material The plume of material is sufficiently excited to emitradiation with some wavelengths that are characteristics of the ma-terial that was vaporized A large parabolic mirror can collect thatradiation and concentrate it on a spectrometer It is hoped that theanalysis of the spectrum leads to an accurate identification of the ma-terial The technique is called laser-induced breakdown spectroscopyor LIBS Figure 73 shows an example of a spectrum that can beremotely detected when a 800 nm filament impinges on a solid inthis case polystyrene The useful information contained in such ameasurement is the narrow spectral lines at specific wavelengthsdue to molecular transitions as indicated in the figure that can beused to identify the target However the IR filaments also produce abroad continuum of light which was exploited in Section 713 as aspectral lamp for probing the atmosphere which is detrimental forlaser-induced breakdown spectroscopy Indeed the conical emissionis partly responsible for the broad continuum observed as a pedestalto the ray spectrum of Figure 73 Only partly because the impact ofa high intensity femtosecond pulse on molecules creates a strongly

42) Only the surface of the suitcase is detected by this method To observe the contentTHz spectroscopy is required

71 Filaments 189

Figure 74 Comparison of laser-inducedbreakdown spectroscopy with UV andIR filaments (a) Experimental setup(b) Comparison of the spectrum of Aland Cu with and without a film of DNTthrough irradiation by a IR filament No

new spectral feature appears (c) Compar-ison of the spectrum of Al and Cu with-out (left) and with a film of DNT Spectrallines characteristic of CNT are clearlyidentified Please find a color version ofthis figure on the color plates

ionized plasma and the ionized molecule undergoes what is calleda raquoCoulomb explosionlaquo decomposing it into unrecognizable frag-ments Rather that identify a bulk solid copper or plastic it would beconsiderably more useful to be able to identify a thin film or residueleft by an explosive substance The UV filament at 266 nm [12] hastwo considerable advantages over the IR filament for remote sens-ing There is no conical white light emission associated with thesefilaments With the longer pulse duration of the UV filament (ns)there is no raquoCoulomb explosionlaquo but a vaporization of the moleculesand partial dissociation in large fragments that have a characteristicspectrum Figure 74a illustrates how remote laser-induced break-down spectroscopy is performed The filament hits the target Theradiation of the plume is collected by a parabolic mirror and focusedonto a spectrometer Data of laser-induced breakdown spectroscopyperformed with UV are shown in Figure 74c (left) bottom picture(from [16]) The target was either a block of copper (solid red lines)or aluminum (dotted green lines) A comparison is made for thebare substrate or the substrate covered with a thin film of DNT Thethin layer of DNT (ammonium perchlorate was also tested) was pro-duced by evaporating a drop of ethanol solution of DNT on the metal


Characteristic spectral lines of DNT are clearly seen in the spectralregion below 390 nm indicated by the dashed ellipse) on copper oron aluminum substrate The same experiment was performed with800 filaments in exactly the same condition [16] The results shown inFigure 74b does not show any spectral feature due to the thin film ofeither DNT or ammonium perchlorate The continuum and spectrallines of copper fluctuate from shot to shot but in each case overpowerthe weaker emission than could be attributed to the thin deposit onthe metal

72 Laser-Induced Lightning

721 Lightning

These days despite centuries of scientific scrutiny it is fair to saythat a basic understanding of lightning and means to control it arestill lacking Yet it is a natural phenomenon with important conse-quences In the United States alone about 20 million flashes hit theground causing forest fires and property damage From 1940 to 1991the National Weather Service of the United States indicated that an av-erage 163 deaths per year are reported [17] The cost to the US utilitiesamounts to $ 1 billion annually in lost revenues and damaged equip-ment It is also the cause of costly delays of rocket launches into spaceFor example during the Apollo 12 launch of 1969 lightning was re-sponsible for temporally disrupting certain vital electronics on thespacecraft In 1987 an Atlas Centaur 67 rocket carrying a communica-tion satellite was struck altering the flight control computerrsquos memo-ry so extensively that the vehicle was destroyed [18] Would it be worththe effort to try to control lightning Any golfer would answer in theaffirmative lightning has made golf one of the deadliest sports [19]

With his famous experiment with a kite Benjamin Franklin estab-lished the connection between lightning and electricity As the legendputs it (Figure 75) kite wire and operator made a perfect lightningrod However the lightning rod is not the foolproof device that it iscracked up to be Most often43) the cumulonimbus cloud itself is a

43) Famous counterexamples are the lightning storms in the sea of Japan where thebottom of clouds can be positively charged [20]

72 Laser-Induced Lightning 191

Figure 75 (a) How Benjamin Franklinis said to have discovered the connec-tion between lightning and electricityThe combination of kite and metallic wire

is the equivalent of a tall lightning rod(b) Space charges provide a shield for thelightning rod reducing the probability ofstrike on the tall conductor

giant capacitor with the bottom charged negatively and the top of thecloud positively The ground itself has a positive polarity in the pres-ence of the negatively charged bottom of the cloud The atmospherebetween cloud and ground is a good insulator but it is not perfectThere is a small background of ions free electrons created by ioniza-tion either from cosmic rays or local field enhancement at sharp ob-jects This background becomes particularly intense in the presenceof an electric field Most of us will have experienced the hissing soundnear high voltage installations this is called the corona The free elec-trons that are created are attracted by the positive charges creating anegatively charged mantel or shield This shield reduces the effective-ness of the lightning rod (Figure 75b) Standing with a needle in yourhand pointing towards a thundercloud will not guarantee that youwill be raquozappedlaquo Space charges shield any conductor put in the atmo-sphere reducing the probability of a strike along the conducting path

722 Lightning Protection

Is there no hope of protecting our village church from the wrathof thunderstorms The lightning rod should be put in place so rapid-ly as not to give time for the space charges to come in place This


Figure 76 Sensors monitor the electricfields under a thundercloud At the in-stant that an imminent strike is detecteda rocket is launched towards the devel-

oping flash trailing a conducting wireThere is however a possibility that spacecharges shield the rocket to the dismay ofthe rooster guarding the local church

has led to the idea of the wire trailing rocket to trigger lightning Asmall missile carries at its base a spool of thin wire that unwindsin flight A rocket is fired towards a thundercloud trailing the cop-per wire as sketched in Figure 76 The speed of the rocket is of theorder of 100 ms Unfortunately the raquoshieldinglaquo electrons are evenfaster traveling at 350 ms44) The wire trailing rocket is a good re-search tool having a success rate of 50ndash70 when fired in the rightdirection at the instant that a lightning strike is in formation Whensuccessful the result can be spectacular as witnessed by the picture ofFigure 77 A first lightning flash follows the copper wire and createsa path of least resistance in the air As the wind displaces and deformsthe conductive path successive strokes of the same flash occur withina fraction of second Even as a research tool the wire trailing rockethas its shortcomings For instance the glow from the vaporized cop-per wire will interfere with the spectral analysis of the lightning Thisis not the ideal tool for the protection of golfers or rock concert audi-ences what goes up must come down

A modern Zeus able to bend the power to thunderstorms to hiswill has yet to appear There is however hope that the laser will oneday be a tool capable of diverting lightning The challenges are how-

44) That is assuming a local accelerating field of 50 kVm and an electron mobility inair of μe D 7 102 m2(Vs)


Figure 77 Rocket triggered lightning A first stroke follows the copper wire trailingthe rocket Successive strokes follow the conductive path blown away by the wind(from [21])

ever nonnegligible and so far there have been numerous unsuccess-ful attempts since the 1970s [22] There was a series of attempts withCO2 lasers in the early 1990s in Japan [23] Such high power laserscan produce a plasma in air but they produce at best a dotted linein the sky rather than a continuous linear path of ionized air For along wavelength laser such as the CO2 laser it is the electric field ofthe laser itself that produces the ionization In the time of an opticalcycle the electrical field of the laser itself is sufficient to accelerate alone electron to the ionization potential of oxygen or nitrogen ioniz-ing it creating in the process another electron that will be acceleratedThis is called an avalanche process In a few optical cycles of the laserall the molecules of air will be ionized This ionized volume is totallyopaque to the laser light that produced it and the laser cannot propa-gate further than the point it ionized It is like constructing a complexrobot whose first task is to turn itself off

723 Laser Filaments to the Rescue

The solution to this problem is to use filaments [24] in the UV [2124] or in the near infrared [25] As discussed above in Section 71


they create a weakly ionized trail over a long distance While the CO2

laser produced a conductivity as good as a metallic wire over a veryshort distance the filaments provide a low conductivity over a longdistance Not only is the resistance of the filament generated wirehigh but the wire itself is short lived The electrons liberated by theionizing filament attach to the oxygen molecule in a time of the or-der of nanoseconds to form negatively charged oxygen ions Becausethese ions are much bigger and slower than the electrons the resis-tance of the filament wire increases a thousand fold It takes a longtime (tens of microseconds which is an eternity in the world of lasers)for a lightning discharge to establish itself over hundreds of metersBy that time some electrons will have attached to oxygen others willhave recombined with the positive ions created when the electronswas ejected and the air will have become a near perfect insulatoragain

There is however light at the end of the tunnel with a scheme thathas been proposed but not yet implemented [26 27] First a high pow-er laser (either UV which can be nanosecond in duration or near IR)sends a pulse towards the thundercloud a pulse that will become afilament (Laser 1 in Figure 78a) The high power short pulse leavesa raquoplasma traillaquo of free electrons and positive ions behind (shownin light blue in Figure 78b) which are only going to live for severalnanoseconds if nothing is made to save them In (b) Laser 2 sendsa long pulse (more than 10 μs) along the same path as the filamentproduced by Laser 1 If the wavelength of Laser 2 is short enough(less than 800 nm) the photons have enough energy to kick the elec-trons out of the negative oxygen ions This process is called photode-tachment and will maintain a cloud of free electrons in the filamentthereby conserving the channel conductivity

There are two effects that will subsequently contribute to the in-crease in density of the channel and its expansion towards the cloudand towards the earth as sketched in Figure 78c The first phe-nomenon is a raquoneedle effectlaquo It is well known that if a needle isput in a uniform electric field (for instance placed between two platesconnected to the positive and negative of a voltage source) there willbe a considerably more intense field at the tip of the needle thanat any point in the space between the two plates This is the situ-ation with the filament the earth (ground electrode) and the baseof the cloud (positive electrode) Even if the filament is only weakly


Figure 78 Pulse sequence to triggerlightning (a) A powerful filamentingpulsed laser (Laser 1) is beamed towardsa thundercloud (b) The laser filament hascreated a weakly ionized needle shapedvolume in the sky Within a nanosecondafter the ionizing pulse a powerful visiblelaser (Laser 2 wavelength shorter than750 nm) or a combination of a visible andan IR laser is sent along the path of the

filament The pulse duration of Laser 2should exceed 10 μs (c) Under the in-fluence of the electrostatic field betweencloud and ground the needle of elec-trons expands and increases its densityFinally as both ends of the needle reachthe reservoir of charges that constitutesthe cloud and ground (d) the lightningdischarge is established

conductive the electric field at the tip of the needle is sufficient toaccelerate some electrons to such a velocity that when they collidewith air molecules they will ionize them creating additional elec-trons Numerical simulations [28] have shown that the density ofelectron increases (implying that the conductivity of air increases)and the raquoneedlelaquo of electrons and ions becomes longer as sketchedin Figure 78d This effect is related to the static electric field betweenground and cloud

The other phenomenon that can increase the channel density isassociated with the field of the laser beam that co-propagates with thefilament We have seen that the electric field of a laser can accelerateelectrons that have been ionized (Sections 18 and 61) Even a lowintensity beam will have an effect on an electron cloud At each halfperiod of the laser light electrons will increase their average velocityTo this average velocity corresponds an average kinetic energy whichcan also be translated as a raquotemperaturelaquo of the electron cloud Theincrease with time of the average electron energy caused by a constant


intensity laser beam is called inverse Bremsstrahlung45) The longerthe wavelength of the laser the faster the plasma heats As the averageelectron energy increases more electrons will have enough energy tocreate other electrons by collision with molecules of air Ultimatelyall the molecules in the needle can be ionized given a sufficient longirradiation at high enough intensity Under the combined effect of thestatic electric field and the field of the long pulse laser the electroncloud will connect the base of the cloud and the ground resulting ina lightning discharge

For successful lightning protection the lasers should induce light-ning at a tenth or twentieth of the natural breakdown field in air Thisrequires putting several lasers in the field simultaneously in adverse

Figure 79 Two examples of UV laser-induced discharge with ps filaments at250 nm The UV laser passes throughtwo profiled holes in the center of theelectrodes (a) The filament starts near

the bottom electrode and the dischargeis guided over the full length (b) Thefilament starts half way between the elec-trodes

45) The name is derived from the opposite effect As electrons decelerate (raquobremsenlaquoin German) they emit radiation (Strahlung in German) hence the nameraquoBremsstrahlunglaquo for that emission See Section 62


conditions that most lasers are not built to sustain and the accuratecombination and synchronization of several beams These tests havenot been performed yet However laboratory tests [29] confirm the im-proved laser triggering achieved by associating to the filament a longpulse co-propagating visible laser for photodetachment of O

2 Thesetests were made with the raquoTeramobilelaquo laser so called because it pro-duces terawatt pulses (1012 W) and is on a mobile platform (a trailer)The pulse duration is 200 fs for a pulse energy of 200 mJ at the nearIR wavelength of 800 nm With pulses of 100 times less energy in theUV (250 nm) and 1 ps duration lightning discharge can be triggeredat atmospheric pressure at 15 of the self-breakdown voltage of air forgap between electrodes of 60 cm as shown in Figure 79 The lightis sent through a hole between electrodes from bottom to top Thedischarge is a straight line when the filament starts near the bottomelectrode (Figure 79a) The guided portion of the discharge is only onthe top half of the interelectrode spacing where the filament starts inFigure 79b

73 Laser TazerndashTeaser

If laser can make a conductive path in air maybe this can be exploit-ed for some other means This section starts like a fairy tale

Once upon a time there was a leader from a powerful countrysupreme leader Foliage46) who had a near panic fear of protesters Anycrowd of demonstrators was to be kept 2 miles away from his passageBut that was not sufficient to alleviate his fears Was there not a betterway to get rid of these people who believed that they could gather andshout their opinions in the streets Machine gunning them That wasnot an option ndash something in the constitution was against that and al-so not raquopolitically correctlaquo Out of the search for a solution was born apowerful agency the raquoNix the troublemaker by any resourcelaquo (NTAR)designed to find means to fight crowds without killing anyone anaction that would have made supreme leader Foliage unpopular Fil-aments seemed to offer a first attractive means and large contractswere given to academic researchers to determine if the pain inflict-

46) This is fiction any resemblance with any living or deceased person is purecoincidence


ed by a filament on the skin was sufficient to disperse a crowd Theanswer was negative but the laser-induced lightning inspired anoth-er approach remote raquozappinglaquo with high voltage discharge guidedby the laser beam Not only would the protesters be eliminated forthe duration of the mandate of the leader but it would eliminate theworse elements in one stroke those that are holding hands Millionsof dollars from the agency and private investors were given to privatecontractors (university academicians were not to be trusted for suchresearch) who devised giant Tesla coils associated with a laser If it suc-ceeded it would be a classified information If it did not that wouldbe an even higher level of classification

Should we expect to see every policeman or policewoman armedwith a laser tazer gun one day There would be no advantage over thetraditional firearm The applied voltage and capacitance required tosustain a discharge would need to be much higher than what is usedin the electrical chair In addition even if incredible progress is madein miniaturization the weight of the equipment would surely inca-pacitate the strongest law enforcer The prospect of having a portableraquolaser gunlaquo capable of killing an assailant is even more improbableraquoLaser gunslaquo are used as target markers in war games It is better thatit stays that way as a game

References

1 Braun A Korn G Liu X Du DSquier J and Mourou G (1994)Self-channeling of high-peak-powerfs laser pulses in air Opt Lett 2073ndash75

2 Zhao XM Rambo P and DielsJC (1995) Filamentation of fem-tosecond UV pulses in air in QELS1995 Vol 16 Optical Society ofAmerica Baltimore MA p 178(QThD2)

3 Akhmanov SA Sukhorukov APand Khokhlov RV (1966) Self fo-cusing and self trapping of intenselight beams in a nonlinear medi-um Sov Phys JETP 23 1025ndash1033

4 Akhmanov SA Sukhorukov APand Khokhlov RV (1967) Develop-ment of an optical waveguide in thepropagation of light in a nonlinearmedium Sov Phys JETP 24 198ndash201

5 Shen YR and Loy MM (1971)Theoretical interpretation of small-scale filaments of light originatingfrom moving focal spots Phys RevA 3 2099ndash2105

6 Freysz E Afifi M Ducasse APouligny B and Lalanne JR(1984) Critical microemulsions asoptically nonlinear media J OptSoc Am B 1 433

73 Laser TazerndashTeaser 199

7 Brodeur A Chien CY Ilkov FAChin SL Kosareva OG andKandidov VP (1997) Moving focusin the propagation of ultrashortlaser pulses in air Opt Lett 22304ndash306

8 Dubietis A Gaisauskas E Ta-mosauskas G and Trapani PD(2004) Light filaments without self-channeling Phys Rev Lett 92253903-1ndash253903-5

9 Couairon A and Mysyrowicz A(2007) Femtosecond filamentationin transparent media Phys Rep441 49ndash189

10 Loriot V Hertz E Fauchet Oand Lavorel B (2009) Measure-ment of high order Kerr refractiveindex of major air componentsOpt Express 17 13439ndash13434

11 Hauri CP Kornelis W Hel-bing FW Heinrich A Coua-iron A Mysyrowicz A BiegertJ and Keller U (2004) Genera-tion of intense carrier-envelopephase-locked few-cycle laser pulsesthrough filamentation Appl PhysB 79 673ndash677

12 Chalus OJ Sukhinin A AcevesA and Diels JC (2008) Propa-gation of non-diffracting intenseultraviolet beams Opt Commun281 3356ndash3360

13 Schillinger H and Sauerbrey R(1999) Electrical conductivity oflong plasma channels in air gen-erated by self-guided femtosecondlaser pulses Appl Phys B 68 753ndash756

14 Rairoux P Schillinger H Nie-dermeier S Rodriguez M Ron-neberger F Sauerbrey R SteinB Waite D Wedeking C WilleH Woeste L and Ziener C(2000) Remote sensing of the at-mosphere using ultrashort laserpulses Appl Phys B 71 573ndash580

15 Fisher M Siders C JohnsonE Andrusyak O Brown C andRichardson M (2006) Control of

filamentation for enhancing re-mote detection with laser inducedbreakdown spectroscopy in ProcSPIE 6219 p 621907

16 Mirell D Chalus O Peterson Kand Diels JC (2008) Remote sens-ing of explosives using infrared andultraviolet filaments J Opt SocAm B 25 108ndash111

17 Kithil R (1999) National light-ning safety institute (NLSI) light-ning losses in the USA Light-ningrsquos social and economic costshttpwwwlightningsafetycomnlsi_llssechtml Last access De-cember 2010

18 Christian HJ Mazur V Fish-er BD Ruhnke LH CrouchK and Perala RP (1989) TheAtlasCentaur lightning strike in-cident J Geophys Res 94 169ndash177

19 Newcott WR (1993) Lightningndash Naturersquos high-voltage spectacleNat Geogr 184(1) 80ndash103

20 Miyake K Suzuki T TakashimaM Takuma M and Tada T (1990)Winter lightning on japan seacoast ndash lightning striking frequencyto tall structures IEEE Trans PowerDeliv 5 1370ndash1376

21 Diels JC Bernstein R StahlkopfK and Zhao XM (1997) Light-ning control with lasers Sci Am277 50ndash55

22 Koopman DW and WilkersonTD (1971) Channeling of an ion-izing electrical streamer by a laserbeam J Appl Phys 42 1883ndash1886

23 Uchida S Shimada Y YasudaH Motokoshi S Yamanaka CYamanaka T Kawasaki Z Tsub-akimoto K Ushio T Onuki AAdachi M and Ishikubo Y (1999)Laser triggered lightning experi-ments in field experiments J OptTechnol 66 199ndash202

24 Zhao XM Diels JC Braun ALiu X Du D Korn G MourouG and Elizondo J (1994) Use


of self-trapped filaments in airto trigger lightning in UltrafastPhenomena IX (eds PF BarbaraWH Knox GA Mourou andAH Zewail) Springer VerlagBerlin Dana Point CA pp 233ndash235

25 Kasparian J Ackermann R An-dreacute YB Meacutechain G Meacutejean GPrade B Rohwetter P SalmonE Stelmaszczyk K Yu J Mysy-rowicz A Sauerbrey R LWoumlsteand Wolf JP (2008) Electric eventssynchronized with laser filamentsin thunderclouds Opt Express 85758ndash5763

26 Zhao XM Diels JC Wang CYand Elizondo J (1995) Femtosec-ond ultraviolet laser pulse induced

electrical discharges in gases IEEEJ Quantum Electron 31 599ndash612

27 Rambo PK Schwarz J andDiels JC (2001) High voltage elec-trical discharges induced by anultrashort pulse UV laser system JOpt A 3 146ndash158

28 Zhao XM Rambo P Diels JCand Elizondo J (1995) Effect of oxy-gen in laser triggering of lightningin CLEO 1995 Optical Society ofAmerica Baltimore MA pp 182(CWE2)

29 Mejean G Ackermann R Kas-parian J Salmon E Yu J andWolf JP (2006) Improved lasertriggering and guiding of megavoltdischarge with dual ns pulses ApplPhys Lett 88 021101


8Laser Sensors

A musician is well aware of the effect of heat and force on hishermusical string Special care and attention is given at the beginningof a performance to tuning the instruments to the same frequencyLaser light is generated in a resonator like a musical note but withhigher precision The laser frequency and intensity changes if the res-onator is modified Just as in the case of the musical instrument thelaser also can be raquotunedlaquo to the raquomaster diapasonlaquo which in the caseof optics is a reference frequency provided by an atomic transition(see Section 541) The absorption of laser light is also modified in apassive cavity (or resonator) Laser can sing and sense the change intheir propagating medium This chapter is about the sensing song ofa laser

81 Passive Sensors

The conventional laser sensor is generally based on resonator prop-erties For the purpose of illustration let us consider a FabryndashPeacuterotcavity that is a resonator made of two parallel mirrors Unlike theraquolaser bodylaquo defined in Section 133 there is no gain medium in thepassive resonator discussed in this section As the light rattles backand forth between the two mirrors we know that the wave will con-tinuously add to itself if the spacing between the two mirrors is aninteger number of wavelengths It is said that the resonator is at reso-nance Independently of the mirror reflectivity the transmission in thecondition of resonance is always unity provided that there is no lossor absorption in the space between the two mirrors

The reflectivity of the mirrors does matter however the higher themirror reflectivity the longer the (injected) wave circulates in the res-onator Recapping Chapter 1 Section 133 we have seen that the


203

Figure 81 (a) A fiber ring resonatorwhere a counterclockwise circulating wavehas been inserted The wave is resonantwith the fiber perimeter that is adds inphase to itself at each round trip The onlyloss of that resonator is a 01 outputcoupler It can easily be calculated thata laser intensity put in circulation in thering will drop to 12 of its initial valueafter 693 round trips The raquoQ-factorlaquo ofthat resonator is the ratio of the raquophotonlifetimelaquo 693 tRT to the light oscilla-tion period T D 1ν (T is the smallest

resolved difference between two wavesracing through the ring) (b) Analogy ofthe racetrack in which two cars are rac-ing The analogy of the photon lifetimeis the time it takes to empty a gas tankThe smallest resolvable time of arrivaldifference is the time it takes for the carto move by a wheel diameter The raquoQ-factorlaquo definition of the fiber resonatorcan be used here also The higher theQ-factor the smaller the difference in ve-locity between the two racing cars thatcan be resolved

higher the reflectivity the longer the distance that the laser wave trav-els between the mirrors (an average of NRT D 693 round trips whenthe mirror reflectivity is 100 and 999) The same applies to a ringresonator for instance a fiber ring as sketched in Figure 81a wherethe light loses (as in the previous example of a linear cavity) 01 tothe external world at each round trip (for instance through a coupler)It takes a time tlife D 693 tRT (often called photon lifetime) for thepower stored in the ring to drop to half of its initial value One definesa raquoquality factorlaquo or raquoQ factorlaquo of a resonator (any resonator) as theproduct of the frequency of the radiation ν by the cavity decay timetlife

One may wonder at this point how these considerations relate tosensors As raquoresonantlaquo light travels around the ring at the speed oflight cn (where n is the index of refraction of the medium in thering) it can survive for a time tlife only because at each round trip thewave adds constructively to itself The wave may cancel itself after afew round trips if there is a small change of refractive index causinga change in wave velocity The smallest change in index of refraction(or in wave velocity) that can be resolved is such that the slower wavelags behind the faster by one light period after a time tlife This isequivalent to saying that the resonator can sense a change of index ofrefraction of nQ

204 8 Laser Sensors

The situation is analogous to a car race on a ring racetrack (Fig-ure 81b) In the latter case tlife is the time that the car can racewith a full tank Let us assume this corresponds to 693 lapses Theanalogy of the light period T D 1ν is the smallest difference inarrival time that can be resolved Assuming that the smallest differ-ence between the race cars on the finish line is the diameter D ofa wheel (which will be the correspondent of the wavelength in thisanalogy) the analogy of the light period is T D Dv where v is thecar velocity of the fastest racing cars As in the optical resonator thesmallest difference in velocities between the two cars that can be re-solved is such that the slower car lags behind the faster by a wheeldiameter after the time tlife to cover 693 lapses This difference isΔv D v T tlife D vQ which is exactly the same expression asfor the optical ring resonator Δ(cn) D c(nQ) Q for the car analogyis the ratio of the full distance run by the cars to the wheel diameterFor a racetrack of 900 m perimeter a wheel diameter of 06 m the Qof the racetrack is 693 90006 1 million For a fiber resonatorsuch as in Figure 81a of 15 m perimeter and a wavelength of 15 μmthe resonator Q-factor is 693 million

Sensors are based on change of wave velocity in the resonator (forinstance by changing the index of refraction) or a change in absorp-tion The change in absorption is also amplified by the number ofround trips For instance in our previous example if the wave is at-tenuated by 1 ppm (one part per million which is not measurable) inone round trip the overall transmission of the resonator we chooseas an example instead of being 1 will be changed by 01 which isquite measurable The higher the raquoQlaquo of a cavity the more sensitiveits transmission will be to a minuscule absorption

811 Various Types of Cavities

Resonators can take many different forms They can be a FabryndashPeacuterot resonator or a ring resonator or a sphere Surprisingly the samegeneral trend applies in space as in time We have seen that the mostaccurate and precise clock even over long time spans ticks at theshortest period (atomic clocks) Similarly the highest raquoQlaquo resonatorsare not large structures but microresonators of dimension close tothe wavelength

81 Passive Sensors 205

8111 The Raindrop as an Optical ResonatorThe first microresonator is as old as the earth and is the major

tourist attraction of Belgium the raindrop However the latter hadto be exported to sunny New Mexico to gain an understanding of thecomplex optical phenomena that can occur in a raindrop An opti-cal ray that is at grazing incidence with a spherical raindrop maybe trapped and suffer continuing total internal reflection inside thedroplet The phenomenon has been known for centuries in acousticsand has been exploited in numerous constructions A famous exam-ple is the whispering wall surrounding the Temple of Heaven nearBeijing shown in Figure 82a A whispering voice launched along thewall can be heard on the diametrically opposite location of the wallthe sound having traveled along the inner wall

8112 Monitoring the Size of an Evaporating DropletThe first laser sensor based on a microresonator consisted simply

of a He-Ne laser a water droplet and a detector In the case of a wa-ter droplet [1] the whispering voice can be a He-Ne laser beam ofwhich a small fraction can be trapped inside the droplet (Figure 82b)A resonance condition exists if the droplet perimeter contains an ex-act integer number of wavelengths and the radiation can exist for alarge number of round trips Some light will be backscattered in thedirection of the incident light The resonance condition can be ob-

Figure 82 (a) The Temple of Heavennear Beijing with the whispering wallin the background The little umbrella(white arrow) hides a lady whispering toher friend at the diametrically oppositeside of the wall not in sight since he isbehind the camera (b) The whispering

gallery mode in a water droplet a lightray incident from the upper left is trappedand bounces inside the sphere by totalinternal reflection Some wavelengths areresonant with the perimeter of the sphereand are trapped for a very large number ofround trips

206 8 Laser Sensors

Figure 83 (a) Recording of the backscat-tered light from a single water droplet asa function of time As the droplet evapo-rates its diameter shrinks and the lightgoes to successive resonances with theperimeter of the droplet Narrow reso-nance corresponds to the whispering

gallery mode resonance the linewidthand spacing between the peaks indicateat least 100 round trips (b) Glory seensurrounding the shadow of a plane overa cloud layer (courtesy of Howard Bryantadapted from [1])

served by monitoring the light reflected back from the droplet As thedroplet evaporates its perimeter decreases going through successiveresonances which are seen as increases in backscattered intensityThese resonances can be used to monitor the diameter of the waterdroplets and eventually their pollution Figure 83a shows a portionof such a recording The broad maxima correspond to a difference inperimeter of a wavelength The grouping of very narrow resonances ismore interesting The successive narrow peaks are separated by 1100wavelengths indicating that they correspond to resonances of 100 cy-cles

Sunlight is not monochromatic but as all wavelengths are com-bined the backscattering results in a well known phenomenon theglory The glory was seen mostly in mountains as a colored ring sur-rounding the shadow of onersquos head projected in a fog bank belowToday it is most often seen surrounding the shadow of a plane fly-ing above a cloud layer as shown by the photograph in Figure 83bA complete description of the glory is beyond the scope of this booksince it involves not only the whispering gallery resonance but alsothe fact that the backscattering is issued from multiple light raquoringslaquo(the annular edge of the droplets) which interfere with each otherThe interferences of these rings cause the concentric ring structure ofthe glory A complete description of this effect can be found in refer-ence [1]


8113 Man-Made MicroresonatorsThere are of course raquoman-madelaquo versions of the raindrop as res-

onator These are crystalline or glass (silica) microspheres integrat-ed semiconductor microringsmicrodisks silica microtoroids withQ-factors ranging from 1 million to 10 billion They are presently ahot topic of fundamental research with promises of applications innumerous fields Figure 84 shows some examples of microcavitiesand a list of related research and applications A discussion of the nu-merous applications contemplated is beyond the scope of this bookWe refer to a few selected citations for communications [2] plasmon-ics [3] biosensing [4] quantum optics [5] quantum computation [6]optomechanics [7ndash9] metrology [10] microwave photonics [11] andnarrow linewidth microlasers [12]

We alluded to some mechanical effects of light in Section 18 Forinstance radiation exerts a pressure on a mirror as it is reflected asmaller push than that given by a flee crashing onto the mirror For thephoton the mirror is a huge mass hence a huge inertia as comparedto the photon momentum hνc In Section 18 we made the radiationpressure take large values for an exceedingly short time by increasingthe laser power to gigantic proportions Another approach to makethe radiation pressure felt is to reduce the size and mass of the mirrorthat the photons are bouncing off The microresonator of a high Q-factor increases the number of photons in a confined space resultingin radiation pressure forces that can be felt by ultralight structures in

Figure 84 (a) fields that are impacted bymicrocavities (b) Examples of microcav-ities (1) A free silica microtoroid (20 μmdiameter) on a silicon chip compared tothe size of red blood cells (2) (3) A 2 mmdiameter LiNbO3 disk (4) A prism cou-pled LiNbO3 microdisk modulator (with

the RF ring resonator on top) (5) A freesilica microtoroid coupled to a silica fiber-taper (6) A silica microsphere and (7) Asilica microtoroid on a silicon pillar (cour-tesy of Professor Mani Hossein-Zadeh ofthe Center for High Technology Materialsat the University of New Mexico)

208 8 Laser Sensors

or near the microresonator This interaction has led to the new fieldof raquooptomechanicslaquo

8114 Micromechanical ForcesThe mechanical action of a laser beam is not limited to pushing (as

in Section 382) it can also twist Circularly polarized light (cf Sec-tion 122) corresponds to an electric field spinning around the lightray at a rate of the light frequency Right-circular polarization will spinto the right and left-circular polarization will spin to the left The pho-ton can be seen as an elementary bullet spinning about the axis ofpropagation Rifles use spin-stabilized bullets the barrelrsquos rifling im-parts spin to the bullet as it passes through the bore a rotation meantto stabilize the bullet in flight Indeed we know that angular momen-tum is conserved so the spinning motion of the bullet will tend tomaintain its axis pointing towards the direction of propagation Asthe bullet hits a body its momenta are exchanged with the targetthe linear momentum producing a recoil (the equivalent of radiationpressure hνc for the photon) and the angular momentum produc-ing a torque The same phenomena of momenta exchanges occur atthe source the gun experiences a recoil when fired and a torque inthe opposite direction to that of the spin The angular momentum Land the kinetic energy K of an object of mass m spinning at a dis-tance r from an axis at a rate of f turnssecond47) are respectivelyL D m(2π f )r2 D mΩ r2 and K D m(2π f )2r2 D mΩ 2 r2 The pho-ton is the ultimate elementary bullet despite the fact that it has nomass it has a linear momentum (mv for the bullet) which is hνcand as any spinning bullet an angular momentum h2π One maywonder whether the angular momentum of a circularly polarized laserpointer may give some strange sensation to its user Would it act as agyroscope moving the beam sideways when one wants to move thespot downwards Or would one feel a recoil torque on the laser whenturning on the laser To get a sense of the magnitude of the angularmomentum of light let us imagine a green laser pointer emitting cir-cularly polarized light as in Figure 85a To the angular momentumN h(2π) (where N is the number of photons) corresponds the kinetic

47) Ω D 2π f is the angular frequency in rads


Figure 85 (a) What is the angular mo-mentum associated with a circularlypolarized green laser pointer of 20 kWpower The angular momentum of thebeam is the value per photon (h(2π))times the number of photons N The

kinetic energy the rate of change of an-gular momentum is equal to the productof the laser power W by the light periodT 15 fs divided by 2π This kinetic en-ergy is that of a 1 g feather on a 1 m armspinning at the rate of 1 turnday (b)

energy of

d Nd t

h2π

D d(N hν)d t

12πν

D W T2π

(81)

where W is the laser power and T 2 fs the period of the laserlight oscillation Even with a laser pointer of 20 kW power () we findthat the kinetic energy associated with all the photons spinning in thesame direction is only 5 1012 J The mechanical system with thesame kinetic energy would be a mass of 1 g held at arms length (1 m)by a man (or polar bear) standing at the North Pole (hence a rotationrate of Ω D (2π rad)day D 000007 rads) In microresonators wheresimilar powers circulate that kinetic rotational energy is concentratedin a volume of the order of a μm3 thus an energy density of 5 Jcm3quite sizable for a micromechanical structure

It is possible to engineer a laser beam with much larger angularmomentum by having the rays skewed with respect to the propaga-tion direction as shown in Figure 85b The envelope of the ray forma hyperboloid the same as can be obtained by attaching string to twocircular bases and twisting the two circles as the bases are pulled apartThe class of beams made of rays that twist around the axis of propaga-tion has been called raquoLaguerre modeslaquo which is a different family to

210 8 Laser Sensors

the raquoGaussian modeslaquo usually emitted by a laser that were referredto in Chapter 1 The linear momentum of the photon hν has a com-ponent hν sin θ in the plane normal to the propagation axis (whichmakes an angle θ with the light rays) The linear momentum timesthe arm w0 (the radius of the beam at the waist) is an angular momen-tum dubbed raquoorbital angular momentumlaquo considerably larger thanthe momentum due to the photon spin For the example of a 20 kWlaser an angle of 6ı and a beam radius of 1 mm the kinetic energy ofsuch a beam W w0 sin θc corresponds to 7 109 J The mechanicalcorrespondent is our North pole experimentalist holding a 13 kg birdat arms length rather than just one feather

It is not conceivable that the kinetic energy associated with the ro-tation of a feather rotating about an axis at the rate of one turndaywould be measurable The raquoprecision of lightlaquo however is such thatthe faintest forces are perceived The minuscule angular momentumof the photon was measured 24 years before the appearance of the firstlaser by Beth [13] We saw in Section 116 that the polarization of lightcan be changed from linear to elliptical to circular with birefringentmaterial or wave plates A half wave plate will change right circularpolarization into left circular polarization In a similar manner as amirror gets a recoil from the momentum of the light that bounces offit the half wave plate having switched the direction of rotation of theelectric field will experience torsion by reaction The torque applied bycircular polarized light on a wave plate (half wave) that converts it fromright circular to left circular was measured by suspending the waveplate on a thin wire creating a very sensitive raquotorsion pendulumlaquo [13]

8115 Tunneling of LightThe higher the raquoQlaquo of a microresonator the more difficult it is for

light to escape but also the more difficult it is to insert light into itHow can one for instance insert light into a perfect toroid such asthe one depicted in Figure 84b We saw in Section 61 that electronsare trapped in a raquopotential barrierlaquo which prevents them from escap-ing from the atom The very high electric field of fs pulse can makethem traverse this raquopotential walllaquo not unlike Harry Potter traversinga brick wall to go to his train platform This phenomenon is calledraquotunnelinglaquo in physics and also exists in optics In optics tunnelingis called raquofrustrated total internal reflectionlaquo or raquoevanescent wave cou-plinglaquo


We saw in Section 144 that if a light ray is incident on an inter-face between a medium of high index of refraction n2 and a lowerindex n1 there will be a critical angle of incidence αcr beyond whichno light is transmitted and all light is reflected by the interface (hencethe name raquototal internal reflectionlaquo) The critical angle is given bysin αcr D n1n2 One would think that interface is an impenetrablebarrier There are different physical phenomena that show this not tobe totally the case One of these is the raquotunnelinglaquo of the light throughthe barrier if another interface is approached Figure 86a shows abeam reflected at a total internal reflection interface of a prism Theelectric field raquoleakslaquo a little through the interface as sketched by thegraph of the field exponentially decaying with distance from the inter-face The decaying field on the low index side is called the raquoevanescentwavelaquo The penetration depth of the field in the low index medium de-pends on the angle of incidence which is largest close to the criticalangle In most practical cases the evanescent wave does not pene-trate deeper than half a wavelength into the low index medium If anidentical prism is approached within range of the evanescent wavethe beam raquotunnelslaquo through the double interface as shown in Fig-ure 86b The transmission factor increases with decreasing distancebetween the prism (Figure 86b) to become 100 when the two in-terfaces merge (optical contact) In addition to the distance between

Figure 86 (a) Total internal reflectionprism The curve shows the exponentialdecay in amplitude of the evanescent fieldas a function of distance from the totalreflecting interface (b) As an identicalprism is approached part of the radia-tion raquotunnels throughlaquo the barrier of theinterfaces There is a gradual increaseof the transmission (and a correspond-ing decrease of the reflection) as (c) the

prisms are brought closer together toreach total transmission when they are incontact This raquotunnelinglaquo is been used toform continuously adjustable beam split-ters [14] (d) The evanescent wave of amicrostripline pumps resonant radiationinto the microring In turn the intensityin the microring is monitored by letting asmall amount tunnel into the microprism(adapted from [11])

212 8 Laser Sensors

prisms other parameters affecting the transmission are the polariza-tion the angle of incidence and the index of refraction of the prismIt was realized soon after the discovery of the laser that this effect hadapplication in making adjustable beam splitter of relatively high dam-age threshold [14] A simple beam splitter can be made by depositingtwo subwavelength thick layers of chromium on the edges of the in-terfaces facing each others in Figure 86b or c and applying pressure(with a screw) in the middle of the opposing face of the prism Theelastic bending of the prism (it is elastic for the displacements areless than 100 nm) brings the two interfaces closer to each other

Frustrated total internal reflection is the main mechanism used tocouple light into and out of microresonators such as shown in Fig-ure 86d The light is fed into the resonant microring through theevanescent wave from a microstripline The amount of light circulat-ing in the resonant ring is sampled by tunneling a sampling of thepower circulating in the ring into a nearby prism

812 Laser Beams to Measure Elongation and Distances

We have seen (Section 39) that short pulse lasers can be used as aradar for three-dimensional imaging of the eye for instance Thesetechniques are limited in resolution by the length of the optical pulserather than the wavelength Since the meter is defined through thespeed of light and the frequency of a laser locked to an atomic stan-dard one would expect the most accurate measurements of lengthto be made by a laser A standard instrument to measure distancewith a single frequency laser is the Michelson interferometer which

Figure 87 (a) The Michelson interferometer (b) The interferometric autocorrelatorto measure distances with a frequency comb (c) Interferometric autocorrrelation of a800 nm pulse of 6 fs duration


is sketched in Figure 87a A detector looks at the reflection of an ob-ject located at a distance L and combines it with the reflection of areference mirror at a distance Lr If the distances L and Lr are equala bright signal will appear on the detector If the mirror L2 is movedby one quarter of a wavelength the difference distance is then a halfwavelength the two reflections make destructive interference result-ing in a minimum signal on the detector D Thus any change in dis-tance within a quarter wavelength increment can be unambiguouslyresolved The difficulty is however to determine the number of quar-ter wavelength differences in the difference L Lr

8121 Frequency Combs to Measure DistancesThe solution to resolving the ambiguity of the return signal pro-

vided by the Michelson interferometer is to use a frequency comband apply a technique called raquointerferometric autocorrelationlaquo [15]The interferometric autocorrelation consists essentially of a Michel-son interferometer such as sketched in Figure 87a but with a non-linear crystal that doubles the optical frequency as a detector (see Sec-tion 1111) The amplitude of the optical oscillation at the doubledfrequency is proportional to the square of the amplitude of the oscil-lation at the fundamental frequency The detector D detects the in-tensity of the second harmonic with the quantity proportional to thesquare of the second harmonic field If the electric fields from botharms of the Michelson interferometer are equal and the difference inoptical path ΔL D L Lr is zero the second harmonic field will beproportional to the square of the fundamental electric field enteringthe nonlinear crystal or (2E)2 D 4E2 The intensity seen by the sec-ond harmonic detector being proportional to the square of the fieldwill be proportional to (4E2) D 16E4 As the optical delay of the refer-ence arm is being changed there will be successive constructive anddestructive interferences of the raquoreferencelaquo and raquosignallaquo arms untilthe two pulses no longer overlap From that delay on the second har-monic intensity will be twice the contribution from each pulse henceit will be proportional to 2E4 For ultrashort pulses each individualfringe of the interferometric autocorrelation between the sample andreference position mirrors can be identified without any ambiguityas shown in Figure 87c The range of the translation of the referencedelay does not need to exceed the distance between two successivepulses of the comb [16] For a well characterized comb the position

214 8 Laser Sensors

of each successive oscillation of the optical field within the pulse en-velope is well known from one pulse to the next It should be notedthat this method requires a stabilized frequency comb and is limitedby amplitude noise and the dynamic range of the detector

813 The Fiber Optical Gyroscope (FOG)

There is a property other than the absorption that is exploited inresonators the length of the resonator In a high Q cavity the waveadds to itself over a very large number of round trips A small changein either the cavity length or the radiation wavelength and the wavemay not add constructively to itself after a large number of round tripswhich again implies a loss of transmission This resonator property isexploited in the fiber laser gyroscope (FOG) which is a ring resonatormade with optical fibers

The FOG is a relatively recent implementation of a century old in-strument the Sagnac interferometer [17 18] This device sketchedin Figure 88 was presented as a proof of the existence of ether afluid medium that would have served as a support for light wavesA sketch of the Sagnac interferometer is shown in Figure 88 Sincethere was no laser source in the days of Sagnac the source was afilament lamp spectrally filtered by a Nicholrsquos prism The light wasconcentrated on a slit and collimated by a lens then injected in aring resonator by a beam splitter B The light reflected by the beamsplitter B went counterclockwise the transmitted light clockwise inthe ring resonator (Figure 88a) Both beams returning at the beamsplitter B will be interfering The result of these interferences is ob-served on a film F To understand the response let us approximatethe interferometer by a circle (of 33 cm diameter in the experiment ofSagnac) At rest the length of the resonator is the same for the clock-wise and counterclockwise directions resulting in a bright fringe inthe middle of the photographic plate When the table on which the in-terferometer is mounted rotates clockwise the beam reflected by thebeam splitter B circulates counterclockwise and will see a perime-ter P shortened by the amount ΔP D v trt D v Pc where cis the speed of light and v D Ω R the velocity at the periphery ofthe circle Since the opposite occurs for the beam circulating clock-wise there will be a difference in optical path between the two beamsreaching the middle of the film amounting to 2Pvc D 4πR2 Ωc


Figure 88 (a) The Sagnac interferometerL is the light source consisting of a fila-ment lamp a slit a collimating lens andspectral filtering B is a beam splitter thatinjects the light into the interferometer inboth directions (reflection sent counter-clockwise transmission sent clockwise)

and extracts the light to make interfer-ences appear on the film F (b) The FOGwhich is simply a Sagnac interferometermade with fibers Instead of a film theinterfering beams extracted from the fiberinterferometer are recorded on a detec-tor D

This is a fraction 4πR2 Ω(cλ) of the wavelength or a phase shiftof 8π2R2 Ω(cλ) With the Sagnac table rotating at 2 turnss (Ω D4π s1) the relative phase shift of the two beams is 018 correspond-ing to 018(2π) D 0029 of the spacing between two fringes consis-tent with the value observed by Sagnac [18] If the Sagnac interferom-eter had been a ring laser instead of measuring a phase shift of 003it would have measured a frequency of 003(2π trt) D 13 MHz Theextreme sensitivity that results from making measurements inside alaser cavity is the subject of Section 822

It is an interesting point to note that Sagnac had the correct mathe-matical expressions for the observed interference yet his experimentwas presented as an irrefutable proof of the existence of ether a theorydiscarded today His interpretation was consistent with the existenceof a medium (ether) to support the propagation of the waves Thetable moving clockwise would drag the ether with it and result in awave velocity of c C v in our notations Sagnac argued that the etherhad a raquowhirlpoollaquo motion countercirculating with the table rotationresulting in an unchanged wave velocity He subsequently used a fanmounted above the experiment to test the whirlpool effect of air andconcluded there was none If his resolution had been better he wouldhave found a minuscule fringe displacement proportional to the ve-locity of air This effect is called Fresnel drag and will be described inSection 822

216 8 Laser Sensors

The Sagnac interferometer enjoyed a huge return to popularity withthe emergence of low-loss single mode optical fibers for telecommu-nication The sensitivity of the Sagnac interferometer is proportionalto its area which can be multiplied by coiling the fiber (only one loopis sketched in Figure 88b) As all passive devices the measurementis based on an intensity measurement the intensity resulting fromthe combination of two beams of the same frequency but differentphase As such the response is sensitive to the amplitude noise of thelaser source We will see that this is not the case for the active sensorsdiscussed in the next section

82 Active Sensors

It has been recognized since the early days of the laser that intra-cavity measurements can outperform in sensitivity any measurementperformed outside of a laser We have seen that lasing action requiresa delicate balance between the gain and losses of the cavity Very smallintracavity absorption will change this equilibrium and result in alarge power change in the laser output This powerful method is notvery widespread because with the commercialization of lasers scien-tists purchase them as a raquoblack boxlaquo that produces light and no longerventure into operating inside the cavity A laser is not only sensitiveto minute changes in losses but also to minute changes in the opti-cal path between the cavity mirrors Note that a change in the opticalpath is not necessarily a change in physical length it can also be achange in the index of refraction We have seen that the wavelengthof a laser has to match an integer fraction of the cavity perimeter (ortwice the cavity length) Since it typically takes 1 million wavelengthsto span the cavity length a change in distance of 11000th of a wave-length will cause a relative change in the optical frequency (1(1000million)) which is still a frequency of the order of MHz easily mea-surable with standard electronics Intracavity phase interferometry ex-ploits this property

821 The Active Laser Gyroscope

A laser gyroscope is basically the Sagnac interferometer sketchedin Figure 88a incorporating a medium with an optical gain such as

82 Active Sensors 217

to make it a ring laser Instead of the beam splitter B which wouldintroduce too many losses the two countercirculating beams are ex-tracted through one of the cavity mirrors and made to interfere Theresponse of a laser gyroscope is the Sagnac phase shift divided by theround trip time of the ring laser From this definition one immedi-ately concludes that there is one essential difference with FOG thereis no increase in response by raquocoilinglaquo the laser gyroscope since theratio of the Sagnac response to the cavity length remains the sameindependently of the number of coils

One can also understand the response of the laser gyroscope with-out invoking the Sagnac effect either in terms of Doppler shift orby considering the standing wave created by the countercirculatingbeams as sketched in Figure 89a Let us consider a circular cavityfor simplicity of radius R in which two beams of the same opticalfrequency circulate in opposite sense The detector or observer ro-tates clockwise around the circle of laser beams at a velocity v DRΩ (Ω being the angular velocity of rotation) It will see the clock-wise beam Doppler-shifted to the red and the counterclockwise beamDoppler shifted towards the blue The difference between the twoDoppler shifts is the gyroscopic response equal to Δν D 2(vc)ν D2RΩλ D [4A(P λ)]Ω where ν and λ are the optical frequenciesand wavelengths respectively and A the area of the laser gyroscope ofperimeter P

An even simpler understanding of the gyroscopic response is byconsidering that the two circulating beams interfere making a stand-ing wave pattern all along their path This standing wave pattern con-stitutes a nonrotating frame of reference48) The observer in a labo-ratory framework rotating with the angular velocity Ω sees the suc-cessive constructive-destructive interferences pass by at a rate Δν D(RΩ(λ2) D 4A(P λ) where A and P are respectively the area andperimeter of the laser gyroscope The sensitivity of the laser gyroscopeis characterized by the factor 4A(P λ) often called the raquoscale factorlaquoA circle is the ideal shape that produces the largest scale factor (thelargest AP ratio) For practical reasons however the typical commer-cial He-Ne laser gyroscope has a triangular cavity which is a shapethat minimizes the number of mirrors Only recently has gyroscopic

48) There is no violation of any law of physics in having an absolute frame of referencefrom the point of view of rotation since rotation involves an acceleration

218 8 Laser Sensors

Figure 89 (a) In a circular laser gyro-scope of radius R the two circulatingbeams of the same optical frequen-cy ν D cλ make a standing wavepattern This standing wave pattern isa fixed reference The detector or ob-server rotating around these interlacedbeams will see successive construc-

tivedestructive interferences at a rate ofΔν D RΩ(λ2) which is the gyroscopicresponse (b) With a continuous laser theresponse of a real gyroscope is not theideal straight (dashed) line but the solidline showing an absence of response orraquodead bandlaquo at low frequencies

response been demonstrated for fiber lasers giving the possibility ofconstructing perfectly circular laser gyroscopes [19] If Sagnac couldhave made a laser of his 0165 m radius interferometer the rotationspeed of 2 turnss would have given him a signal at a frequency ofΔν D 13 MHz instead of the barely resolvable phase shift of 003 rad

There are however two main challenges that have limited the per-formances of the laser gyroscope both related to the difficulty of cre-ating a laser with two independent countercirculating beams In thebrighter regions of interference of the two countercirculating beams(Figure 89a) the electric field of the combined waves is twice as largeas the field of either circulating wave hence the intensity if four timeslarger This implies that the gain will saturate more if two beamscountercirculate in the laser (bidirectional operation) than if thereis only one beam circulating in one direction (unidirectional opera-tion)49) Therefore in most cases the laser will operate in unidirec-tional mode and there will be no gyroscopic response Gas lasers arean exception where the two countercirculating beams are not mutu-ally exclusive which is the reason that commercial laser gyroscopesare He-Ne lasers (continuous gas lasers of shortest wavelength) Thesecond challenge is the requirement that there be no coupling be-

49) A phenomenon generally designated as raquomutual gain saturationlaquo and raquomodecompetitionlaquo


tween the two circulating beams The laser cavity mirrors (as well asany transparent component) will scatter some light from one circulat-ing beam into the other This causes a phenomenon called raquoinjectionlockinglaquo the weak light that is back-scattered from one sense of circu-lation is amplified and forces the countercirculating beam to have thesame frequency effectively nullifying the gyroscopic response Thiscreates a raquodead bandlaquo in the gyroscopic response An example of adead band caused by a back-scattering on only 0000 000 000 022 of theintensity of the incoming beam is shown in Figure 89b The sensitiv-ity to backscattering is so extreme that an active Sagnac interferome-ter can be used to detect surface defects in optics that backscatter aslittle as one part in 1015 [20 21] Two solutions have been implement-ed to limit the impact of the dead band in commercial He-Ne lasergyroscopes (i) designing raquosuper mirrorslaquo of ultralow scattering and(ii) mechanically shaking the laser in all directions to ensure that theoperation is never within the dead band An He-Ne laser and a laserpointer create a bright visible spot on any surface including a mirrorThe raquosuper mirrorslaquo that have been developed for the He-Ne laser gy-roscope have reached such a degree of perfection that the impact ofthe beam on the mirror is totally invisible These mirrors are howev-er very expensive and fragile (standard cleaning techniques cannot beapplied) All commercial He-Ne laser gyroscopes for navigation havemechanical parts that move their operation outside the dead bandThis mechanical solution defeats the advantage of the laser gyroscopewhich would be to operate without any moving part

The solution to both the raquomode competitionlaquo that restricts the ac-tive Sagnac interferometer to the He-Ne gain medium and the deadband lies in the use of mode-locked lasers This solution has givenrise to a new field of intracavity phase interferometry presented in thenext section

822 Two Pulse Waltzing in a Laser CavityIntracavity Phase Interferometry

The conventional laser sensor is based on high-Q resonator proper-ties The inverse of the quality factor Q of a resonator defined as theratio of the photon lifetime to the light period is the ultimate resolu-tion of a phase sensor This is because as resonant light circulates ina resonator it can survive for the photon lifetime only because at each

220 8 Laser Sensors

round trip the wave adds constructively to itself which is a conditionthat is destroyed for a phase shift larger than 2πQ the ultimate res-olution of a sensor based on a change of index phase velocity or res-onator length Instead of increasing the resonator Q through techno-logical marvels (mirrors of extreme reflectivity lossless waveguides)one can reach the ultimate quality factor by inserting a gain mediumthat is making a laser Various methods have been devised to exploitthe extreme quality factor of a laser interferometer for phase mea-surement The difficulty is that the laser will chose to oscillate at theresonant frequency of the oscillator The solution is to use two lasersin one that is with one mode affected by the external parameter tobe measured and a reference mode The only method to have twononinteracting signals sharing a cavity is to have ultrashort pulses cir-culating in the resonator one as a reference the other as a probe Theprobe will be given a phase shift proportional to the parameter beingsensed per round trip Two pulse trains issued by this resonator cor-responding respectively to the circulating reference and probe areinterfered on a detector The signal is a frequency or beat note equalto the phase shiftround trip There are two main advantages to intra-cavity phase interferometry (i) exploiting the high Q factor of an activelaser and (ii) measuring a frequency rather than an amplitude

To better appreciate the power of intracavity phase interferometryFigure 810 shows a comparison between a Michelson interferome-ter and IPI both applied to a measurement of length change with amode-locked laser In Figure 810a a mode-locked laser sends a trainof identical optical pulses onto the two arms of a Michelson interfer-ometer made of a raquoreferencelaquo and raquosignallaquo arm As the length of thesignal arm L is varied the pulses add in or out of phase resultingin the variation of detected signals (as a function of L) sketched nextto the detector D The sensitivity to length of this arrangement is theratio of the measured change in detected intensity Δ I to the lengthchange ΔL

In the case of IPI (Figure 810b) the Michelson interferometer is in-side the mode-locked laser [22] operating in such a way as to have twopulses circulating simultaneously inside its cavity Some optical deviceperiodically sends one of the pulses into the reference arm and theother pulse into the signal arm Since these two arms are part of thelaser the pulse circulating in the reference cavity will have a differentfrequency to the pulse circulating in the signal cavity The detection is


Figure 810 Comparison of Michelsoninterferometry and intracavity phaseinterferometry A mode-locked laser isused producing a train of identical ul-trashort pulses (a) The train of pulsesis sent onto a Michelson interferometerThe successive constructivedestructiveinterferences recorded as the length Lbeing varied give within a certain range achange in intensity Δ I proportional to theelongation ΔL In (b) a similar measure-ment is performed inside a mode-locked

laser cavity in which two pulses circulateA device (not shown) diverts one of theintracavity pulses upwards towards theraquoreference armlaquo while the other pulseis directed towards the raquosignal armlaquo ofvarying length L The signal obtained bymaking the two pulse trains extractedfrom the laser interfere on a detector hasa frequency Δν proportional to the elon-gation relative to the cavity length Lcavwhere the proportionality constant isprecisely the optical frequency ν

made by extracting the pulse trains corresponding to each of the in-tracavity pulses from the cavity giving them a relative delay such as tomake them overlap on a detector The detector will record an alterna-tive signal at a frequency proportional to the difference in optical fre-quency between the signal and reference As the length of the signalarm L is being scanned the measured quantity which is the recordedfrequency will vary linearly This frequency Δν generally called theraquobeat frequencylaquo50) is equal to the product of the optical frequen-cy of the laser by the displacement relative to the cavity length LcavΔν D νΔLLcav The goal of the measurement is of course to deter-mine the small optical length change ΔL from the measurement ofthe beat frequency Δν ΔL D Lcav Δνν Measurements of changesof Δν as small as 02 Hz have been detected [23] with a laser at anoptical frequency of ν D c(13 μm) D 23 1014 thus correspondingto an elongation of ΔL 1015 m D 1 fm One can justifiably lookat such a figure with surprise a femtometer is less than the distance

50) Δν is called beat frequency or beat note because it results from the raquobeatinglaquo ofthe two pulse trains on the detector

222 8 Laser Sensors

between atoms in a crystal thus also considerably less than the sur-face irregularities in the best polished mirror How could the cavitylength be defined with much better precision than the surface of thelaser mirrors The answer lies in the fact that the wave surfaces of thelaser after thousands of bounces on the mirrors take the sphericalshape that best matches the curved mirror surfaces

Implementation of this device is a challenge it is not particularlyeasy to design a mode-locked laser where two pulses circulate inde-pendently of each other Despite these challenges successful systemsand applications have been demonstrated and are briefly mentionedbelow

Measurement of air currents The laser used in this application is a ringdye laser mode-locked by a saturable absorber jet The saturable ab-sorber has a double role that of being the raquoshutterlaquo that opens itselfat every round trip to create the mode-locking The same saturableabsorber also ensures bidirectional operation with the countercircu-lating pulses meeting at the location of the absorber Two counter-propagating pulses meeting in the absorber saturate the latter moreefficiently than a single pulse traveling through the absorber (as is thecase in unidirectional operation) The first application of intracavityphase interferometry was to measure air flow [24] It was mentionedthat Sagnac unsuccessfully attempted to measure a phase shift due tothe flow of an air fan blowing over the interferometer In the measure-ment of [24] air was flown through a tube inserted in the cavity andthe beat note recorded as a function of the flow velocity The observedlinear dependence of beat note versus flow rate [24] does not implythat the electromagnetic wave is raquocarriedlaquo by air The effect is calledraquoFresnel draglaquo As the Sagnac experiment it was seen as a proof of theexistence of ether the medium assumed to carry the electromagneticwaves It was theorized by Fresnel [25] that a transparent mediummoving along a light beam would raquodraglaquo the ether with it Thereforethe velocity of light cn (n being the index of refraction) would beaffected a change characterized by a raquodrag velocity adjustmentlaquo vd

proportional to the velocity of the moving medium The correctionterm is vd D v (1 1n2) where 1n2 is interpreted as being the ratioof the ether density to the density of the moving medium The inter-pretation of Fresnel has long been forgotten but the expression forthe velocity of light in a moving medium remains cn C v (1 1n2)


In the ring laser the beam moving along the air velocity presents a dif-ferent index of refraction than the countercirculating beam resultingin a beat note

Measurement of minuscule scattering In order to have a linear responseof the intracavity phase interferometer there should be absolutely nocoupling between the countercirculating pulses Any backscatteringresults in a dead band as discussed in Section 821 Conversely themeasurement of a dead band can be used to measure minusculebackscattering coefficients The measurement of Figure 89b was ob-tained by inserting an interface with a backscattering coefficient of22 1011 at the location of the pulse crossing point The dashedline showing an absence of dead band was obtained by removing thebackscattering interface [20]

Various measurements by intracavity phase interferometry Measurementsof rotation [26] and magnetic fields [27] have been performed withring Tisapphire lasers Electro-optic coefficients measurements usedlinear Tisapphire lasers [28] Sensitive low power measurements ofa nonlinear index of refractions used an optical parametric oscilla-tor [23] in a linear configuration

References

1 Bryant HC and Jarmie N (1974)The Glory Sci Am 231 60ndash71

2 Hossein-Zadeh M and Vahala KJ(2008) Photonic RF down-converterbased on optomechanical oscilla-tion IEEE Photonics Technol Lett20 234ndash236

3 Min B Ostby E Sorger V Ulin-Avila E Yang L Zhang X andVahala K (2009) High-Q surface-plasmon-polariton whispering-gallery microcavity Nature 457455ndash458

4 Armani AM Kulkarni RP Fras-er SE Flagan RC and Vaha-la KJ (2007) Label-free single-molecule detection with optical mi-crocavities Science 317 783mdash787

5 Aoki T Dayan B Wilcut EBowen WP Parkins AS Kip-penberg TJ Vahala KJ andKimble HJ (2006) Observation ofstrong coupling between one atomand a monolithic microresonatorNature 443 671ndash674

6 Ralph T and Pryde G (2009)Optical quantum computation inProgress in Optics Vol 54 pp 209ndash269

7 Hossein-Zadeh M Rokhsari HHajimi A and Vahala KJ (2006)Characterization of a radiationpressure driven optomechanical os-cillator Phys Rev A 74(2) 023813

8 Hossein-Zadeh M and Vahala KJ(2010) Optomechanical oscillator

224 8 Laser Sensors

on a silicon chip J Sel Topics inQuantum Electron 16 276ndash287

9 Kippenberg T and Vahala K(2008) Cavity optomechanics Back-action at the mesoscale Science321 1172

10 DelrsquoHaye P Schliesser A ArcizetO Wilken T Holzwarth R andKippenberg TJ (2007) Optical fre-quency comb generation from amonolithic microresonator Nature450 7173

11 Hossein-Zadeh M and Levi AFJ(2006) 146 GHz LiNbO3 microdiskphotonic self-homodyne RF receiv-er IEEE Trans Microwave TheoryTechn 54(2) 821ndash831

12 Lu T Yang L van Loon RVPolman A and Vahala KJ (2009)On-chip green silica upconversionmicrolaser Opt Lett 34 482ndash484

13 Beth RA (1936) Mechanical de-tection and measurement of theangular momentum of light PhysRev 50 115ndash125

14 Court IN and von Willisen FK(1964) Frustrated total internalreflection and application of itsprinciple to laser cavity designAppl Opt 3 719ndash726

15 Diels JC Stryland EV and GoldD (1978) Investigation of theparameters affecting subpicosec-ond pulse durations in passivelymode-locked dye lasers in Proc 1stConf Picosecond Phenomena HiltonHead South Carolina pp 117ndash120

16 Ye J (2004) Absolute measurementof a long arbitrary distance to lessthan an optical fringe Opt Lett 291153ndash1155

17 Sagnac MG (1913) Lrsquoeacutether lu-mineux deacutemontreacute par lrsquoeffet duvent relatif drsquoeacutether dans un inter-feacuteromegravetre en rotation uniforme Cr 157 708ndash710

18 Sagnac MG (1913) Sur la preuvede la reacutealiteacute de lrsquoeacutether lumineuxdeacutemontreacute par lrsquoexpeacuterience de

lrsquointerfeacuterographe tournant C r157 1410ndash1413b

19 Braga AP Diels JC Jain RKKay R and Wang L (2010) Bidi-rectional mode-locked fiber ringlaser using self-regenerative pas-sively controlled threshold gatingOpt Lett 35 2648ndash2650

20 Navarro M Chalus O and DielsJC (2006) Mode-locked ring lasersfor backscattering measurement ofmirror Opt Lett 31 2864ndash2866

21 Quintero-Torres R Ackerman MNavarro M and Diels JC (2004)Scatterometer using a bidirectionalring laser Opt Commun 241 179ndash183


23 Velten A Schmitt-Sody A andDiels JC (2010) Precise intracavityphase measurement in an opticalparametric oscillator with two puls-es per cavity round-trip Opt Lett35 1181ndash1183

24 Dennis ML Diels JC and LaiM (1991) The femtosecond ringdye laser a potential new lasergyro Opt Lett 16 529ndash531

25 Fresnel A (1818) Ann Chim Phys9 57

26 Lai M Diels JC and DennisM (1992) Nonreciprocal measure-ments in fs ring lasers Opt Lett17 1535ndash1537

27 Schmitt-Sody A Velten A Ma-suda K and Diels JC (2010)Intra-cavity mode locked laser mag-netometer Opt Commun 2833339ndash3341

28 Bohn MJ Diels JC and JainRK (1997) Measuring intracavityphase changes using double puls-es in a linear cavity Opt Lett 22642ndash644


9Future Perspectives

Fifty years ago nobody in his right mind could have imagined theimpact that lasers would have in the near future More often thannot this device was claimed to be a raquosolution looking for a problemlaquoIn those days research was supported in a different way Companieslike Bell (ATampT) Philips and others dedicated large sums of moneyto the advancement of science Researchers were not in a raquostraightjacketlaquo ndash their survival did not depend on producing something thatmakes the grass greener or reduces wrinkles Let the imagination andwisdom span our horizons and increase our understanding of natureand voilaacute applications emerge Applications were not the motivationbut the natural result of the learning process When electricity wasfound no one expected that this newly discovered force of nature thatpowered light bulbs would one day run computers The laser did leadto applications more than could be cited in this book Are we anywiser now to predict the future of lasers One can always try to drawsome lessons from the past

Laser Development From Dinosaurs to Bacteria

Most popular in the early years were gas lasers followed by pumpeddye lasers (ion argon lasers) It appears that these lasers are slowly fad-ing into the sunset to make place for a more efficient smaller gen-eration of sources of coherent light Argon ion lasers held for sometime the limelight as sources for pumping dye lasers and Tisapphirelasers and entertaining crowds at rock concerts Contributing to theirdownfall is their amazing inefficiency It takes a power source of 480V3 phase 60 A per phase to power a 20 W laser which can pump amode-locked dye laser producing a frequency comb of a few mW av-erage power Most of the power consumed has to be evacuated in cool-ing water involving even more power wasted in heat exchangers In


227

all the average power in the dye laser beam resulting from this chainrepresents a fraction of the order of 1 part in 10 million of the powerconsumed

The efficiency of laser chains has increased considerably throughminiaturization as well as through the replacement of incoherentpump sources such as flashlamps arc lamps by semiconductorlasers Not only can the wall-plug efficiency of semiconductor lasersexceed 70 [1] but their emission spectrum can be engineered tomatch the absorption of the laser medium to be pumped Further-more as compared to a flashlamp the semiconductor laser is consid-erably more efficient as a pump source because of its directionalityThere is a simple physical reason for the extreme miniaturization oflasers The efficiency will never reach 100 but can be improved Thehigher the power density inside the laser the more the heat that hasto be dissipated Efficient cooling requires a large surface-to-volumeratio which for a given shape is inversely proportional to the lineardimension For a given size the shape can be chosen to maximizecooling Disk-shaped lasers are playing an increasing role in high-power small-size lasers Another shape with larger area-to-volumeratio making huge strides in power capability is the fiber laser Largearrays of spaghetti will be competing with stacks of pancakes for theultimate laser power

What is the limit in laser size What is the ultimate power Every-thing else being equal laser power is proportional to its size Mid-size lasers are commercially available and increasingly used for appli-cations in medicine and industry Seeking laser designs in the twoextremes ndash micro and macro ndash are the main interests of laser en-gineers As for the resonator cavity the lower size limit is the lightwavelength Micro-resonators are designed in various shapes in thesize of a bacteria It is safe to predict that progress in laser sourceswill be linked to material development For instance progress in thesynthesis of cheaper diamond an ideal heat conductor will spur thedevelopment of a new generation of high power miniature lasers Onemajor challenge in material development is the creation of solid statelasers at short wavelength violet and UV A giant step has been thedevelopment of GaN lasers (reaching lasing wavelength as short as360 nm) not only for purple laser pointers but for High DefinitionDigital Video Discs (HDVD) and raquoBlue Raylaquo In most applications in-volving miniaturization of semiconductor lasers the laser is just a low

228 9 Future Perspectives

maintenance resource like the ideal husband () ndash a checkbook not tobe seen and not to be heard

As we are seeing the extinction of the medium-size dinosaurs citedabove some super-giants are being hatched requiring funding on thescale of a continent rather than a single country The European ELI(raquoExtreme Light Infrastructurelaquo) project is one example promisingto reach laser powers sufficient to create matter out of light Thesemegaprojects will be the Tyrannosaur Rex that will slowly gobble upNational and International particle accelerator facilities since the highpower ultrashort pulse laser promises to create more compact andefficient particle accelerators

Silent Lasers

One can still question the importance of lasers in our daily life Af-ter all the invention of wheels light bulbs and computers were morenoticeable than lasers If we choose to ignore the laser as a scientifictool to explore nuclear and chemical reactions and material process-ing we can search for its footprints at home The silent existence oflasers continues in our CDs DVDs HDVDs etc Quietly surrepti-tiously the laser has squeezed itself into the leading position in oneof the biggest markets of our modern society A walk around the houseshould reveal many more hidden applications of lasers which may bedifficult to trace back to the building components Bills are printed bylaser printers cell phones and other electronics are made with laserlithography [2] (microfabrication of circuits) It may not be unreason-able to expect lasers to play an increasing role in lighting as well Weare not yet using laser cooling as a refrigerator or picking up dust withan optical tweezer or chopping tomatoes with a laser scalpel As razorand cream were replaced by electric shavers should we expect to havelaser beard sculpting take over the daily shaving operation Now thatwe have cheap laser power at hand is it going in the direction of hav-ing laser drills laser cookers A reader with a wild imagination mayat this point look around and see the possibility of replacements of orbenefits from lasers in our daily apparatuses With more curiosity onemay imagine that lasers as a scientific tool will enlighten the myster-ies of the universe It is not steam power that replaces a horse and thelaser will not lead to defenestration of mechanics or electromagnetics

9 Future Perspectives 229

It is a fine tool that steers an electron in an atom and can be so intenseas to imitate the sun in a laboratory

Laser Applications

Laser applications in every area cover a wide umbrella from small tomedium and giant sizes as dedicated by its design and required pow-er level In most cases mid-range lasers are used in our daily applica-tions In machining we benefit from CO2 and semiconductor lasersboth in continuous and pulsed operations to cut steel blocks and drillwith miminum damage and highest precision With the control in theposition of the focus patterns and structures can be formed inside ablock and nanostructures sculpted onto semiconductors with ultra-violet lasers By the use of laser filaments we can also transfer ener-gy into further hitherto unreached distances across the atmosphereOne would expect lasers to harness the energy deposition and materi-al modification in all scales more frequently

In electronics lasers will steer currents in atoms and moleculesWith the recent realization of molecular transistors [3] the evershrinking electronic component would ultimately be the size of anatom Lasers will revolutionize our understanding of chemistry andbiology as chemical bond formation and dissociation are monitoredand controlled with laser pulses Since the laser beam can guide nervecells to grow and nerve fibers can be stimulated by lasers it will bepossible to change the message of neurons with a laser beam

A laser cannot read the mind but new ultrasensitive and miniatur-ized laser magnetometers will make it possible to provide direct im-ages of the activities in the brain hence reading the mind In symbio-sis with the development of cameras lasers will contribute to expandour vision beyond the narrow range of visible light

Lasers as active elements in quantum optics and quantum infor-mation will change our binary logic and transfer our deductions ofraquoyesraquoand raquonolaquo to that of raquomaybelaquo With short laser pulses communi-cation will not be restricted to electronic barriers Lasers will not washthe dishes but will be important components of robots (sensors forinstance)

The laser was barely born when raquoGoldfingerlaquo inspired the miscon-ception of the raquolaser gunlaquo Chemical explosives will remain the toyof choice to blow up a wall We can expect to see more lasers for fine


surgery down to the cellular level and for connecting or splicing tinybroken molecular bounds

References

1 Botez D (2005) High-power highbrightness semiconductor lasersin Semiconductor and Organic Op-toelectronic Materials and DevicesVol 5624 (ed ST Chung-En ZahYi Luo) SPIE Bellingham WA5624 203ndash212

2 Xia D Ku Z Lee SC andBrueck SRJ (2011) Nanostruc-

tures and functional materialsfabricated by interferometric lithog-raphy Advanced Materials 23

3 Song H Kim Y YHJang JeongH MAReed and Lee T (2009)Observation of molecular orbitalgating Nature 462 1039ndash1043


Index

aAbove barrier ionization 164Absorption 11 76Accelerator 172Acne laser treatment 108Acoustic analogy 17Actinic keratoses (AK) treatment 107Active sensors 217Acupuncture 113Aerodynamic window 185Air turbine 37Albert Einstein 10Amplified spontaneous emission

(ASE) 176Amplifier with feedback 17Angular momentum 209Atomic force microscope (AFM) 138

139Attosecond 160

ndash recollision 166ndash short and long trajectory 166

Audience scanning 98Aurora Boreal 187Avalanche 194

ndash ionization 185Axons 102

bBand gap 26Barcode reader 86

ndash camera barcode reader 86ndash CCD barcode scanner 86ndash laser barcode scanner 86ndash pen type 86

Basal cell carcinoma (BCC)treatment 107

Beam divergence 13Beam waist 42BeerndashLambert law 105

Biostimulation lasers 113Birefringent medium 38 211Blink reflex 100Braking radiation 173Bremsstrahlung 173 197

ndash inverse Bremsstrahlung 185Brewster angle 23Brownian motion 9

cCarbon dioxide laser 22Carrier to envelope offset (CEO) 69Carrier to envelope phase (CEP) 69Cascade ionization 77Cavity 203

ndash lifetime 19ndash modes 48

CD 87ndash pit 88

Cesium clock 150Charge coupled devices (CCD) 83Chirp 50Chirped pulse amplification 65Circular polarization 12

ndash helicity 12CO2 laser 194Coherence 8

ndash spatial 44ndash temporal 44

Colliding pulse mode-locking 53COLTRIMS 169Compact disc (CD) 87Compton wavelength 63 174Conduction band 26Conical emission 187Corona 192Coulomb explosion 190Coulomb force 172Crookes radiometer 62

232

Crowd scanning 98Cutting 134

dData storage 87Dendrites 102Dermis 104Diagnodent 114Dielectric mirror 33Difference frequency generation 73Diffraction 13 41Diode laser 26Dipole oscillation 167Directionality 59Dispersion 48 49

ndash negative dispersion 50Divergence 13Doppler anemometry 122Doppler blood anemometry 123Doppler effect 121Doppler shift 177 218Doppler velocimetry 122Drilling 134Droplet 206DVD 87

ndash groove 88ndash multilayer 89ndash multiplexing 89ndash pit 88ndash reader and writer 87ndash three dimensional recording 89

Dye laser 51

eElectro-optic effect 39 145Electron attachment 195Electron levels 6Electronndashpositron pair 171Electronic Q-switching 38ELI 64Emission 10

ndash stimulated 10Energy levels 9Engraving 133Epidermis 104Ether 3 215Evanescent wave 211

ndash coupling 211Extreme light infrastructure 175Eye refractive surgery 97

fFabryndashPeacuterot 203Feedback 18Fiber gyroscope 215Fiber ring 204Filament 60 181

ndash conical emission 187ndash continuous 182ndash explosive detection 188ndash Kerr effect 184ndash remote sensing 187ndash THz spectroscopy 188ndash UV 185

Fine structure constant 152Fission 172FOG 215Frequency combs 68 149Frequency generation

ndash difference frequency generation 73ndash sum frequency generation 73

Frustrated total internal reflection 211Fused silica 138

gGain 11

ndash lifetime 16ndash saturation 35

Gamma radiation 172Gaussian probability 59Glaucoma treatment 97Glial cells 102Glory 207Group velocity 48Gyroscopic response 218

hHe-Ne lasers 20Helicity 12HHG 166High harmonic generation 166 169High Q 19

ndash optical resonators 121

iImpulsive stimulated Raman 115Incoherence 8Index of refraction 49Injection locking 20Inkjet printer 83Interference 8 13 204Interferometric autocorrelation 214

Index 233

Intracavity phase interferometry(IPI) 220

inverse Bremsstrahlung 185Ionization

ndash above barrier 164ndash avalanche 185ndash multiphoton 164ndash potential 162ndash tunneling 164

kKeldysh parameter 164Kerr effect 38 49 184Kinesin 118KramersndashKroumlnig 11Krypton emission 150

lLADAR 85Laguerre modes 210Laser

ndash cavity 15ndash high Q 19

ndash cavity lifetime 19ndash cavity round trip 19ndash cooling 117 177ndash damage

ndash photochemical damage 99ndash thermal 99

ndash directionality 41ndash gain 15 16 161ndash gyroscope 217ndash in construction 90ndash level 90ndash lithotripsy 111ndash mode-locking 47ndash output coupler 19ndash pointer 90ndash printer 81ndash pump 15ndash Q-switching 36ndash resonator 15ndash scanner 83ndash seed 20ndash slave 20ndash threshold 18 20ndash Tisapphire 170ndash type

ndash carbon dioxide 22ndash dye 51

ndash fiber 29ndash He-Ne 20ndash nitrogen 24ndash semiconductor 26ndash TEA 24ndash Tisapphire 56

ndash welding 135Laser-induced breakdown

spectroscopy 189Laser-induced fission 171Laser-induced lightning 191Levitation trap 121LIBS 189LIDAR 84Light emitting diode (LED) 82Light mill 62Lightning 191Linear polarization 13Lithotripsy 111Low level laser therapy (LLLT) 113

mMagneto-optical trap (MOT) 178Marking 133Mars orbital laser altimeter 85Mendeleev table 1Meter standard 150Methane stabilized He-Ne 150Michelson 213Microscopy

ndash fluorescence 142ndash multiphoton 142ndash nonlinear 143ndash two-photon 142

Microsphere 206Microstructure fibers 152Mitosis 118Modal dispersion 29Mode competition 219Mode-locked laser 47 48Mode-locking

ndash colliding pulse 53Molecular alignment

ndash revival 168Momentum 62 208Moving focus 182 183Multimode fiber 29Multiphoton 140

ndash absorption 76

234 Index

ndash fluorescence 77ndash ionization 77 164

Multiplexing 90 146ndash time multiplexing 147ndash wavelength multiplexing 146

nNegative dispersion 50Neural network 102Neurones 102Niels Ryberg Finsen 93Nitrogen laser 24Nonlinear

ndash index 182ndash lensing 182ndash Schroumldinger equation 57

Nonsequential double ionization 166Nuclear fission 171Nucleon 172Numerical aperture 15

oOffset frequency 69Optical coherence tomography

(OCT) 126Optical lattice 119Optical parametric generator 75Optical rectification 73Optical stretching (OS) 119Optical tweezers trap 121Optomechanics 209Orbital 161Orbital angular momentum 211

pPair production 171Parametric gain 73Passive Q-switching 39Passive resonators 203Periodically poled crystal 72Permittivity 11Phase matching 71Photochemical damage 99Photodetachment 195Photodynamic therapy (PDT) 107Photoelectric 173

ndash effect 159Photon 2 209

ndash energy 4Photon lifetime 204

Photosynthesis 159Pion 171Planckrsquos constant 3 4Plane wave 14Plasma heating 185Plasma shutter 77Pockelrsquos cell 38Point source 44Polarizability 120Polarization 12

ndash circular 12ndash linear 13

Polarizers 38Polarizing beam splitter 38Pondermotive potential 166Population inversion 16PPLN 72Preform 31Printer

ndash inkjet 83ndash laser printer 82

Probabilityndash Gaussian 59

Probability distribution 59Psoriasis treatment 108Pulse shaper 154

qQ factor 204Q-switching 36QED 174Quasi phase matching 72

rRadar 84Radiation 10 20

ndash spontaneous 10ndash stimulated 10

Radiation pressure 62 117 177 208 209ndash gradient force 118ndash scattering force 118

Raindrop 206Raman spectroscopy 114Rayleigh

ndash criterion 14 88ndash length 43 181

Recollision 166Resonance Raman spectroscopy 115Resonator 18

Index 235

Restorationndash monuments 135

Retinal photo-coagulation 97Revival 168Rotating mirror 37Round trip 19

sSagnac interferometer 215Saturable absorber 39Saturable absorption 52Saturation 35 97

ndash gain saturation 35ndash mutual 219ndash rate 35

Scale factor 218Scanning

ndash audience 98Scanning electron microscope 138Second harmonic 70 185Seed laser 20Self-focusing 185Self-induced waveguide 183Self-phase modulation 55Semiconductor lasers 26ShackndashHartman 130Short range nuclear force 171Single mode fiber 29SLAC 175Slave laser 20Soliton

ndash communication 145ndash compression 55

Spatial coherence 44Speed of light 45 49 67 172Spontaneous radiation 10 176Spontaneous Raman scattering 115Squamous cell carcinoma (SCC)

treatment 108Standing waves 18Stimulated radiation 10 176Sum frequency generation 73Surface enhanced Raman scattering 116Susceptibility 11

tTEA laser 24Temporal coherence 44Thermal damage 99Thin disk laser 135

Three step model 162Threshold 20Tisapphire 56Time of flight 84Time-space duality 147Time standard 150Total internal reflection 29Triangulation 84Tunnel effect 211Tunnel ionization 164Tunneling 211Two-photon absorption 76 89

uUltrashort pulses 45Upchirp 49Uranium 171

vVacuum fluctuation 3 75Valence band 26Velocity map imaging 165Vibrational modes 23VIPA 155Vitiligo treatment 108

wWater droplet 206Wave 2

ndash amplitude 2ndash packet 49ndash period 2ndash plate 211ndash speed 2ndash velocity 2 49

Waveguide 138Wavelength 2Waveplate 38Whispering gallery mode 206Wire trailing rocket 194Wood cutting 136Work function 159

xx-ray free-electron laser 175Xerography 81

zZero point energy 3

236 Index

Color Plates

Figure 12 Different objects that radiate electromagnetic waves and the wavelength andelementary energy associated with them


237

Figure 16 (a) Diffraction of a beamthrough an aperture The path differencevaries across the screen showing moreintensities where peaks from waves ofdifferent parts of the opening coincideand darker regions where peaks and valleycoincide on the screen This results in animage (red pattern) of the aperture that isnot so clear (b) It is shown how far twopoints can be from each other in order to

be distinguished In order to resolve twoimages the raquoRayleigh criterionlaquo definesthe distance between the two points to besuch that the first minimum ring overlapsthe central maximum of the other image(case II) If the distance between the twopoints is larger (case I) the images arebetter resolved while if the distance issmaller (case III) the resolution is lost

Figure 18 Short (12 cm) stable He-Ne laser with flat optical elements directly boundedto the fused silica body (courtesy of Dr Haisma with permission from KoninklijkePhilips Electronics NV Eindhoven from [1])

238 Color Plates

Figure 19 Typical low pressure CO2 laserThe two windows (BW) can be madeof germanium or salt (transparent tothe wavelength of 10 μm emitted by thelaser) They are at an angle such thatthere are no reflection losses for a beampolarized in the plane of the figure (called

the Brewster angle) The electrodes canbe small cylinders of nickel The reflec-tivity of a flat plate of germanium (80)is sufficient to achieve lasing action Theother reflector can be a flat metallic mirror(a concave mirror ndash typically 20 m radiusof curvature ndash is generally used)


to the upper plate pointing towards theground plate or a car spark plug) Theshort circuit propagates towards the rightbrings the left electrode to ground poten-tial inducing a discharge across the tubelasting until the complete capacitanceis discharged (about 1 ns) The tube isclosed by two windows or one windowand a mirror Pure nitrogen at 2550 torrpressure is pumped through the tube (aircan also be used but the performancesare reduced)

Color Plates 239


potential adds to the electron energiesresulting in slanted bands (a) The currentof electrons flows down the raquoriverlaquo ofthe conduction band to cascade down tothe valence band at the junction just as awaterfall (b)

240 Color Plates

Figure 112 (a) Beam incident from thebottom on the interface between twoglasses of different index of refractionncore gt ncladding Rays incident at an an-gle larger than or equal to αcr are totallyreflected without any loss in the mediumof index ncladding (b) Total internal reflec-tion takes place between the core of anoptical fiber and the cladding provided

that the rays make an angle with the axisof the fiber smaller than the critical valueθ D 90ı αcr The smallest beam diam-eter D that can be trapped is the one forwhich the diffraction angle λD (see Sec-tion 123) corresponds to the critical θ Ifthe core diameter is equal to D the fiberis said to be single mode

Figure 113 Erbium doped fiber glowing in the dark upon excitation by the pump radia-tion at 980 nm

Color Plates 241

Figure 115 (a) A CO2 laser tube is closedat one end by a partially reflecting mirroran uncoated germanium plate or a coat-ed ZnSe plate The other end is sealedwith an enclosure containing the rotatingmirror In position (a) with the rotatingmirror at a nonzero incidence with re-spect to the tube axis the gain developsinside the discharge tube As the rotatingmirror arrives in position (b) the outputmirror and the rotating mirror are paral-

lel forming a resonator in which a laserpulse forms and depletes the gain As themirror pursues its rotation (c) there isno longer a resonator and the gain canrecover until the next position (b) (d)Exploded view of an air turbine used forQ-switching The rotation speed couldreach 60 000 revolutionsmin limitedby the centrifugal expansion of the shaft(courtesy of Koninklijke Philips Electron-ics NV Eindhoven 1970)


with time (c) To release the energy storedin that cavity in the shortest amount oftime one of the cavity mirrors is raquore-movedlaquo in a time short compared withthe time it takes light to make a completeround trip in the cavity

242 Color Plates


rors Curved mirrors lead to the situationof (b) the raquoringslaquo are twisted with re-spect to each other The envelope of therays (that are perpendicular to the surfaceof the mirror) draw an hyperboloid whichcan often be seen with a laser beam in adusty environment If the curvature of themirrors is equal the minimum diameterraquoDlaquo ndash the waist ndash is at the midpoint ofthe cavity

Color Plates 243

Figure 119 (a) The illustration of coher-ence at source is given by comparing apoint source with an extended one like aflash lamp filament If all rays come froma tiny (compared to the light wavelength)source they all generate waves ( photons)with the same oscillation phase With ide-al lenses and mirrors one can generatea parallel beam to infinity (b) The sameapplies in reverse if a beam is parallelit can be focused to one spot (c) Sincewe do not live in an ideal word all these

terms are relative such that as the sourceget more extended the collimation is lessIf the source emission is not spatially co-herent the radiation is like having spearsout of a trash can that are all in differentdirections An extended filament evenif emits light at the same time will notgenerate a well collimated beam and willnot be able to merge to a focal point Thesmallest beam at the focus correspondsto imaging the filament

Figure 120 Five waves are added on top of each other such that at a given time all thecrests coincide

244 Color Plates

Figure 121 (a) Generation of new opti-cal frequencies by propagation of a pulsein a medium where the wave velocity in-creases with intensity The optical signalof increasing intensity is shown as hav-ing a stepwise increase on its leadingedge (the time axis points to the left fora better visualization of a pulse propagat-ing to the right) The different intensitiespropagate at velocities v1 v2 v3 and v4with v4 lt v3 lt v2 lt v1 As a resultthe pulse optical frequencies decreasewith time along the pulse (or the wave-lengths increase along the pulse) after

some propagation distance (b) Throughthe process shown in (a) one has gen-erated an raquoupchirpedlaquo pulse that is apulse of which the optical frequency in-creases with time This is exactly what thelittle bird at the bottom of the picture issinging This pulse is now sent through amedium with negative dispersion (ie amedium in which the higher frequencies(blue) propagate faster than the lower fre-quencies (red)) As a result the tail of thepulse catches up with the pulse leadingedge resulting in pulse compression

Color Plates 245

Figure 122 A ring dye laser The dye jet isseen in the middle of the picture pumpedby the bright blue beam of an argon ionlaser The mirror in the foreground focus-es the argon leaser beam at a tiny spot

in the dye jet This gain spot is at the fo-cus of two curved mirrors which direct acollimated beam in the other part of thecavity The red intracavity beam of the dyelaser can be seen on the picture

246 Color Plates


one jet and mirrors with square spectralbandwidth [15 16] In (d) with the raquocol-liding pulselaquo mode-locking implementedin a ring cavity the prism is reinstatedbut at the center of curvature of a mir-ror [17] In (e) a four prism sequence isintroduced in the ring to produce negativedispersion [18]

Color Plates 247

Figure 124 A Tisapphire laser The Tisapphire crystal is pumped through one ofthe two curved mirrors projecting the gain spot into the cavity by a frequency doubledvanadate mirror

Figure 127 (a) The annular display seenon a door 25 m away from the intenseshort pulse laser source The beam hascollapsed into a single filament whichhas produced these concentric colorfulcones (b) A filament produced in glassThe color spectrum is displayed horizon-

tally (from long wavelength to the left toshort wavelengths to the right) and theangle the individual rays make with thehorizontal is the vertical axis The intensebeam propagates along an horizontal axis(shown in black) The directions of therays is indicated for different colors

248 Color Plates


tial dependence of the index of refractionresults in a lensing effect The wavefrontswill curve and the rays perpendicularto the wavefronts will bend towards theaxis A waveguide is formed by the beamitself similar to the fiber sketched in Fig-ure 112

Color Plates 249

Figure 129 The electric field of a pulsenear the peak of a cycle is sufficientlyhigh to eject an electron from its orbit (a)The electron is accelerated away fromthe atom then decelerated to a halt thenext half cycle as the light electric fieldreverses sign (b) During the next quar-ter cycle of the light pulse the electronis accelerated back towards the atomNumerous complex physical phenomena

can occur during that recollision one ofthem being the emission of an extremelyshort (typically 100 as) burst of x-ray ra-diation (d) The pressure of sunlight or aHe-Ne laser is not sufficient to make theraquolight milllaquo (or raquoCrookes radiometerlaquo)spin However the radiation pressureat intensities used to create attosecondpulses is 10 000 times larger than that atthe bottom of the ocean (e)

250 Color Plates

Figure 130 (a) Any amplifier stage hasto be matched to the size of the amplifiedpulse For a given amplifier diameter thesaturation limits the maximum pulse en-ergy that can be extracted as the diameterof the tube limits the size of the elephant

that can pass through it (b) Instead of in-creasing the diameter of the tube why notstretch the elephant to make him passthrough a narrower tube and give him theoriginal proportion after amplification

Figure 131 Chirped pulse amplificationAn ultrashort pulse is sent through astretcher which can be constructed withdiscrete elements (gratings prism) or bea piece of glass or a fiber The differentfrequency components of the pulse aredelayed with respect to each other re-sulting in chirp and pulse stretching The

10 000 to 100 000 times pulse stretchingratio allows considerable amplification be-fore the damage limit to the componentsof the amplifier is reached The action ofthe stretcher is reversed in the amplifierresulting in the creation of an extremelyintense ultrashort pulse

Color Plates 251

Figure 133 The mode-locked pulse trainin the time domain (top) is shown as awave at a single carrier frequency modu-lated by and envelope The correspondingcomb of optical frequencies is represent-ed on the bottom (a) A general case

where the envelope spacing is not an in-teger number of optical cycles (b) Theenvelope spacing is an integer number oflight periods and in addition the carrierto envelope phase is zero


plane B (SHB the two fields cancel out toform a zero second harmonic SH) (c) isthe case of a periodically poled crystalWith the optic axis oriented as shown bythe arrows the propagation and secondharmonic generation from plane A to Bare the same as in case (b) In case (c)the optic axis is reversed after plane Band the second harmonic generated in Bis reversed as compared to cases (a)and (b) Consequently the two fields SHAand SHB add in phase to create a largesecond harmonic SH

252 Color Plates

Figure 136 (a) An optical parametric oscillator in a ring cavity (b) An optical paramet-ric generator (c) A seeded optical parametric generator

Figure 137 Absorption can be interpretedas being due to the incoming light ex-citing dipoles that radiate with oppositephase In (a) A CO2 laser pulse is sentthrough a resonant absorber (typicallyheated CO2) The excited molecules emita wave that destructively interferes withthe incoming wave resulting in a nullsignal on the detector In (b) a plasma iscreated in air which abruptly cuts the tail

of the ns pulse There is no more incom-ing wave to destructively interfere with theradiation from the excited molecules Anintense pulse is observed on the detectorwhich has a duration determined by thetime that the excited molecules remain inphase That time is related to the collisiontime between an excited molecule and anyother atom or molecule in the cell

Color Plates 253

Figure 21 Schematic of a laser printerThe computer digital data of the imageis transferred to brightness and darknessof the laser Then the laser is steered witha mirror and a lens to discharge the neg-ative charge of the drum where there is

brightness (ones) Based on the electro-static charge attraction negative tonerswill ride on the discharged points of thedrum The toner is picked up by paperand the image is transferred for a particu-lar toner color (picture from Wikipedia)

Figure 22 Principle of laser scanning based on triangulation The object and imageare fixed in space and only the laser light is steered across the sample Reflection fromfront and back faces and corners of the object end up on different spots on a CCD

254 Color Plates

Figure 31 (a) The LASIK operation procedure (b) Wavefront LASIK which not onlylooks at correcting the focal point on the retina but also follows the whole wavefront ofthe eye as seen and collected on the retina

Figure 33 (a) The skin has a layeredstructure of epidermis and dermis withmany small structures embedded (b) Ab-sorption spectra of the skin main ab-

sorbers water (blue) melanin (brown)and hemoglobin (red) Also shown arewavelengths of some important dermato-logical lasers

Color Plates 255


for a gradient intensity profile we can fol-low this force as normal to the beam raybending in the sphere The thickness ofthe line representing each ray is an indi-cation of the intensity of that portion oflight (b) With proper adjustment of thelight intensity radiation pressure can beused to make a levitation trap If the forcedue to radiation pressure cancels theweight of the particle a stable suspensionis achieved


within the eye The pulse length (pulseduration c) is shorter than even thethickness of the epithelium (membranein front of the cornea) The time of flightmeasurement is performed as a pure op-tical coincidence method the raquoblack boxlaquoonly detects a signal if the raquoreferencelaquoand raquosignallaquo (from the eye) pulses arriveat the same time

256 Color Plates

Figure 38 (a) Typical set-up for opticalcoherent tomography The source is ei-ther an ultrashort (femtosecond) pulsesource or a low coherence semiconductorsource coupled to a fiber which is dividedinto two arms at the beam splitter BS Ascanning retroreflector AC at the end ofthe reference arm returns a signal back

towards the beam splitter BS The otherfiber arm is collimated by the lens L givena transverse scanning (in x and y) by thescanner TS before being sent to the eyeby a set of lenses L The backscatteredradiation from the eye is mixed with thereference signal in the detector D

Color Plates 257

Figure 39 Successive steps of tomographic reconstruction (a) The object under in-vestigation (b) One-dimensional scanning (c) Scanning from four different directions(d) The planes that define the object

Figure 51 (a) Conventional fluorescence(single photon) microscopy If the fluo-rescing material is uniformly distributedin the sample the entire spectral volume

will emit fluorescence radiation (b) Inthe case of two-photon fluorescence thefluorescence is confined to the center ofthe focal volume

Figure 52 (a) Third harmonic generat-ed picture of sections of a live neuron(courtesy of httpwwwweizmannacilhomefeyaronindexhtm) (b) Two-photon fluorescence of horse chestnut

bark From httpwwwuni-muensterdePhysikAPFallnichForschenNichtlineareMikroskopiehtml (c) A pic-ture of the horse chestnut

258 Color Plates

Figure 54 The principle of wavelengthmultiplexing Several words (pulsestrings) from various sources modu-late a difference color channel in a fiber

Filters (resonators) are used at the detec-tion to separate the different wavelengthhence restituting the individuality of eachchannel

Figure 57 (a) A standard pulse shaperA first grating displays the spectrum ofeach pulse of a pulse train onto a pro-grammable mask The mask manipulatesthe spectral components in amplitudeand phase The transformed spectralcomponents are brought back together by

a second grating Each pulse of the origi-nal train has given birth to a sequence ofpulses controlled by the mask (b) Com-bination of a VIPA and a grating to isolateevery single tooth of a frequency comb(courtesy of Scott Diddams [12])

Color Plates 259

Figure 61 (a) A laser pulse takes the elec-tron and accelerates it just like a slingshottaking a stone For the light photon of800 nm the electron wavelength after thisacceleration is only between 10 to 03 Aring(b) The electron in an atom or moleculeis held in a potential well by Coulomb at-traction to the positive nucleus Althoughin quantum mechanics contrary to clas-sical physics a particle has a chance topass a barrier beyond its energy the prob-ability of this event is negligible when

the particle is at rest (c) With the highelectric field of the laser the atom is ion-ized and the electron oscillates with thelaser field The three curves on the rightside represent three different moments ofionization which will lead to different ac-celeration and ultimate speed of electronThe trajectory of the electrons with ap-plied laser field is calculated by classicalphysics (d) The ejected electron travelswith the laser field and may return andrecombine with its parent ion

260 Color Plates

Figure 63 (a) Tunneling with high laserfield The ejected electron from the tun-nel carries the information about theorbital that it left (b) Recording of themomentum distribution of aligned andanti-aligned molecules is used to producea normalized image of the electron or-bital The image recorded of low energytunneled electrons with the highest elec-tronic orbital calculated for nitrogen andoxygen is in agreement with the imageof direct electrons [9] (c) A schematic ofa COLTRIM to synchronously record themomentum of the ejected electrons and

ions The source is the gas jet that movesup in the picture to meet with the laser(the red light from the left) at its focalspot After the reaction the charged prod-ucts are guided to their proper recordingdevice The high voltage bias separatesthe ions from electrons The magnetic coilon the COLTRIMS overpowers the earthmagnetic field and extends the travel timeof electrons COLTRIMS are made of vari-ous chambers to separate the interactionand detection procedures (courtesy ofAndre Staudte and Mortiz Meckel)

Color Plates 261

Figure 65 (a) Bremsstrahlung radiationor braking radiation of an electron Theelectron trajectory is affected by the pos-itive charge of the nucleus This energyloss due to the deceleration of the elec-tron is transferred to a photon in the x-rayand gamma ray range (b) Compton scat-tering the high energy photon is deflectedby collision with electrons in matter Thephoton energy is reduced (its wavelength

is increased) and the energy difference isgiven to the electron (c) Pair productionwhen a light photon has high enough en-ergy that can produce an electron and apositron pair (D 2 511 keV) a pho-ton can be annihilated and be replacedby matter The excess energy is given askinetic energy to the electron and positrongoing in opposite direction to conservethe momentum

Figure 71 Comparison of the mov-ing focus model and true self-inducedwaveguide For the moving focus suc-cessive slices in intensity reach a focusat a different point along the beam axisgiving the illusion of a filament True self-waveguiding is observed in suspensionsof nanospheres which tend to aggregate

in the most intense part of the beam (onthe axis in the case of the figure) As theparticles accumulate on the axis theyincrease the average index of refractionof the suspension and create a lens TheBrownian motion counteracts this effectby dispersing the nanoparticles

262 Color Plates

Figure 72 UV Filament A 2 cm diameterhigh power laser beam at 266 nm is fo-cused through a 3 m long vacuum tubeThe focal spot is located 1 to 2 cm in frontof the aperture of an aerodynamic win-dow where a supersonic flow of air servesas seal between vacuum and atmosphereThe various colors inside the expansionchamber of the aerodynamic window in-dicate the local pressure (from dark blue0 torr to red 700760 torr) At low inten-sity the beam diverges after the focus

covering the entire aperture of the CCD at1 m distance At high intensity the beamdiameter remains constant at 300 μm ofthe 4 m propagation distance availablein the laboratory To attenuate the beamwithout any distortion a 15 cm diametermirror at grazing (89ı) incidence first re-duced the filament intensity by a factor of10 million Further attenuation can there-after be made by simple absorbing grayfilters (raquoneutral density filterslaquo)


new spectral feature appears (c) Com-parison of the spectrum of Al and Cuwithout (left) and with a film of DNTSpectral lines characteristic of CNT areclearly identified

Color Plates 263

Lasers

Contents

Preface

References

1 A Scenic Route through the Laser



112 Photon Energy

113 Energy and Size






131 The Pump

132 Gain



141 He-Ne Lasers



144 Fiber Lasers

15 Pulsed Lasers


152 Saturation



161 Directionality

162 Intensity





174 The Real Thing From Splashing Dyes to Crystal Lasers to Semiconductor Lasers











References

2 Laser Coherence at Home






241 Laser Level

242 Laser Pointers

3 The Laser in Medicine

31 Introduction



















References

4 Lasers in Industry

41 Laser Machining

411 Marking


421 Laser Welding




References

5 Laser Time Capsule

51 Introduction


53 Communication

531 Introduction


533 Multiplexing

54 Frequency Combs





References

6 Light in Matter





63 Laser Cooling

References

7 High Power Lasers (TazerTeaser)

71 Filaments







721 Lightning




References

8 Laser Sensors

81 Passive Sensors




82 Active Sensors


822 Two Pulse Waltzing in a Laser Cavity Intracavity Phase Interferometry

References

9 Future Perspectives

References

Index

Color Plates

Jean-Claude Diels and Ladan ArissianLasers

Related Titles







Lasers



The Authors











ISBN Print 978-3-527-41039-2




Jean-Claude Diels

V

Contents





VII








Index 232

Color Plates 237

VIII Contents

Preface




IX





X Preface








Preface XI




References








XII Preface








1











112 Photon Energy






E D hν D hcλ

(11)





113 Energy and Size






























































131 The Pump




132 Gain































141 He-Ne Lasers








































144 Fiber Lasers


































15 Pulsed Lasers







152 Saturation




15 Pulsed Lasers 35













15 Pulsed Lasers 37













15 Pulsed Lasers 39












161 Directionality










θ D 06λD

(12)




162 Intensity


























































































































































































References















































81













































density D 18

area06 λ

NA

2 (21)








241 Laser Level


242 Laser Pointers









31 Introduction





93

















































































































































































































References



















4Lasers in Industry

41 Laser Machining


411 Marking




133








421 Laser Welding






























References










5Laser Time Capsule

51 Introduction




141














53 Communication

531 Introduction








533 Multiplexing




















54 Frequency Combs

































Figure 58 VIPA











References
















6Light in Matter





159






















































































λ0 λ D hmc

(1 cos (θ )) (61)

















63 Laser Cooling











References


















71 Filaments



181










71 Filaments 183









71 Filaments 185









71 Filaments 187







41) 1 THz D 1012 Hz







71 Filaments 189







721 Lightning















































References




































8Laser Sensors


81 Passive Sensors




203





204 8 Laser Sensors












206 8 Laser Sensors











208 8 Laser Sensors








energy of

d Nd t

h2π

D d(N hν)d t

12πν

D W T2π

(81)



210 8 Laser Sensors









212 8 Laser Sensors










214 8 Laser Sensors










216 8 Laser Sensors


82 Active Sensors









218 8 Laser Sensors











220 8 Laser Sensors









222 8 Laser Sensors









References









224 8 Laser Sensors





























227







Silent Lasers




Laser Applications








References






Index



139Attosecond 160












CD 87ndash pit 88





232





Dye laser 51









gGain 11






Index 233



















ndash absorption 76

234 Index
























Index 235



















236 Index

Color Plates



237




238 Color Plates





Color Plates 239



240 Color Plates




Color Plates 241





242 Color Plates



Color Plates 243




244 Color Plates



Color Plates 245



246 Color Plates



Color Plates 247




248 Color Plates



Color Plates 249



250 Color Plates





Color Plates 251





252 Color Plates




Color Plates 253




254 Color Plates




Color Plates 255





256 Color Plates



Color Plates 257






258 Color Plates





Color Plates 259



260 Color Plates



Color Plates 261





262 Color Plates





Color Plates 263

Lasers

Contents

Preface

References




112 Photon Energy

113 Energy and Size






131 The Pump

132 Gain



141 He-Ne Lasers



144 Fiber Lasers

15 Pulsed Lasers


152 Saturation



161 Directionality

162 Intensity
















References







241 Laser Level

242 Laser Pointers


31 Introduction



















References


41 Laser Machining

411 Marking


421 Laser Welding




References


51 Introduction


53 Communication

531 Introduction


533 Multiplexing

54 Frequency Combs





References

6 Light in Matter





63 Laser Cooling

References


71 Filaments







721 Lightning




References

8 Laser Sensors

81 Passive Sensors




82 Active Sensors



References


References

Index

Color Plates

Related Titles







Lasers



The Authors











ISBN Print 978-3-527-41039-2




Jean-Claude Diels

V

Contents





VII








Index 232

Color Plates 237

VIII Contents

Preface




IX





X Preface








Preface XI




References








XII Preface








1











112 Photon Energy






E D hν D hcλ

(11)





113 Energy and Size






























































131 The Pump




132 Gain































141 He-Ne Lasers








































144 Fiber Lasers


































15 Pulsed Lasers







152 Saturation




15 Pulsed Lasers 35













15 Pulsed Lasers 37













15 Pulsed Lasers 39












161 Directionality










θ D 06λD

(12)




162 Intensity


























































































































































































References















































81













































density D 18

area06 λ

NA

2 (21)








241 Laser Level


242 Laser Pointers









31 Introduction





93

















































































































































































































References



















4Lasers in Industry

41 Laser Machining


411 Marking




133








421 Laser Welding






























References










5Laser Time Capsule

51 Introduction




141














53 Communication

531 Introduction








533 Multiplexing




















54 Frequency Combs

































Figure 58 VIPA











References
















6Light in Matter





159






















































































λ0 λ D hmc

(1 cos (θ )) (61)

















63 Laser Cooling











References


















71 Filaments



181










71 Filaments 183









71 Filaments 185









71 Filaments 187







41) 1 THz D 1012 Hz







71 Filaments 189







721 Lightning















































References




































8Laser Sensors


81 Passive Sensors




203





204 8 Laser Sensors












206 8 Laser Sensors











208 8 Laser Sensors








energy of

d Nd t

h2π

D d(N hν)d t

12πν

D W T2π

(81)



210 8 Laser Sensors









212 8 Laser Sensors










214 8 Laser Sensors










216 8 Laser Sensors


82 Active Sensors









218 8 Laser Sensors











220 8 Laser Sensors









222 8 Laser Sensors









References









224 8 Laser Sensors





























227







Silent Lasers




Laser Applications








References






Index



139Attosecond 160












CD 87ndash pit 88





232





Dye laser 51









gGain 11






Index 233



















ndash absorption 76

234 Index
























Index 235



















236 Index

Color Plates



237




238 Color Plates





Color Plates 239



240 Color Plates




Color Plates 241





242 Color Plates



Color Plates 243




244 Color Plates



Color Plates 245



246 Color Plates



Color Plates 247




248 Color Plates



Color Plates 249



250 Color Plates





Color Plates 251





252 Color Plates




Color Plates 253




254 Color Plates




Color Plates 255





256 Color Plates



Color Plates 257






258 Color Plates





Color Plates 259



260 Color Plates



Color Plates 261





262 Color Plates





Color Plates 263

Lasers

Contents

Preface

References




112 Photon Energy

113 Energy and Size






131 The Pump

132 Gain



141 He-Ne Lasers



144 Fiber Lasers

15 Pulsed Lasers


152 Saturation



161 Directionality

162 Intensity
















References







241 Laser Level

242 Laser Pointers


31 Introduction



















References


41 Laser Machining

411 Marking


421 Laser Welding




References


51 Introduction


53 Communication

531 Introduction


533 Multiplexing

54 Frequency Combs





References

6 Light in Matter





63 Laser Cooling

References


71 Filaments







721 Lightning




References

8 Laser Sensors

81 Passive Sensors




82 Active Sensors



References


References

Index

Color Plates


Lasers



The Authors











ISBN Print 978-3-527-41039-2




Jean-Claude Diels

V

Contents





VII








Index 232

Color Plates 237

VIII Contents

Preface




IX





X Preface








Preface XI




References








XII Preface








1











112 Photon Energy






E D hν D hcλ

(11)





113 Energy and Size






























































131 The Pump




132 Gain































141 He-Ne Lasers








































144 Fiber Lasers


































15 Pulsed Lasers







152 Saturation




15 Pulsed Lasers 35













15 Pulsed Lasers 37













15 Pulsed Lasers 39












161 Directionality










θ D 06λD

(12)




162 Intensity


























































































































































































References















































81













































density D 18

area06 λ

NA

2 (21)








241 Laser Level


242 Laser Pointers









31 Introduction





93

















































































































































































































References



















4Lasers in Industry

41 Laser Machining


411 Marking




133








421 Laser Welding






























References










5Laser Time Capsule

51 Introduction




141














53 Communication

531 Introduction








533 Multiplexing




















54 Frequency Combs

































Figure 58 VIPA











References
















6Light in Matter





159






















































































λ0 λ D hmc

(1 cos (θ )) (61)

















63 Laser Cooling











References


















71 Filaments



181










71 Filaments 183









71 Filaments 185









71 Filaments 187







41) 1 THz D 1012 Hz







71 Filaments 189







721 Lightning















































References




































8Laser Sensors


81 Passive Sensors




203





204 8 Laser Sensors












206 8 Laser Sensors











208 8 Laser Sensors








energy of

d Nd t

h2π

D d(N hν)d t

12πν

D W T2π

(81)



210 8 Laser Sensors









212 8 Laser Sensors










214 8 Laser Sensors










216 8 Laser Sensors


82 Active Sensors









218 8 Laser Sensors











220 8 Laser Sensors









222 8 Laser Sensors









References









224 8 Laser Sensors





























227







Silent Lasers




Laser Applications








References






Index



139Attosecond 160












CD 87ndash pit 88





232





Dye laser 51









gGain 11






Index 233



















ndash absorption 76

234 Index
























Index 235



















236 Index

Color Plates



237




238 Color Plates





Color Plates 239



240 Color Plates




Color Plates 241





242 Color Plates



Color Plates 243




244 Color Plates



Color Plates 245



246 Color Plates



Color Plates 247




248 Color Plates



Color Plates 249



250 Color Plates





Color Plates 251





252 Color Plates




Color Plates 253




254 Color Plates




Color Plates 255





256 Color Plates



Color Plates 257






258 Color Plates





Color Plates 259



260 Color Plates



Color Plates 261





262 Color Plates





Color Plates 263

Lasers

Contents

Preface

References




112 Photon Energy

113 Energy and Size






131 The Pump

132 Gain



141 He-Ne Lasers



144 Fiber Lasers

15 Pulsed Lasers


152 Saturation



161 Directionality

162 Intensity
















References







241 Laser Level

242 Laser Pointers


31 Introduction



















References


41 Laser Machining

411 Marking


421 Laser Welding




References


51 Introduction


53 Communication

531 Introduction


533 Multiplexing

54 Frequency Combs





References

6 Light in Matter





63 Laser Cooling

References


71 Filaments







721 Lightning




References

8 Laser Sensors

81 Passive Sensors




82 Active Sensors



References


References

Index

Color Plates

lasers: the power and precision of light

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