fVCC

THE LASER

THE LASERA Module on Modern Optics and Quantum Mechanics

FVCCGary S. Waldman, Florissant Valley Community College

Bill G. Aldridge, Florissant Valley Community CollegeA. A. Strassenburg, State University of New York at Stony Brook

Bill G. Aldridge, Project Director

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The Physics of Technology modules were produced by the Tech Physics Project, whichwas funded by grants from the National Science Foundation. The work was coordinated bythe American Institute of Physics. In the early planning stages, the Tech Physics Projectreceived a grant for exploratory work from the Exxon Educational Foundation.

The modules were coordinated, edited, and printed copy produced by the staff at IndianaState University at Terre Haute. The staff involved in the project included:

Philip DiLavoreJulius Sigler ..Mary Lu McFallB. W. Barricklow.Stacy Garrett. . .Elsie GreenDonald Emmons.

. . . . . . . . . . . Editor

. . . . . . Rewrite EditorCopy and Layout Editor

. Illustrator. . . . . . Compositor. . . . . . CompositorTechnical Proofreader

In the early days of the Tech Physics Project A. A. Strassenburg, then Director of the AlPOffice of Education, coordinated the module quality-control and advisory functions of theNational Steering Committee. In 1972 Philip DiLavore became Project Coordinator andalso assumed the responsibilities of editing and producing the final page copy for themodules.

The National Steering Committee appointed by the American Institute of Physics hasplayed an important role in the development and review of these modules. Members ofthis committee are:

J. David Gavenda, Chairman, University of Texas, AustinD. Murray Alexander, DeAnza CollegeLewis Fibel, Virginia Polytechnic Institute & State UniversityKenneth Ford, University of Massachusetts, BostonJames Heinselman, Los Angeles City CollegeAlan Holden, Bell Telephone LabsGeorge Kesler, Engineering ConsultantTheodore Pohrte, Dallas County Community College DistrictCharles Shoup, Cabot CorporationLouis Wertman, New York City Community College

This module was produced through the efforts of a number of people in addition to theprincipal authors. Laboratory experiments were developed with the assistance of DonaldMowery. Illustrations were prepared by Robert Day. John Yoder, III, coordinated art work,and he also prepared the Instructor's Guide. Reviews were provided by the members of thePhysics of Technology Steering Committee and participants in the NSF ChautauquaProgram. Finally, Wendy Chytka typed the various module drafts, coordinated prelim-inary publication efforts, and acted as a liaison person with the Terre Haute ProductionCenter where final copy was being produced. To all these persons, we are indebted.

Copyright © 1975 by Florissant ValIey Community ColIege. AII rights reserved. Printed inthe United States of America. No part of this publication may be reproduced, stored in aretrieval system, or transmitted, in any form or by any means, electronic, mechanical,photocopying, recording or otherwise, without the prior written permission of thepublisher.

Except for the rights to material reserved by others, the publisher and copyright ownerhereby grant permission to domestic persons of the United States and Canada for use ofthis work without charge in the English language in the United States and Canada afterJanuary 1, 1982. For conditions of use and permission to use materials contained hereinfor foreign publication or publications in other than the English language, apply to theAmerican Institute of Physics, 335 East 45th Street, New York, N.Y. 10017

Section ALaser Light: How It Differs from Ordinary LightIntroduction .Some Facts about Light .Experiment A-I. Observations of Light .Discussion of Experimental ObservationsInterference Patterns .The Nature of Light .Advantages of Laser LightLaser ApplicationsSummary ...

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Section BDeveloping a Model for LightSpeed of Light ..What Is Light? .A Model for Light . . . .Particle and Wave ModelsExperiment B-1. Particles and WavesWhich Model Accounts for Interference?Young's Double-Slit Experiment . . . . .Constructive and Destructive InterferenceWavelength and Color .How the Slit Separation Mfects an Interference PatternExperiment B-2. The Interference of Light .Conclusions Based on Experimental ResultsWhat about Large Angles? (Optional)Light Waves Have Short WavelengthsLight Waves Have High Frequency . .The Electromagnetic SpectrumMonochromaticity and Temporal CoherenceSpatial Coherence .Interference .Waves and HolographyWaves and CommunicationsSummary . . . . . . . . .

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Section C (Optional)An Analysis of Laser LightBandwidth .Coherence Length . . . . .Interference Requires CoherenceExperiment C-l. Spatial and Temporal CoherenceLine Spectra of GasesAtoms and Light . . . .A Model of an AtomPhotons . . . . . . . . .The Waveand Particle Nature of LightInteraction of Electrons and PhotonsSpontaneous EmissionStimulated EmissionNatural Linewidth ...Doppler LinewidthInverted Population Needed for Laser ActionOptical Pumping in Ruby Laser ..Pumping Scheme for He-Ne Laser . . .Amplification between End Mirrors . .Standing Waves in the Laser (Optional)Axial and Non-Axial Modes (Optional)Coexisting Axial Modes (Optional)Line Narrowing (Optional)Other LasersSummary .. . . . . . . . .

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Work SheetsExperiment A-IExperiment B-1Experiment B-2Experiment C-l

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The Laser

INTRODUCTION AND SPECIALPREREQUISITES

In this module, you will use the laser tolearn some of the principles of wave motion,physical optics, and modem physics.

Even though most of the conceptsneeded to understand the laser are presentedwithin the module, there are a few things youshould know to start with. These prerequisitesconcern wave motion and the concepts ofenergy, electric charge, electric potential dif-ference (voltage), and kinetic energy.

Sections A and B of the module requireonly the prerequisites on wave motion, andthese may be met by meeting the goals of TheGuitar module. Other equivalent materialcould teach you the same concepts.

The prerequisites of Section C will bemet if you have achieved goals similar tothose in The Pile Driver module and TheIncandescent Lamp module. These goals in-volve concepts of kinetic energy, potentialenergy, and thermal radiation. Several otherPhysics of Technology modules include theessential prerequisites for this module.

This module puts an emphasis on labo-ratory experience. As you come to the experi-ments, tear out the corresponding work sheetsat the end of the module and fill them out.

The following goals state what youshould be able to do after you have com-pleted this section of the module. These goalsmust be studied carefully as you proceedthrough the module and as you prepare forthe post-test. The example which follows eachgoal is a test item which fits the goal. Whenyou can correctly respond to any item likethe one given, you will know that you havemet this goal.

1. Goal: Explain the observational evi-dence for straight line propagation oflight.

Item: Why does an extended sourceproduce fuzzy shadows while a pointsource produces sharp shadows?

Goal: Know the characteristics of inter-ference patterns produced by thin films(e.g., a layer of air between two glassplates).

Item: Two optical flats in contact areilluminated from one side with a laserbeam. On the opposite side, light anddark bands appear on a screen. Whathappened to the laser light that wouldhave been in the dark bands if theoptical flats were absent?

Goal: Knowdouble- andpatterns.

the characteristics ofsingle-slit interference

Item: When a laser beam is shinedthrough two closely spaced slits, a num-ber of spots of light can be seen on ascreen. What change in the slits canreduce the number of light spots seenwithout changing their spacing?

Goal: Understand the concept of spec-tral and non-spectral colors.

Item: Is white a spectral or non-spectralcolor?

5. Goal: Know the special properties oflaser light which make it more usefulthan ordinary sources in special applica-tions.

Item: Which of the following laser lightproperties is most important in align-ment applications:

a. collimationb. powerc. pure colord. short pulse time

Answers to Items AccompanyingPreviousGoals

1. The edge of an obstacle will block eitherall or none of the light traveling instraight lines from a point source to anobservation point. With an extendedsource, the obstacle can block only partof the light to the observation point,giving a gray or fuzzy region to theshadow.

2. It appears in the reflected interferencepattern.

3. Make the slits wider without changingtheir center to center separation.

4. Non-spectral because it does not appearin the spectrum.

Laser Light: How It Differs from Ordinary Light

The laser* is a relatively new type oflight source. Invented in 1960, the laser hasbeen extensively developed since that timeand many interesting uses have been foundfor it. (Actually, although we often speak ofthe laser, there are now many different kindsof laser, having some kinds of characteristicsin common and others which are quitedifferent.)

The light from some kinds of laser canbore a hole through a sheet of metal. Lasersare already being used to weld tiny wires inelectronic circuits, to perform delicate surgeryon human eyes, to cut suit patterns intocloth, and to do many other useful things.They soon may be used to build super-fastcomputers and to send thousands of simulta-neous messages across long distances. Reflec-ted laser light has been used to measure thedistance to the moon within a few centi-meters.

In this module, you will learn how laserlight differs from ordinary light and you willuse a laser to reveal the wave properties oflight. The first laser was built in 1960 by T.H. Maiman at Hughes Aircraft Company.Energy was supplied to this first laser, whosemain component was a ruby crystal rod, by aflash tube wrapped around the rod. Figure 1shows a simplified diagram of an early rubylaser.

Ruby lasers produce light only in shortpulses. That is, light is emitted during a shortperiod of time; then no light is produced untilthe next pulse. In 1961 a continuouslyoperating laser was built by Ali lavan, at BellTelephone Laboratories. He used a glass tubecontaining a mixture of helium and neongases as the central element of the laser. Such

*The word laser is formed from the first letters ofLight Amplification by Stimulated Emission ofRadiation.

FLASHLAMP

RUBY ROD

LASER

POWERSOURCE

a continuously operating device is called acontinuous-wave (cw) laser. A schematic draw-ing of a simple helium-neon laser appears inFigure 2. Since then a great variety ofpulsed and cw lasers have been made. Theycan produce a wide range of different poweroutputs (and light of almost any color).

\..He-Ne MIXTURE.---ELECTRODES---'

There are many properties of light whichall of us have obsetved at one time or anotherin our lives. Let us list a few of the things

which may be considered common knowledgeabout light. Most of these observations arenecessary knowledge for what follows in thismodule. Some of these observations will beexpanded in the module to add to yourunderstanding of light, especially laser light.

Light travels in straight lines if theproperties of the matter through which thelight travels do not change along the lightpath, and if no obstacles or apertures areinserted in the path. What evidence do wehave to justify this statement? One commonobservation is that light casts rather distinctshadows of most objects which get in its way.For example, you can see the curve of theearth as its shadow crosses the moon during alunar eclipse. "Sharp" shadows can be castonly if light travels in straight lines. (Do yousee why?) Another way we know that lighttravels in straight lines is by observing a lightbeam from a spotlight in fog or in a smoke-filled area. As shown in Figure 3, you can seethe path of the light beam as the light isscattered by the particles of fog or smoke.

Question 1. If light travels in straight lines,how can you account for the fact that inside ahouse in the daytime with the lights turnedoff you can see your surroundings? That is,how does the sunlight, which travels instraight lines, get into all parts of the house?

Transparent, Translucent, andOpaque Materials

Another fact about light is that it can gothrough some materials and not others. Weknow that light travels through air and emptyspace (vacuum). Light also travels throughglass, water, and many other materials. Mate-rials like clear glass, clear plastics, and waterwhich let almost all the light through just as ifthe materials were not there are called trans-parent. However, light will not travel throughmany solid materials such as metal and wood.Substances which will not allow light to passare said to be opaque. Other materials, likethin pieces of paper or frosted glass, let someor most of the light through but prevent youfrom seeing the detailed shape of things onthe other side. Such materials are said to betranslucen t

Question 2. In what way is fog like atranslucent material?

Some materials reflect ("bounce" back)the light from an object in such a waythat an object in front of the reflectingsurface appears to be behind it. As you know,such a surface is called a mirror.

Another common observation may ap-pear to contradict the fact that light travelsin straight lines. When you observe a spoon

partly submerged in a cup of water as shownin Figure 4, the handle of the spOon appearsto be bent at the surface of the water. If youexperiment further with this situation, youwill find that light does travel in straight linesin a given material or medium. However,when light reaches the boundary between twodifferent materials, the light may be bent. Thisphenomenon is known as refraction.

The properties of light we have discussedin the preceding paragraphs apply to allkinds of light, including laser light. The lightin a laser beam has very special propertieswhich distinguish it from the light of ordinarysources. You will now discover some of thesedifferences by doing Experiment A-I.

CAUTION: You will be working with alaser when performing experiments inthis module. Although you are workingwith a low-power gas laser, there aresome precautions which should betaken:

1. Do not look directly into a laserbeam or its reflection from a shinysurface.

2. Since you are probably working ina lab with other students, do notpoint the beam where others mightaccidentally look directly into thebeam or its reflection.

You have been provided with two piecesof glass called optical flats. Place these opticalflats one on top of the other on a clean whitesurface. Touch only the edges and be carefulnot to touch or scratch the surfaces of theoptical flats. Now look down at the top of theoptical flats so that you see the reflection ofroom light (from a fluorescent lamp orincandescent lamp). This arrangement isshown in Figure 5. (You may have to pressthe flats firmly together, touching only theedges.)

2. Do you see colors at the edges of thebands? What colors?

Now let's see what happens when laserlight is used. Place the flats one on top of theother on the special holder. Pass the laser

IIROOMLIGHT

beam through the lens system which has beenprovided. This lens expands the laser beam sothat it can shine on a larger area. The beamshould be reflected from a mirror placedabove the optical flats so that the beamilluminates most of the surface of the flats.Place a white screen beneath the flats andposition another white screen above the flatsso that the light reflected from the flats willstrike this upper screen. Your apparatusshould be arranged as shown in Figure 6.

Next, dim the room lights so that youcan see the reflection of the laser beam on theupper screen and the transmitted portion ofthe beam (the part which passes through theoptical flats) on the lower screen.

4. Sketch the reflected pattern (seen on theupper screen).

5. How is this pattern similar to what yousaw using white light?

(f~ IOCM)LENS

PINHOLE(AT FOCAL POI NT OF LENS)

perpendicular to its surface while holding thelower flat stationmy.

8. What happens to the pattern as theupper flat is rotated?

9. Now look at and sketch the transmittedpattern (seen on the lower screen).

10. How is the transmitted pattern differentfrom the reflected pattern?

Place a pointed object (such as a pencil)lightly on the surface of the upper flat.(Better still, just hold the pencil point slightlyabove the flats.) Position the pencil point sothat it is on a bright band in the transmittedpattern. If the point is observed at more thanone position on each screen, look at thedarkest point

11. Is the pencil point then on a bright ordark band of the reflected pattern?

You should now observe the effects ofpassing light through narrow slits. You have

OPTICALFLATS

been provided a glass slide containing singleslits of various widths and pairs of slits ofvarious separations. Find a pair of closelyspaced slits. Hold the glass slide close to youreye and look through the pair of slits at afrosted light bulb about a meter away.

1. Describe what you observe. (Do you seetwo slits? Is the light uniform all the wayacross?)

2. Now use a straight-filament, clear lightbulb. Turn the glassslide so that the slitsare perpendicular to the filament; thenlook through the slits at the bulb.Describe what you see.

3. While looking through the slits, slowlyrotate the glass slide until the slits areparallel to the filament. Describe whathappens.

4. What colors do you observe? What arethe relative positions of these colors?

5. Place the red and blue filters over thebulb (Figure 7) so that the filters meetbut do not overlap. Look through thedouble slits at the bulb. Do the redbands and blue bands of light exactlyline up? Sketch what you observe.

OBSERVER~

Now place the glass slide as shown inFigure 8, so that the double slits are in thelaser beam; observe the resulting pattern on awhite screen about two meters away. (DONOT LOOK THROUGH THE SLITS AT THELASER BEAM.)

DOUBLESLIT

8. Try other pairs of slits with differentspacing between them. Sketch the pat-

terns you observe as the spacing betweenslits changes.

Next place one of the single slits in thelaser beam.

10. Use single slits of various widths. Sketchthe pattern you get for different slitwidths.

11. Place the double slits in the beam. Arethere any differences between this pat-tern and the singl~-slit pattern? What arethey?

You should now find how much a beamof light spreads out along its length. Take thelight from a small bright source, and try toproduce a narrow beam which doesn't spreadout very much. This is what a headlight does.

To do this, use the small bright source.Place a diaphragm* in front of it and adjustthe opening to about 0.5 cm in diameter.Place the lens supplied between the dia-phragm and a flat mirror as shown in Figure9. Adjust the mirror so that the reflected lightfalls back on the source itself. Now move thelens back and forth until the light reflectedback to the diaphragm produces the smallestpossible spot. Leave the lens at this positionand remove the mirror from the other side.Adjust the diaphragm until the resultant beamhas a diameter of about 2 cm. The beam oflight produced has rays which are as closelyparallel as can be obtained with thisapparatus. This beam is called a collimatedbeam, and the process you just used toachieve it is called auto-collimation.

1. At a distance of one meter from the lensplace a white screen, so that you canmeasure the diameter of the collimatedbeam.

*A diaphragm is an opaque disc which has a variable-sized hole in its center.

PLANEMIRROR

LIGHTSOURCE

2. Measure the diameter of the beam at adistance of two meters from the lens.

5. Turn on the laser and measure the diam-eter at two meters.

3. What is the ratio obtained by dividingthe measurement of step 2 by themeasurement of step I?

6. What is the ratio obtained by dividingthe measure men t of step 5 by themeasurement of step 4?

4. Measure the diameter of the laser beamat a distance of one meter from the frontof the laser.

7. What can you conclude about the differ-ence in spread between a collimated lightbeam and a laser beam?

DISCUSSION OF EXPERIMENTALOBSERVATIONS

Light sources can be classified in terms ofvarious properties such as the color andbrightness of the light produced, and so on.One very important classification is that ofextended source versus point source. A pointsource is an idealization and it occupies nospace. However, if the real source is small andthe obsetver is far away, it may be a goodapproximation to a point source. An extendedlight source, such as a frosted light bulb, or theclouds on an overcast day, does not producesharp shadows. Thus such sources cannot beused for projecting the pattern of spotsproduced by double slits, as you did with thelaser. In order for extended sources to be usedfor such experiments, it is necessary to firstpass the light through a slit to approximate aline source, which is like a point source in onedimension and an extended source in the other.This greatly reduces the amount of lightavailable for the experiment. Often it is alsoadvantageous to filter the light, allowing onlyone color to reach the slits.This further reducesthe amount of light which reaches the screen,and the pattern produced isextremely dim.

You can demonstrate the effect of anextended source yourself. Find a fixture whichhas a singlestraight fluorescent lamp in it. Holda pencil under the light, but as far away from itas you can. Obsetve the shadow produced on anearby surface when the pencil isparallel to thelamp. Then turn the pencil so that it isperpendicular to the lamp, and look at theshadow. The fluorescent lamp may be consid-ered a point source in one direction and anextended source in the other.

A point source is one which is sufficientlysmall and/or far away so that all of the lightfrom the source appears to come from a point.We may also define a point source in terms ofeffects which can easily be seen or measured.One effect is, at least for large objects, that apoint source willcast a sharp shadow. Any lightsource behaves as a point source if it issufficiently far away. The stars are point

sources by this definition, and even the sunmay be considered a point source for someobsetvations. A frosted light bulb about ameter away from you definitely is not a pointsource (as you might have discovered inExperiment A-I).

We know that visible light includes avariety of colors. Generally we think of the

.color of light as. a property of the source ofthe light or of the object which we see byreflected light. To some extent this is true.Different sources do give off different colorsof light, and different objects do appeardifferently colored when seen in the samelight. However, color is really a sensationcaused by the light which is detected by oureyes. Therefore, color has as much to do withhow we perceive the light as it does with thelight itself. Later, we will define a quantitywhich corresponds to the color of the light.We must be careful to remember, however,that "color" is primarily a physiological andpsychological process in the eye and brain.

In experiments like that with the double-slit apparatus, "white" light sources createdpatterns in which colors were visible at theedges of the bright bands. The laser producedsimilarly shaped light and dark patterns ofone color. Such results suggest that the singlecolor (monochromatic) light of a laser mightin some way be simpler than white light.

In the seventeenth century Sir IsaacNewton (1642-1727) proved with a simpleexperiment that white light is a combinationof light of various colors. He passed a narrowbeam of sunlight through a prism, as shown inFigure 10.

As it passes through the prism, the whitelight is spread out into a band of colors: red,orange, yellow, green, blue, violet. This bandof colors is called a spectrum, and the colorsare called spectral colors. Some colors, such astan and pink, can be produced by mixingspectral colors, but they appear nowhere in

NARROWBEAM OFSUNLIGHT

WHITESCREEN

the spectrum. They are therefore called non-spectral colors. For example, the non-spectralcolor purple is ~ mixture of the spectral colorsred and blue. To assure that the color was notadded by the prism, but was actually presentin the white light, Newton refined the exper-imen t further as shown in Figure 11.

When the light from the first prism ispassed through a second prism, white lightagain emerges from the other side. Further-more, passing anyone of the spectral colorsthrough a second prism does not further changeits color. These experiments lead to the

conclusion that white light is composed of allthe colors of the spectrum. The prism bendsdifferent colors by different amounts toproduce the separation of colors observed. Thephenomenon of different colors bending bydifferent amounts is called dispersion. We canconclude that "white" is the sensation pro-duced by all of the spectral colors properlymixed together. As you may know, thesensation of white light may also be producedby properly mixing only three colors, like red,green, and blue, as used in color television.

Question 3. What non-spectral colors are you .familiar with?

Question 4. Could a mixture of two spectralcolors produce another spectral color? Why orwhy not?

The colored patterns produced whenwhite light was used in certain parts ofExperiment A-I were not due to dispersion.They arose, however, because white light is amixture of colors. The colored patterns can bethought of as the display of many differentmonochromatic patterns, each similar to thatproduced with laser light.

The previous discussion does not explain.the observed alternating light and dark patternsproduced by the double slits. Many people findthese alternating light and dark bands partic-ularly surprising. Why are there not just twobright bands coming through the two slits? Wecan only say at this point that the behavior oflight is more complex than one might guessfrom everyday observations of light andshadows. Only detailed observations, similar tothose you have done in the first experiment,can lead to a more basic understanding of light.

The single-slit pattern is also unexpected.In this case there is a bright band in the center,

and a number of smaller light bands on eachside.

Both the single-slit and double-slit pat-terns you have observed suggest that lighthas a tendency to spread out into areas whichyou would expect to be in shadows. Thesmaller the opening through which the lightpasses, the greater the spreading. The bendingof light around sharp edgesinto shadow areasiscalled diffraction. It is always present, butusually ishard to see.

Question S. Look at a distant street lightthrough a fine-mesh screen or through a linenhandkerchief. Describe the pattern you see.Are there similarities between this pattern andthe double-slit pattern you observed with alaser source? What are the major differences? Inwhat ways does the pattern change when youlook first at a mercury-vapor light (bluish-white) and then at a sodium-vapor light(yellow)?

In many lasers conditions are present forproducing a nearly perfect parallel beam. Sucha beam is said to be collimated. The fact thatthe divergence of a laser beam is extremelysmall is a feature which has a wide variety ofapplications. The slight spreading that doesoccur in a laser-spreading whichyou measuredin Experiment A-I-is similar to single-slitdiffraction. The edges of the laser tube itselfbehave as a slit opening and thus diffractionoccurs.

The light and dark patterns you haveseen are interference patterns of light. Ingeneral, interference patterns are produced bycombining two beams of light which origi-nally came from the same source. In theexperiments using flat glass plates, the lightfrom a source was split into two parts. Then itwas recombined by being partially reflected

and partially transmitted at each side of theair film between the plates. In the double-slitexperiment, the light was split by allowingonly a part of it to pass through each opening;it recombined because of its own naturaltendency to spread on the other side of theslits. White light interference patterns aremulti-colored, and they have the same generalshape as monochromatic light patterns. Mono-chromatic light is a component of white light.It is much easier to get bright, clear interfer-ence patterns with laser light than with lightfrom ordinary white light sources, even if thelatter is passed through a color fl1ter.

Diffraction, the tendency of light tospread out into shadow areas, is particularlyeasy to see using laser light. In the absence ofother optical components, it is often the mainreason for the spreading of the laser beam. Inspite of diffraction, laser beam collimation isgenerally much better than one can obtainwith ordinary light sources.

Many of the properties of laser light,such as a single spectral color, clearer inter-ference patterns, and better collimation,suggest that laser light is somehow simplerthan light from other sources.

In general, pulsed lasers are more power-ful than continuous (cw) lasers. The highpower of pulsed lasers results from the factthat, in a pulsed laser, a substantial amount oflight energy is emitted in a very short time.Early ruby lasers typically had output powersof several kilowatts, with pulse times ofseveral milliseconds. Later versions of rubylasers have produced pulses of energy lastingfor times as short as a nanosecond (ns,

-910 second). The average power in such ashort pulse can be as much as hundreds ofmegawatts.

Typical output powers of cw He-Nelasers likely to be used in the classroom areabout one milliwatt or less. However, cwlasers have been made using carbon dioxide as

the active material that produce an invisiblebeam of infrared light with power as high asten kilowatts.

The power density (power per unit area)which can be attained with lasers is even moreimpressive. This is because the simple, purenature oflaser light allows one to focus it into

-4 2unusually tiny areas as small as 10 cm. A10-kW beam focused onto that area wouldproduce a power density of 108 W/cm2

•

Such extremely large power densities canmelt or even vaporize most materials. Conse-quently lasers have been used to drill tinyholes or make small welds. One example is theuse of a pulsed laser to drill holes in diamondsfor industrial purposes, cutting the time re-quired from two days for previous methods totwo minutes. Another example is the use of acw carbon-dioxide laser to automatically cuttailor-made suits, reducing the time over handlabor by a factor of 20. Lasers may soon beused to read codes on items at the grocerystore, so that bills can be automaticallytotaled.

Properties of laser light have been usedin a number of medical applications. Forexample, tiny "spot welds" can be made inthe eye to correct a condition known as"detached retina." The retina is the light-sensitive surface at the back of the eyeball.Under certain conditions the retina can peelaway from the eyeball, causing blindness. Aburst of laser light into the eye and focusedon the retina will produce a tiny scar whichprevents further detachment. The treatment iseffective, painless, and requires no hospital-ization. Another possible medical applicationtakes advantage of the fact that dark materialsabsorb more light than do lighter materials.Skin cancers, which are darker than healthytissue, may possibly be destroyed with large

laser pulses. The same principle may be usedto "drill" decayed teeth, since the decayedarea is darker than the healthy tooth. Laserpulses are focused on the decayed area of thetooth. The darker decayed part absorbs thelaser light and is vaporized without heatingthe healthy part of the tooth.

It might seem that these destructiveproperties of the laser could be used forweaponry. Although this aspect of lasersseems to have fascinated movie and televisionscriptwriters more than others, it is not a verypromising area. Once it appeared to some that"laser guns" might have significant advantagesin anti-ballistic missile defenses because the"light bullet" would reach the target ex-tremely fast. Because of this speed, therewould be no need for the complicated compu-tations that are required if a slow projectile isto be launched at a moving target. However,tremendously powerful lasers are needed todo even a small amount of damage in the lab,and the emitted light is affected by atmo-spheric conditions. Fog or clouds or even dustin the air may quickly reduce the laser beamto a harmless intensity. As for putting holes inpeople, James Bond notwithstanding, ordi-nary metal bullets are much cheaper and workin all weather. There is still the possibilitythat large, pulsed lasers could be used asblinding weapons, since the eyes are muchmore susceptible to damage from light thanthe rest of the body, but other weapons usesare still highly speculative.

Besides using lasers as weapons, there aremilitary applications which overlap with civil-ian applications. A laser beam can be used toilluminate a target for a guided missile. In thiscase, a very precise color fIlter in front of themissile's sensor will block essentially every-thing from its view except the laser light.Laser pulses used for range-finding ("laserradar") have both civilian and military use. Ashort pulse of light is reflected from an object

and the distance to the object is computedfrom the time it took the pulse to get thereand back. A pulse of one nanosecond dura-tion is only about one foot long, since lighttravels about one foot per nanosecond. Thispulse length allows range measurements toone foot accuracy. The technique has beenused to measure the distance to the moon towithin six inches. The laser beam is trans-mitted through a large telescope to a reflectorpackage left on the surface of the moon bythe Apollo 11 astronauts. A tiny fraction ofthe reflected beam is observed in the sametelescope back on earth.

For military applications, the narrowbeam of an infrared laser can be aimed muchbetter and is less likely to be detected thanthe beam from a conventional (microwave)radar set.

An even simpler use of the laser is foralignmen t. The beam from a cw laser makes astraight line for lining up equipment. A laserwas used to align equipment digging a tunnelunder San Francisco Bay for a new rapidtransit system. Likewise the two-mile-longlinear particle accelerator at StanfordUniversity is kept in a straight line with theaid of a laser beam.

One of the most spectacular applicationsof lasers has been their use in a three-dimensional photographic technique calledholography. Holography was invented in1947, considerably before the laser, by theEnglish physicist Dennis Gabor. However, thespecial properties of laser light makeholograms easier to produce and more impres-sive. It is difficult to explain the techniquefully, but a hologram is a photograph of aninterference pattern, with laser light reflectedfrom a scene. When the hologram is illumi-nated with laser light, a striking three-dimensional image of the original scene isproduced. This process could have obviouspoten tial uses in entertainment andadvertising. Other possible uses will be dis-

cussed after you have learned more aboutlight The best way to appreciate the remark-able properties of holograms is to look at one,if one is available.

The following statements summarize theconcepts, definitions, and principles you havelearned so far in this module.

The word laser is formed from the firstletters of light amplification by stimulatedemission of radiation.

In a given material, and in the absence ofobstacles and openings, all light, includinglaser light, travels in a straight line.

A translucent material is one whichallows some light to travel through it, butdoes not permit one to see clearly details ofthe light source on the other side.

A transparent material is one whichallows most light to pass through it so thatobjects on the other side are clearly seen.

An opaque material is one which doesnot allow light to travel through it.

In general, light changes direction as itcrosses a boundary between two transparentmaterials. This phenomenon is calledrefraction.

Color is a sensation in the brain and is acombination of a property of the light and ofthe physiological and psychological process inthe eye and brain we call seeing.

A point source of light is one which iscapable of producing sharp shadows of largeobjects. Alternatively a point source is anylight source which, compared to its size, is avery large distance from the observer.

A collimated light beam is one whichdoes not diverge.

Monochromatic light is light of a singlecolor.

White light is a combination of all thecolors in the spectrum. The sensation of whitelight can also be produced by a combinationof other colors.

The fact that different colors bend dif-ferent amounts when crossing a boundarybetween two different transparent materials iscalled dispersion.

A color filter is any material which isopaque to some colors and transparent to anarrow band of colors.

The alternating pattern of bright anddark bands produced when two light beamsare brought together is called an interferencepattern.

When light travels through very smallopenings or encounters small objects in itspath, it is diffracted and produces an inter-ference pattern (also often called a diffractionpattern).

The following goals state what youshould be able to do after you have com-pleted this section of the module.

1. Goal: Understand the implications ofthe wave and particle models of light.

Item: What would be the expectedresult in a double-slit experiment usingthe particle model if you widened bothslits without changing their separation?

2. Goal: Understand the correspondenceof wavelength to color.

Item: If the light emitted by a helium-cadmium laser has a wavelength of442 nm, what color will it be?

3. Goal: Know the relationship betweenthe angular separation of the bright spotsin Young's double-slit experiment, thewavelength of the light, and the slitseparation.

Item: Light from a helium-neon laser(A.= 633 nm) is shined through a pair ofslits and produces an interferencepattern with an angular separation of

4. Goal: Be able to calculate the frequencyof light whose wavelength is given.

Item: What is the frequency of lightfrom the laser in Item 3?

5. Goal: Understand the wave modelexplanation of temporal and spatialcoherence.

Item: What temporal coherence con-dition on the waves passing throughdouble slits is necessary for an inter-ference pattern?

Answers to Items AccompanyingPreviousGoals

3. 2.11mm

4. 4.74 X 1014 Hz

5. Wave trains must have a fixed relation-ship from one crest to the next.

Developing a Model for Light

Light originates at a source such as thesun, a flame, or a lamp. It travels away fromthe source and falls on objects. When lightstrikes an object, it can cause a temperatureincrease in the object, it can induce a chemi-cal reaction (e.g., photosynthesis), or it canproduce other effects. Light can enter oureyes directly from the source or after reflec-tion from objects about us. When light entersour eyes, we "see." Seeing is largely respon-sible for our impressions of the shapes andcolors of things in our environment.

Although light travels very fast, we knowthat some time always elapses between theinstant light leaves a source and the instant itstrikes an object. Several ingenious methodshave been devised for measuring the speed atwhich light travels. The simplest of these(although not necessarily the easiest) is tomeasure a very large distance carefully, andthen measure the time required for light totravel that distance. The speed of light is thensimply the distance traveled divided by thetime required to travel that distance. Inempty space, the speed of light has beenfound to be 2.997925 X 108 meters persecond (3 X 108 mls ~ 186,000 mils).

Despite the fact that most of our percep-tions of the world around us involve light andthe sense of sight, light is not easy to study orunderstand. We cannot catch it, inspect it, ormanipulate it the way we can a piece of mat-ter. Perhaps we can better understand thedifficulty in determining what light is byconsidering the following situation. YouobseIVe two people tossing some object backand forth between them. The object is movingtoo fast for you to see what it is, but youwould like to examine it. You step in and

catch the object and closely examine it. Let'ssay it turns out to be an ordinary baseball.The baseball in your hand is exactly the samebaseball that was previously being tossed. Themotion of the baseball had nothing to do withits being a baseball.

We would like to examine a light beamin the same manner, so we step in and"catch" the light beam in some appropriatematerial. As soon as we stop (absorb) it, weno longer have a light beam. We may havesomething else-heat, for example-but wedon't have light. The motion of light is anintrinsic part of light. Without motion, lightdoesn't exist.

We cannot answer the question of whatlight is in this module, but we can learn agreat deal about it. Wewill probe more deeplyinto the behavior of light, and try to predictits effects. We also wish to reveal any connec-tions that might exist among the seeminglyunconnected phenomena we obseIVe.In orderto do this we will try to develop a set ofsimple concepts that will help us to visualizewhat light is and how it behaves. Such a set ofideas is often called a model. A model issomething people invent, thus a model forlight is not light itself. Light reveals its truecharacteristics only through its observedbehavior. In fact, the model we create mayvery well have some flaws in it which we canrecognize but not know how to fix. Neverthe-less, the model may help us to construct a setof mathematical equations that describe andpredict the things that light does.

The model plus the set of equationsconstitute a theory. Because of their inter-pretive and predictive power, theories are veryuseful, though they must be discarded ormodified if facts are discovered that areinconsistent with them.

Models of various kinds have playedextremely powerful and useful roles inscientific thought. They have also proved tobe tricky in many respects. For example,some models have proved to be consistentwith limited ranges of measurements.

We shall develop a model for thebehavior of light that has proved to beextremely useful in the range of macroscopicphenomena. In this module macroscopicimplies situations like those we explored inthe first part of this module, where lightinteracts with objects of substantial size suchas reflecting and refracting boundaries, slits,gratings, films, etc. When it became possibleto study the interaction of light with matteron a much smaller, microscopic scale (Le., theinteraction between light and atoms, mole-cules, electrons), it was found that a differentmodel was needed to interpret that new rangeof experience.

Since light seems to involve some kind ofmotion, we shall refer to those kinds ofmotion with which we are familiar in every-day experience.

We know that light carries energy fromone place to another, and so far no one hasdiscovered or thought of any way to moveenergy that does not involve either themotion of matter (particles) or the propa-gation of a disturbance in matter without anyflow of matter (waves). Does light behave like

a stream of particles flowing from one placeto another, colliding with and bouncing offobstacles as billard balls do? Or can we betterunderstand the way light behaves by thinkingof it as a wave? Our job is to try to predicthow light would behave if it were either astream of particles or some kind of wavemotion. We must then compare these predic-tions with experimental observations, to deter-mine which model fits the facts-if either does.

The two models we have mentioned, theparticle model and the wave model, are by nomeans new ideas. As long ago as the seven-teenth century, both were offered as explana-tions of the behavior of light. Many eminentscientists of the day strongly supported thewave theory, and other equally eminent scien-tists argued strongly for the particle theory.In order to decide between two models, onemust design an experiment whose outcome ispredicted differently by the two theories.Then if the experiment is done carefully, theresults from the actual performance willdecide which model may be accepted. Eventhen, the model may be changed by newinformation.

You may now obselVe some of thebehavior of waves and particles, and comparethis with your earlier obselVationsof light.

In this experiment you will study thebehavior of particles and of waves and com-pare results with those for the behavior oflight In order to study particles, you havebeen provided with a box containing severalsmall, spherical particles and several compart-ments in a row along the bottom of the box.This apparatus is shown in Figure 12. Severalstrips with single or double holes (analogousto slits) are also provided. These strips can beplaced in the box. Select the strip with themost widely spaced pair of holes. Insert thisstrip through the slot on one side of the boxand center the holes in the box. Turn the boxupside down and shake it to get all of theparticles in the upper portion of the box.

ROTATE ABOUTTHIS LINE

Now, turn the box upright by rotating itabout an axis parallel to the strip with theslits (keep the strip horizontal). Let theparticles fall through the slits. (It may benecessary to tap the front of the box to getthe particles to fall.)

1. Make a bar graph that shows the heightof the column of balls found in eachcompartment.

2. Is the number of balls in the compart-ments between the slits larger than or

smaller than the numbers in adjacentcompartmen ts?

Now change the strip in the box to onewith the two slits closer together. Repeat theabove procedure.

3. Make a bar graph showing the newdistribution of balls in the compartmentsalong the bottom of the box.

4. Did the distance between the two tallestbars on your graph increase or decreaseafter the slits were placed closer to-gether?

Replace the strip with the one having thelargest single slit. Repeat the procedure in 1and 2.

5. As before, show the distribution ofparticles along the bottom of the box.

Change the strip to the one having thenarrowest single slit. Repeat the procedure in1 and 2.

6. As before, show the pattern of particlesalong the bottom of the box.

7. Did the pattern become wider or morenarrow as the slit width became smaller?

In order to examine the behavior ofwaves, you will use a ripple tank arranged asshown in Figure 13. With the ripple tank, wecan produce water waves and observe theirbehavior. Water waves are similar to otherkinds of waves in many respects, and they areeasy to observe. We study them here as atypical kind of wave.

Turn on the lamp above the tank andlook at the white screen under the rippletank. Using an eye dropper, release a drop ofwater so that it falls in the center of the tank.

RIPPLETANK

7

Observe the resulting waves on the screen.You should see light and dark rings movingaway from a center. This center correspondsto where the drop hit. If the rings are notdistinct, lift up the screen until the rings areclearly seen on the screen. The light ringscorrespond to regions where the water isdeepest (wave crests) and the dark ringscorrespond to regions where the water is mostshallow (wave troughs).

You have been provided with a straight-wave generator. This generator consists of astraight piece of wood with a motor attached.Put the wood in the water and connect themotor to the battery . You should thenobserve straight waves moving away from thewave generator. Adjust the supports for thewave generator to give the straightest waves.Place three barriers about 10 cm in front of,and parallel to, the wave generator, as shownin Figure 14. The center barrier should beabout 3 cm long and the width of the slitopenings about 1 cm.

This arrangement provides a pair of slitsthrough which the waves can pass. Thus it isanalogous to the two-hole arrangement in theparticle experiment and to the two-slitarrangement in the light experiment.

Sketch the pattern of waves seen on thescreen beneath the ripple tank. Do thisfor waves on both sides of the barrier.The following questions will refer to theside of the barrier away from the wavegenerator.

2. Look at the surface of the water andidentify the areas of maximum andminimum wave activity. Then identifythe corresponding areas on your sketch.

3. Is the region along a line which isequidistant from the two slits one ofmaximum or minimum wave activity?

4. Draw a line along the central region ofmaximum wave activity (which is calleda maximum). Draw a line along theadjacent region of minimum waveactivity (which is called a minimum).Then draw another line along the maxi-mum which is next to this minimum.Label each of these latter two lines andmeasure the angle which each line makeswith the central maximum line.

Change the distance between the slits byreplacing the center barrier by another barrierof a different length. Then readjust the outer

WAVEGENERATOR

// ·~~~tt:!!r=r t!f1!f t!1!f!·ftff ·ff frr:!~t\ ...~'•.\

j I \ \ ,

/ \ \ \

\

barriers so that the width of each slit is thesame as before.

5. Is the pattern seen on the screengenerally the same as before? In whatways is it different?

6. As before, draw a line along the centralmaximum, the first minimum, and thenext maximum. Measure the angles eachof the latter two lines makes with thecentral maximum line.

7. How did the "spread" (the angles be-tween lines drawn along adjacentmaxima) of the pattern change as thedistance between the slits changed?

Reduce the speed of the motor. Thisreduction of motor speed increases the dis-tance between successivewaves. (The distancebetween corresponding points on successivewavesis called the wavelength.)

8. What effect does changing the wave-length have on the double-slit pattern?

Remove the center barrier and move theouter barriers to produce a single slit of about10 to 15 cm width.

narrower slit (about 5 cm). Sketch thepattern.

11. Did the pattern become wider or morenarrow as the slit width became smaller?

12. Place the barriers very close together(about 1 cm separation). Sketch the pat-tern as seen on the screen.

13. Do you see areas of maximum andminimum wave activity?

Look at the results obtained with light inExperiment A-I, Part II. Compare thoseresults with the observations of this experi-ment.

1. When light passes through narrow slits,do you think it is behaving as particles orwaves?

2. Why? (For example, compare the rela-tive intensities of laser light at and nearthe center of a screen for a double-slitpattern with your answers to Question 2,Part I, and Question 3, Part II. Orcompare the way the width of thecentral light band in a single-slit patternvaries with slit width and your answersto Question 7, Part I and Question 11,Part II of Experiment B-1.)

WHICHMODEL ACCOUNTS FORINTERFERENCE?

If you now compare observations ofExperiment 8-1 with those from ExperimentA-I, you should be able to decide whether thewave model or the particle model bestexplains interference. Your experience withwater waves in the second experimentindicates that an interference pattern isformed when waves pass through two smallopenings. This pattern is formed by theoverlapping of the two sets of waves createdby the two slits. The interference patternspreads out when the two slits are movedcloser together. This same behavior wasobserved with laser light in Experiment A-I.On the other hand, the particle modelpredicts that just two spots of light would beproduced by the particles coming through thetwo slits. We may therefore conclude that thedouble-slit experiment strongly supports theidea of a wave model oflight.

The double-slit experiment was one of thecritical experiments which led to theacceptance of the wave model of light. Allthrough the eighteenth century, a particlemodel of light was widely accepted, primarilybecause of the great influence of Newton.However, early in the nineteenth century, anumber of interference experiments andcalculations by the English scientist ThomasYoung (1773-1829), and the French scientistAugustin Fresnel (1788-1827), changed theopinions of many. The double-slitexperiment, first performed by Young, isoften called Young's experiment.

CONSTRUCTIVE AND DESTRUCTIVEINTERFERENCE

Young's explanation of the double-slitinterference pattern can be understood withthe aid of Figure 15.

In this figure, the straight lines to the leftof the slits represent wave crests as viewedfrom the top. As the straight waves strike the

double slits, the waves diffract and spread outfrom one slit as semicircular waves. Thispicture is much like the water-wave patternobtained in Experiment B-1. In Figure 15, weare assuming that a straight-wave crest (ortrough) hits both openings at the same timeand that the two circular waves which formthen spread out in the region beyond the slits.That is, each opening acts as a new source ofcircular waves. A circular-wave crest emergesfrom the upper slit at the same time thatanother circular-wave crest emerges from thelower slit. As these waves move away fromthe slits, they overlap everywhere. Theoverlapping waves from the two slits interferewith each other to produce a characteristicpattern. Where crest and crest (or trough andtrough) meet, constrnctive interferenceproduces a larger crest (or a deeper trough).Correspondingly, where crest and troughmeet, destructive interference produces can-cellation of the wave. Although the wavesare continuously moving through the rip-ple tank, the pattern of destructive andconstructive interference does not move. (Forexample, there is always constructive

interference along the perpendicular bisectorof the line connecting the two slits.) As younoticed in Experiment B-1, increasing thewavelength of the waves spreads out theinterference pattern.

Question 6. Using the particle model, wouldyou expect the center of the double-slitpattern to be brighter or darker than theplaces immediately to each side of the center?What does the wave model predict? Does theparticle model predict more than twomaxima? What about the wave model? Howdo these predictions compare with yourobservations of light made in ExperimentA-I?

The results of Experiment A-I andExperiment B-1 have a number ofimplications for light. The appearance of aninterference pattern, when light passesthrough two slits, rather than two spots oflight, indicates that light is behaving likewaves instead of like particles. The brightspots in the pattern occur at positions ofconstructive interference, where the resultantwave is large, and the dark spots are at thepositions of destructive interference, wherethe resultant waves are very small. Theinterference pattern observed in ExperimentA-I for blue light, where the bright spots werecloser together than for red light, suggests

that blue light has a shorter wavelength thanred light. Let us assume that differentwavelengths of light give rise to differentcolor sensations. Since red and blue are at thetwo ends of the visible spectrum, it is logicalthat the color red is caused by the longestwavelength we can see, and the color violet bythe shortest. All the other spectral colorsperceived are then produced by intermediatewavelengths. Then a prism separates whitelight, which is a mixture of all visiblewavelengths, into all the spectral colors whereeach color corresponds to a certainwavelength of light. A non-spectral color isone that does not correspond to a singlewavelength (actually a "single wavelength" isalways a small interval of adjacentwavelengths). Non-spectral colors aremixtures of somewhat widely separatedwavelengths.

Question 7. Would you expect light of asingle wavelength to give rise to the sensationof brown? Why or why not?

HOW THE SLIT SEPARATION AFFECTSAN INTERFERENCE PATTERN

You have already seen that changing theseparation between two slits affects aninterference pattern. You can discover therelationship between slit separation and theangles between a maximum and the centralmaximum in an interference pattern by doingExperiment B-2.

For this experiment you will need theglass slide containing different single anddouble slits which you used in ExperimentA-I. The slide contains a number of doubleslits; the separation between the two slits ofeach pair is different. You will need to knowthe separation in each case. This informationmay be given to you by your instructor, or hemay ask you to measure slit separations withan appropriate instrument, such as a travelingmicroscope.

Place the narrowest set of slits in a laserbeam and observe the pattern on a screenplaced two meters from the slits. Figure 16shows this arrangement as seen from above.

GLASSSLI DE

r-= D=2m

82LASER-BEAM

The lines from the double slit representthe light paths leading to bright spots in theinterference pattern. The numbers 0, 1, and 2are placed where the various spots appear onthe screen. The Greek letter theta (0) is usedto represent the angle between the line to thecentral bright spot, labeled 0 on the screen,and the line for any other bright spot in thepattern. For example, the angle O2 is shownfor the second bright band from the center ofthe screen. The angle between lines Corre-sponding to each of the bright bands islabeled D.O. The Greek letter delta (D.) is usedto represent "a change in" some quantity; inthis case, in an angle.

Since the angular separations, D.O, arequite small, the angle (in radians) may becalculated by dividing the distance a (inmeters) between the bright bands on thescreen by the distance D from the slits to thescreen (2 m).

3. What is the distance d between the slitsin meters?

Repeat the above procedure for threemore pairs of slits with different values of d.Record your data in the table in the worksheets at the end of the module.

If D.O decreases as d increases, onepossible relationship is that D.O is proportionalto lid. To test for this relationship calculatethe values of lid and record them in the tablein the work sheets. (From now on we will usethe symbol "m" to represent "meter" and"m-1

" to represent "reciprocal meter"(l/meter).

Plot a graph of D.O on the vertical axis\

and lid on the horizontal axis.

6. Draw the best straight line through yourpoints which passes through the origin.(If this relationship is really a propor-tionality, the line must go through theorigin.) Calculate the slope of the line.

CONCLUSIONS BASED ONEXPERIMENTAL RESULTS

In Experiment B-2 you discovered therelationship between the angular separation,118, of two adjacent spots in an interferencepattern (diffraction pattern), and the separa-tion between the slits, d. This relationship, forsmall angles, is expressed as

where 118 is the radians and d is in meters.The constant in Equation (I) is a very smalllength, about 6 X 10-7 m. Since increasingthe wavelength in a double-slit experimentspreads out the interference pattern (increases118), then the constant must have somethingto do with wavelength. As a matter of fact,the constant is the wavelength. Equation (1)can be used as a defmition of wavelength. Ifwe let the Greek letter lambda (A) stand forthe wavelength, and substitute A for theconstant in Equation (l), we obtain

This formula is valid for small angles (11() lesso

than about 10 ).

Problem l. When a light source which emitsviolet light is used to produce a double-slitpattern, the bright bands are found to beseparated by 0.40 cm. If the screen is 2.00 mfrom the slits, and the slit separation is0.20 mm, what is the wavelength of this violetlight? (Note that we can calculate very smallwavelengths from measurements of the muchlarger distances of interference patterns.)

WHAT ABOUT LARGE ANGLES?(Optional)

What is the correct equation for theseparation of bands when the angle 8 is large?Although we do not have time in this sectionof the module to examine the case experi-mentally for larger angles, we can describe theresults of such experiments. For any double-slit interference pattern, the relationship

between wavelength slit separation and angleof "spread" is found to be given by

Here the angle 8 is measured from the centralbright spot to the first adjacent bright spot.The correct relationship for the sixth,seventh, or Nth bright spots, for instance,would be

N = 0 refers to the central bright spot, N = Irefers to the first adjacent bright spot oneither side of the central spot, N = 2 refers tothe next spot, and so forth.

This equation may be represented in adifferent form by multiplying both sides by d,giving

A, d, and 8 have already been defmed, and N,the number associated with each bright spot,counting from the central bright spot, iscalled the order of that spot.

Problem 2. Sound is a wave which travelsthrough air and other materials. Suppose thatthe wavelength of a certain pitch of sound is80 cm. What separation would you needbetween two "slits" to produce an inter-ference pattern of sound with a first ordermaximum at an angle of 300 with respect tothe central maximum?

UGHT WAVES HAVE SHORTWAVELENGTHS

We conclude that light behaves likewaves, and that this behavior is clearly shownby the formation of interference patterns.What sort of wave is light? For example, whatis it that causes the light to move from oneplace to another? Such questions are verypuzzling. For now, we simply note that nomaterial seems to be necessary, since lightcrosses the empty regions of outer space.

Different wavelengths of visible light are

seen as different spectral colors. The wave-lengths for visible light are quite small, forexample, about 6.5 X 10-7 m for red light,and the wavelength of blue light is about4.5 X 10-7

ffi.

Problem 3. The prefix nano means 109•

Express the wavelength of violet light innanometers (nm). Do the same for the wave-length of red light.

The small wavelength of light and itshigh speed imply a very high frequency forthe light waves. The sreed of light in emptyspace is about 3 X 10 m/s. We can use thewave relationship which connects the speed,wavelength, and frequency of any wave, tofmd the frequency v of a light wave*

For green light, with A = 500 nm, solvingEquation (5) for v

3 X 108m/s =0.5 X 10-6m

This result means that six hundred trillionwaves per second are emitted by the sourceand, correspondingly, six hundred trillionwaves pass a given point in the path of thislight every second.

Problem 4. Find the frequency of deep violetligh t. Which has the higher frequency, redlight or violet light?

The small wavelength of light was animportant reason why its wave propertieswere not discovered for a long time. Thevisible spectrum ranges from about 700 nm

*The Greek letter nu (v) is commonly used forfrequency.

(red) to 400 nm (violet) in wavelength. Actu-ally, we know now that the visible spectrum isjust a small part of a much larger electro-magnetic spectrum. Light is one type ofelectromagnetic wave; all electromagneticwaves travel at the same speed in emptyspace, c ~ 3 X 108 mis, and they are identicalexcept for wavelength. Our eyes respond onlyto those wavelengths we call light. Figure 17is a diagram of the electromagnetic spectrum.

The wavelengths of light from availablelasers extend into the ultraviolet and infra-red portions of the spectrum. Table 1 is ashort listing of the more common laser mate-rials and wavelengths.

Table I.Laser Materials and Wavelengths

RubyHelium-NeonNeodymium in glassGallium ArsenideCarbon DioxideArgonArgonHelium-Cadmium

694.3632.8

1060840

10,600488514.5442

MONOCHROMATICITY AND TEMPORALCOHERENCE

Any laser produces light which is verynearly a single wavelength. Light of a singlewavelength is called monochromatic light.Truly monochromatic light does not exist.However, the term is also applied to lightwhich has a very narrow spread of wave-lengths. In this sense, laser light is monochro-matic. Ordinary light sources may be madenearly monochromatic by using good fIlters.However, the filtering of such a sourcereduces the use able light output to a levelwhich is extremely low. Laser light does notrequire fIltering; it is nearly monochromaticand very intense.

The monochromaticity of laser light isclosely related to another important property

104 106 108 10'° 10'2 1014 10'6 10'8 1020 FREQUENCY(Hz)

AM.FM radio and micro- infra- ultra- gammaTel ev, s ion wa ves waves red violet x- rays rays

1014 10'2 1010 108 106 104 102 10° 10-2 10-4 WAVELENGTH(nm)

called temporal (time) coherence. To say thatlight has temporal coherence means that thelight waves emitted by a source at one timehave a fixed relation to the waves emitted at alater time. As indicated in Figure 18, tempo-rally coherent light is in the form of longwave trains, instead of shorter, unrelated wavepulses.

Suppose, for example, that you could sitand watch waves move past some point inspace. If the waves possess temporal coher-ence, then the time between passage ofsuccessive wave crests is always the same. Asimilar statement can be made about the timeof passage of any other part of the wave, suchas wave troughs. If the waves do not havetemporal coherence, the time from crest tocrest will vary. If we could start at a crestwith light which does not possess temporalcoherence, and wait a whole number ofperiods as the wave passes by, we would be aslikely to arrive at a trough or any other pointon the wave as we would a crest.

400 WAVELENGTH(nm)

Laser light possesses another kind ofcoherence which light from an ordinarysource does not have. It is called spatialcoherence (coherence in space). Spatial coher-ence means a fixed relationship betweenwaves that are in different regions of space.For example, one might imagine two parts ofa laser beam as they pass through differentpoints of a plane which is perpendicular tothe beam. Then, the two parts of the beammay pass through the plane in such a way thatboth have crests (or troughs) at the plane atthe same time. In that case, the two waves aresaid to be in phase, and spatially coherent. Ifthe crest of one wave passes the plane everytime a trough of the other wave passes, thetwo waves are said to be out of phase. Theyare still spatially coherent. If the phaserelationship (relationship between the crestsand troughs of one part of the wave and thoseof the other part) remains the same for someperiod of time, the waves are said to possesstemporal coherence for that period of time.The period of time during which the wave istemporally coherent is called the coherencetime.

Figure 19A shows two waveswhich haveboth temporal and spatial coherence passingthrough a plane in phase.

Figure 19B shows two waveswhich haveboth temporal and spatial coherence passingthrough a plane out of phase.

If there is no fixed relationship betweenthe light at two separate points of. the plane(i.e., no relationship that persists for longerthan the time of a simple wave cycle), thelight is spatially incoherent. However, inco-herent light tends to "smooth out" as itmoves away from the source. This can beunderstood by considering the wavefronts ofthe light. For a wave which consists of manysmall pieces, the adjacent crests (or troughs)can be connected together to form a surface,as indicated in Figure 20A. If this surface is aplane, the wave is called a plane wave. Ifwavefronts are constructed through successivecrests, the result is a set of parallel surfaces

separated by one wavelength and movingtogether, as shown in Figure 20B. To makethe drawing easier, lines are customarilydrawn to represent cross sections of thewavefronts, as shown in Figure 20C. For asmall source, the wavefronts are spherical.Figure 21A represents a portion of sphericalwavefronts for a coherent source. In theripple tank, the wavefronts were seen asstraight lines (on the source side of the slits)or as semicircles (on the other side of theslits). If the light is incoherent, the wavefrontsare "wrinkled" in random ways, as shown inFigure 21B.

You can also use a small aperture(opening) to obtain spatially coherent lightwithout the inconvenience of moving so faraway from the source. By allowing only asmall portion of the wavefront to comethrough the opening, a smoother portion ofwavefront is obtained, which then spreads outas shown in Figure 22. At a great distancefrom the source this "wrinkling" becomesrelatively less important because one usesonly a small fraction of the whole wavefront.But the improved coherence at great distancesis at the expense of decreased intensity. Thesmoothing action of the small aperture can

COHERENT

(D:.. ) ).::::..:::.:.::

INCOHERENT

INCANDESCENTLAMP

FILTER SINGLESLIT

best be explained by considering the extremecase where only one point of the wavefront isallowed to pass through. One point of thewavefront has no irregularities at all. It isexactly the same as if a perfectly smoothwavefront hit the opening. The smaller theaperture, the better the smoothing effect.However, the smaller the aperture, the lowerthe light intensity.

All of the various methods of producingspatially or temporally coherent light fromordinary sources reduce the amount of lightavailable. The better the coherence obtained,the less light there is to work with. Lasersproduce light which is spatially and tempo-rally coherent and quite intense.

Question 8. Explain how you would obtainlight that is both spatially and temporallycoherent from an incandescent lamp.

When two waves of the same kind meetin space, they add together. This basic prop-erty of all waves is called superposition.

Imagine that you have two identical lightsources, such as two lasers, which producelight beams which are perfectly coherent witheach other (this is theoretically possible, butvery difficult to do in practice). You could

then aim the two beams at the same point ona screen. If the two waves were in phase, theywould add up to create a bright spot on thescreen. Such "adding up" of waves is calledconstructive interference. If the two beamswere completely out of phase, they wouldcancel each other out and produce a dark spot(no light). This process is called destructiveinterference.

In the ripple-tank experiments, the twoslits serve as sources of two coherent waveswhose crests and troughs you can actually see.Further, you can see that the two waves showconstructive interference at some points, anddestructive interference at other points. Atstill other points, there are various mixturesof the two types of interference. The relation-ship between phase and distance traveled bythe waves from the source to the screen (thepath length) is that the two waves are in phaseif they travel the same distance from the twosources (equal path lengths), or if one travelsany whole number of wavelengths furtherthan the other. If one wave travels a half-wavelength, or any odd number of half-wavelengths, farther than the other, the twowaves are out of phase. Figure 23 illustratesthe relationship for waves in a ripple tank.

At the point on the right side of the tankmarked "0," the two waves have traveled thesame distance from the slits and are in phase,producing constructive interference. At thepoints labeled "Y2," one wave has traveled ahalf-wavelength farther than the other, sothey are out of phast(, At the points marked"1," the two waves are in phase again becauseone of the waves has traveled a full wave-length farther than the other, and so on.

The double-slit experiments with lightare slightly more subtle. Since laser light hasboth temporal and spatial coherence, aninterference pattern is created whenever alaser beam passes through two closely spacedslits. The light diffracts and spreads out as itpasses through each slit, causing two coherentwaves which then interfere in the same way asdo water waves. The bright spots in theinterference pattern are points of constructiveinterference, and the dark spots are points ofdestructive interference. Interference patterns

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are more difficult to obtain with ordinarylight because it lacks coherence. More will besaid about the relationship between the num-ber of interference spots observed and thecoherence of the light in Section C of themodule.

In Experiment A-I, you observedanother type of interference. The interferencebands seen with the two optical flats arecaused by interference between light beamsreflected from the glass on the top andbottom surfaces of the "sandwich" of airbetween the flats. Referring to Figure 24, thelight entering the eye from point A reachesthe eye by two different paths. One of theseis a path which is reflected from point A. Theother is light which has been reflected frompoint B through point A to the eye. Since thetwo light beams reaching the eye from pointA have traveled different distances, they maynot be in phase. Whether or not they are in

GLASSAIR

B GLASS

21/2211/2I1/2o1/2I11/2221/2

phase depends on the difference in pathlength of the two light beams, and on thewavelength of the light. The dark bands arecaused by destructive interference, while thelight bands are caused by constructive inter-ference. The fact that the bands you observedwere parallel is an indication that the glasssurfaces of the optical flats are really "flat."The interference patterns created by an opti-cal flat on a non-flat surface are complexswirls of light and dark bands, instead ofparallel, straight bands.

With the aid of the wave theory of light,we can study some of the applications of thelaser in more detail. For instance, the theoryof holography was worked out, using the ideathat light is a wave, before lasers wereinvented. Coherent light is necessary to makeholograms, therefore they were very difficultto make before laser light was available. Thehologram does not have to be made with thesame wavelength light as is used to view theimage. In terrain-mapping radar systems, forexample, holograms are made from the re-flected radar wave information. The holo-grams are then viewed with visible light.

Holograms can also be made by using acombination of sound and light waves. Suchacoustic holograms are then viewed with light.This technique has promising medical applica-tions because sound waves can penetrate the

body. Someday this technique may surpassthe x-ray in importance for viewing internalorgans. The advantages of holography overx-ray include the possibility of a much moredetailed picture, particularly of soft tissues,and the absence of radiation danger.

Light can be used to transmit informa-tion. Radio and television broadcasting areexamples of the use of other electromagneticwaves for the transmission of information.Before lasers, there were no powerful sourcesof coherent light waves that could be used forcommunication. The advantage of using lightfrequencies for communication lies in thehigh frequency that is available. The higherthe frequency of the wave, the greater theamount of information which can be carriedby it. Presently available radio, television, andmicrowave broadcast bands cover a range ofabout 9.5 X 109 Hz, but the visible and near-by infrared frequencies cover a range of about9 X 1014Hz. This great frequency rangeimplies that a great deal of information couldbe carried by light waves, at least theoreti-cally. The problem is that an effective waymust be found to modulate and demodulatelight waves. Modulation means varying thewave in some manner in order to have it carryinformation. Correspondingly, demodulationmeans translating the modulated wave backinto the desired information at the receivingend. These techniques are not near.y so welldeveloped at optical frequencies as they are atlower frequencies. Still, we might expect thattelephone conversations will at some futuredate be carried on laser light beams propa-gating down long, evacuated tubes.

The following statements summarize theconcepts, definitions and principles you havelearned in this part of the module.

Light travels from its source at anextremely great speed: 1.86 X 105 mils or3 X 108 mls in empty space.

A model for the behavior of light is a

mental picture that can be used to visualizethe effects and processes that light exhibits.

Macroscopic refers to objects of substan-tial size, usually large enough to be seen withthe eye.

Microscopic refers to objects the size ofatoms or molecules.

The color of a light wave as seen by theeye corresponds to the wavelength of thatlight wave.

The angular separation of the brightbands in an interference pattern (diffractionpattern) is inversely proportional to the sepa-ration between the slits. In equation form, forsmall angles, this relationship is

The quantity A.is the wavelength and d is theseparation of the slits.

The number of bright bands (maxima)from the central maximum in an interferencepattern to another given maximum is calledthe order of that maximum.

(Optional) For all angles of separation,and for all orders (N), the relationship amongangular separation, wavelength, slit sepa-ration, and order number is

The wavelengths of the visible spectrum-7vary continuously from about 7 X 10m for

the lo~~st visible wave (red), down to about4 X 10m for the shortest visible wave(violet).

The frequencies of the visible spectrum1 4range from about 4 X 10Hz to

147.5 X 10 Hz.Monochromatic light refers to light that

is very nearly a single color, or likewise asingle wavelength.

Temporal coherence (coherence in time)is a measure of the extent to which lightwaves are continuous and uninterrupted intime.

Spatial coherence (coherence in space) isa measure of the extent to which wavefrontsare smooth and coordinated.

Laser light has a high degree of spatial

and temporal coherence in a beam whichdivergesonly slightly.

White light (from an incandescentsource) is highly incoherent, both spatially

and temporally. It can be made more coher-ent by means of a filter and a slit. To bring itto a high degree of coherence requires a greatloss of intensity of light.

The following goals state what youshould be able to do after you have com-pleted this section of the module.

1. Goal: Understand the concepts of band-width and fractional bandwidth.

Item: A mter is centered at 500 nm andhas a 1Q-nm linewidth. What is thefrequency bandwidth of the light itpasses?

2. Goal: Understand the concepts ofcoherence time and coherence length.

Item: A laser emits wave trains 100waves long with a wavelength of 442 nm.What is the coherence time of thissource?

3. Goal: Understand the nature of spatialand temporal coherence required forinterference experiments.

Item: The air mm between two opticalflats is 0.03 mm thick. What is themaximum bandwidth of sodium light(X = 589 nm) that would give goodinterference fringes?

4. Goal: Understand how the concepts ofatomic energy levels and photons arerelated to the emission and absorption oflight.

Item: What frequency of light would beemitted by a hydrogen atom when itfalls from the fifth to the third energylevel?

neous emIssIOn, stimulated eIDlSSlon,natural linewidth, and Doppler line-width.

Item: Which of the previous four termsbest fits the description "it can beroughly calculated from the lifetime ofthe excited state?"

6. Goal: Understand the concept of popu-lation inversion and the methods forachieving it.

Item: In the ruby laser how short wouldthe lifetime of the intermediate stateneed to become before an inverted popu-lation would be impossible?

7. Goal: Understand how the end mirrorsof a laser produce a narrow bandwidth.

Item: How long should the resonantcavity of a He-Ne laser be in order toproduce ten axial modes within theDoppler broadened line with-sb.vDI:::::: 10 ?

Answers to Items AccompanyingPrevious Goals

1. 1.2 X 1013 Hz

2. 1.47 X 10-13 s

3. 5 X 1012 Hz

4. 2.34 X 1014 Hz

5. Naturallinewidth

6. About 10-9 s

SECTION C (OPTIONAL)

An Analysis of Laser Light

The monochromaticity of light can berelated mathematically to its temporal coher-ence. To do this we need a quantitativemeasure of monochromaticity. The range offrequencies emitted by any light source isusually referred to as the bandwidth orlinewidth. Laser light has a spread of frequen-cies (a non-zero bandwidth) although it isusually small compared to light from othersources. It is important to remember thatbandwidth refers to a range of frequencies,not to the actual frequencies. For example,we might speak of the "bandwidth" ofheights of people in a classroom: such a"bandwidth" might be 1 foot, the differencebetween the tallest and shortest persons in theroom, whereas the average height itself mightbe 5 feet 9 inches. Similarly, the bandwidthof laser light may be about 108 Hz, spreadabout a central light frequency of more than1014Hz. If we use .Av to represent bandwidthand v to represent frequency, then for atypical helium-neon (He-Ne) laser the ratio ofbandwidth to central frequency is

The bandwidth of laser light may be onlyabout 0.0001% of the average frequency,whereas in the previous example of heightsthe "height bandwidth" was about 15% of theaverage value.

The ratio of the bandwidth to theaverage frequency, called the fractional band-width, is a common way of expressing howmonochromatic a source is. A small range offrequencies, .Av, implies a small range ofwavelengths, .AA, because wavelength andfrequency are related through Equation (5),and the fractional ranges are equal.

The small bandwidth of laser light is one ofthe things that distinguishes the laser from allother light sources and leads to the very purecolor of laser light.

Problem 5. About what range of wavelengthswould be expected from the typical He-Nelaser if the center wavelength is 633 nm?

The fractional bandwidth is a measure ofthe monochromaticity of a source; the lengthof an emitted wave train, .AL, is a measure ofthe temporal coherence of the source. Thislength is called the coherence length. Becausethe wave travels at a constant speed, thecoherence length can be written in terms ofthe time interval, .At, during which the wavetrain is emitted (also called coherence time).

It turns out that we can relate, in anapproximate manner, the time of emission tothe bandwidth of frequencies emitted. Sincethe relationship is simple, while the derivationof it is not, we shall just state it for use at thistime:

where .At is in seconds (s) and .Av is in hertz(Hz). Combining Equations (8) and (9), weobtain a relationship between coherence lengthand band width

Equation (l0) states that a small bandwidth(highly monochromatic light) means a largecoherence length (high temporal coherence),and vice versa. The temporal coherence of laserlight is another aspect of its monochromaticity.

Example Problem. What is the coherencelength of a He-Ne laser whose bandwidth is108 Hz?

Solution. Given is .::lv = 108 Hz, and we8know already that c = 3 X 10 m/s. These

values may be substituted directly intoEquation (l0).

8IlL = 3 X 10 mls

108 Hz

Problem 6. What is the coherence length of aruby laser with bandwidth 2 X 109 Hz?

Problemproblem694 nm,emitted?

7. If the ruby laser of the abovehas an average wavelength ofwhat range of wavelengths is

Problem 8. If white light is passed through afilter with center wavelength of 500 nm and abandwidth of 1 nm, what is the resultingcoherence length of the light?

INTERFERENCE REQUIRESCOHERENCE

Considerable spatial coherence and sometemporal coherence are required to produce adouble-slit interference pattern. Spatial coher-ence is the major factor because'the inter-ference is between different parts ofwavefronts emitted at the same, or verynearly the same, time. In other words, theinterference is between different portions ofthe same or nearby wavefronts, and theseportions must have a fixed relationship witheach other to produce a stationary inter-ference pattern.

In Figure 25, the points a and b repre-sent the portions of the wavefronts which willpass through the two slits and spread out intonew coherent wavefronts. After passingthrough the slits the wave from point a onwavefront 1 will add constructively with that

from point b of the same wavefront in thecenter of the screen. This produces the centralmaximum of the interference pattern. (Thisis also called the zeroth-order maximum.)Similarly, the waves produced from points aand b of wavefronts 2 and 3 will add at latertimes to produce the same central maximum.To produce an adjacent maximum, called thefirst-order, the wave from point la interferesconstructively with that from point 2b, 2awith 3b, etc. This maximum is at an off-center position which must be closer to thelower slit in the figure, for the two waves toarrive in phase. The next, second-order, maxi-mum is produced by constructive interferencebetween points la and 3b, 2a and 4b, etc.Thus we can conclude that very little tempo-ral coherence is required for the center of theinterference pattern, but more temporalcoherence is required for the edges of thepattern where wavefronts are interfering withothers several wavelengths away.

For an interference pattern containingten orders, besides the central one, the wavetrain must contain at least eleven equallyspaced wavefronts. The tenth-order maximumis produced by constructive interference ofthe first wavefront passing through one slitwith the eleventh wavefront through theother slit.

The time required for eleven wavefrontsto pass through the slits is very short. Forlight having an average wavelength of6 X 10-7 m, the coherence time !:J..t required isgiven by the equation

Total length of wavetrain= speed X coherence time

or for n waves, measuring from the first to thenth wavefront

6 X 10-6!:J..t = 8 = 2 X 10-14 S

3 X 10

This temporal-coherence time corresponds to-6a coherence length of 6 X 10m or ten

wavelengths. The slit separation you haveused in the laboratory is about 0.1 mm, orabout 100 wavelengths. In order to get astationary interference pattern, the wavesmust be spatially coherent for about thisdistance along the wavefronts. Thus even iftemporal coherence is poor, compared withthe spatial coherence, we can still get double-slit interference with several orders.

You should now do Experiment C-l.

Suppose two beams of light leaving asingle source in different directions passthrough slits, diffract, and thus overlap in thespace beyond the slits. They will form inter-ference patterns only if the light is spatiallycoherent over the distance separating the slits.

Place an incandescent lamp at one end ofan optical bench. Immediately in front of thelamp place a piece of frosted glass that hasbeen masked except for a strip two or threemillimeters wide running vertically down thecenter. From a distance of about two meters,look at the frosted glass through a pair ofclosely spaced slits. With the slits parallel tothe unmasked strip of the frosted glass, lookfor an interference pattern of bright and darkfringes.

While looking through the slits, movecloser to the frosted glass.

2. Do you observe any change in theinterference pattern?

Continue moving closer to the frostedglass until the slits are just a few centimetersfrom the frosted glass.

3. Is there now evidence of interference?How would you explain this?

CAUTION: Never look directly intolaser light.

Now place a white screen at the end ofthe optical bench and a pair of slits about10 cm in front of the screen. Mount the laserat the other end of the optical bench andilluminate the pair of slits with the laserbeam. Look for an interference pattern on thescreen.

Move the laser toward the slits until it isas close as possible while still illuminatingboth slits.

5. Do you observe any change in theinterference pattern?

6. From these observations, what can yousay about the spatial coherence of laserlight compared with that from the incan-descent lamp?

Part II: Temporal Coherence (CoherenceLength)

The purpose of this experiment is tocompare the coherence length of two kinds ofsingle-color light: the almost "pure" (narrowbandwidth) light from a laser, and the less"pure" (wider bandwidth) light from aftltered mercury 'lamp. To do this you willcompare the quality of different interferencefringes obtained with a Michelson inter-ferometer. An interferometer is a devicewhich uses the phenomenon of interferenceto measure very small distances. In theMichelson version, a beam of light from thesource shines on a special mirror(beamsplitter) which transmits half of thelight beam and reflects the other half of thelight beam. The transmitted part of the beamtravels to a regular mirror and is reflectedback. The reflected half of the original beamtravels (in a direction perpendicular to that ofthe transmitted beam) to another mirror andis also reflected back. These two parts of theoriginal beam are then recombined by thebeamsplitter to produce interference fringessimilar to those you saw in Experiment A-I.These interference fringes arise because thetwo parts of the beam travel slightly differentdistances between the point where the beamis split and the point where the two beamsrecombine. The interference pattern is deter-mined by this path difference.

Set up the interferometer and mercurylight source with a green filter (Figure 26).

I•• ~I

LIGHTSOURCE

MIRROR2

¥OBSERVER

On your interferometer one of themirrors is moveable along the light path andone or both of the mirrors can be tilted.Adjust the moveable mirror so that the twolight paths are as nearly equal as you can getthem by measuring with a meter stick. Holdthe point of a pencil just in front of the lightsource and look through the beamsplitter atthe images of the source. If you see more thanone image of the pencil point, one or both ofthe mirrors is tilted. Adjust the tilt of themirrors to merge the images of the pencilpoint into one image. As the images mergeexactly, a pattern of interference fringes,alternate light and dark bands, should popinto view. You can then further adjust the tilt

of the mirrors to get a circular pattern offringes similar to that shown in Figure 27.

Now change the distance L1 by movingthe moveable mirror slowly and observe whathappens to the fringes. Continue this until thefringes disappear. Then move the mirror inthe other direction until the fringes disappearagain.

1. What happens to the fringes as you movethe mirror? About how far can youmove the mirror and still see fringes?

In order to produce interference fringes,the path difference, 21L1 - L2 I, must be lessthan the coherence length.

ence length of the filtered mercury-vaporlight?

Replace the mercury-vapor light andfilter with the laser. Use a lens to expand thebeam and direct it into the interferometer.Place a white screen in front of the beam-splitter and adjust the mirrors to give aninterference pattern on the screen.

3. How does this pattern compare with thatof the previous light source?

4. By changing the path difference, whatcan you determine about the coherencelength of the laser light?

5. Compare the coherence lengths of thefiltered mercury-vapor light and the laserlight.

In Experiment C-l you saw that thecoherence length of a He-Ne laser is muchlonger than that of a filtered mercury-vaporsource. The filtered mercury-vapor light, inturn, has a longer coherence length than lightfrom an incandescent lamp, because the greenlight from a filtered mercury-vapor source hasa much smaller bandwidth than that producedby allowing light from an incandescent lampto pass through the same filter. This smallerbandwidth is related to the group of wave-lengths, called the spectrum, emitted by a hotgas such as mercury vapor. Light from a hotsolid, such as that from the filament of anincandescent lamp, contains all visible wave-lengths from 400 nm to 700 nm. But when agas is heated or electrically caused to emitlight, only certain wavelengths are emitted.This kind of spectrum is called a line spectrumbecause it appears as a set of colored lineswhen viewed th!"ougha wavelength-measuringinstrument such as a spectrometer. Eachcolored line corresponds to a differentemitted wavelength (and frequency).

The green filter used with the mercury-vapor source passes only the green line andabsorbs the other lines in the mercuryspectrum. The wavelengths of the absorbedlines are not too close to the wavelength ofthe green line. The green light emitted bymercury vapor has a much narrower band-width than the bandwidth passed by the filterif "white light" is used.

To understand how gases emit linespectra and how laser light has a narrowerbandwidth than the lines emitted by a gas, weneed to study the interaction of light withatoms.

How the atoms of a substance emit andabsorb light has been of great interest toscientists for many years. The optical proper-ties of gases depend strongly on the structureof the individual atoms or molecules of thegas. This is true because particles in a gas arerelatively independent of one another. But in

solids, interactions between atoms occur,resulting in more complex optical properties.

The idea that all matter might be con-structed of large numbers of very smallbuilding blocks, called atoms, occurred to theGreeks several thousand years ago. A morerefined version of this concept was developedin the wake of experiments performed byDalton and others early in the nineteenthcentury. Originally the atom was thought tobe indivisible. Late in the nineteenth centuryevidence accumulated to indicate that atomshave internal parts and that these parts showelectrical properties. Pieces of atoms, calledelectrons, can easily be separated from theremaining portions of the atoms. The sepa-rated parts are called ions; the electron is anegative ion and the remainder of the atom isa positive ion. All electrons appear to beidentical, regardless of their origins. Anelectron has a mass which is less than 0.1% ofthe mass of small atoms, and a negativeelectrical charge. When an electron is removedfrom a neutral atom, the charge of thepositive ion left behind is equal and oppositeto that of the electron. The number ofelectrons in an atom varies from element toelement.

Questions arose about the internal struc-ture of atoms. For example, what is thenature of the massive positive ions? How areelectrons arranged within an atom?

A number of "models" for the structureof atoms have been proposed, with varyingdegrees of success in predicting atomicbehavior. The structure of atoms is stillnot fully known, but, as a result of manyexperiments, organized with the help oftheories, we now know a great deal abouthow atoms are put together and why theybehave as they do. One well-established fact isthat most of the mass of an atom is in thenucleus, a tiny core that occupies only a smallfraction of the volume of the atom. Sur-rounding this nucleus are electrons, which areconstantly in high-speed motion. Eachnucleus, which has a positive charge, tends to

attract and hold just enough electrons so thattheir total negative charge is equal in size tothe charge of the nucleus. The surroundingelectrons determine the chemical propertiesof the atom; when an electron is removedfrom an atom, the resulting ion has differentchemical properties.

For the purposes of this module, themost important characteristic of atoms is thateach atom possesses a certain energy which isinternal to the atom. This energy is due to thearrangement of the nucleus and the electronsand has nothing to do with any other energythe atom may have because of its motion orits interactions with other atoms. Further,this "internal" energy, which we shall simplycall the "energy of the atom," has the rathersurprising property that, for a given atom, itcan have only certain values, called energylevels.

The lowest energy level is called theground state, and atoms are normally found inthe ground state. An atom can absorb energyin various ways provided just enough energy isavailable to cause the atom to "jump up" to ahigher energy level, called an excited state. Ifleft alone long enough, the atom returns to itsground state. When it does so, it emits theradiation we see as a particular colored line(or lines) in the spectrum of a gas.

Analysis of the spectrum of a gas canlead to knowledge of the energy structure. Adiagram showing the energy levels of thehydrogen atom is shown in Figure 28.

What happens when atoms in an excitedstate "drop" to the ground state? We knowthat the atom emits radiation of a particularcolor. It is this radiation phenomenon that ledto the idea of energy levels in the first place.A complete theory must include a model forthe atoms that emit the radiation and also amodel for the radiation itself. In the earliersections of this module, we discussed a wavemodel for light, which successfully explainedphenomena such as interference and diffrac-tion. However, the wave model previouslydiscussed does not adequately explain other

tJOULES (eV)

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phenomena such as the spectrum of radiationemitted by glowinggases.

Historically, an important clue toanother aspect of light came from experi-ments involving the photoelectric effect. *When light falls on certain materials under theright circumstances, electrons are ejected. Aclose examination of this phenomenonshowed that a wave model of light cannotaccount for the observations. For example,the kinetic energy of the electrons which arekicked out of the material does not dependupon the intensity of the light, but it doesdepend upon the wavelength. Also, physicistsexpected that a bright light would cause thefirst electrons to come out of the surfacesooner than would a dim light, and thisproved not to be the case. In 1905, AlbertEinstein showed that the characteristics of thephotoelectric effect support a photon modelfor light. He argued that the light consists oftiny bundles of energy, called photons, andthat these photons have the characteristics ofparticles. (Nearly twenty years passed beforeEinstein's strange idea was generally

*This effect is made use of in photocells, which areused in some kinds of exposure meters, automaticdoor openers, and burglar alarms, among other things.

accepted.) If one measures the frequency oflight, the energy of each photon is given bythe formula

-34where h = 6.63 X 10 joule-second (J ·s).The constant h is known as Planck's constant.The very small value of Planck's constantimplies a small energy for one photon, even atthe very high frequency of visible light.

Question 9. Which have higher energy, pho-tons of red light or photons of blue light?

Problem 9. What is the energy of a photon ofgreen light with frequency v = 6 X 1014Hz?

THE WAVE AND PARTICLENATURE OF liGHT

We have just stated that one gets theenergy of a photon, which has particle proper-ties, by measuring the frequency of thelight, which is a wave property. Is light awave? Is light a particle? By now you may bethoroughly confused. Interference, diffrac-tion, and refraction, as well as effects notmentioned in this module, are wave phenom-ena The photoelectric effect and the emissionof light from an atom, as well as other effects,are particle phenomena.

An experiment using light of extremelylow intensity has helped to resolve thisapparent dual character of light. It is possibleto make the intensity of light so low that onlyone photon of light can pass through one orthe other of a pair of slits. When we do thisexperiment, a photographic plate registerssingle particles of light, one after the other.Thus, as the light strikes the film, the inter-action is particle behavior. After a largenumber of particles have passed through theslits, we find that they have formed aninterference pattern on the film. This statis-tical behavior of large numbers of photonscan be explained using a wave model.

This dilemma illustrates the basicproblem of "model building" in modemscience. Scientists, as well as others, prefer

models that can readily be visualized, modelsthat correspond to everyday things in theworld around us (a light wave is "like" awater wave; a photon is "like" a marble).Unfortunately, the models that seem to beforced upon us by the facts of modemphysics are not like this. Some of our modemmodels mix seemingly incompatible ideas anddefy simple visualization.

The importa:nt point is that, for light,both models are needed. In the case of particleinteractions you need the energy or momen-tum of a photon; but to get these quantities,you need the frequency or wavelength associ-ated with the photons' statistical behavior. Inthe case of interference, you need the accumu-lation of individual photon collisions witha photographic plate or screen.

INTERACTION OF ELECTRONSAND PHOTONS

When an atom absorbs light, the energyof the atom changes to a higher energy level.When the atom emits light, it jumps to alower energy level. Each such jump or trans-ition is associated with the absorption oremission of a single photon. If no energy islost, then the change in energy of the atommust equal the energy of the photon absorbedor emitted

where En and Em refer to the higher andlower energy levels, respectively.

Example Problem. What is the energy of aphoton emitted by a hydrogen atom, whenthe atom jumps from the third to the firstenergy level?

Solution. You are only given the numbers ofthe energy levels involved in the transition.Use Figure 28 to find

-19E3 = -2.42 X 10 J

-(-21.76 X 10-19) J

= 21.76 X 10-19 J - 2.42

Problem 10. What is the energy of a photonemitted from a hydrogen atom, when theenergy of the atom falls from the second tothe first level?

Problem 11. What frequency light will causethe hydrogen atom to jump from the secondto the third energy level?

Question 10. In a certain atom, green lightwill cause an atom to jump from the first tothe third energy level. Would a shorter or alonger wavelength be required to produce atransition from the first to the second energylevel?

If an atom is excited (raised to a higherenergy) by some outside source of energy,such as by the absorption of a photon, theatom eventually gives up that energy and fallsback to the ground state. The ener~y thus lostby the atom may appear as light or as otherforms of energy. For a given excited atom, itis impossible to tell exactly when such atransition will take place, but there is someaverage time for a large collection of identicalatoms. This average length of time that anatom spends in the excited state beforeemitting a photon and returning to a lowerstate is called the lifetime of the excited state.Atomic lifetimes are usually very short, onthe order of 10-8 s for the excited states thatproduce visible light. The emission of radia-tion by a group of excited atoms whichundergo transitions to the ground state, withno outside influence, is called spontaneous

emiSSIOn. Ordinary light sources emit theirlight by spontaneous emission.

Excited atoms can also emit light andreturn to the ground state by another processcalled stimulated emission. If a photon of thecorrect frequency passes close enough to anexcited atom, it can "stimulate" the atom toemit its excitation energy in the form ofanother photon corresponding to exactly thesame frequency. Stimulated emission is possi-ble only when the incoming photon hasenergy (frequency) exactly equal to thedifference in energy between the excitedenergy level and a lower energy level. Thisprocess is the inverse of absorption, in whicha photon corresponding to just the rightfrequency is absorbed by an atom in theground state, thereby raising the atom to anexcited state. A light wavecan cause each of acertain number of atoms in the ground stateto absorb a photon. The same light wave cancause each of the same number of atoms inthe excited state to emit a photon. Thatmeans that if there were only the ground-stateand one excited-state level, as many atomswould lose energy as would gain energy. Thisis the reason why lasers must be made withmaterials having more than two energy levels.

The interesting feature of the stimulated-emission process for the study of lasers is thatthe emitted light wave is exactly alignedcrest-to-crest with the stimulating wave, isexactly the same frequency, and is traveling inexactly the same direction. The two wavesarecoherent. Lasersemit their light by stimulatedemission. The three processes - absorption,spontaneous emission, and stimulated emis-sion - are illustrated in Figure 29A, B, and C.

You might wonder why laser light has anarrower linewidth than the light emitted byglowing gases. The spectrum of the light froma gas does contain narrow lines of color, buteach line contains not just one frequency, butrather a small spread of frequencies. If for a

E ABSORPTION~----O •EI •

Figure 29A. For absorption the atom absorbs aphoton of just the right energy and jumps to ahigher energy level.

SPONTANEOUS EMISSION:~--_·--OFigure 29B. In spontaneous eIlliSslon, the excitedatom simply drops to a lower energy state.

STIMULATED

E • ~~ VE----

I

EMISSION

~~•

Figure 29C. In stimulated emission the excited atomis affected by a photon of just the right energy andtwo identical photons go off together.

particular excited state, At is the time duringwhich light is emitted, we can use Equation (9)to find the bandwidth of the spontaneouslyemitted light. This bandwidth is called thenaturallinewidth, AVN.

The naturallinewidth of an optical transitionis roughly the same as the linewidth of ahelium-neon laser.

Since the natural linewidth of a spectralline is about the same as the linewidth of laserlight, you might wonder why laser light is somuch more nearly monochromatic than lightof a single color emitted by a gas discharge.The reason is that there are other processes ina gas discharge that tend to spread out, orbroaden, spectral lines. The most importantof these, called Doppler broadening, is causedby the motion of the atoms or moleculeswhich emit the light. The particles in a gashave sufficient thermal (heat) energy at room

temperature to be moving at fairly highspeeds. But a motion of the source of a waveaffects the wave frequency observed. Motionof the source toward the observer causes anincrease in the frequency observed, whilemotion away from the observer leads to adecrease in the frequency observed. You mayhave noticed this effect in connection withsound waves; when a car is approaching itshorn sounds higher-pitched than when it isleaving.

In a gas, the sources of the light waves,the atoms or molecules, are moving at differ-ent speeds and in random directions, sometoward and some away from the observer.Since each line we see results from the sametransition in many of these moving atoms, thefrequencies are spread out, some higher andsome lower than that from a stationary atom.This results in a general broadening of the lineover a range of frequencies, as indicated inFigure 30. At room temperature, this Doppler

,-,NATURAL ::

I I

L1NEWIDTH-: :I II II I

DOPPLERL1NEWIDTH

1I I

I ,

II

Figure 30. The graph is badly distorted since thebroadened linewidth is about 100 times the naturallinewidth and, for the same number of atoms, thenatural linewidth peak is much higher.

linewidth, AVD, is on the order of ten toone hundred times the natural linewidth.Thus:

The green light from the mercury-vaporlamp may have a linewidth this large or larger.Laser light is considerably moremonochromatic.

INVERTED POPULATION NEEDEDFOR LASER ACTION

The light in a laser originates in theatoms of the active material. In the firstoperational laser, the material used was apiece of ruby. Ruby is aluminum oxide withchromium ions in it. Although they composeonly about 0.05% of the ruby, the chromiumions are the active material and they emit thelaser light. Lasers with many other activematerials have been built since the ruby laser,but we shall confine our attention primarilyto the ruby laser and the helium-neon lasersince they are still the most common.

The chromium in ruby is in the form ofpositive ions with three electrons missing.These ions take the place of some aluminumions in the crystalline structure of the solidaluminum oxide. The energy levels of thechromium ions in the aluminum oxide crystalare similar to those of the simple atoms.However, some energy levels are spread into"bands" as a result of the electrical forceswhich hold the solid together. An energyband can be thought of as a great manyclosely spaced energy levels, and an ion canhave essentially any energy within the band.This is indicated in the energy-level diagramof Figure 31.

To achieve laser action there must bemore ions in the right excited state than inthe ground state. Otherwise more photons arelost in exciting ground-state ions than aregained by stimulated emission. A populationinversion exists when there are more excited-than ground-state ions.

Various methods of adding energy to theactive materials are used to obtain populationinversions. One of the most straightforward,called optical pumping, is used to excite theruby laser. The chromium ions are excited byabsorbing photons from an initial burst oflight supplied by a flashlamp. The flashlampsused are similar to the electronic flashlampsused by photographers. However, an invertedpopulation cannot be obtained simply by

adding energy to ions in the ground state andthereby raising them to a single excited state.If the atom had only two energy levels, itwould be impossible to get an inverted popu-lation by optical pumping. Once half of theatoms were excited, as many would be stimu-lated to emit as would be excited by thepumping radiation, and a balance would beachieved that would involve no gain in thenumber of photons. In the ruby laser, thereare actually two levels and two bands involvedin the population inversion. In the energy-level diagram of Figure 31, only the singleband and the single energy level which areinvolved in the laser action are shown. Lightfrom the flash tube excites chromium ions toan energy band. These excited ions lose someof their energy by collisions within the crystaland thus fall to the excited-state energy level,as shown in Figure 31.

_______ I ENERGY BAND

\ EXCITED,STATE

LASERLIGHT

EMITTED

EXCITEDBY

GREENLIGHT

J GROUNDSTATE

Figure 31. A simplified energy-level diagram of chro-mium ions in a ruby. The excited-state level has beenmoved to the right just to make room on the diagram.

The process of losing energy by colli-sions without emitting a photon is calledthermal relaxation. Thermal relaxation pro-ceeds very rapidly (10-9 s), transferringenergy to the ruby in the form of heat. Onthe other hand, the excited-state energy level

is relatively long-lived, with a lifetime on theorder of 10-3 s; and this energy level istherefore called metastable. The net result isthat ions "pile up" in the metastable energylevel. Thus an inverted population is achieved.The transition between the metastable stateand the ground state will then occur. The firstfew photons, which are produced by sponta-neous emissions, stimulate more ions to emit,and the result is a laser beam at a wavelengthof 694.3 nm.

A completely different scheme is used toenergize the atoms in a He-Ne laser. Theenergy originates in an electric dischargethrough the gas which is about six partshelium to one part neon. The discharge isstarted by accelerating electrons through thegas toward a positive electrode.

The free electrons moving through thegas collide violently with the atoms and givethem the energy to jump to excited energylevels. Although neon is the active material ofthe laser, a fortunate closeness of energylevels makes it helpful to use a mixture ofhelium and neon. As shown in Figure 32,helium happens to have an excited energylevel which has just the same energy as one ofthe neon levels.

Neon can be made to "lase" by itself,but it turns out to be easier and much moreefficient to excite the helium atoms in thedischarge; those excited helium atoms giveenergy to the neon atoms in collisions. Thiscan happen because the energy levels of thetwo gases are so nearly the same.

Although, with a great deal of effort,ruby lasers can be run continuously, they areusually pulsed. Helium-neon lasers are usuallyrun continuously. A comparison of Figures 31and 32 indicates why this is the case. For theruby laser to work, it is necessary to producea population inversion between an excitedenergy level and the ground-state level. How-ever, at room temperature most of the ionstend to be in the ground state and well overhalf of them must be raised to the excitedstate. On the other hand, the helium-neon

-'-1-2

LASERLIGHT

EMITTED

~I

Figure 32. A simplified energy-leveldiagram for heli-um and neon. The first excited level of neon reallyconsists of 10 closely spaced levels, and level 2 isreally 4 levels. Other multiple levels are omitted.

laser requires only a population inversionbetween level 2 and level l. Fortunately,level I has almost no atoms in it at roomtemperature. This means that only a relativelyfew atoms need be in level 2 for a populationinversion to occur. Also, spontaneous tran-sitions from level I to the ground state occurvery rapidly, so it is easy to maintain thepopulation inversion continuously. The stim-ulated transitions from level 2 to level Iproduce visible laser light at a wavelengthof 632.8 nm, but by using other transitionshelium-neon lasers have been made to pro-duce laser light at many different wave-lengths, especially in the infrared.

AMPLIFICATION BETWEEN ENDMIRRORS

Once a population inversion has beencreated in the active material, laser actionstarts with a spontaneous emission. Anyphoton emitted spontaneously by an atommay pass close enough to an excited atom to

cause a stimulated emission. The two coher-ent photons resulting may then cause stimu-lated emissions in other atoms which are stillin the excited state, and a kind of "chainreaction" may occur, building up the numberof mutually coherent photons as it proceeds.This is indicated in Figure 33, where a singlephoton starts the process in a number ofexcited atoms.

~" .....~. r ..

~?7'.';;r ..'

Figure 33. In a group of excited atoms a spontaneousemission starts a "chain reaction" of stimulatedemissions and a coherent beam of light emerges.

In the usual case, the active medium iscontained in a cylindrical shape, as indicatedin Figure 34A. Then when a spontaneousemission occurs and produces some stimu-lated emissions, the resultant wave is likelyto simply escape out the side, as in Figure34B. However, occasionally a spontaneousemission will start out exactly along thelength of the cylinder and, after having a longdistance to build up, the wavewill emerge outthe end, as in Figure 34C. However, eventhough it has built up a great deal thecoherent wave is still very tiny. To build it upeven more, a mirror is placed so that the wavegoes back through the active material andcauses many more stimulated emissions, as inFigure 34D. Finally, a second mirror is placedon the other end, so that the wave makesrepeated passes through the medium, gainingintensity with each pass. The region betweenthe two mirrors is called the laser cavity. Oneof the mirrors is made only partially reflectingso that a small fraction of the light passesthrough it. We see this fraction as laser light.

I' . , ' 'I.: : . .4. . : :. • ....: •....•................: .0.::: "0"": .

r: : :.... :<7, :"1'.. ' .. r· . . . ...• . (.'. ...... " .... .• .• .... .• .• .• ..

I" ' , =.""~~'r--'!.'''-'-.'~ .~. ~ .. ....~., . '.' . . .. ~"

li~I'" :.' : .' . :- ',: .~o } ...'.' .: .. - . . .. ".

STANDINGWAYES IN THE LASER(OPTIONAL)

Actually, the role of the end mirrors ismore important than indicated above. To seewhy, we can consider the light as a wavereflecting back and forth between the mirrors.At each mirror surface the wave is reflected.Inside the laser then, a standing wave patternis created.

Some points on a standing wave nevermove at all and are called nodes. Halfwaybetween successive nodes are positions ofmaximum variation called antinodes. For aguitar string the variation is the transversedisplacement of the string. In the laser thevariation involveschanges in the electrical andmagnetic forces that charged particles wouldfeel if put at these points in space. Themirrors guarantee that the electromagneticwaves will have nodes at some particularpoints in space near the mirror surfaces. Thisis analogous to the guitar string which,because of being clamped at its ends, hasnodes there.

Thus, the end mirrors will pick outwavelengthssuch that a standing wavejust fitsin with nodes at the right places; all otherwavelengths die out rapidly. For this reasonthe region between the end mirrors is said toform a resonant cavity. The internal laser lightcan be thought of as a standing wave that

grows rapidly as more and more excitedatoms are stimulated to emit photons.

For a guitar string, some possible stand-ing waves are shown in Figure 35. Each

different standing wave is called a mode ofoscillation. The distance between adjacentnodes is % X. Thus, the possible wavelengthscan be seen from this figure to be

'\ _ 2LI\n -

n

Here L is the length of the string and n is thenumber of half-waves which exactly fit in.

For a laser, we can make the approxi-mate assumption that there is a node at eachmirror. However, because the wavelength oflight is so small, there will always be a verylarge number of nodes in the laser cavity.

Problem 12. What is the longest wavelengthof a standing wave, with nodes at both ends,that will fit into a 10-cm cavity? Could this bea light wave?

Problem 13. Assuming nodes at both ends,how many half-waves of green light(X = 500 nm) will fit in a 5O-cm resonantcavity?

AXIAL AND NON-AXIAL MODES(OPTIONAL)

There is one complication to this analy-sis that should be considered. Standing wavesthat are slightly inclined with respect to theaxis are also possible, as indicated in Figure36. This fact would allow many more possible

wavelengths to be supported in the laser ifthere were not some way to keep these modesfrom gaining too much energy. To distinguishbetween these standing waves and the onesparallel to the axis, we shall call the latter axialmodes and the former non-axial modes. Asnoted earlier, the non-axial modes will tend to"walk off" the mirrors after a few passes, andso do not get a chance to build up bystimulated emission. By making the resonantcavity long with respect to the size of the endmirrors, the non-axial modes are eliminated.

COEXISTING AXIAL MODES(OPTIONAL)

Even when the non-axial modes areeliminated, several different axial modes cancompete for the energy stored in the invertedpopulation. This competition arises becauseseveral axial mode frequencies usually fallwithin the Doppler-broadened emission line-

width of the active material. We calculate theseparation between two successive axial modefrequencies using Equations (14) and (6).

The frequency difference between these twomodes is

The fractional frequency separation is thengiven by

Vn+1-Vn c/2L 1--=-- =- (15)

Vn nc/2L n

The number n is the number of half wave-lengths that fit in the resonant cavity. Forlight it is quite large, say

vn+l -Vn -6---~ 10Vn

This last figure may be compared with theDoppler linewidth noted earlier

~VD -5-- ~ 10

v

This implies that one can expect up to tenaxial modes within the Doppler-broadenedemission line of the active material. A typicalsituation is shown in Figure 37. As a popula-tion inversion is created in the active material,the axial mode closest to the center of theDoppler linewidth begins to oscillate. If thepumping process is powerful enough to over-come the loss of excited atoms due to thismode, then the next closest modes also beginto oscillate. The final laser spectrum mayappear as several "sharp spikes" which aremuch closer together than the Doppler line-width of the active material.

LINE NARROWING(OPTIONAL)

This process of producing "sharp spikes"which are much narrower than the Dopplerlinewidth is called line narrowing. This linenarrowing occurs automatically within thelaser cavity.

One way of understanding this is

DOPPLERWIDTH

through the standing wave discussion of thepreceding section. But the same phenomenonmay be looked at in a somewhat differentway. First, a given wave in the cavity stimu-lates emissions of those atoms which aremoving at just the proper speed so that theirphotons have exactly the same frequency asthe stimulating wave. Each wave which getsstarted picks out the right atoms to addcoherent radiation to itself. Secondly, after anumber of passes between the mirrors, onlythose waves which reinforce themselves growand the others destroy themselves. Saying thisanother way, if a portion of the wave hasmade two passes through the cavity, it adds toportions which have made four passes, or ten,or twenty, only if all of the portions are inphase. Since the waves all travel at the samespeed, for a given cavity length only waves ofthe right wavelength reinforce themselves.Other waves will arrive at the same spot outof phase with themselves and die out. This isindicated in Figure 38.

Figure 38A. Two portions of a wave which happensto have the right wavelength for a particular cavityreinforce because they are in phase.

Figure 38B. In the same cavity, a wave of anotherwavelength destroys itself by destructive interferencebecause its two parts are out of phase.

Since the development of the first rubyand helium-neon lasers, a great many othermaterials, including even a gelatin dessert,have been made to undergo laser action. Someof these other lasers are important because ofsome properties not possible with the firsttwo types. For example, argon lasers producegreen light and cadmium (metal-vapor) lasersproduce blue light. A carbon dioxide (molec-ular) laser can produce extremely powerfulinfrared radiation. Diode lasers, which use thesame kinds of semiconductors as do tran-sistors, produce only a small amount of light,but they are very small and easy to power;they may have application in super fastcomputers. Organic-dye lasers have relativelyvery large linewidths, but they can easily betuned to produce a wide range of colors oflight.

The monochromaticity of any lightsource can be measured by its bandwidth, ~v,or fractional bandwidth ~v/v.

For the very monochromatic light of alaser the fractional bandwidth might be~v/v = ~A/A ;:::,:10-6•

The temporal coherence of any source ismeasured by the coherence length, ~L, whichis directly related to bandwidth

Monochromatic light is temporally coherentand vice versa. The two terms mean exactlythe same thing.

Light has both wave and particle prop-erties. A photon (light particle) has an energy

where h = 6.63 X 10-34 J·s (Planck's con-stant) and v is the frequency of the associatedwave.

Gases emit light only at certain frequen-cies or wavelengths. The resulting spectrum iscalled a line spectrum. A gas will absorb just

those frequencies it emits. The frequenciesabsorbed or emitted by a gas depend on theenergy levels of its atoms.

An atom can absorb one photon andjump to a higher energy level, or it can emitone photon and jump to a lower energy level.In either case, the change in the energy of theatom will equal the energy of the photon:

When an atom falls to the ground statefrom an excited state without any outsideinfluence, the process is called spontaneousemission. Spontaneous emission accounts formost of the light from ordinary sources.

When an excited atom is stimulated toemit by a light wave of just the rightfrequency, the process is called stimulatedemission. In stimulated emission, the emittedlight is of the same wavelength and exactly inphase with the stimulating light. Laser light is

produced by stimulated emISSiOnfrom theatoms of the active material.

The naturallinewidth, ~VN, of a spectralline depends on the lifetime of the ex-cited state. Thus, it is usually quite narrow:~VN IVN ~ 106

• However, Doppler broad-ening can increase this value by a factorof ten or more so that ~VD Iv ~ 10-5

•

To make a laser work, there must bemore excited atoms than ground-state atoms.This condition is known as inversion. A rubylaser uses the energy from a flashlamp toproduce population inversion in a processcalled optical pumping. In a helium-neonlaser, an electric discharge excites the heliumatoms, which transfer their energy to neonatoms by collisions, producing the requiredpopulation inversion.

Because of the way they build up in thelaser cavity, the resulting waves are highlycoherent (monochromatic) and well collimated(non-diverging).

Work SheetsExperiment A-I

Part II:

1.

10. Part III:

l. Diameter = em

2. Diameter = em

3. Difference = em

4. Diameter = em

5. Diameter = em

6. Difference = em

7.

Work SheetsExperiment B-1

Part Ill:

1.

Work SheetExperiment C-l