Laser and its applications

Chapter (1): Theory of Lasing (2)

Chapter (2): Characteristics of laser beam ( )Chapter (3): Types of laser sources ( ) Chapter (4): Laser applications ( )

Contents page

Chapter (1) Theory of Lasing1.Introduction (Brief history of laser)

The laser is perhaps the most important optical device to be developed in the past 50 years. Since its arrival in the 1960s, rather quiet and unheralded outside the scientific community, it has provided the stimulus to make optics one of the most rapidly growing fields in science and technology today.

The laser is essentially an optical amplifier. The word laser is an acronym that stands for “light amplification by the stimulated emission of radiation”. The theoretical background of laser action as the basis for an optical amplifier was made possible by Albert Einstein, as early as 1917, when he first predicted the existence of a new irradiative process called “stimulated emission”. His theoretical work, however, remained largely unexploited until 1954, when C.H. Townes and Co-workers developed a microwave amplifier based on stimulated emission radiation. It was called a maser.

Following the birth of the ruby and He-Ne lasers, others devices followed in rapid succession, each with a different laser medium and a different wavelength emission. For the greater part of the 1960s, the laser was viewed by the world of industry and technology as scientific curiosity.

In 1960, T.H.Maiman built the first laser device (ruby laser). Within months of the arrival of Maiman’s ruby laser, which emitted deep red light at a wavelength of 694.3 nm, A. Javan and associates developed the first gas laser (He-Ne laser), which emitted light in both the infrared (at 1.15mm) and visible (at 632.8 nm) spectral regions..

1.Einstein’s quantum theory of radiation In 1916, according to Einstein, the interaction of

radiation with matter could be explained in terms of three basic processes: spontaneous emission, absorption and stimulated emission. The three processes are illustrated and discussed in the following:

Before After

(i) Stimulated absorption

ii) Spontaneous emission (

)iii (Stimulated emission

)ii) Spontaneous emission Consider an atom (or molecule) of the material is existed

initially in an excited state E2 No external radiation is

required to initiate the emission. Since E2>E1, the atom will

tend to spontaneously decay to the ground state E1, a

photon of energy h =E2-E1 is released in a random direction as shown in (Fig. 1-ii). This process is called “spontaneous emission”

Note that; when the release energy difference (E2-E1) is delivered in the form of an e.m wave, the process called "radiative emission" which is one of the two possible ways “non-radiative” decay is occurred when the energy difference (E2-E1) is delivered in some form other than e.m radiation (e.g. it may transfer to kinetic energy of the surrounding)

(iii) Stimulated emission Quite by contrast “stimulated emission” (Fig. 1-iii)

requires the presence of external radiation when an incident photon of energy h =E2-E1 passes by an atom

in an excited state E2, it stimulates the atom to drop or

decay to the lower state E1. In this process, the atom

releases a photon of the same energy, direction, phase and polarization as that of the photon passing by, the net effect is two identical photons (2h) in the place of one, or an increase in the intensity of the incident beam. It is precisely this processes of stimulated emission that makes possible the amplification of light in lasers.

Growth of Laser Beam

Atoms exist most of the time in one of a number of certain characteristic energy levels. The energy level or energy state of an atom is a result of the energy level of the individual electrons of that particular atom. In any group of atoms, thermal motion or agitation causes a constant motion of the atoms between low and high energy levels. In the absence of any applied electromagnetic radiation the distribution of the atoms in their various allowed states is governed by Boltzman’s law which states that:

The theory of lasing

if an assemblage of atoms is in state of thermal equilibrium at

an absolute temp. T, the number of atoms N2 in one energy level

E2 is related to the number N1 in another energy level E1 by the

equation.

Where E2>E1 clearly N2<N1

K Boltzmann’s constant = 1.38x10-16 erg / degree

= 1.38x10-23 j/K

T the absolute temp. in degrees Kelvin

KT/)1E2E(12 eNN

At absolute zero all atoms will be in the ground

state. There is such a lack of thermal motion among the electrons that there are no atoms in higher energy levels. As the temperature increases atoms change randomly from low to the height energy states and back again. The atoms are raised to high energy states by chance electron collision and they return to the low energy state by their natural tendency to seek the lowest energy level. When they return to the lower energy state electromagnetic radiation is emitted. This is spontaneous emission of radiation and because of its random nature, it is incoherent

As indicated by the equation, the number of atoms decreases as the energy level increases. As the temp increases, more atoms will attain higher energy levels. However, the lower energy levels will be still more populated.

Einstein in 1917 first introduced the concept of stimulated or induced emission of radiation by atomic systems. He showed that in order to describe completely the interaction of matter and radiative, it is necessary to include that process in which an excited atom may be induced by the presence of radiation emit a photon and decay to lower energy state.

An atom in level E2 can decay to level E1 by emission

of photon. Let us call A21 the transition probability per

unit time for spontaneous emission from level E2 to

level E1. Then the number of spontaneous decays per

second is N2A21, i.e. the number of spontaneous decays

per second=N2A21.

In addition to these spontaneous transitions, there will induced or stimulated transitions. The total rate to these induced transitions between level 2 and level 1 is proportional to the density (U) of radiation of

frequency , where

= ( E2-E1 )/h , h Planck's const.

Let B21 and B12 denote the proportionality constants for

stimulated emission and absorption. Then number of stimulated downward transition in stimulated emission per second = N2 B21 U

similarly , the number of stimulated upward transitions per second = N1 B12 U

The proportionality constants A and B are known as the Einstein A and B coefficients. Under equilibrium

conditions we have

by solving for U (density of the radiation) we obtain

U [N1 B12- N2 B21 ] = A21 N2

212121

212

BNBNAN

)(U

N2 A21 + N2 B21 U =N1 B12 U

SP ST

A b

1

)(

2

1

21

1221

21

NN

BBB

AU

KT/hKT/)EE(

1

2 eeNN 12

1e

BBB

A)(UKT/h

21

1221

21

According to Planck’s formula of radiation

1e1

ch8)(U KT/h3

3

)2)

)1)

from equations 1 and 2 we have B12=B21 (3)

213

3

21 Bch8A

equation 3 and 4 are Einstein’s relations. Thus for atoms in equilibrium with thermal radiation.

)4(

21

21

212

212

A)(UB

AN)(UBN

emissioneoustansponemissionstimulate

from equation 2 and 4

1e1

ch8

h8c

)(Uh8c

emission.sponemission.stim

KT/h3

3

3

3

3

3

1e1

emission.sponemission.stim

KT/h

)5(

Accordingly, the rate of induced emission is extremely small in the visible region of the spectrum with ordinary optical sources ( T10 3 K .(

Hence in such sources, most of the radiation is emitted through spontaneous transitions. Since these transitions occur in a random manner, ordinary sources of visible radiation are incoherent.

On the other hand, in a laser the induced transitions become completely dominant. One result is that the emitted radiation is highly coherent. Another is that the spectral intensity at the operating frequency of the laser is much greater than the spectral intensities of ordinary light sources.

Amplification in a Medium Consider an optical medium through which radiation is

passing. Suppose that the medium contains atoms in various energy levels E1, E2, E3,….let us fitt our attention to two levels E1&

E2 where E2>E1 we have already seen that the rate of stimulated

emission and absorption involving these two levels are proportional to N2B21&N1B12 respectively. Since B21=B12, the rate of

stimulated downward transitions will exceed that of the upward transitions when N2>N1,.i.e the population of the upper state is

greater than that of the lower state such a condition is condrary to the thermal equilibrium distribution given by Boltzmann’s low. It is termed a population inversion. If a population inversion exist, then a light beam will increase in intensity i.e. it will be amplified as it passes through the medium. This is because the gain due to the induced emission exceeds the loss due to absorption.

x,o eII

gives the rate of growth of the beam intensity in the direction of propagation, an is the gain constant at

frequency

Quantitative Amplification of light

In order to determine quantitatively the amount of amplification in a medium we consider a parallel beam of light that propagate through a medium enjoying population inversion. For a collimated beam, the spectral energy density U is related to the intensity in the frequency interval to + by the formula.

Due to the Doppler effect and other line-broadening effects not all the atoms in a given energy level are effective for emission or absorption in a specified frequency interval. Only a certain number N1 of the N1 atoms at level 1 are available for absorption. Similarly of the N2 atoms in level 2, the number N2 are available for emission. Consequently, the rate of upward transitions is given by:

cIU

vI

U

1LI

U

cIU

221221 N)c/I(BNUB

and the rate of stimulated or induced downward transitions is given by:

Now each upward transition subtracts a quantum energy h from the beam. Similarly, each downward transition adds the same amount therefore the net time rate of change of the spectral energy density in the interval is given by

U)NBNB(h)U(dtd

112221

where (h B NU)= the rate of transition of quantum energy

cI)NBNB(h)

cI(

dtd

112221

In time dt the wave travels a distance dx = c dt i.e

dxc

dt1

then

IB)

NN(

ch

dxdI

2112

I

dxdI

dxI

dI

x.,o eII

in which is the gain constant at frequency it is given by:

1212 B)NN(

ch

an approximate expression is

1212max B)NN(ch

being the line width

Doppler width This is one of the few causes seriously affecting equally

both emission and absorption lines. Let all the atoms emit light of the same wavelength. The effective wavelength observed from those moving towards an observer is diminished and for those atoms moving away it is increased in accordance with Doppler’s principle.

When we have a moving source sending out waves continuously it moves. The velocity of the waves is often not changed but the wavelength and frequency as noted by stationary observed alter.

Thus consider a source of waves moving towards an observer with velocity v. Then since the source is moving the waves which are between the source and the observer will be crowded into a smaller distance than if

the source had been at rest. If the frequency is o , then

in time t the source emit ot waves. If the frequency had

been at rest these waves would have occupied a length AB. But due to its motion the source has caused a

distance vt, hence these ot waves are compressed into

a length where \\BA

vtBAAB \\

vttt \oo thus

o

\ v

o

\ v

)v1(o

\

Observer

)cv1(\

)cv1(cc

o

where n=c

)cv1(cc

o

)cv1(o

cv1

o

cv

o

o

)(cv oo

Evaluation of Doppler half width :

According to Maxwelliam distribution of velocities, from the kinetic theory of gasses, the probability that the velocity will

be between v and v+v is given by:

dveB 2Bv

So that the fraction of atoms whose their velocities lie between v and v+ v is given by the following equation

veBN

)(N 2Bv

where B= m = molecular weight, K=gas constant, T=absolute temp

KT2m

Substituting for v in the last equation from equation (1) and since the intensity emitted will depend on the number of atoms having the velocity in the region v and

vv then, i. e. N)(N)(I

I() = const . 2)o(2

o

2cB

e

= at

I(

=(I

=const

) )= max= const

There for

max 2)o(

2o

2cB

e

21e

I)2/(I 4

2

2o

2cB

max

o

being the half width of the spectral line it is the width at

2Imax , then

4cB2ln

2

2o

2

2lnmkT2

c2 o