laser and its applications1
TRANSCRIPT
Laser and its applications
young man
By
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 2 No external radiation is
required to initiate the emission. Since 2>1, the atom will
tend to spontaneously decay to the ground state 1, a
photon of energy h =2-1 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 (2-1) 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 (2-1) 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 =2-1 passes by an atom
in an excited state 2, it stimulates the atom to drop or
decay to the lower state 1. 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. , the number of atoms 2 in one energy level 2 is
related to the number 1 in another energy level 1 by the equation.
Where 2>1 clearly 2<1
Boltzmann’s constant = 1.38x10-16 erg / degree
= 1.38x10-23 j/K
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 2 can decay to level1 by emission
of photon. Let us call21 the transition probability per
unit time for spontaneous emission from level 2 to level
1. Then the number of spontaneous decays per second
is 221, i.e. the number of spontaneous decays per
second=221.
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
= ( 2-1 )/h , h Planck's const.
Let 21 and 12 denote the proportionality constants for
stimulated emission and absorption. Then number of stimulated downward transition in stimulated emission per
second = 2 21 U
similarly , the number of stimulated upward transitions per second = 1 12 U
The proportionality constants and are known as the Einstein and coefficients. Under equilibrium conditions
we have
by solving for U (density of the radiation) we obtain
U [1 12- 2 21 ] = 21 2
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 ( 10 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 1, 2, 3,….let us fitt our attention to two levels 1&
2 where 2>1 we have already seen that the rate of stimulated
emission and absorption involving these two levels are proportional to 221&112 respectively. Since 21=12, the rate of
stimulated downward transitions will exceed that of the upward transitions when 2>1,.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.
gives the rate of growth of the beam intensity in the direction of propagation, an is the gain constant at
frequency
x,o eII
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 1 of the 1 atoms at level 1 are available for absorption. Similarly of the 2 atoms in level 2, the number 2 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 U)= 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
Calculation of Doppler width:1- Calculate the Doppler’s width for Hg198 . where =1.38x10-16 erg per degree at temp=300k and =5460Ao solution
vm
KT2ln2c
2 o
=
molecular weight m = const. ( atomic mass m\ ) const.=1.668x10-24 gm
\o
mT
.contK2ln2
c2
\o7
mT1017.7 wave number o
1=
=.015 cm-1
2- Calculate the half-maximum line width (Doppler width) for He-Ne
laser transition assuming a discharge temperature of about 400K
and a neon atomic mass of 20 and wavelength of 632.8nm.
(Ans., =1500MHz)