LASER Engineering Physics

1. Introduction:-

The word laser stands for Light Amplification by Stimulated Emission of Radiation.

It is a device that amplifies light and produces a highly directional, high-intensity

beam that most often has a very pure frequency.

2. Characteristics of laser:-

The important characteristics of laser are

1. High directionality
2. High degree of monochromaticity
3. High degree of coherence
4. High intensity
1. High directionality:-

The conventional light sources emit light in all directions due to spontaneous
emission. Laser other hand emit light in one direction due to stimulated emission.
The directionality of laser beam is expressed in terms of divergence.

The degree of directionality is expressed in terms of divergence. The curvature of the

mirrors confines the light within the cavity and causes the beam to narrow down to a
radius ( 0 ) called “minimum spot size”.

The beam divergence  is given in terms of the minimum spot size 0

1.22

20

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 LASER Engineering Physics

The divergence tells how rapidly the beam spreads when it is emitted form the laser.

At d1 and d 2 distances from the laser window, if the diameters of spot are measured

to be a1 and a2 . Then the angle of divergence is

a2  a1

2(d 2  d1 )

2. High monochromaticity:-

Due to stimulated emission, the light emitted by laser is more monochromatic than
that of any congenital monochromatic source.

The degree of monochromaticity will be explained by using line width (or) band
width of source which is the frequency spread of spectral line. Now the degree of
non-monochromaticity  is given by





And for a highly stable gas laser   500Hz and   5 1014 Hz

500
  1012
5 1014

But for a conventional monochromatic source, the degree of non-monochromaticity

is 105 . Therefore the monochromatic source is poorer than the laser source.

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3. High degree of coherence:-

Coherence is related to phenomenon of interference. Interference is observed only

with coherent sources. The property of exciting either zero (or) constant phase
difference between two (or) more waves is known s coherence. The laser beam is
temporally and spatially coherent to an extraordinary degree. Temporal coherence is
referred to longitudinal coherence while the spatial coherence is called lateral
coherence.

Spatial coherence:-

Spatial coherence also referred to as transverse coherence describes how far apart
two sources (or) two portions of the same source can be located in a direction
transverse to the direction of observation and still exhibit coherent properties. This is
some times also referred to as the lateral coherence

Assume two source are separated by a distance ‘s’ in the transverse direction to the
direction of observation and are at a distance ‘r’ from the point of observation. If the
two sources exhibit interference effects at a point ‘a’ and ‘b’. Then the transverse
coherence length lt is the transverse distance from point ‘a’ to point ‘b’ where

r
lt 
s

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 LASER Engineering Physics

Temporal coherence:-

The case of temporal coherence refers to the relative phase (or) coherence of the
two waves at two separated locations along the propagation direction of two beams.
It is some times referred as longitudinal coherence.

If we assume that the two waves are exactly in phase at first location then they will
still be at least partially in phase at second location up to a distance lc , where lc

referred to coherence length

2
lc 


Where  difference in wave length between two waves and  is their average wave
length.

4. High intensity:-

The laser beam is highly intense as compared to ordinary source of light. That is why
it can be used for such operations as welding of metals which involve high
temperature.

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 LASER Engineering Physics

The above fig shows the focusing of laser beam by means of simple lens of radius ‘r’
and focal length ‘f’. The beam has full width angular divergence ‘  ’. The distance ‘ d1 ’

of the focused beam is approximately equal to the focal length of lens ‘f’, multiplied
by the divergent angle  i.e. d1  f  .

Now the area of the focused spot is

 f    0.785 f  2
2
d12
Aspot     
4 4

The intensity (or) power density at focused spot is

P P
I 
Aspot 0.785  f  2

3. Pumping:-

The population inversion cannot be achieved thermally. To achieve population

inversion suitable form of energy must be supplied. The process of supplying suitable
form of energy to a system to achieve population inversion is called pumping.

Most commonly used pumping methods are

1. Optical pumping
2. Electric discharge
3. Inelastic atom-atom collision
4. Direct conversion
5. Chemical reaction

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 LASER Engineering Physics

1. Optical pumping:-

In optical pumping a light source is used to supply luminous energy. Most often this
energy comes in the form of short flashes of light. This method was first used by
maiman in his ruby laser.

2. Electric discharge method:-

In this method the atoms are excited by collision with fast electrons in an electric
discharge. This method is preferred in gaseous ion laser. In this method electrons
emitted by the cathode to be accelerated towards the anode. Some of these
electrons will collide with the atom of the active medium, ionize the medium and
raise it to the higher level.

3. Inelastic atom- atom collision:-

This method is used in gas lasers consisting of two species of atoms. Pumping by
electrical discharge raises one type atoms to their excited states. These atoms collide
inelastically with another type of atoms. It is these latter atoms that provide the
population inversion need for the laser emission. An example for this is the helium-
neon laser.

4. Direct conversion:-

This method is used in semiconductor p-n junction lasers. In this laser electrons and
holes are made to combine across the depletion region by applying a forward bias.
Electrons and holes recombine to emit radiation. Thus direct conversion of electrical
energy into radiation occurs in semiconductor laser and in LED’s.

5. Chemical reactions:-

In this method the energy comes from a chemical reaction without any need for
other source. Hydrogen can react with fluorine to produce hydrogen fluoride
according to the reaction

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 LASER Engineering Physics

H 2  F2  2HF  heat

This reaction generates enough heat to pump a Co2 laser.

4. Population inversion:-
1. Lasing action requires p op ulati on inversion. Population inversion
cannot be obtained in two level pumping systems it can be obtained in multilevel
system.
2. In thermal equilibrium the number atoms in the higher energy level is less than
in lower energy. If there are more atoms in higher energy level than in lower energy
level is called Population inversion.
3. For this life time of the spontaneous emission should be greater i.e. the life
time of the upper energy level should be longer and the light source must be highly
monochromatic.

4. The simplest energy-level system for laser operation is a three-level system. In

this system, the ground state is the lower energy level E1 , and a population

inversion is created between this level and a higher-energy metastable state with
energy E2.

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 LASER Engineering Physics

5. The three-level laser system is operated in the pulsed mode for continuous
mode we have use four- level laser system which shown in the fig. the energy
level structure is similar to that in the three-level system, except that after the
atoms drop from the highest level E4 to the metastable state E3 . The
population inversion is takes place between ground state E 1 and metastable
state E3 . So lasing action occurs between E1 and E3 .
6. Lasing action:-
1. Intense laser beam requires a large number of excited atoms at higher energy
level compared to ground level. This condition is called population inversion.
Population inversion is the process in which the number of atoms in excited state is
more than number of atoms in ground state.
2. Population inversion is the important condition to achieve lasing action. In
general atoms excited to a level that is two or three levels above the ground state.
3. The atoms in excited state release the energy just as they absorb it. The energy
is released in the form of photon. Here lasing action starts spontaneously when an
excited atom in metastable state decays spontaneously by emitting photon.
4. The emitted photon now stimulate the atom which in metastable and bring it to
ground state within the life time by emitting two photons which are in the same
phase, and travels in the same direction. This process is continued until intense
laser beam is emitted. Therefore lasing action occurs spontaneously but laser

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radiation is due to stimulated emission.

7. Interaction of radiation with matter:-

Absorption:-

Let us consider two energy levels with energies E1 and E2 , where E1 ground state is

and E2 is excited state. Usually atoms are present in ground state E1 . When a photon

of energy h is incident on the atom lying in ground state then it excites to higher
state E2 . This phenomenon is known as “absorption”.

Spontaneous emission:-

Let us consider two energy levels with energies E1 and E2 , where E1 ground state is

and E2 is excited state. Usually atoms are present in ground state E1 .let us assume

that the atom is in the excited state E2 .after life time the atom de-excites to its

ground state spontaneously emitting photon of energy h . This phenomenon is

known as “spontaneous emission”.

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 LASER Engineering Physics

Stimulated emission:-

We know that average life time of an atom in the excited state is 108 s. During this
short interval let a photon of energy h is incident on the atom which is in the
excited will return to the ground state within the life time by emitting two photons.
This phenomenon is known as “stimulated emission”.

The direction of propagation, phase and energy emitted photon is exactly same as
that of incident stimulating photon.

6. Main components of laser:-

The main components of laser are

1. Active medium
2. Energy source
3. Optical resonator
1. Active medium:-

It is medium in which metastable state is present. In metastable state only the

population inversion takes place. It can be a solid, liquid, gas or semiconductor
junction.

2. Energy source:-

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 LASER Engineering Physics

It supplies suitable form of energy to the active medium to achieve population

inversion. It performs pumping process.

3. Optical resonator:-

It is an enclosure of the active medium and essentially consists of two mirrors facing
each other. One mirror is fully reflective and other one is partially reflective. The
function of resonator is to increase the intensity of laser beam.

7. Einstein’s coefficients:-

Absorption:-

Let us consider two energy levels 1 and 2 . The probable rate of transition from 1  2
depends upon properties of states 1 and 2 and it is proportional to energy density
u ( ) of radiation of frequency  .

Energy density u ( ) is defined as the radiant energy per unit volume in the frequency
interval  and   d .

The probable rate of occurrence of absorption

P12  u ( )

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 LASER Engineering Physics

P12  B12u( ) ------------------------------ (1)

Where B12 is called “Einstein’s coefficient of absorption”.

Spontaneous emission:-

In spontaneous emission the probable rate of transition from 2  1 is depends upon

properties of states 1 and 2 and it is independent of the energy density.

 P21 spon  A21 ------------------------------ (2)

Stimulated emission:-

In stimulated emission the probable rate of transition from 2  1 is depends upon

properties of states 1 and 2 and and it is proportional to energy density u ( ) of the
stimulating radiation and is given by

( P21 )stimu  u( )

( P21 )stimu  B21u( ) ------------------------------ (3)

The total probability for an atom in state 2 to state 1 is therefore

P21  A21  B21u( ) ---------------------------- (4)

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 LASER Engineering Physics

Relation between different Einstein’s coefficients:-

Let us consider an assembly of atoms in thermal equilibrium at temperature T with

radiation of frequency  and   d and energy density u ( ) . Let N1 and N 2 be the

number of atoms in lower energy state 1 and higher energy state 2 respectively.

The number of atoms in state 1 that absorb a photon and rise to state 2 per unit time
is given by

N1P12  N1B12u( ) --------------------------------- (5)

The number of atoms in state 2 to state 1, either by spontaneous emission or by

stimulated emission is given by

N1P21  N2  A21  B21u ( ) --------------------------------- (6)

Under the condition equilibrium, the number of atoms absorbing radiation per unit
time is equal to the number of atoms emitting radiation per unit time. Hence

N1P12  N1P21

N1B12u( )  N2  A21  B21u( )

N1B12u( )  N2 B21u( )  N2 A21

[ N1B12  N2 B21 ]u( )  N2 A21

N 2 A21
u ( ) 
N1 B12  N 2 B21

N 2 A21
u ( ) 
N B 
N 2 B21  1 12  1
 N 2 B21 

A21 1
u ( )  ---------------------------------- (7)
B21  N1 B12 
 N B  1
 2 21 

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 LASER Engineering Physics

According to Boltzmann distribution law, the ratio of N1 and N 2 is given by

 E 
N 0 exp   1 
N1
  k BT 
N2  E 
N 0 exp   2 
 k BT 

N1  E  E1 
 exp  2 
N2  k BT 

N1  h 
 exp   ------------------------------------ (8)
N2  k BT 

Substitute equation (8) in equation (7), we get

A21 1
u ( )  ------------------------------- (9)
B21   h  B21 
exp    1
  k BT  B12 

According to plank’s radiation law

8 h 3 1
u ( )  ----------------------------------- (10)
c 3
  h  
exp    1
  k BT  

Comparing eq (9) and eq(10), we get

A21 8 h 3

B21 c3
--------------------------------------------- (11)
B21
1
B12

Equation (11) shows the relation between Einstein’s coefficients B12 , B21 and A21 .this

shows that the ratio of Einstein’s coefficient of spontaneous emission to Einstein’s

coefficient of absorption is proportional to the cube of frequency.

The second relation shows the rate of probability of induced emission and
absorption is equal, when the system is equilibrium.

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8. Types of lasers:-

On the basis of active medium used systems, lasers are classified into several types
and most popular methods are

1. Solid-state laser (Ruby laser)

2. Liquid laser (Europium laser)
3. Gaseous laser (He-Ne laser)
4. Dye laser (coumarin dye laser)
5. Semiconductor laser (GaAs laser)
1. Ruby laser:-

Ruby laser is a solid state three-level laser system developed by Maimen in 1960.

It produces pulsed laser which is useful for various industrial applications like surface
hardening, hard facing cladding of various industrial products.

It is a high power laser which has hundreds of MW. Each pulse will come out in
duration of 10 nano seconds. The main components of ruby laser are

Source of energy: - xenon flash lamp

Active medium: - ruby crystal rod

Optical cavity: - arrangement of silver polished surface on either sides of the ruby
rod.

Construction:-

The schematic diagram of ruby laser is is shown in fig.

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 LASER Engineering Physics

Ruby is taken in the form of a cylindrical rod of about 4 cm length and 1 cm in

diameter. Ruby crystal is basically Al2O3 crystal containing about 0.05% of chromium
3
atoms. The Al 3 ions in the crystal lattice are replaced Cr ions will play main role in
the emission of laser beam.

The two ends of a ruby crystal are grounded and polished and one face is silvered to
achieve 100% reflection while the opposite face is partially silvered to make it
semitransparent. A xenon flash tube is arranged around the ruby rod. Which supplies
green colour flash light of wave length 5600A0 to active medium to active population
inversion. Only a part of flash light is used for the pumping the Cr 3 , while the rest
heats up the apparatus. A cooling arrangement is provided to keep the experiment
setup at normal temperature.

Working principle:-

1. The energy level of Cr 3 ions in the crystal lattice is shown in fig. they form
basically a three level system.
2. The xenon flash lamp generates an intense white light lasting for a few
milliseconds. The green component of the light having wavelength 5600A0 is
absorbed by Cr 3 ions raising them from the ground state E1 to the excited

state E3 . The excited levels are highly unstable.

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 LASER Engineering Physics

3. The Cr 3 ions rapidly lose part of their energy  E2  E3  to the crystal lattice

and undergo non-radiative transition to the E2 is metastable state. Therefore

Cr 3 ions accumulate there.

4. If pumping occurs at a faster rate the population at the level E2 exceeds that

of the ground level E1 in a short time. The state of population inversion gets

established between E2 and E1 level.

5. A spontaneous photon emitted by a Cr 3 ion at E2 level initiates the

stimulated emission by the other Cr 3 ions in the metastable state.

6. Photons traveling along the axial direction are repeatedly reflected and
amplified, and emerge out of the semi-transparent mirror in the form of a
strong laser beam.
7. The beam is red in colour and corresponds to a wavelength of 6943A0 and
frequency 4.32 1014 Hz .

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2. He-Ne laser:-

The main drawback of ruby laser is that the output beam is not continuous through
very intense. The laser is very highly directional, monochromatic, coherent and
stable. But the output power is moderate when it is compared with solid state laser.
It is very useful in making holograms and interferometric experiments.

Source of energy: - R.F oscillator

Active medium: - helium-neon gas mixture

Optical cavity: - arrangement of fully and partially reflective mirrors on either sides
of quartz tube.

Construction:-

The gas laser consists of a fused quartz tube with diameter about 1.5 cm and 80 cm
long. In this laser active medium is a mixture of ten parts of helium to one part of
neon. The neon atoms provide the energy level for laser transition. Through helium
atoms are not directly involved in the laser transition, they provide an efficient
excitation mechanism for neon atoms. In He-Ne gas laser electric discharge method
is used for pumping process.

Working:-

When an electric discharge is posses the He-Ne gas mixture, helium atoms are
excited to higher levels He2 and He3 through collisions with accelerated electrons.

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 LASER Engineering Physics

In this neon atom contain six energy levels Ne1 , Ne2 , Ne3 , Ne4 , Ne5 and Ne6 . Here it

should be noted that Ne4 and He2 have same energy and life time and similarly Ne6

and He3 .

The states He2 and He3 are metastable states from which there are no allowed

transitions. The excited helium atoms then collide inelastically with neon atoms still
in ground state and transfer energy to them. This interaction excites the neon atoms
to their metastable states Ne6 and Ne4 . After collision, the helium atoms are

returned to ground state He1 .

A population inversion is thus created between Ne6 and ( Ne5 , Ne3 ) group and also
between Ne4 and Ne3 . There are three possible transitions in between Ne6 , Ne5 , Ne4
and Ne3 .

1. Ne6  Ne3 Transition: - This transition generates a laser beam of red colour of

wave length 6328A0 .

2. Ne6  Ne5 Transition: - during this transition electromagnetic radiation of wave

length 3390A0 .

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 LASER Engineering Physics

3. Ne4  Ne3 Transition: - during this transition an electromagnetic radiation of

1150A0 is emitted.

Whereas 3390A0 and 1150A0 transitions are in infrared region where as 6328A0
transition is in visible region. Thus build up of 1150A0 and 3390A0 transitions reduce
6328A0 transition. To overcome this problem in order to get only 6328A0 output, the

laser tube windows are made up of glass (or) quartz. That absorb strongly 1150A0 and

3390A0 .

When an excited neon atom passes from metastable state Ne6  Ne3 it emits

photon. This photon travels through the gas mixture. If the photon is moving parallel
to the axis of tube, it reflects back and forth by mirror ends until it stimulates an
excited neon atom by emitting photon with same phase and direction.

The stimulated transition is a laser transition. This process continues till a beam of
coherent radiation build up in the tube. When the beam becomes sufficiently intense
it escapes through the partially silvered end.

3. Co2 Laser:-

The carbon dioxide laser is very useful and efficient to produce high power laser of
several kilowatts. Therefore, it is widely used in medical field, communications and
weaponry. It is a four level laser and emit continuous laser.

The carbon dioxide laser was invented by C.K.N Patel in 1963. The active medium is
Co for efficient excitation of Co molecules N molecules are used. Addition of He
2 2 2
to the gas mixture the increases efficiency. The ratio of pressure of Co : N : He is
2 2
1: 4 : 5 .

Construction:-

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 LASER Engineering Physics

The schematic diagram of Co laser is shown in fig. it is basically a discharge tube

2

having cross-section of about 1.5mm2 and length of about 260mm . The discharge tube
is filled with a mixture of carbon dioxide, nitrogen and helium gases at the ration of
1: 2 : 3 . In Co laser electric discharge method is used for pumping.
2

Energy levels of Co laser:-

2

Co molecules have a more complicated structure and have energy levels that
2
correspond to rotation (or) vibration motion of entire molecule structure.

The Co molecule is a composed of two oxygen atoms and a carbon atom between
2
them, undergoes three different types of vibrational oscillations known as the
“vibrational modes”.

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 LASER Engineering Physics

At any one time, the molecules can be vibrating in any combinations of these

 
fundamental modes. A set of three quantum numbers 1,2,3 are used to denote

the modes of vibration. Where  represents symmetric modes of vibration 

1 2
represents bending mode of vibration and  represents the asymmetric mode of
3
vibration.

For example the set (001) represents a molecule vibrating in pure symmetric mode
and (020) indicates that the molecule is vibrating with pure bending with two units of
energy.

In addition to these vibrational the molecule can also rotate and thus it has closely
spaced rotational energy levels associated with each vibrational energy level.

Simplified energy level diagram for Co laser is shown in fig.

2

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 LASER Engineering Physics

In Co laser, the excitation is provided by electric discharge. Excited N molecules

2 2
transfer their energy to the Co molecule in resonant collisions exciting them to
2
(001) level which are metastable level with relatively longer life time.

With sufficient pumping, a population is produced between (001) state and (100) and
(020) states and laser transition begins. The possible laser transitions are

 The laser transition between  001   020 level will produces 9.6 m wavelength

of radiation

 And the transition from  001  100 level will produces 10.6 m wavelength of

radiation.

 Since the laser transition from  001  100 has higher gain than from
 001   020 , so the laser beam usually oscillates at 10.6 m .

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 LASER Engineering Physics

This process leads to accumulation of population at (010) level. The presence of

helium along with Co helps to decrease the population density at (010) level. It de-
2
excite the Co molecules through inelastic collisions.
2

The Co laser operates in continuous wave mode and is capable of generating high
2
power of the order of several kilowatts at a relatively high efficiency of about 40%.
Therefore it is mostly used laser.

12. Semiconductor laser:-

Semiconductor lasers are unique when compared to other types of lasers. They are
very small, they operate with relatively low power input, and they are very efficient.
They also operate in a different way in that they require the merging of two different
materials and the laser action occurs in the interface between those two materials.
One of the materials has an excess of electrons (n-type) and the other material (p-
type) has excess of holes. When forward bias voltage is placed across this junction
electrons are forced into the region from the n-type material and holes are forced
into junction from the p-type material. These electrons with a negative charge and
the holes with a positive charge are attracted to each other, and when they collide
they neutralize each other and in the process emit radiation this process is known as
recombination.

On the basis of recombination processes, semiconductors are classified into two

categories

 Direct band gap semiconductors are those in which conduction electrons

recombine direct with holes

 Indirect band gap semiconductors are those in which conduction electrons

recombine with holes via intermediate energy levels

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 LASER Engineering Physics

There is large possibility to emit electromagnetic radiation during the direct

recombination process, but not in case of indirect recombination. Therefore direct
band gap semiconductors are useful to construct semiconductors laser.

Semiconductor lasers are classified into two types, they are

1. Homo-junction diode laser system

2. Hetero-junction diode laser system
A homo-junction laser is formed between n-type and p-type semiconductor of same
materials where as hetro-junction is formed between n-type and p-type
semiconductors of different materials.

Construction of homo-junction GaAs diode laser:-

In this laser system, the active medium is PN-junction diode formed between n-GaAs
and p-GaAs. The impurities germanium and tellurium are dopped into GaAs
semiconductor to obtain p- type GaAs and n-type GaAs respectively. The thickness of
the pn-junction layer is very narrow so that the emitted laser radiation has large
divergence and poor coherence. At the junction two sides which are parallel to each
other are well polished through which laser is emitted. And the other sides are
roughened to avoid laser emission.

To provide forward bias two metal contacts are provided in the top and bottom of
the diode.

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 LASER Engineering Physics

Construction of hetero-junction diode laser:-

Hetero-junction means that the material on one side of the junction differs from that
on the other side of the junction. A layer of GaAs is sandwiched between two layers
of GaAlAs that has a wider energy gap than and also lower refractive index. Fig shows
a double hetero structure strip laser diode in which the numbers 1,2,3,4 and 5 are
indicating the various layers. The laser emission takes place between the layers 2 and
4. Where 1, 2 and 4 are GaAlAs layers and 3, 5 are GaAs layers.

Working principle:-

The working principle is same for the homo and hetero junction diode laser systems.
The population inversion can be obtained by injecting electrons and holes into the
junction from the n-region and p-region respectively by means of forward bias
voltage. When forward bias is not connected then energy diagram will be shown in
fig. i.e. no electrons and holes present in the depletion region.

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 LASER Engineering Physics

When a small forward bias is given to the pn-junction then small number of electrons
and holes will be injected into the depletion region from respective region.

When a relatively large current is passed through the junction then large number of
electrons and holes will be injected into depletion region and direct recombination
process takes place. Further the emitted photon increase the rate of recombination.
Thus more number of photons produced. Hence the emitted photons from induced
recombination are having the same frequency as that of original inducing photons.

The wavelength of emitted radiation depends upon the concentration of donor and
acceptor atoms in GaAs.

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