Module V

Double and Multiple Slit’s interference –

Diffraction gratings – Thin films – Anti-reflection
coatings – Newton’s Rings, Air Wedge and their
applications –
Michelson Interferometer –
The Diffraction Limit

Module VI
Lasers – Principles and applications – Einstein’s
Coefficients – Laser Resonator – Semiconductor Laser
 Young’s Double Slit Interference

A monochromatic light source is incident on the first screen which contains a slit S0 . The
emerging light then arrives at the second screen which has two parallel slits S1 and S2 .
which serve as the sources of coherent light. The light waves emerging from the two slits
then interfere and form an interference pattern on the viewing screen. The bright bands
(fringes) correspond to interference maxima, and the dark band interference minima.
Diffraction Gratings

Remember the double-slit interference pattern from the

chapter on interference?

2  d sin 
I = Imax cos  
  

If the slit width (not the spacing

between slits) is small (i.e.,
comparable to the wavelength of
the light), you must account for
diffraction.
interference only
Single Slit
Double Diffraction with a  
SlitDiffraction

r1
y
a
S1 r2
a 

P
O
d
S2

L
 Diffraction Gratings
A diffraction grating consists of a large number of equally
spaced parallel slits.

The path difference between

rays from any two adjacent
slits is  = dsin .


If  is equal to some integer
multiple of the wavelength
then waves from all slits will
d
arrive in phase at a point on
a distant screen.
 = d sin 

Interference maxima occur for d sin = m, m =1, 2, 3, ...

Diffraction is not the same as refraction!
 double-slit interference
d sin = m, m =1, 2, 3, ... constructive

diffraction grating
d sin = m, m =1, 2, 3, ... constructive
Diffraction Grating Intensity Distribution

Interference Maxima:
d sin = m

 = d sin 
The intensity maxima are
brighter and sharper than for
the two slit case
 Thin films – Antireflection Coatings
Whenever light passes through a boundary, part of the light is lost due to reflection. The
reflectivity r at a boundary between two media of refractive indices 1 and 2 at normal
incidence is given by
2
   
r  2 1
 2  1 

For example, at a boundary between air (1 = 1) and glass (2 = 1.5) , the reflectivity is 0.04
which means that when light falls on a glass surface, 4% of the light is reflected and lost.
There are ways of reducing such losses :

1. Reflection will not occur if 1 = 2. But then no refraction will occur.

2. Another way of eliminating reflection is by interference, applying a suitable

coating to the surface.
 Monolayer Antireflection Coating
Consider that light is incident on a glass surface coated with a thin film of transparent
material as shown in the Figure. Some light will be reflected from the front surface of the
film and some light will be reflected from the back surface of the film. These reflections
can be made to cancel if the two reflected waves are out of
phase by 180 and approximately they have the same
amplitude A1 = A2.

Amplitude condition : 0 1 glass

A1 = A2
2 2
 1  0    g  1  Where 0 is the refractive index of air
 

  
   g  1  1 is the refractive index of the coated film and
 1 0   
g is the refractive index of the glass substrate.
1 1  g  1

1  1  g  1 2 12  2  g

1 g  12   g  1  1 g  12   g  1 1  g

 Monolayer Antireflection Coating
Out of phase condition :
2 1 d = (n + ½)  d

1 d  for n = 0
4
0 1 g

This means that the optical thickness of the coating should

be equal to one-quarter of a wavelength


A coating of refractive index 1   g and thickness gives anti-reflection.
4 g

If coating is transparent no light will be absorbed or scattered. The entire light is

transmitted. The coating material should be insoluble and scratch resistant. The best
material known is magnesium fluoride MgF2; Its refractive index is 1.38.
 Multilayer antireflection coatings
• A single layer coating is effective only for one
wavelength. The wavelength chosen is usually near
the centre of the visible spectrum, causing part of
the blue and red to be reflected. This makes the
coating on the camera lens appear purple. A wider
coverage of wavelength is possible with multiple
coatings called multilayers.
• In a two layer anti-reflection coating, each layer is
made /4 thick. This is called quarter-quarter
coating. No reflection will occur if the following
condition is satisfied :  2 
 0
1 g

2 2
 Multilayer antireflection coatings
• In three layer anti-reflection coatings, the centre layer is
made /2 thick, the other two layers are /4 each. This is
called quarter-half-quarter coating. Such coatings are
effective over most of the visible spectrum.
• The first outside layer is often /4 coating of magnesium
fluoride, the next is /2 zirconium dioxide ZrO2, with
refractive index 2.10 and the next layer close to the
substrate is /4 cerium fluoride CeF3 with refractive index
1.63 or aluminum oxide Al2O3 with refractive index 1.76.
• Modern antireflection coatings have upto 100 layers of
alternating high and low index materials.
 Air Wedge
Air Wedge is formed using two optically flat glass plates with a thin paper or hair or thin wire
at one end. The two glass plates may he held together with the help of a rubber band.

The light from the Sodium lamp is

made to fall on a 45 glass plate. The
reflected light from the Air Wedge set
up is made to pass through the 45
glass plate and captured in a travelling
microscope. The path difference
between the reflected wave from the
bottom surface of the top glass plate
and the top surface of the bottom glass
place overlap with each other in the
region above the airwedge forming
interference fringes.

By measuring the distance between the thin sheet and the line of contact of glass plates and
from the fringe width, the thickness of the thin sheet or hair or wire can be calculated.
 Air Wedge

Let  be the small angle formed by the glass plates. ‘’ is the ref.index of the medium
between the plates. Consider a point at a distance x1 from the line of contact of the plates.
Let the thickness of the air film be ‘t’ at the distance x1. The path difference between the
two reflected wave fronts coming from the top surface of the bottom glass plate and the
bottom surface of the top glass plate is ‘2t’.
An additional path difference of /2 is produced d
since the second wave front is reflected from a  
l
denser to rarer medium. Hence, the net path
difference is 2t + /2 d t

2t + /2 = n  bright fringe condition 
2t + /2 = (n + ½)  dark fringe condition x1
t
2t = n  dark fringe 
x1
2 x1 = n  dark fringe
2 x2  = (n +1)  next dark fringe at distance x2 from the line of contact

2 ( x2 - x1)  =  where x2 - x1 is the fringe width 

On substituting for , we get

d d l Thickness can
2  ( x2  x1 )   or 2    or d 
l l 2  be determined
 Michelson Interferometer
An interferometer is a device that can be used to measure lengths or changes in length
with great accuracy by means of interference fringes.
A.A. Michelson showed that the international standard of
length ‘meter’ was equivalent to 1553163.5 wavelengths
of a certain monochromatic red light emitted from a
cadmium light source with his careful measurement with
his interferometer, which he originally devised and built.
For this, he received the 1907 Nobel Prize in Physics

Interference is modification of intensity obtained by the

superposition of two or more beams of light, derived from Albert Abraham Michelson
the same source. When they are derived from the same (1852 – 1931)
source, they are coherent1.

In 1800 A.D, Thomas Young obtained two interfering sources by division of wavefront
originated from the same source and observed interference fringes. Later in 1881 A.D,
A.A. Michelson obtained two interfering sources by division of amplitude originated from
the same source and observed interference fringes in their region of overlap
 Constructive and destructive interference
When the interfering waves arrive in phase with each other at a given point in space, the
intensity is maximum at that point. In other words, when the phase difference between the
two coherent waves which superpose at a point in space is zero, a bright fringe is formed.
When the modified intensity is greater than the two separate intensities, it is called
constructive interference. When the modified intensity is smaller than the two separate
intensities, it is called destructive interference and a dark fringe is formed.

The relation between the phase difference and path difference between two waves is
given by Phase difference  2
Path difference   where k =
k 
Phase / path difference between Maxima Minima
the two interfering waves

     
Phase difference = 0, 2 , 4 , 6 , 8 ,.... , 3 , 5 , 7 , ....


   
Path difference  = 0,  , 2  , 3 , 4 , .... /2, 3/2 , 5/2 , , ....
  or (n + ½) 
or n where n = 0, 1, 2, 3, ... where n = 0, 1, 2, 3, ...
 
 Construction of Michelson Interferometer
Consider a beam of monochromatic light coming from an extended source S falls on a
beam splitter B that is kept at 45. The beam splitter is a semi silvered mirror that transmits
half of the incident beam (horizontal component) and reflects the other half light beam
(vertical component). The transmitted beam goes to a fixed mirror M 1 and the reflected
beam goes to a movable mirror M2. The mirrors M1 and M2 are kept exactly perpendicular
to each other with the help of three equidistant screws kept behind the mirrors. A
compensator plate C, made of the same glass and with the same thickness as beam splitter, is
kept at the same angle of 45 in the path of the transmitted beam. This is to compensate the
extra path length traversed by the reflected component inside the beamsplitter glass.
Movable M
2
mirror

The two beams traveling towards the

mirrors M1 and M2, get reflected from
them and they are made to overlap with
each other by the beamsplitter. An S
interference fringe pattern can be viewed B C
through a telescope T. The whole Fixed
mirror M1
apparatus is very rigidly mounted on a
frame using very fine screws for accuracy
and high precision.
T

,.
Working of Michelson Interferometer

An extended source emits a monochromatic beam of light which falls on a beamsplitter.

Two interfering beams are obtained by division of amplitude using the beam splitter. The
transmitted beam travels through the compensator plate C towards the fixed mirror M 1 and
falls on it normally. The beam gets reflected and retraces its path back to the beamsplitter.
The reflected component on the beamsplitter reaches the telescope T.

The transmission phenomenon involves no Movable M

2
phase reversal; but each reflection mirror

phenomenon involves a phase change of , as

each reflection happens from rarer medium to
denser medium.
S
The reflected beam travels towards the B C
movable mirror M2. The beam undergoes Fixed
mirror M1
reflection with normal incidence and retraces
its path back to the beamsplitter. Here, the
transmitted component on the beam splitter T
reaches the telescope T.
 Theory of fringe formation
When the two mirrors M1 and M2 are kept exactly at equal distances from the beam splitter,
the two interfering beams travel equal length and the total path difference between them is


2
which corresponds to a phase difference of  =  Virtual source1 M2'

2d cos r
This is due to the additional phase reversal of the 2d
r
transmitted beam which goes to M1. When the
movable mirror M2 is kept at a distance ‘d’ away Virtual source M1'
from its current position, the transmitted beam
travels an additional distance of ‘2d’. r
Therefore, the total path difference is   2d 

2
The telescope captures the rays which appears to emerge from the normal
two mirrors M1 and M2 in a field of view, where slightly inclined
rays which make an angle ‘r’ with the normal to the mirrors,
make concentric circles of alternate bright and dark bands of
interference fringes. The total path difference between the rays

emerging from virtual sources of M1 and M2 is given by   2d cos r 
2
 Interference conditions

Condition for bright fringes :


  2d cos r  = n where n = 0, 1, 2, 3, ...
2

Condition for dark fringes :


  2d cos r  = (n + ½)  Fringes of equal inclination
2
where n = 0, 1, 2, 3, ... form concentric circles in the
telescopic field of view
Larger the ‘d’ value, greater is the number
A particular dark or bright ring has a constant
of concentric circles appearing in the field
value of ‘r’, where ‘r’ is the angle of
of view. Smaller the ‘d’ value, less number
inclination of the slightly off – axis rays which
of concentric circles appearing in the field
manage to reach the telescopic field of view.
of view. For d = 0, both the mirrors M1 and
Therefore, these bright and dark rings are also
M2 are at equal distances and this known as fringes of equal inclination. The
corresponds to a uniform dark broad values of ‘r’ are very small close to zero and
circular fringe. the factor cos r can be approximated to unity.
 Formation of circular fringes with
increasing values of ‘d’ in steps of /4

 3
d=0;  d = /4    d = /2   d = 3/4   2
2 2

5 7
d =  ;  d = 5/4   3 d = 6/4   d = 7/4   4
2 2
 Types of fringes formed

M2'
d=0
M1',M2' 2d

M1'

Formation of hyperbolic and straight fringes

with movement of tilted movable mirror
M2'
M2'
M1' M1'
M1'
M2'


Determination of wavelength of monochromatic light

Initial adjustment of Michelson interferometer:
 When the telescope is focused, normally hyperbolic fringes would appear. The
movable mirror M2 is moved in a direction such that the curvature of the fringes
decrease and become straight fringes. The two mirrors are set approximately at equal
distances.
 The three screws behind the movable mirror are adjusted to obtain circular fringes.
The two mirrors are exactly set perpendicular to each other.
 The movable mirror M2 is moved using a micrometer vernier set up (for movement of
very small distances) in a direction such that the number of fringes decreases slowly to
obtain a single broad circular dark fringe. The cross wire is set on the central fringe.

The initial micrometer reading can be noted after the initial adjustment. The movable mirror
M2 is moved slowly, simultaneously counting the number of fringes (choose either dark or
bright) which collapse in or emerge out of the centre of the concentric ring pattern. The
difference between the initial and final micrometer reading will give the distance moved by
the movable mirror ‘L’. Then the unknown wavelength  of the source can be determined
from the equation 2L = n  where ‘n’ is the number of fringes that collapse in / emerge out
or crossing the field of view.
 Determination of thickness of a thin transparent film
After initial adjustment and noting down initial micrometer reading, insert the thin film of
unknown thickness ‘t’ in the path of any one of the interfering beams of the Michelson
interferometer. Then, the path difference introduced due to insertion is 2 ( - 1) t = n 
where  is the refractive index of the
thin film. ‘n’ is the number of fringes Movable mirror M1
shifted across the field of view due to
the path difference introduced. Move Thin film t
the movable mirror in a direction such
that the number of fringes decreases
slowly and get back the original broad
Source
circular central fringe pattern. If ‘L’ is
the distance moved by the mirror, then
2 ( - 1) t = n  = 2 L Fixed
M
mirror 2
If the refractive index of the thin film ‘’ is known,
then its thickness ‘t’ can be determined as Telescope

2L n
t = (   1) or t =
(   1)

Or if thickness is known, then its refractive index  of the thin film can be determined.
 The Diffraction Limit of a Telescope

S1


S2

The minimum angular separation of two sources that can be distinguished by a

Telescope is called Diffraction Limit.

1.22 
 
a

a is the telescope diameter

Lasers
 Introduction
In 1953, Charles H. Townes and graduate students James P. Gordon and Herbert J.
Zeiger produced the first Maser an acronym for “Microwave Amplification by
Stimulated Emission of Radiation”, a device operating on similar principles to the laser,
but producing microwaves rather than optical radiation.

And in 1960, Theoder H.Mainman achieved a similar amplification in the optical (light)
region using a ruby rod (ruby laser - red light at 694 nanometres wavelength). It was
named LASER2, an acronym for “Light Amplification by Stimulated Emission of
Radiation”. Later in the same year the Iranian physicist Ali Javan, together with William
Bennet and Donald Herriot, made the first gas laser using helium and neon. The concept
of the semiconductor laser was proposed by Basov and Javan; and the first laser diode
was demonstrated by Robert N. Hall in 1962.
In 1970, semiconductor diode laser with a heterojunction structure and continuously
operation at room temperature was independently developed by both Zhores Alferov in
the Soviet Union and Izuo Hayashi and Morton Panish of Bell Telephone Laboratories.
 Einstein’s theory of emission
For interaction to occur, first of all, the energy of the interacting photon h must match
with the energy difference between the two states of the atoms involved in the interaction.

Under this condition, if the radiation interacts with atoms in the lower energy state say E 1,
the atoms absorb the energy and get excited to the higher energy state E 2 by a process
called stimulated absorption. Instead, if the radiation interacts with atoms which are
already in the excited state E2, then de-excitation of those atoms to the lower energy state
E1 occurs with emission of photons of energy h. This process is called stimulated emission.
Another emission process is called spontaneous emission, where in atoms in the excited
state drop to the lower energy state after its lifetime
 Einstein’s theory of emission
In a collection of atoms, all the three transition processes – stimulated absorption,
spontaneous emission and stimulated emission occur simultaneously.

Let N1 be the number of atoms per unit volume with energy E 1 and N2 be the number of
atoms per unit volume with energy E2 . Let ‘n’ be the number of photons per unit volume at
frequency  such that h = E2 - E1 . Then the energy density of the interacting photons is
given by () = n h. When these photons interact with atoms, both upward (absorption)
and downward (emission) transitions occur. At equilibrium, these transition rates must be
equal.
 Einstein’s theory of emission
Upward Transition :
Stimulated absorption rate depends on the number of atoms available in the lower energy

state for the absorption of these atoms as well as the energy density of the interacting
radiation.
Stimulated absorption rate R12  N1
  ( )
or R12  N1  ( ) B12

B12 is a constant called Einstein coefficient of stimulated absorption

 Einstein’s theory of emission
Downward Transition :
Once the atoms are excited by stimulated absorption, they stay in the excited state during

their lifetime. Then they move to the lower energy level spontaneously emitting photons.
The spontaneous emission rate depends on the number of atoms in the excited state.
Spon tan eous emission rate R21  N 2
 N 2 A21

A21 is a constant called Einstein coefficient of spontaneous emission

 Einstein’s theory of emission
Downward Transition :
Before the excited atoms de-excite to their lower energy states by spontaneous emission,

they may interact with photons resulting in stimulated emission of photons. Therefore, the
stimulated emission rate depends on the number of photons available in the excited state
and the energy density of the interacting photons;
Stimulated emission rate R21  N 2
  ( )
or R12  N 2  ( ) B21

B21 is a constant called Einstein coefficient of stimulated emission

 Einstein’s theory of emission
At steady state :
Total Absorption Rate = Total Emission Rate

N1  ( ) B12  N 2  ( ) B21  N 2 A21

N 2 A21
 ( ) 
N1 B12  N 2 B21
A21 / B21
 ( ) 
N1 B12
1
N 2 B21
 Einstein’s theory of emission

N1  N 0 exp ( E1 / kT )

N 2  N 0 exp ( E2 / kT )

N1  E2  E1  We get B12
 exp    1
N2  kT  B21
N1 h B12  B21
 exp
N2 kT
A21 8  h 3
Plank’s law of Black body radiation says 
B21 c3
8  h 3 1
 ( ) 
c3 exp h  1 These two equations are called
kT Einstein’s Equations
On comparing it with the eq.n. A21 / B21
 ( ) 
N1 B12
1
N 2 B21
 Spontaneous emission predominates
over stimulated emission
8  h 3 1 A21 8  h 3
 ( )  and 
c3 exp h  1 B21 c3
kT
A21 h
 exp 1
B21  ( ) kT

Ratio of Spontaneous emission rate to Stimulated emission rate R is given by

N 2 A21
R
N 2  ( ) B21

h
R  exp 1
kT
Absorption and emission process occur simultaneously. Even for sources operating at
higher temperatures and lower frequencies h >> kT, R is found to be R >> 1. This confirms
that under the conditions of thermal equilibrium, spontaneous emission predominates over
stimulated emission.
 Population inversion

Ratio of Stimulated emission rate to Stimulated Absorption rate is given by

Stimulated emission rate N 2  ( ) B21 N2

 
Stimulated absorption rate N1  ( ) B12 N1

N2
At thermal equilibrium,  1
N1
At thermal equilibrium, stimulated absorption predominates over stimulated emission.
If we create a situation such N2 > N1, stimulated emission will predominate over
stimulated absorption. If stimulated emission predominates the photon density
increases and lasing occurs. Therefore, in order to achieve more stimulated emission,
population of the excited state (N2) should be made larger than the population of the
lower state (N1) and this condition is called the population inversion.

In two energy level lasers, population inversion is not possible. In three energy level
lasers and Four Energy level lasers, it is possible to achieve population inversion.
 Amplification of Light

Consider light of intensity I0 entering a medium of length x.

The intensity of light leaving the medium on the other side x
under thermal equilibrium condition is given by Beer’s law I0 I(x)
I ( x)  I 0 exp (  x)

where  is the absorption coefficient of the medium.

Stimulated absorption results in falling in intensity of light.

If we can create population inversion in the medium, stimulated emission will

predominate over stimulated absorption and hence the light passing through the
medium undergoes amplification instead of attenuation.

I ( x)  I 0 exp (  x)

Where  is the gain or amplification coefficient. Thus the medium is under the condition
of population inversion, the density of photons passing through the medium increases
and the output light intensity I(x) increases.
 Pumping mechanisms and Population inversion
The population inversion required for light amplification is a non-equilibrium distribution of
atoms among the various levels of the atomic system. There are different mechanisms
applied to pump the atoms of the active medium to higher energy states to create
population inversion.
They are
1. Optical pumping
2. Electric Discharge
3. Chemical reaction
4. Injection current etc.

Optical Pumping :
Optical pumping is the very first mechanism applied to Ruby laser. Solid state lasers are
optically pumped using xenon flash lamps. Since these materials have very broad band
absorption, sufficient amount of energy is absorbed from the emission band of flash lamp
and population inversion is created. Flash lamps are replaced by laser diodes making the
laser systems more efficient in recent days.
Examples of optically pumped lasers are Ruby laser, Nd: YAG lasers, Nd: Glass lasers,
dye lasers, etc.
 Pumping mechanisms and Population inversion

Electric Discharge :
Since gas lasers have very narrow absorption band, pumping them using any flash lamp is
not possible. In most of the cases, population inversion is created by means of electric
discharge. Accelerated electrons collide with gas particles to excite them to the higher
energy levels. Examples of such laser systems are He-Ne laser, Argon ion laser,
Carbon dioxide laser, etc.

Chemical reaction :
Chemical reaction will result in excitation and creation of population inversion in a few
systems. Examples of such lasers are HF laser and atomic iodine lasers.

Injection current :
In semiconductor lasers, the injection current through the junction results in creation of
population inversion among the charge carriers within the junction.
 Optical Laser Resonator

The process of excitation results in amplification of laser

beam. Light amplification takes place by stimulated emission of
radiation but the amount of amplification provided by most
active medium in a single-pass of reasonable length is much low
to be useful. Practically, it is impossible to increase the length
beyond certain value and keep the entire length of the medium
under population inversion.
The limitation is overcome by the use of two end mirrors to
direct the amplified light to travel back and forth through the
active medium many times. This multiple pass provides
sufficiently larger amplification. By keeping one of the mirrors
100% reflecting and another slightly lower than 100%, a fraction
of the amplified light is drawn as output through the partially
reflecting mirror.
 Optical Laser Resonator
With plane mirrors, it is extremely difficult to align them exactly parallel to each other and
perpendicular to the cavity axis of the active medium. This problem is overcome by the
use of curved mirrors to form the resonator
cavity instead of plane parallel mirrors.
Resonator mirrors are generally coated with
multi layer dielectric materials to reduced
the absorption loss in the mirrors. Moreover,
these resonators act as frequency selectors
and also give rise to directionality to the
output beam. Since the resonator mirrors
provide positive feedback to the photons
amplified by the active medium, this is
called laser oscillator.
The three requisites for laser action are :
1. Suitable active medium
2. Creation of population inversion
3. Proper optical feedback
 Characteristics of Laser

The most striking features of laser beam are

1. High monochromaticity
2. High degree of coherence
3. High directionality (less divergence) and
4. High brightness
 Monochromaticity

So far, we have assumed that the energy levels of atoms are discrete and sharp. It is not
so in reality. Transition of an atom between two energy levels will result in emission of
photon whose frequency lies between  and  + . This results in spectral broadening.
 Monochromaticity

Spectral line width of a source  is related to the wavelength spread as

 c 
    2  
 

To appreciate relatively better the monochromaticity of laser, let us compare

the wavelength spreads of white light with light from a commercial discharge
lamp and a laser. For white light source   300 nm whereas for a gas
discharge line   0.01 nm. For a laser,   0.001 nm and using the
techniques to control the output still much lower linewidths are possible.
 Coherence
A predictable correlation of the amplitude and phase at any one point with
other point is called coherence.

P1

P2

The maximum separation between any two points on the cross-section of the
wavefront which maintain phase correlation between them. (ie. which are in
phase with each other all the time) is called spatial coherence. It is also called
as transverse coherence.
 Temporal coherence

The maximum separation between any two points on the length of the
wavetrain which maintain phase correlation between them is called temporal
coherence. It is also called as longitudinal coherence

P1 P2

Coherent length
Coherent time 
Velocity of light

White light from sun has a coherent length of nearly a few hundreds of nm. Sodium vapor
lamp has a few hundreds of micron. A He-Ne laser has coherent length of few hundreds of
mm. In Michelson interferometric experiment, the maximum path difference between the
two beams upto which interference can be observed is a measure of temporal coherence.
 Directionality

Conventional light sources emit light in all directions. The beam drawn from the output
mirror of the laser is highly parallel and directional. The degree of directionality is
expressed in terms of divergence. The divergence tells how rapidly the beam spreads
when it is emitted from the laser.

Laser a1 a2
d1
d2

If the diameter of the laser spots are measured to be a1 and a2 respectively at distances d1
and d2 from the laser, then angle of divergence can be expressed as
a2  a1

2 ( d 2  d1 )
For a typical small laser, the beam divergence is about 1 milliradian. It can be shown that
for a beam divergence of 1 milliradian, the size of the laser beam increases by about 1 mm
for every meter of beam travel.
 Brightness
Lasers are bright and intense light sources. An one milliwatt
He-Ne laser is 100 times brighter than the sun. This is because
of coherence and directionality. We know that when two
photons each of amplitude a are in phase with each other,
then by the principle of superposition, the resultant amplitude
is 2a and the intensity is proportional to 4a2.

Laser has many photons (n photons) in phase with each

other. The amplitude of the resulting wave becomes na and
the intensity is proportional to n2a2. Thus due to coherent
addition of amplitude and negligible divergence, the intensity
increases enormously.
 Semiconductor Lasers

Homojunction laser :
Semiconducting lasers are very similar to light emitting diodes. A p-n junction provides the
active medium. To obtain laser action,
we have to create population
inversion and provide optical
feedback. To obtain stimulated
emission, there must be a region in
the device where there are many
excited electrons and holes present
together. This is achieved by forming a
homojunction from a heavily doped n
and p materials. In such n+ type
material, the Fermi level lies within
the conduction band. Similarly for the
p+ type material, Fermi level lies in
the valence band.
 Semiconductor Lasers
When the junction is forward biased with a voltage that is nearly equal to the energy gap
voltage (Eg/e), the electrons and holes are injected across the junction in sufficient numbers

to create population inversion in a narrow zone called the active region. GaAs diode has
a higher probability of radiative recombination. The photons thus produced may either
interact with the valence band electrons and be absorbed thereby stimulating radiative
recombination (stimulated emission) producing further photons of the same energy.
 Semiconductor Lasers

If the injected carrier concentration is large, the stimulated emission can exceed the
absorption so that optical amplification is achieved in the active region.
To provide optical
feedback, there is no
need to use external
mirrors in the case of
diode lasers. The diode
is cleaved along the
natural crystal plane
normal to the plane of
the junction so that the
end faces are perfectly
parallel and reflecting.
Laser oscillations occur
when the round trip
exceeds the total
losses.
 Semiconductor Lasers

In the active region, the additional charge carriers present increases the refractive index
above that of the surrounding material, thereby forming a dielectric waveguide.

Since the difference in refractive index between the central waveguiding layer and the
surrounding region is very less (0.02 only), the waveguiding effect is not very efficient.
Therefore, the radiation generated in the active region extends to some extent beyond
the active region, thereby forming the mode volume.
 Semiconductor Lasers

Homojunction lasers require vigorous

pumping. They can be operated only in
the pulsed mode at room temperature
because of very high threshold
pumping density (typically of the order
of 400 A/mm2). At very low
temperatures homojunction lasers can
be operated in Continuous Wave mode.
The onset of laser action at the
threshold current density is indicated
by a sudden increase of light output
intensity at the emitting region. Below
the threshold, the emission is
spontaneous and has broad spectral
emission. When the current density is
above the threshold, laser mode
dominates and emission has narrow
spectrum.
 Semiconductor Lasers

The GaAs laser emits light at

900nm (infrared) while a
GaAsP laser radiates at
650nm (visible). Unlike other
lasers, for diode lasers
divergence is high since the
active region emitting
radiation acts as a narrow
single slit diffracting the
output.

Divergence is around 10

along the direction parallel to
the layer.
 Semiconductor Lasers

Heterojunction lasers :
The threshold current density for homojunction lasers is very large due to poor optical
and carrier confinement. Heterojunction lasers have high efficiency even at room
temperatures. A heterojunction laser is composed of various doping combinations of

GaAs and AlGaAs. In this arrangement, the p-layer of GaAs has an active region that is only
0.1 – 0.2m thick. AlGaAs layers on either side serve as potential barriers and provide
confinement for charge carriers to flow within the active region. Hence, excitation and
recombination can occur only within this active region.
 Semiconductor Lasers

This arrangement also provides additional refractive index variation thus guiding the
optical wave to confine within the active region. In addition to the control of layer
thickness during fabrication, the side walls of the active region are narrowed via
lithographic techniques. This confines the laser to a narrow region and reduces the

Threshold current even further. Heterojunction lasers have a high efficiency even at room
temperatures. Threshold current density reduces to 10 A/mm 2 and continuous wave
operation is possible.
 Semiconductor Lasers

Due to multilayers in the laser structure, carriers are confined to a narrow region so that
population is built up at lower current levels. With operating currents of less than 50 mA,
output powers of about 10mW can be produced. Lasers with lifetimes in excess of 40,000
hours are now available in continuous wave operation.

In optical fiber communications, it is desirable to have a laser emitting at wavelengths in the

region 1.1 m to 1.6 m, since optical fibers have minimum attenuation and dispersion in
this region. Lasers made of quarternary alloy GaInAsP is most suitable to get emission of
this range.
 Semiconductor Lasers

• Semiconductor lasers are the cheapest and smallest lasers

available.

• They are mass produced and easily fabricated into arrays

using the same techniques developed for transistors.

• The laser output can be easily modulated by modulating the

current through the laser diode.

• Also they are small in size and highly efficient.

These properties have made these lasers well suited as light

sources for fiber-optic communication system
 Important Properties of Lasers that make
them suitable for applications
1. Monochromaticity
– Lasers have very narrow spectral width better than 0.001 nm.

2. Coherence
– Lasers have longitudinal coherence of more than few hundreds of mm and spatial
coherence of few tens of mm

3. Directionality
– Lasers travel without much of divergence. Lasers have divergence less than 1
milliradian.

4. High Intensity
– Since photons have better coherence and travel without much of divergence, lasers
have high intensity. Highly energetic beam could be delivered in a small area
 Important Properties of Lasers that make
them suitable for applications
5. High Focusability
– Using proper lenses to focus, one can focus the laser to the order
of  or less (ie) one can focus to a spot of less than one micron
size.

6. Ultrashort pulse generation

– Lasers with femtosecond (10-15 seconds) pulse duration could be
generated for study of ultrafast reactions.

7. Fiber as a waveguide
– Lasers could be carried through optical fibers to any ‘difficult to
reach’ areas also
 Lasers in Metrology

When Neil Armstrong landed in

the moon in 1969, he placed a
reflecting mirror there. A laser
pulse was sent from the earth
to the moon. Its reflected
signal was received back and
the distance between earth
and moon was calculated with
centimeter accuracy.
Nowadays for surveying,
alignment lasers are used.
Using laser interferometry,
displacement can be measured
with an accuracy of a micron.
 Lasers in Material processing

Welding :
It is possible to use the laser(primarily CO2)
with increased power output as a welding tool.
The advantages of laser welding are :
1. Very high welding rates are possible (with a
10KW CO2 laser, 5mm thick stainless steel
plates can be welded at a speed of
10cm/sec)
2. Dissimilar metals can be welded.
3. Minimum amount of distortion of the
surrounded area (very less heat affected
zone)
4. Any extremely complex shaped contours
can be welded using computers for
controlling the deflection of the beam
5. Microwelding is done with great ease
6. The work piece is not stressed.
 Lasers in Material processing

Cutting :
Lasers cut through a wide variety of
materials, rapidly and precisely
1. Any desired shape can be cut.
2. Cut finish is very smooth requiring no
further treatment such as grinding
and polishing.
3. Lasers are used to cut a large number
of models and sizes of dresses and
suits. Synthetic fabrics are particularly
suited to this technique. Since the cut
edges are melted by the beam and
any fraying is prevented
4. With high power levels, glass and
quartz are easily cut with CO2 laser.

With 250 Watt CO2 laser, 3mm thick quartz plate can be cut at a rate of 2cm/second. With
the same laser power, oxygen assisted laser cutting can be done at a rate of 1cm/sec in a
low carbon steel plate of 1cm thick.
 Lasers in Material processing

Drilling :
Most drilling systems operate in pulsed
mode. To get the drill of desired depth
and size, number of pulses and the
energy of each pulse are to be
controlled.
1. To drill diamond dies used in the
extrusion of wire
2. Lasers are used to drill aerosol
nozzles and control orifices within
the required precision.
3. Lasers are used to drill holes in
‘difficult to drill’ materials such as Surface hardening :
ceramics Surface hardening and heat treatments are done
4. Holes of micron order can be easily to harden surfaces like automobile piston, etc.
drilled using lasers (In this small
range, drill bits cannot be used

Lasers drill holes at the rate of ten holes per second in 1 cm thick stainless steel plate.
 Lasers in medicine
Eye treatment :
1. Opthalmologists started using Argon ion lasers for welding retinal detachment. The
retina is the light sensitive layer at the back of the eye. If it is torn, it may lead to
blindness. The green beam of Argon ion laser is strongly absorbed by red cells of the
retina and welds the retina back to the eye ball. Since this beam passes through the
eye lens and the vitrious chamber without being absorbed, this treatment is done
without surgery.
2. Lasers are used for cataract removal
3. Using ultraviolet radiation from Excimer laser, curvature
correction of eye lens is carried out. This is based on
photo-ablative effect
4. Laser scalpels are used for bloodless surgery. When the
tissues are cut, the blood veins cut are fused at their tips
by the infrared laser and hence there is no blood loss.

Cancer diagnosis and therapy :

1. When growth region is illuminated with uv laser, the porferin, a natural dye
accumulated in cancerous region glows with red colour indicating the presence of
cancerous cells. Cancer cells alone can be destroyed
 Lasers in medicine
Laser Angioplasty :
Nd: YAG lasers are sent through fiber to the region of block. It burns the excess growth
and regulates the blood flow without need for bypass surgery.

• In Dermatology, lasers are used to remove freckles, acne, birth marks and tattoo
• Lasers are used in breaking kidney stones and gallstones into smaller pieces. Laser
pulses are sent through optical fibers to shatter the stones.
 Lasers in Defence
Lasers are finding wide range of applications such as ranging, guiding weapons to the
intended target and the beam itself acting as a weapon.

Pulsed laser beam directed towards

the target returns after reflection.
The time delay in its round trip is
measured to determine the range of
the target. If the object is in motion,
the reflected signal is Doppler shifted
and by measuring the shift, the
velocity of the moving object is
calculated. Nd: YAG or Nd: Glass
lasers are used for this purpose.
Military tanks built at Heavy Vehicle
Factory (HVF), Avadi is housed with
such laser sytems.
 Lasers in Defence
Lasers are used to guide the missiles. The head of the missile sends a laser beam to the
target and from the collection of light scattered from the target, the angle of line of sight
is determined. The difference, if any, between the glide angle of the trajectory of bomb
and the angle of line of sight is fed
to servo loop acting as the error
signal. The error correcting signal
controls the direction of motion of
the bomb and brings it onto the
target. Since infrared radiation is
not absorbed by the fog or smoke
in the atmosphere, CO2 lasers are
used for this purpose.
Laser weapons have two uses
in defense. One to disable the
enemy weapons and other to
destroy them.
Lasers with moderate powers are used to damage the infrared sensors on guided missiles
or the sensitive electronic eyes of spy satellites. To destroy the weapons, very high powers
are required.
 Lasers in nuclear energy

Nuclear fusion offers a low cost

and pollution free energy.
Extremely high temperatures and
pressures are required in order to
make light nuclei to overcome the
mutual repulsion and combine to
release energy. Laser assisted
inertial confinement method
generates highly compressed
plasma of heavy isotopes of
hydrogen, namely deuterium D
and tritium T. In the presence of
such high compression, the core
reaches a temperature of about
108K. To achieve this condition
enormous amount of laser pulse
energy is needed. Many countries
are in the process of development
of laser fusion projects.
 Lasers in nuclear energy

Isotopes are chemically almost identical. Each isotope absorbs light at different
characteristic wavelength. Using a tunable dye laser, it is possible to ionize one
isotope without disturbing the other.

Ionized isotopes
can be separated
from the other
using electrostatic
fields. From
natural U-238,
ionized U-235
atoms are
separated using
this method.
 Lasers in Optical Communications

The amount of information that can be sent over an electromagnetic wave is

proportional to the bandwidth of the wave. Since lasers operate with exceedingly large
bandwidth, optical communication using lasers is very attractive.

Lasers are used in two types of communication : one, open space communication and
another fiber optic communication. Open space communication requires the environment
free from fog, dust and rain.

Fiber optic communication has the following advantages :

1. Enormous bandwidth (as large as 105GHz)
2. Electrical isolation
3. Immunity to interference and cross talk
4. Signal security
5. Small size and weight
6. Low transmission loss
7. Ruggedness and flexibility
8. Low Cost
 Lasers in electronic industry

Scribing:
Scribing involves drawing fine lines in brittle ceramic and semiconductor wafers. When
bent, they break along the lines scribed. Low power CO2 lasers are generally used

Scribing :
Scribing involves drawing fine lines in brittle
ceramic and semiconductor wafers. When bent,
they break along the line
 Lasers in electronic industry

Soldering :
Difficult to solder materials such as platinum, silver and palladium are soldered using
Nd: YAG lasers without any flux. Sheets as thin as 25 micron can be soldered without any
damage to the sheet.

Trimming :
Using Nd:YAG pulsed laser, the resistance material is gradually removed from the surface
without causing thermal damage to the substrate and the resistance is continuously
controlled and monitored accurately.
 Optical data storage using CD

The optical data storage techniques have resulted in increased storage capacities.

The audio, video and text data to

be stored is first converted into
binary form as 0’s and 1’s. It is
then stored in the form of
reflecting and non-reflecting
micro points in spiral path on a
disc.
During the readout process,
variation in the reflected intensity
of laser is converted back to data.

To read and write in a CD, laser beam is focused using a convex lens. Shorter the
wavelength, sharper will be the focus. Hence shorter wavelength of blue light with small 
and shorter focus lens are used for larger storage capacity.