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Module 2: Lasers and applications

Light from a source comes as the sum of total radiations by billions of atoms or molecules in the

source. The phase is different at different times. Therefore, the ordinary light is incoherent. Laser is

the phenomenon in which radiation from different atoms of a given source is made in phase, in

direction of emission and same polarisation i.e. coherence of a given source.

Important feature of Laser:

(1) High degree of coherence

(2) High directional

(3) Monochromatic

(4) Highly intense

Absorption of radiation:

When the atoms absorb energy by any means in the ground state, the electrons of the atom absorb

energy and reach to higher energy level. Now the atom is said to be in excited state.

Let us consider two energy levels 1 and 2 of an atom with energies E1 and E2. If the atom is initially in

the lower energy state E1 ,it can be raised to energy state E2 by absorbing a photon of energy E2-

E1 = υh . This process is called stimulated absorption.

Fig. 1 Absorption phenomenon

Usually the number of excited particles (atoms) in the system is smaller than the non –excited

particles. The time upto which the particle can remain in excited state is known as life time. For

Hydrogen atom, it is around 10-8

second.

Spontaneous emission of radiation:

The excited state with higher energy E2 is not a stable state. After a short interval of time, the atom

jumps back to ground state by emitting a photon of frequency υ. This type of emission is called

spontaneous emission.

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Fig.2 Spontaneous emission

The spontaneous emission is random in character. If there is an assembly of atoms, the radiation

emitted spontaneously by each atom has a random direction and a random phase. Thus the radiation in

this case is a random mixture of quanta having various wavelengths. Thus spontaneous emission is

incoherent and has broad spectrum.

Stimulated (induced) emission of radiation:

In 1917, Einstein proposed this kind of emission. In this phenomenon, an incident photon of energy

hυ causes a transition from E2 to E1.So the radiated light emits an addition photon of same frequency

υ. Hence two photon two photon move together. This phenomenon is called stimulated emission of

radiation. The direction of propagation, phase and energy of the emitted photon is exactly same as

that of incident photon. Thus result is an enhanced beam of coherence light. Emitted photons are in

same state of polarisation.

Fig. Stimulated emission of radiation

Einstein Coefficients:

Suppose the rate of transition between the two energy state 1 and 2 having energies E1 and E2. The

probable rate of occurrence of absorption transition 1→2 depends upon the properties of states 1 and

2. This is proportional to the energy density u(υ) of the radiation of frequency υ incident on the atom.

Energy density is defined as radiant energy per unit volume in the frequency interval υ and υ+ dυ.

Therefore, probable rate of occurrence of absorption transition is

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)(1212 υuBP =

Here B12 = proportionality constant known as Einstein’s coefficient of absorption radiation.

The probability of spontaneous emission 2→1 is determined only by the properties of states 2 and 1.

This is denoted by A21 and is known as Einstein’s coefficient of spontaneous emission of radiation.

This is independent of energy density u(υ).

The probability of stimulated emission transition 2→1 is proportional to energy density u(υ) of the

stimulating radiation and is given by

)(2121' υuBP = (1)

Here B21 is Einstein’s coefficient of stimulated emission of radiation. Total probability for an atom in

state 2 to 1 is

)(212121 υuBAP += (2)

Relation between Einstein’s coefficients:

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

frequency υ and υ+dυ and energy density u(υ). Let N1 and N2 be the number of atoms in lower

energy state 1 and higher energy state 2 respectively. The number of atoms in state 1 that absorbs a

photon and rise to state 2 per unit time is given by

)(121211 υuBNPN = (3)

The number of atom in state 2 that drop to state 1, either by spontaneous emission or by stimulated

emission is given by

)]([ 21212212 υuBANPN += (4)

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

the number of emitting radiation per unit time, hence

212121 PNPN =

)]([)( 21212121 υυ uBANuBN +=

212212121 )(][ ANuBNBN =− υ

1

1)(

21

12

2

121

21

212121

212

−

×=

−=

B

B

N

NB

A

BNBN

ANu υ (5)

Thermodynamically it was proved by Einstein that the probability of stimulated absorption is equal to

the probability of stimulated emission i.e.

B12=B21

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Hence

1

1)(

2

121

21

−

×=

N

NB

Au υ (6)

Now according to Boltzmann distribution law, the ratio of N1 and N2 is given by

=

−=

kT

h

kT

EE

N

N υexpexp 12

2

1 (7)

Here k is Boltzmann constant. From (6) and (7)

1exp

1)(

21

21

−

×=

kT

hB

Au

υυ (8)

According to Planck’s radiation law, the energy density of radiation is given by

1exp

18)(

3

3

−

×=

kT

hc

hu

υ

υπυ (9)

From (8) and (9) we have

3

3

21

21 8

c

h

B

A υπ= (10)

Equation (10) shows the ratio of Einstein’s coefficients of spontaneous emission to stimulated

emission is directly proportional to the cube of frequency. This shows the probability of spontaneous

emission increases rapidly with the increase of energy difference between two states.

Condition for light amplification:

At the thermal equilibrium

)()(

tan 21

21

221

221 υυ

uA

B

NA

uNB

transitioneousspon

transitionstimulated== (11)

1

2

112

221

)(

)(

N

N

uNB

uNB

transitionabsorption

transitionstimulated==

υ

υ since B12 = B21 (12)

From (11) it is concluded that in order to enhance the number of stimulated transitions the radiation

density is to be made larger.

From(12), the stimulated emission will be larger that absorption only when N2>N1, otherwise N2<N1

absorption phenomenon dominates.

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Coherence:

If two light sources are in constant phase different, it is called coherence sources.

Incoherent light Coherent light

Temporal coherence: If the phase difference of waves crossing the two points lying along the

direction of propagation of the beam is time dependent then a beam of light is said to possess

temporal , time or longitudinal coherence.

Fig. Temporal coherence

The average time interval for which the field remains sinusoidal (i.e., a definite phase relationship

exists) is known as the coherence time . The distance for which the field remains sinusoidal is called

coherence length, L=τ c.

Spatial Coherence: In spatial coherence the phase difference of the waves crossing the two points

lying on a plane , perpendicular to the direction of propagation of the beam is time independent. It is

also called as transverse or lateral coherence. Spatial coherence is the measure of the minimum

separation between the wavefront where two waves remain coherent.

Fig. spatial coherence

Laser beam characteristics:

(1) High directionality: Directionality is the characteristic of laser light that causes it to travel in

a single direction with a narrow cone of divergence. It is defined in terms of divergence angle.

The angular spread of beam on one side of the axis :

d

λβθ =

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Divergence angle is twice the angle made by the outer edge with the axis of the beam.

(2) High intensity: In laser the energy is concentrated in a very small region.

(3) Divergence: Light from convection source spread out in the form of spherical wave forms.

Hence, they are divergent but divergence or angular spread of laser is extremely small.

(4) Monochromacity: Light from normal monochromatic source spread over a wavelength range

of the order of 100 A0 to 1000A

0. But in case of laser, the spread of wavelength is order of a

few angstroms.

(5) Coherence: It is completely coherence and it is easily observed the phenomenon of

interference from two laser light.

Population Inversion:

Normally number of particles N2 in high energy level 2 is less than population N1 of low energy level

1. Suppose E1 and E2 (E2> E1) are two energy state with population energy N1 and N2, then

−=

kT

EE

N

N 12

2

1 exp

For laser action to take place the higher energy level should be more populated than the lower energy

state i.e. N2> N1.

The process by which the population of a particular high energy state is made more than that of a

specific lower energy state, this phenomenon is called population inversion and the system in which

population inversion is achieved is called a s active system.

The process of achieving the population inversion is known as pumping of atoms. There are following

methods for pumping-

1. Optical pumping (in Ruby laser)

2. Electric discharge (in He-Ne laser)

3. Direct conversion (in semiconductor diode laser)

4. Chemical reaction(in CO2 laser)

Meta stable state:

In order to achieve the population inversion, there should be an energy state which has a long life time

(~10-3

sec). Such an energy state is called Meta stable state. The Meta stable sate allows accumulation

of large number of excited atoms at this level. Hence population inversion can be achieved.

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Process of population inversion:

Suppose an appropriate energy from an external source is applied to the system. As a result some

atoms from lower energy state E1 are excited to higher energy state E3. Most of the atoms from E3 go

to E1 but some atoms transit to E2. Since atom will stay at E2 larger time than E1. Thus after some

time, population of atoms in E2 energy state increases than E1 i.e. N2>N1.

Laser Principle:

Let us consider an assembly of atoms of some kind that has Meta-stable. After achieving population

inversion, following steps take place-

Step (1) Pumping

Step (2) Population inversion

Step (3) Stimulated emission

Fig. Laser Principle

Main Components of a Laser:

1. Active region: When the active medium is excited, it achieves population inversion. Active

medium may be liquid, solid or gas. Depending upon medium we different types of laser such

as Ruby laser (solid), He-Ne laser (gas).

2. Energy source: The energy source raises the system to an excited state.

3. Optical resonator or resonant cavity: Optical resonator consists of two mirrors facing each

other. The active medium is enclosed by this cavity. One of the mirror is partially silvered and

another is fully silvered. Function of the optical resonator is to increase the intensity of the

Laser beam.

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Fig. Components of a laser

Action of optical resonator:

Initially active centres are in non-excited state. Using suitable pumping process, the material is taken

into population inversion state. For this purpose energy source is used. At the initial stage,

spontaneous photons are emitted in all directions. The photons that travel in specific direction are

selected rest are rejected. The simulated photons are to be made to pass through the medium a number

of times. The mirrors constituting the resonator cause the directional selectivity. The photons

travelling in random directions are lost. On reaching the partially reflective mirror, some photons are

transmitted while remaining are reflected back. The reflected photons de-excite more and more atoms.

At fully reflecting mirror, some photons are absorbed and major number of photons are reflected. The

beam is now amplified. The amplified beams undergo multiple reflection at the mirrors and gain in

strength. When the amount of amplified light becomes equal to the total amount of light lost (through

the sides of the resonator, through the mirrors, through the absorption of the medium), the laser beams

start to oscillate. When the oscillation builds upto enough intensity then they emerge through the front

mirror as a highly collimated intense beam i.e. Laser beam.

Three-level Laser System:

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Four level laser: In a four level laser, four energy levels are involved as shown in fig.

Fig. A four-level laser energy diagram.

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He-Ne laser (Gas laser):

In this laser system a quartz tube is filled with a mixture of He and Ne gas in the ratio 10:1

respectively at a pressure of about 0.1 mm of mercury. This mixture acts as the active medium. The

length of the tube is equal to an integral number of half wavelength of laser light. An electric

discharge is produced in the gas by means of electrodes outside the tube connected to a source of high

frequency alternating current. The collisions with electron from discharge excite He and Ne atoms to

meta stable states respectively 20.16 and 20.66 eV above their ground state.

Some of the excited He atoms transfer their energy to Ne atoms in collisions with the 0.05eV of

additional energy being provided by kinetic energy of the atoms. Such an energy transfer is only

possible when two colliding atoms have same identical state. Therefore, He atom is used to help in

achieving the population inversion in the Ne atoms. He atoms do not return to ground state by

spontaneous emission but transfer the energy to Ne atoms. The laser transition in Ne is from the meta

stable at 20.66 eV to an excited state at 18.70 eV with the emission of light with wavelength 6328 A0.

Then another photon is spontaneously emitted in a transition to a lower meta stable state. But this

transition yields only in coherent light. The photon of wavelength 6328 A0 travel through the gas

mixture parallel to the axis of the tube and stimulates the surrounding Ne atoms present in the meta

stable state. This way we get other photons that are in phase with the simulating photons. These

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photons reflect back and forth by the silvered mirror and number of photons gets amplified through

stimulated emission every time and finally a portion of these intensified photons passes through the

partially silvered end. Since the electrons that excite the He atoms and Ne atoms occur all the times,

He-Ne laser operates continuously. This laser is used in super markets to read bar codes.

Applications of laser:

1. It is used to measure long distances.

2. Lasers are suitable for communication.

3. Lasers (such that CO2 laser, which carries high power) are used for welding, cutting of

materials etc..

4. Used in eye surgery, in skin disease and other medical field.

5. Used in 3D holography.

6. Used as bar code scanner and laser printer.

Nd:YAG laser

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The CO2 laser possesses an extremely high efficiency of ∼30%. This is because of efficient

pumping to the (001) level and also because all the energy levels involved are close to the

ground level. Thus the atomic quantum efficiency which is the ratio of the energy difference

corresponding to the laser transition to the energy difference of the pump transition, i.e.,

is quite high (∼45%). Thus a large portion of the input power can be converted into useful

laser power. Output powers of several watts to several kilowatts can be obtained from CO2

lasers.

Holography:

Theory was developed in 1947 by scientist Dennis Gabor winning the Nobel Prize in 1971. Word

Origin : Holography is derived from from the Greek word hólos, "whole" + grafē, "writing, drawing”

Holography is the process or technique of making three-dimensional image of the object. A hologram

is produced by the interference of two beams of laser light : one is the object beam coming through

the object and other is the reference beam coming directly from the source. holography is a two step

process:

1. Construction of the image : During the recording process, object wave (wave illuminating the

object) and the reference wave (coming directly from source) interfere in the plane of the recording

medium & produce interference fringes. This photographic plate carrying the interference pattern is

called Hologram. The interference fringes contain all the information about the intensity and the

phase of the scattered beam from object.

2. Reconstruction of the image: In the reconstruction process, the hologram acts as diffraction

grating. This is illuminated by a wave called the reconstruction wave (in most cases this is similar to

the reference wave used for recording the hologram) and the image of the object is reconstructed from

the hologram. A real image is formed in front of the hologram and a virtual image behind the

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hologram. The virtual image has all the characteristics of the object. The real image can be

photographed directly without using a lens.

Construction of the image

Reconstruction of the image

Holography vs. Photography: Photography is 2D record of a 3D object whereas holography gives a

three dimensional form of original object. If any object is hidden just behind another object then the

observer can see the hidden object in viewing the hologram. Hologram is the positive pattern whereas

in conventional photography negative pattern is produced.

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In ordinary photography each region contains separate and individual part of the original object.

Destruction of a portion of a negative leads to an irrepairable loss of information corresponding to the

destroyed part. On the other hand, each part of a hologram contains information about the entire

object. Destruction of a part of hologram does not cause a loss of information about the object, each

seaparate fragment is capable of producing image with a reduced clarity. The information holding

capacity of a hologram is extremely high by recording several images of the object whereas in

ordinary photography a photofilm cannot be used to record several images.

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