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Lasers
Absorption, Spontaneous and stimulated emissions – Einstein’s Quantum Theory of Radiation –
population inversion and lasing action –– properties and types of lasers- - He-Ne, Nd
...
Applications in medicine and Industry

Introduction
Stimulated absorption
Consider a two level energy system of energies E1 and E 2 respectively for lower and
upper levels
...
If the energy of the interacting photon hv is equal to the energy difference
between the two levels of the atom , i
...

hv = E2 - E1, then the atom at the lower
energy level E1 absorb the incident
energy and it jumps to the upper energy
level E2
...


Spontaneous Emission
The atoms in the excited state will stay for a short
duration of time 10-9s called their lifetime and drop to the lower
energy state
...
e
...
The process by which an atom in an excited state
undergoes a transition to the ground state and emits a photon
by itself without the help external radiation is called as
emission process or spontaneous emission
...
The energy of the atom is raised to the upper energy level
2
...
It
then spontaneously returns to the lower state 1 with the emission of a photon of light
...
So Einstein introduced a new
type of emission called Stimulated emission process along with spontaneous emission
...
One photon interacting with an excited atom results in two photons being emitted
...

Rate of downward transition ( stimulated) R21 (st)  B21N 2  (v)
Rate of downward transition ( spontaneous) R21 (sp)  A21N 2
Rate of downward transition  R21 (sp)  R21 (st)

…(8)

At equilibrium
Rate of upward transition = Rate of downward transition
R12  R21 (sp)  R21 (st)

B12 N1  (v)  A21N 2  B21N 2  (v)

 (v)( B12 N1  B21N 2 )  A21N 2
 (v ) 

Substituting the value of

A21 N 2
A21

B12 N1  B21 N 2 B N1  B
12
21
N2

N2
given by the equation (5) in (9), we get
N1

 (v ) 

A21
 hv 
B12 exp    B21
 kT 

by comparing equation (10) and ( 7) , we get

B21  B12 and

…(9)

A21 8hv 3

B12
c3

…(10)

 (v ) 

A
B

1
 hv 
exp    1
 kT 

…(11)

From B21  B12 , the probability of stimulated emission is equal to the probability of
induced absorption
...

the ratio of stimulated emission to spontaneous emission

R21 ( st ) B21 N 2  (v)

R21 ( sp)
A21 N 2
B
 21  (v)
…(12)
A21
From the above equation the radiation density or energy density  (v) should be high for
stimulated emission to predominate over spontaneous emission
...

the ratio of stimulated emission to absorption

R21 ( st ) B21 N 2  (v)

R12
B12 N1  (v)
N
 2
N1

…(13)

for stimulated emission to predominate over absorption the population in the higher
energy N2 should be greater than N1
...

If the above two conditions are satisfied stimulated emission will occur and a photon will
be emitted in same direction of incident photon
...
Light amplification by stimulated
emission of radiation is achieved i
...
Create population inversion
2
...


Nd-YAG laser
Nd-YAG laser is a four level solid-state laser
...
It is abbreviated as YAG and the
molecular formula Y3Al5O12
...
5% are doped as impurities
which provides the energy levels for lasing action
...
The crystal field modifies the transition probabilities between the
various energy levels of Nd3+
...

The length of Nd-YAG laser rod varies from 5cm to 10 cm depending on the power of
the laser and its diameter is generally 6 to 9 mm
...
Krypton flash tube is used to excite
the Nd3+ ions from ground state to excited state
...
During
the transition from higher energy level to lower energy level, a laser beam of wavelength 1
...

Construction
The laser rod and a linear flash lamp
are kept in an elliptical reflector cavity
...
The optical
cavity is formed by using fully reflecting
mirror and partially reflecting mirror
...

Working
i) When the krypton flash tube is switched on neodymium ions are excited from ground level E0
to excited energy level E3 and E4 by absorbing a photon
ii) The excited neodymium ions from E3 and E4 make a radiation less transition and enter into E2
energy level
...
Hence population inversion
condition is achieved between the energy level E2 and E1
...
This emitted photon will trigger the
neodymium ions in E2 hence a chain of stimulated photons are emitted
...

vi) After enough strength has been attained high intensity of laser beam of wavelength
1
...


Gas laser
Helium- neon Gas laser
Gas lasers are the most widely used laser, they range from low power He-Ne laser to high power
CO2 laser
...
1 mm of Hg)
...
The helium atoms are not directly involved in the laser transition , they provide
efficient excitation mechanism to neon atoms
...
The end faces of the
discharge tube are tilted at the Brewster angle to get
polarized output
...
H e-Ne laser is excited by applying 2 to 4
KV in the range of radio frequency
...
During electric discharge
,the electrons with kinetic energy by impact with He atoms
...
This collision is called as first kind
...
In the
discharge tube as helium and neon ratio is 10:1, all the Ne atoms will collide with He atoms and
raised to higher energy levels
...

He * + Ne  He + Ne*

where (*) represents an excited state

Working
Collision of the excited helium atoms with
the ground-state neon atoms results in transfer of
energy to the neon atoms, exciting them into the
2s and 3s states
...
Spontaneous
emission between the 3s and 2p states results in
emission of 632
...
After this,
fast radiative decay occurs from the 2p to the 1s
energy levels, which then decay to the ground
state via collisions of the neon atoms with the
container walls
...
\
With the correct selection of cavity mirrors, other wavelengths of laser emission of the
HeNe laser are possible
...
39 μm
and 1
...


Molecular lasers- the carbon dioxide laser
The first molecular carbon dioxide laser invented in the year 1963 by C
...
N
...

Principle
In carbon dioxide laser the laser action takes place between
the vibrational energy levels of carbon dioxide molecule
...
Symmetric stretching and the quantum numbers are (100)
2
...
Bending vibration and the quantum numbers are (010)
The active medium
The active medium is CO2 gas and N2 is used for efficient excitation of CO2 molecules
...
The ratio of CO2 : N2 : He are 1:4:5
...
During electric discharge ,the
electrons with kinetic energy by impact with N2
...
This collision is called as first kind
...
In
the discharge tube, the CO2 and N2 ratio is 1:4, all the CO2 molecule will collide with N2 and
raised to higher energy levels
...

N2 * + CO2  N2 + CO2*
where (*) represents an excited state
Working
The vibration level structure of CO2 and
N2 is shown in the figure
...

The excited N2 molecules transfer energy
to CO2 molecule and exciting them to 001 level
which are metastable state relative to 100 and
020 states
...
The laser transition undergoes from 001 state to 100 with
10
...
6m photon in IR region
...
6m is suppressed by
He speeding up the non-radiating transition from 100 to ground level
...

CO2 lasers are capable of producing very high output powers approximately 10KW
...
Depending on the
semiconductor material used, the emission wavelength can be further refined by using band
structure engineering,
Principle
They are basically a diode junction (depletion region)
...

This is achieved using heavily doped n and p material and applying a forward bias to the
junction
...
The semiconductor are heavily doped
...
The pumping energy comes from the diode
current
...
The faces are polished
perpendicular to the junction which will serve as an optical
cavity
...

Achievement of population inversion:
When p-n junction diode is forward biased, then there will be
injection of electrons into the conduction band along n-side
and production of more holes in valence band along p-side of
the junction
...


Working
If the junction is forward biased with an applied
voltage nearly equal to the band gap voltage
...
In the active region both
excited electron states in the conduction band and holes
valance band are present, where condition for population
inversion is achieved
...
Laser light is emitted from the active
region
...

Double heterostructure GaAs/AlGaAs laser
Very effective carrier and optical confinement can be simultaneously accomplished with double
heterostructures
...
The middle layer is a narrow-gap
material
...
g
...
In the active region (GaAs) the
electrons are confined in conduction band and holes
in the valence band
...


APPLICATIONS OF LASERS
Lasers find variety of applications in various fields due to their properties which are
much different from the ordinary light
...

The major property of laser is its high power, high directionality
...

LASER DRILLING
In case of a conventional drilling a drill bit is held to the specimen with large amount of
force between them apart from the force used to hold the drilling machine and the specimen
...

These practical problems can be overcome by using high power lasers as there is no
mechanical contact between the laser and the specimen and the highly directional laser can also
be concentrated on a narrow space
...

High energetic pulses of 10-4 to 10-3 s duration are made to fall on the material
...

Nd-YAG laser is used for metals and the CO2 laser is
used for metallic and non-metallic materials
...
A typical schematic diagram is shown in
figure 11
...
Since lasers can be concentrated on a small
space very small drills can be created
...
Laser welding are
generally used for welding multilayer in which the thermal properties differ at interfaces
...
The laser welding process is as explained below
...
Because of high intensity of the
beam falling over a smaller region generates lot of heat
energy which melts the material with in that small region
...


Problems
1
...
If it emits light of wavelength
632
...

Energy of one photon= hv 

hc

 3
...
96eV


output _ power
No of photons emitted =
energy _ of _ one _ photon
=

5  10 3
 1
...
14  10 19

2
...
8nm,
calculate the energy of emitted photons
...
141  10 19 J  1
...
The band gap of GaAs is 1
...
What is the wavelength of the laser emitted
...
794  10 7 nm
Eg

4
...

N1
 hv 
 hc 
41
From eqn (5)
 exp    exp 
  5
...
Examine the possibility of stimulated emission at 300K and =600nm
...
762  10 35
 hc 
exp 
 1
 kT 
The ratio is very small so stimulated emission is not possible
...
A laser beam of wavelength 632
...

Angular spread  


d

 6

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