It has all the discription about LASER with derivations related to this.

2. Light Amplification by Stimulated Emission of Radiation
LASER
Properties Of Laser Light
* Monochromatic Light
* Extremely Coherent Beam
* Highly Directional
* High Intensity

3. Absorption
E1 = Energy of Ground Sate
E2 = Energy of Excited State
In presence of suitable energy ∆E, the ground state atom can
absorb it and jumps to excited state.
According to Einstein, the Probability of Absorption
P12 α u(ʋ)
P12 = B12 u(ʋ) here u(ʋ) is incident energy density
and B12 is Einstein's Coefficient of Absorption and contains information
about the transition of atoms from state 1 to state 2
2
1
Excited state
Ground state
------------------------------ E2
∆E = E2 – E1
----------------------------- E1

4. Spontaneous Emission
The atom in excited state has a life time of ≈ 10-8 sec.
It undergoes a spontaneous emission during this time span and
comes to ground state by emitting a photon .
According to Einstein, the Probability of spontaneous emission
P21 = A21
i.e it is a random process and does not need energy here A21 is
Einstein's Coefficient of spontaneous emission and contains information
about the transition of atoms from state 2 to state 1
life time ≈10-8 sec
------------------------------ E2
one photon
(Random direction)
----------------------------- E1
2
1

5. Stimulated Emission
The atom in excited state has a life time of ≈ 10-8 sec.
According to Einstein, if incident energy happens to interact with this atom which is
already excited, then this excited atom does not absorb this, but at once comes down
to ground state by emitting a photon identical to the interacting photon.
According to Einstein, the Probability of Stimulated emission is
proportional to the interacting energy density
P21 α u(ʋ)
P21 = B21 u(ʋ) here u(ʋ) is incident energy density
life time ≈10-8 sec
-------------------------------------- E2
two identical photon
(same direction)
-------------------------------------- E1
2
1
here B21 is Einstein's Coefficient of stimulated emission
and contains information about the transition of atoms from
state 2 to state 1

6. Consider an atom described by state 1 as ground state having energy E1 and has N1 number of electrons
And state 2 as higher excited state with energy E2 and has N2 number of electrons.
In the presence of photon(s) of suitable energy ∆E = E2 – E1 the ground state atom can absorb it and can
move to excited state. The probability of absorption, spontaneous emission and stimulated emission are
given below
Relation Between Einstein’s Coefficients
P12 = B12 u(ʋ) ------------(1)
P21 = A21 ------------(2)
P21 = B21 u(ʋ) ------------(3)
multiplying the probability with number of atom in state gives the rate of transition
Rate of Absorption
R1→2 = B12 u(ʋ) x N1 ---------------------------------------(4)
Rate of Spontaneous emission
R2→1 (Spontenous) = A21 x N2 ------------------(5)
Rate of Stimulated emission
R2→1 (Stimulated) = B21 u(ʋ) x N2 -------------------(6)
Rate of Emission = [Rate of Spontaneous Emission + Rate of Stimulated Emission]
= [ A21 x N2 + B21 u(ʋ) x N2 ]
Rate of Emission = [ A21 + B21 u(ʋ) ] . N2 -------------------------(7)

7. Rate of Absorption = Rate of Emission
B12 u(ʋ) . N1 = [ A21 + B21 u(ʋ) ] . N2 ---------------------- (8)
In the state of thermal equilibrium
Re-arranging the equation, we gets
A21 / B21
u(ʋ) = ------------------------ --------------------------- (9)
B12 . N1
------------ - 1
B21 N2
According to Maxwell-Boltzmann Distribution law, The ration of number of atoms in excited
state to ground state is given as
N1 -(E1 –E2)/kT (E2 –E1)/kT ∆E/kT
---- = e = e = e
N2
N1 hʋ/kT
---- = e --------------------------------------- (10)
N2
…

8. Putting equation (10) in equation (9), we gets the spectral energy
density in terms of Einstein’s Coefficients
A21 / B21
u(ʋ) = ------------------------ ----------------- (11)
B12 . hʋ/kT
------ e - 1
B21
Also according to Planks Radiation law, the spectral energy density is given as
8πhʋ3 / c3
u(ʋ)dʋ = ------------------------ dʋ ----------------- (12)
hʋ/kT
e - 1
Comparing equation (11) and (12)
A21 8πhʋ3
----- = --------- ----------------------------- (13)
B21 c3
B12 = B21 -------------------------(14)

9. 1. The Rate of Emission should be greater than the rate
of Absorption.
Principle of Laser Action
2. Stimulated emission should dominate
over Spontaneous emission

10. Stimulated emission should dominate
over Spontaneous emission
Principle of Laser Action
Probability of spontaneous emission A21
Consider the ratio ------------------------------------------------ = --------------
Probability of stimulated emission B21 u(ʋ)
A21 / B21
Putting u(ʋ) = ----------------------------------
hʋ/kT
e - 1
Probability of spontaneous emission hʋ/kT
--------------------------------------------------- = e - 1
Probability of stimulated emission
 If hʋ > kT Probability of Spontaneous emission will be larger
 If hʋ < kT Probability of Stimulated emission will be larger --- LASER
If hʋ <<< kT Stimulated emission dominates over spontaneous emission
MASER : Microwave Amplification by Stimulated Emision of Radiation

11. The Rate of Emission should be greater than the rate
of Absorption.
Principle of Laser Action
Rate of Emission [ A21 + B21 u(ʋ) ] . N2
Consider the ratio ------------------------- = --------------------------------
Rate of Absorption B12 u(ʋ) . N1
A21 B21 u(ʋ) N2
= ( ------------------ + ------------------- ) ‘ ------- since B12 = B21
B21 u(ʋ) B21 u(ʋ) N1
Rate of Emission N2
------------------------- = -------
Rate of Absorption N1
=> For Rate of emission > Rate of absorption
N2 > N1
N2 > N1 This is the condition termed as POPULATION INVERSION
Here A21/B21u(v) quantity can be neglected

12. B12 = B21 ------------------------------(14)
A21 8πhʋ3
----- = --------- ----------------------------- (13)
B21 c3
Equation (14) can be re-written as B12 u(ʋ) = B21 u(ʋ)
Absorption and Stimulated emission are equally probable
The First Principle of Laser action i.e Rate of Emission > Rate of Absorption
is satisfied only when N2 > N1
This is the condition termed as POPULATION INVERSION
*

13. For Laser action, population inversion is the essential condition . In 2-Level
system the thermal equilibrium is established and due to the condition
(Rate of absorption = Rate of Emission) the 2-level system behaves like a optical
cavity.
POPULATION INVERSION
To achieve the population Inversion,
the concept of METASTABLE STATE is used.
Metastable state is a state lying below and closer to the excited state
having a life time of 10-3 sec and the transition to metastable state is
just by atomic collision and hence it is non radiative transition i.e.
radiation less transition.
So in comparison to excited state, the life time of metastable state is 105 times more
Excited atoms goes into metastable state via excited state and thus Population
Inversion is established between ground state and metastable state.
*

14. The Excited atoms moves to metastable state via excited
state and there is establishedt a Population Inversion
between ground state and metastable state.
So in comparison to excited state, the life time of
metastable state is 105 times more
Once population Inversion is achieved, The stimulated emission
dominates and LASER ACTION takes place
.
.
.

15. 1. Lasing Material
Requirements for Laser device
2. Pumping System
3. Optical Resonator Cavity
.
.

16. 1. Pumping
Necessary Steps in Laser Action
2. Pupulation Inversion
3. Triggering
.
.

17. 1. Lasing Material : Chromium ion Cr+3 doped
in AL2O3
RUBY-LASER
2. Pumping System : Xenon Flash tube wrapped
around the Ruby Dod
3. Optical Resonator Cavity : Two Mirrors
one is 99.9% reflector (fully reflector)
another is 99% reflector (partially reflector)
.
.

18. Ruby-laser
Maiman (1960):
Ruby: Al2O3 + Cr
Xe
cavity
L =n l

20. four level laser
• atoms are pumped from the
ground state to level 4 from where
they decay rapidly to level 3,
creating population inversion with
respect to level 2
• the pumping to level 4 can be
optical (from a flashlamp or
another laser) or electrical
• the decay rate from level 2 to
ground state (level 1) must be fast
to prevent atoms accumulating in
that level and destroying the
population inversion

22. 1. Lasing Material : Neon atoms
He-Ne LASER
2. Pumping System : Electron Impact Pumping
3. Optical Resonator Cavity :
Two Mirrors kept at Brewester Window to obtain
Polarized Laser
one is 99.9% reflector (fully reflector)
another is 99% reflector (partially reflector)
.
.
*

23. Anode
---------- ----------- ----------
He + Ne
(10:1)
---------- ----------- ----------
R F Excitor
Brewster
window
632.8 nm
He-Ne Laser
99.9%
reflector
99 %
reflector
Cathode

24. HeNe laser
•pump He to metastable state (20.61 eV)
•transfer excitation to Ne metastable state (20.66 eV)
•laser transition
•spontaneous emission (2 times) to deplete lower level ( low pumping)
•not very efficient! (20.6 eV vs 2 eV)

25. F3 _____________ E 6____________
3.39 μm
He-Ne E 5______________
Collision
F 2_____________ E 4__________ 632.8 nm
1.15 μm
E 3 ______________
ELECTRON IMPACT
PUMPING Spontaneous
emission
E 2 ___________________
decay by atomic collision
F 1 _____________ E 1___________________
Helium atom Neon atom
Ground State

26. 1
Here ∆t = ----- here ∆ʋ is broadening of spectral line
∆ʋ