An essential Lecture on Lasers physics basics

1. B A S I C P R I N C I P L E S O F L A S E R
E I N S T E I N ’ S C O E F F I C I E N T S
C H A R A C T E R I S T I C S O F L A S E R B E A M
LASERS

2. What is LASER????
Light Amplification by Stimulated Emission of
Radiation
• A device that produces a coherent beam of optical
radiation by stimulating electronic, ionic, or
molecular transitions to higher energy levels.
• When they return to lower energy levels by
stimulated emission, they emit energy.

3. Basic concepts for a laser
 Absorption
 Spontaneous Emission
 Stimulated Emission
 Population inversion

4. Lasers: Basic Principle
Absorption and Radiation Processes

5. Absorption
An electron in an atom can be excited from an energy level E1 to a
higher energy level E2 by absorption:
photon absorption─ hν = E2 – E1.
h
E
E 1
2 



6. Spontaneous Emission
The atom decays from level 2 to level 1 through the
emission of a photon with the energy hv. It is a completely
random process.

7. Stimulated Emission
Atoms in an upper energy level can be triggered or stimulated
in phase by an incoming photon of a specific energy.

8. Stimulated Emission
The stimulated photons have unique properties:
In phase with the incident photon
Same wavelength as the incident photon
Travel in same direction as incident photon

9. Einstein Coefficients
N2 E2
N1 E2
)
(
12
12 
u
B
P 
21
tan
21 A
P eous
Spon

)
(
21
21 
u
B
P Stimulated


10. Relation between Einstein’s coefficients
Under equilibrium conditions we have :
 An atom in level E2 can decay to level E1 by emission of photon. Let us call
A21 the transition probability per unit time for spontaneous emission from
level E2 to level E1. Then the number of spontaneous decays per second is
N2A21, i.e. the number of spontaneous decays per second=N2A21.
 In addition to these spontaneous transitions, there will induced or
stimulated transitions. The total rate to these induced transitions between
level 2 and level 1 is proportional to the density (U(ν)) of radiation of
frequency ν, where ν = ( E2-E1 )/h , h Planck's constant.
 Let B21 and B12 denote the proportionality constants for stimulated emission
and absorption. Then number of stimulated downward transition in
stimulated emission per second = N2 B21 U(ν)
 Similarly , the number of stimulated upward transitions per second = N1 B12
U(ν)
 The proportionality constants A and B are known as the Einstein A
and B coefficients.

11. Contd..
N2 A21 + N2 B21 U(ν) =N1 B12 U(ν)
By solving for U(ν) (density of the radiation) we obtain
U(ν) [N1 B12 - N2 B21 ] = A21 N2
21
2
12
1
21
2
)
(
B
N
B
N
A
N
U


 









1
)
(
2
1
21
12
21
21
N
N
B
B
B
A
U 

12. Contd..
KT
/
h
KT
/
)
E
E
(
1
2
e
e
N
N 1
2 

















1
e
B
B
B
A
)
(
U
KT
/
h
21
12
21
21
According to Planck’s formula of radiation
 
1
e
1
c
h
8
)
(
U KT
/
h
3
3




 
)1)
)2)
From Boltzmann distribution:

13. Contd..
from equations 1 and 2 we have
B12=B21 =1 (3)
21
3
3
21
8
B
c
h
A



equations 3 and 4 are Einstein’s relations.
Thus for atoms in equilibrium with thermal radiation.
)4 (
)
(
)
(
tan
21
21
21
2
21
1

 U
B
A
U
B
N
A
N
emission
stimulated
emission
eous
spon


3
21
21


B
A It means that the probability of spontaneous emission
dominates above stimulated emission more and more as the
energy difference between the two states increases.

14. Interpretation of Einstein’s Coefficients
3
3
21
21 8
c
h
B
A 

 Indicates that at a given frequency an atom in a given energy state
Can undergo either spontaneous or stimulated emission
Further it means that at high frequencies spontaneous emission is more likely
to occur than the stimulated emission. This makes the laser mechanism more
difficult at higher frequencies such as ultraviolet frequencies.
B12=B21 means that an atom in a given energy state can have the mechanism
of spontaneous and stimulated emission with equal probability.
Though the coefficients of upward and downward transition are equal , the
rate of upward or downward transition differ. This is because there rates
depend on the population densities N 1& N2

15. Population Inversion
 A state in which a substance
has been energized, or
excited to specific energy
levels.
 More atoms or molecules are
in a higher excited state.
 The process of producing a
population inversion is
called pumping.
 Examples:
→by lamps of appropriate
intensity
→by electrical discharge

16. Metastable states
 An atom or molecule in an excited state remains
there for a certain time called the lifetime of that
state, before making a transition to a lower state. The
lifetime of a state is characteristic of the energy level
and varies over a wide range. Most of the states have
a short lifetime, of the order of 10-8 s. However, some
energy states have very long lifetime of the order of
10-3 s or higher. Energy states with such long life
times are called meta-stable states.

17. Pumping
 The population inversion can be achieved by exciting the
medium with suitable form of energy. This process is called
Pumping.
 There are several methods of pumping a laser and
producing population inversion necessary for the
occurrence of stimulated emission :
(a) Optical pumping
(b) Electric Discharge
(c) Inelastic atom-atom collision
(d) Direct Conversion
(e) Chemical reactions

18. Characteristics of Laser Beam
 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.
Divergence angle is twice the angle made by the outer edge with the
axis of the beam.
The angular spread of beam on one side of the axis :
d


 

19. High Intensity
The intensity of light is defined as the energy passing per unit area per
second through a point normal to the direction of flow. For a spherical
source with output power P , intensity at a point distant r from the source
is given as:
Laser beam is highly intense because it emits light as a narrow beam and
intensity remains high even at large distance from the source.
2
4 r
P
I



20. Extraordinary monochromacity
If ∆ν is the frequency of a spectral line of frequency ν0then the degree of
monochromacity is defined as:
ε=∆ν/ν0
Smaller is the value of ε, higher is the monochromacity of light.
For laser source ε=10-12 while for ordinary source ε≈10-5

21. High Coherence
Degree of coherence is the measure of phase correlation in the radiation field
at different locations and different time.
Incoherent
Coherent

22. 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.
 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
X′ X
P Q

23. 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.
Spatial coherence length of the source – lω=λ/θ, where θ is the angle
subtended by the slit in plane of observation.