3. 3
What makes lasers special?
• Intensity: The laser
beam is highly
intense
• Directionality: They
produce a directional
beam.
• Monochromaticity: They have
a narrow spectrum (or
bandwidth).
• Coherence: They are
coherent (constant phase
relation)
4. Principles of working of a laser
In lasers, photons are interacted in three ways with the
atoms:
1. Absorption of radiation
2. Spontaneous emission
3. Stimulated emission
4. Population Inversion
5. Pumping
5. Absorption of radiation.
Absorption of radiation is the process by which electrons in the ground state absorbs
energy from photons to jump into the higher energy level.
Lasers: the basic idea
6. Spontaneous emission.
Spontaneous emission is the process by which electrons in the excited state
(unstable state) return to the ground state (stable state) by emitting photons.
The electrons in the excited state can stay only for a short period. The time up
to which an excited electron can stay at higher energy state (E2) is known as
the lifetime of excited electrons. The lifetime of electrons in excited state is
10-8
second.
Lasers: the basic idea
7. Stimulated emission.
Stimulated emission is the process by which an incoming photon of a specific frequency can
interact with an excited atomic electron causing it to drop to a lower energy level. In stimulated
emission, two photons are emitted (one additional photon is emitted), one is due to the
incident photon and another one is due to the energy release of excited electron. Thus, two
photons are emitted.
Lasers: the basic idea
8. 8
Hence we need a population inversion,
i.e. more atoms in the upper level than in the lower level.
We want lots of this.... ... but not much of this
Lasers: the basic idea
POPULATION INVERSION
9. 9
Need to pump (add energy to) the gain medium to get an inversion
POPULATION INVERSION
10. Population inversion is the process of achieving greater population
of higher energy state as compared to the lower energy state.
Population inversion technique is mainly used for light amplification.
The population inversion is required for laser operation.
Consider a group of electrons with two
energy levels E1
and E2
.
E1
is the lower energy state and E2
is the
higher energy state. N1
is the number of
electrons in the energy state E1
. N2
is the
number of electrons in the energy state E2
.
The number of electrons per unit volume in
an energy state is the population of that
11. Population inversion cannot be achieved in a two energy level
system.
Under normal conditions, the number of electrons (N1) in the
lower energy state (E1) is always greater as compared to the
number of electrons (N2) in the higher energy state (E2).
N1 > N2
When temperature increases, the population of higher energy
state (N2) also increases. However, the population of higher
energy state (N2) will never exceeds the population of lower
energy state (N1).
At best an equal population of the two states can be achieved
12. 12
3 and 4 level lasers
• Can’t get a population inversion in 2 level system.
• So lasers broadly categorised as 3 or 4 level systems.
• 3 level - N2 > N1 – 1 thermally populated so need raise lots of population from 1 – 3
• 4 level - N2 = 0, so any population in 3 is an inversion – less pump, more efficient!
• Not necessarily monochromatic:
• Some lasers have broad emission range (although not white light!)
DN1
Rate of change of population population density x pumping rate
Absorption & stimulated emission equally likely
Best we can do is N2 = N1 - no population inversion in 2 level laser
13. 3-level Laser
Consider a system consisting of three energy levels E1, E2, E3 with N number of
electrons.
It can be simply written as E1 < E2 < E3. That means the energy level of E2 lies in
between E1 and E3. .
The energy level E1 is known
as the ground state or lower
energy state and the energy
levels E2 and E3 are known as
excited states. The energy
level E2 is sometimes referred
to as Meta stable state (10-3
sec). The energy level E3 is
sometimes referred to as
14. To get laser emission or population inversion, the population of higher energy state (E2)
should be greater than the population of the lower energy state (E1).
Under normal conditions, the higher an energy level is, the lesser it is populated. For
example, in a three level energy system, the lower energy state E1 is highly populated as
compared to the excited energy states E2 and E3. On the other hand, the excited energy
state E2 is highly populated as compared to the excited energy state E3. It can be simply
written as N1 > N2 > N3.
Under certain conditions, the greater population of higher energy state (E2) as compared to
the lower energy state (E1) is achieved. Such an arrangement is called population inversion.
Let us assume that initially the majority of electrons will be in the lower energy state or
ground state (E1) and only a small number of electrons will be in excited states (E2 and E3).
When we supply light energy which is equal to the energy difference of E3 and E1, the
electrons in the lower energy state (E1) gains sufficient energy and jumps into the higher
energy state (E3). This process of supplying energy is called pumping.
We also use other methods to excite ground state electrons such as electric discharge and
15. The lifetime of electrons in the energy state E3 is very small as compared to the
lifetime of electrons in the energy state E2. Therefore, electrons in the energy
level E3 does not stay for long period. After a short period, they quickly fall to
the Meta stable state or energy state E2 and releases radiation less energy
instead of photons.
Because of the shorter lifetime, only a small number of electrons accumulate
in the energy state E3.
The electrons in the Meta stable state E2 will remain there for longer period
because of its longer lifetime. As result, a large number of electrons
accumulate in Meta stable state. Thus, the population of metal stable state
will become greater than the population of energy states E3 and E1.
It can be simply written as N2 > N1 > N3.
In a three level energy system, we achieve population inversion between
16. After completion of lifetime of electrons in the Meta stable state, they fall
back to the lower energy state or ground state E1 by releasing energy in the
form of photons. This process of emission of photons is called spontaneous
emission.
When this emitted photon interacts with the electron in the Meta stable state
E2, it forces that electron to fall back to the ground state. As a result, two
photons are emitted. This process of emission of photons is called stimulated
emission.
When these photons again interacted with the electrons in the Meta stable
state, they forces two Meta stable state electrons to fall back to the ground
state. As a result, four photons are emitted. Likewise, a large number of
photons are emitted.
As a result, millions of photons are emitted by using small number of photons.
17. Einstein Coefficient Relation derivation and discussion:
Einstein showed the interaction of radiation with the matter with the help of
three processes called stimulated absorption, spontaneous emission, and
stimulated emission. He showed in 1917 that for a proper description of
radiation with matter, the process of stimulated emission is essential. Let us
first derive the Einstein coefficient relation on the basis of the above theory:
Let N1 be the number of atoms per unit volume in the ground state E1 and
these atoms exist in the radiation field of photons of energy E2-E1 =h v such
that the energy density of the field is E.
E2
E1
Einstein Coefficient for Stimulated
Absorption:
Let R1 be the rate of absorption of
light by E1 E2 transitions by the
process called stimulated absorption
(Refer beside figure):
18. This rate of absorption R1 is proportional to the number of atoms N1 per unit volume in
the ground state and proportional to the energy density E of radiations.
R1∞ N1 E
Or R1 = B12N1 E (1)
Where B12 is known as the Einstein’s coefficient of stimulated absorption and it
represents the probability of absorption of radiation. Energy density e is defined as the
incident energy on an atom as per unit volume in a state.
Einstein Coefficient for Spontaneous Emission:
Now atoms in the higher energy level E2 can fall to the ground state E1 automatically
after 10-8 sec by the process called spontaneous emission (as shown in figure).
The rate R2 of spontaneous emission E2-> E1 is independent of energy density E of the
radiation field.
R2 is proportional to number of atoms N2 in the excited state E2 thus
R2∞ N2
19. Where A21 is known as
Einstein’s coefficient for
spontaneous emission and it
represents the probability of
spontaneous emission.
Einstein Coefficient for Stimulated
Emission:
Atoms can also fall back to the ground
state E1 under the influence of the
electromagnetic field of an incident
photon of energy E2-E1 =hv by the
process called stimulated emission
(Refer beside Figure):
E2
E1
E2
E1
20. Rate R3 for stimulated emission E2-> E1 is proportional to energy density E of the
radiation field and proportional to the number of atoms N2 in the excited state, thus
R3α N2 E
Or R3=B21N2 E (3)
Where B21 is known as the Einstein coefficient for stimulated emission and it represents
the probability of stimulated emission.
In steady-state (at thermal equilibrium), the two emission rates (spontaneous and
stimulated) must balance the rate of absorption.
Thus R1=R2+R3
Using equations (1,2, and 3) ,we get
N1B12E=N2A21+N2B21E
Or N1B12E –N2B21E=N2A21
Or (N1B12-N2B21) E =N2A21
Or E= N2A21/N1B12-N2B21
21. [by taking out common N2B21from the denominator]
Or E= (A21/B21) {1/N1/N2(B12/B21-1)) (4)
Einstein proved thermodynamically, that the probability of stimulated absorption is
equal to the probability of stimulated emission. thus
B12=B21
Then equation(4) becomes
E=(A21/B21) (1/N1/N2-1) (5)
From Boltzman’s distribution law, the ratio of populations of two levels at
temperature T is expressed as
N1/N2=e(E
2–E
1
)/KT
N1/N2=ehv/KT
Where K is the Boltzman’s constant and h is Planck’s constant.
Substituting value of N1/N2in equation (5) we get
E= A21/B21 (1/ehv/KT
-1) (6)
22. Now according to Planck’s radiation law, the energy density of the black body
radiation of frequency v at temperature T is given as
E = ( 8πhv3
/c3
) (1/ehv
/KT) (7)
By comparing equations (6 and 7),we get
A21/B21=8πhv3
/c3
This is the relation between Einstein’s coefficients in laser.
Significance of Einstein coefficient relation: This shows that the ratio of Einstein’s
coefficient of spontaneous emission to the Einstein’s coefficient of stimulated
absorption is proportional to the cube of frequency v. It means that at thermal
equilibrium, the probability of spontaneous emission increases rapidly with the
energy difference between two states.
23. 23
• Gas lasers:
• Usually electrically pumped
• Wide range of wavelengths
• Low gain
Types of laser
• Liquid lasers
• Solution of complex organic dyes
• Widely tunable
• Solid state lasers
• Widest class of laser systems
• Lasing ion doped in crystalline host - Nd:YAG, Ti:sapp
• Ion in glass -Nd:glass
• Fibre lasers – Er, Yb in glass
• Semiconductor diode lasers
But you don’t get every colour! Dependent on lasing transition
24. Application:
1. It is widely used in fiber optic communication
2. It is used to heal the wounds by infrared radiation
3. It is also used as a pain killer
4. It is used in laser printers and CD writing and reading.
![[by taking out common N2B21from the denominator]
Or E= (A21/B21) {1/N1/N2(B12/B21-1)) (4)
Einstein proved thermodynamically, that the probability of stimulated absorption is
equal to the probability of stimulated emission. thus
B12=B21
Then equation(4) becomes
E=(A21/B21) (1/N1/N2-1) (5)
From Boltzman’s distribution law, the ratio of populations of two levels at
temperature T is expressed as
N1/N2=e(E
2–E
1
)/KT
N1/N2=ehv/KT
Where K is the Boltzman’s constant and h is Planck’s constant.
Substituting value of N1/N2in equation (5) we get
E= A21/B21 (1/ehv/KT
-1) (6)](https://image.slidesharecdn.com/lc-01-laser-250524063750-c448bafd/85/LC-01-Laser-pptx-laser-basic-idea-Einstein-s-coefficient-derivation-21-320.jpg)
