Laser physics for BSc students and engineering

Laser Physics
(UNIT III)
Asst. Prof. SHIVANAND B. H
TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI
May 28, 2024

Introduction
Syllabus
Interaction of radiation with matter: Induced absorption, spontaneous emission and
stimulated emission.
Einstein's A and B coecients Derivation of relation between Einstein's coecients and
radiation energy density;
Condition for amplication of light;
Population inversion; Methods of pumping; Requisites of laser energy source, active
medium and laser cavity;
Three level energy diagram.
Construction and Working principle of Ruby Laser.
Characteristics of laser light and its applications.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Introduction
The wordLASERwas coined as an acronym for
Emission of Radiation.
The special nature of laser light has made laser technology a vital tool in nearly every
aspect of everyday life including communications, entertainment, manufacturing, and
medicine.
A laser device is a source of highly intense, monochromatic, coherent and highly directed
beam of light produced by stimulated emission of radiation. T. Maiman produced rst
laser device using ruby crystal in 1960.
The idea of stimulated emission of radiation was given by Albert Einstein in 1917.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Interaction of radiation with matter:
An isolated atom can exist in its ground state of energyE1or in an excited state of higher
energyE2.
The atom can change from one of these states to the other through following three
processes. They are
1. Stimulated absorption,
2. Spontaneous emission
3. Stimulated emission.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Interaction of radiation with matter:
Stimulated absorption
Consider an atom initially in the ground state of energyE1.
If an electromagnetic radiation of frequencyis incident on the atom, the atom absorbs
energyhfrom the radiation and move to the higher energy stateE2ifh=E2E1.
The process by which an atom in a lower energy state can be raised to a higher energy
state by absorbing a photon of energyhis called
ATOM + PHOTON !ATOM*
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Interaction of radiation with matter:
Stimulated absorption
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Interaction of radiation with matter:
Spontaneous emission :
Consider the atom in the excited state of energyE2.
The atom will remain in this state for a time of about 10
8
s.
The atom will fall on its own to the ground state emitting radiation of energyh.
The process by which an excited atom jumps from a higher energy state to a lower energy
state with emission of a photon is called
ATOM*!ATOM + PHOTON
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Interaction of radiation with matter:
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Interaction of radiation with matter:
Stimulated emission :
Consider an atom in the excited state of energyE2. If an electromagnetic radiation of
frequencyhis incident on the atom, the atom moves to the ground state of energyE1
by emitting a photon of energyhalong with the incident photon of energyh.
This stimulated emission is possible only if the frequencyhof the radiation satises the
relationh=E2E1.
The process in which an atom in a higher energy state jumps to lower energy state with
the emission of a photon identical to the incident photon is called as
ATOM* !ATOM + 2 PHOTON
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Interaction of radiation with matter:
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Relation between Einstein coecients
Consider an atomic system present in a radiation eld of energy density(v)under
equilibrium conditions.
LetE1andE2be the energy levels of the atom withE2>E1. The number of atoms per
unit volume in the two levels respectively areN1andN2.
The photon emitted due to transition between the levels will have energyhv=E2E1.
Postulations made by Einstein are
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Relation between Einstein coecients
1
proportional to (a) the number of atoms per unit volume in the lower levelN1and (b)
density(v)of radiation energy incident on these atoms.
Mathematically
dN1
dt
/N1(v)or
dN1
dt
=B12N1(v): : : ::(1)
whereB12is the proportionality constant calledEinstein coecient for induced
absorption.
The rate of spontaneous emission
lower level is proportional to the number of atoms per unit volume in the higher levelN2
only.
i.e.
dN2
dt
/N2or
dN2
dt
=A21N2: : :(2)
whereA21is the proportionality constant calledEinstein coecient for spontaneous
emission.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Relation between Einstein coecients
The rate of stimulated emission
lower level is proportional to (1) the number of atoms per unit volume in the higher level
N2and (2) density of radiation energy incident on these atoms.
i.e.
dN2
dt
/N2(v)or
dN2
dt
=B21N2(v): : : ::(3)
whereB21is the proportionality constant calledEinstein coecient for stimulated
emission.
Under thermal equilibrium, the absorption rate or the number of photons absorbed per
second is equal to the sum of the number of photons emitted per second by spontaneous
and stimulated emissions.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Relation between Einstein coecients
Thus RHS of equation (1) is equal to sum of RHS of equations (2) and (3)
B12N1(v) =A21N2+B21N2(v)or
(v) [B12N1B21N2] =A21N2(v) =
A21N2
B12N1B21N2
or(v) =
A21N2
B21N2

B12N1
B21N2
1
or(v) =
A21
B21

N
1
B
12
N
2
B
21
1
: : : ::(4)
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Relation between Einstein coecients
According to Boltzmann, the atomic population at dierent energy levels at a given
temperatureTis given by (Boltzmann distribution law)
N1=N0e
(E1=kT)
andN2=N0e
(E2=kT)
.
whereN0is the total number of atoms andkis the Boltzmann constant.
Dividing the above equations,
N1
N2
=
e
(E
1
=kT)
e
(E
2
=kT)
=
e
(E2E1=kT)
or
N1
N2
=e
(hv=kT)
: : :(5)
(sinceE2E1=hv)
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Relation between Einstein coecients
substituting for
N1
N2
from (5) in (4) we get(v) =
A21
B21
2
4 1

B
12
B
21
e
(hv=kT)
1

3
5: : :(6).
The energy density of radiation at a given temperature as per Planck's radiation formula is
(v) =
8hv
3
c
3
"
1

e
(hv=kT)
1

#
: : :(7)
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Relation between Einstein coecients
Comparison of equations (6) and (7), we get
A21
B21
=
8hv
3
c
3. and
B12
B21
=1.
This impliesB12=B21: : :(9) By substituting (8) in (7)
(v) =
A21
B21

1
(e
(hv=kT)
1)

Rearranging, we have
spontaneous emission probability
Stimulated emission probability
=
A21
B21(v)
=

e
(hv=kT)
1

: : :(10)
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Relation between Einstein coecients
Case 1 : hv>kT;e
(hv=kT)
1 From eqn. (10),
A21
B21
1 then spontaneous
emission probability is greater than stimulated emission probability which is the case in
electronic transition in atoms and molecules.
Case 2 : hvkT;e
(hv=kT)
will be low and comparable to 1 . ThenA21will be
comparable toB21i.e. the phenomena of stimulated emission becomes signicant.
Case 3 : hv<kT;

e
(
hv
kT)
1

1. From eqn. (10),
A21
B21
1, then stimulated
emission probability is greater than spontaneous emission probability which is the case in
atomic transitions in microwave regions and visible regions. This leads to laser action.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Principle of Laser
The action of laser is based on stimulated emission and amplication of light. In producing
laser, the following conditions must be satised
State of population inversion,
Existence of metastable state and
connement of emitted photons to achieve population inversion.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Population inversion
Consider a sample having a number of atoms in thermal equilibrium at a certain
temperature.
If the numberN1of these atoms are in the ground state of energyE1and the numberN2
are in a state of higher energyE2then according to Boltzmann's law
N2
N1
= exp
h
(E2E1)
kT
i
ThusN2<N1. There will always be less atoms in the excited state than in the ground
state.
The number of atoms present in a given energy state of a substance at thermal
equilibrium is calledpopulationof that energy state.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Population inversion
The condition when the number of atoms in an excited state is more than that in the
ground state is called population inversion.
The process of supplying energy from an external source, to achieve population inversion
in a sample, is calledpumping.
The process in which the atoms in a given sample are raised to higher energy states using
light energy is called optical pumping.
In this process, the sample is illuminated with light of frequencyvsuch that
hv=E2E1. The atoms in the ground state absorb the energy of incident photons and
jump to the higher energy state.
In an excited state, the atom remains for a short duration of time of around 10
8
s.
An excited state in which atoms can stay for a comparatively longer duration of time of
around 5msis calledmetastable state.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

metastable state
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Pumping methods
Pumping can be classied into the following types based on the type of source of pumping.
Optical pumping:
optical source. The atoms absorb energy from the photons and raises to excited state.
(e.g.) Ruby Laser, Nd-YAG Laser
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Pumping methods
Electrical pumping:
electric eld and they collide with gas atoms and these atoms are raised to excited state.
(e.g.) Argon Laser,CO2Laser
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Pumping methods
Direct Conversion:
GaAs etc., the combination of electrons and holes takes place and electrical energy is
converted into light energy directly. (e.g) Semiconductor Laser.
Inelastic collision between atoms:
collision with electrons. The excitedA

atoms now collide with "B" atoms so thatB
goes to excited stateB

(e.g.)HeNeLaser.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Pumping methods
Thermal pumping
except that in this method heat is used as pump source instead of light or electric
discharge
Figure:
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Components of laser :
The components of a laser are
active medium -
amplifying light by way of population inversion.
the pumping source to achieve population inversion.
electric discharge or any other method to move the atoms to metastable state from
ground state.
the optical resonator -
forth in the active medium with the help of mirrors to achieve amplication.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Laser action
Consider a system of atoms that exist in three dierent energy states namely, ground
state(E1), excited state(E2)and metastable state(E3)as shown in the diagram.
In the excited state an atom can exist only for a time interval of 10
8
s. In the
metastable state an atom can remain stable for a longer duration of time (5ms).
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Laser action
The system of atoms in the ground state are illuminated by radiation such that they get
excited and move to excited state(E2)by absorbing photons of energyhv
0
=E2E1.
This is called optical pumping.
Since the life of excited atoms is very small, they jump to metastable state(E3)by non
radiative transition. The atoms can remain in this metastable state for longer time. Thus
there will be more atoms in metastable state than in the ground state. Thus population
inversion is said to be achieved.
The atoms in the metastable state are bombarded by photons each of energy
hv=E3E1The atoms make transition to the ground state by stimulated emission.
This results in emission of photons each of energyhv=E3E1. These photons along
with the bombarding photons have same energy and are in same phase. Thus the number
of photons is multiplied by a factor of two. This process repeats and light amplication by
stimulated emission of radiation or LASER occurs.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Ruby laser
construction and working principles of Ruby Laser
Ruby laser is a three level solid state laser and was constructed by Mainmann in 1960.
Ruby(Al2O3+Cr2O3)is a crystal of Aluminium oxide, in which 0:05%ofAl
+3
ions are
replaced by theCr
+3
ions. The colour of the rod is pink. The active medium in the ruby
rod isCr
+3
ions.
Figure:
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

construction and working principles of Ruby Laser
Construction
In ruby laser 4cmlength and 5mmdiameter rod is generally used. Both the ends of the
rods are highly polished and made strictly parallel.
The ends are silvered in such a way, one becomes partially reected and the other end
fully reected.
The ruby rod is surrounded by xenon ash tube, which provides the pumping light to
excite the chromium ions in to upper energy levels.
Xenon ash tube emits thousands joules of energy in few milli seconds, but only a part of
that energy is utilized by the chromium ions while the rest energy heats up the apparatus.
A cooling arrangement is provided to keep the experimental set up at normal temperatures
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

construction and working principles of Ruby Laser
Construction
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

construction and working principles of Ruby Laser
Working
The energy level diagram of chromium ions is|shown in gure. The chromium ions get
excitation into higher energy levels by absorbing of 5600A
0
of wave length radiation.
The excited chromium ions stay in the levelHfor short interval of time

10
8
Sec

. After
their life time most of the chromium ions are de-excited fromHtoGand a few
chromium ions are de-excited fromHtoM.
The transition betweenHandMis non-radioactive transition i.e. the chromium ions
gives their energy to the lattice in the form of heat.
In the Meta stable state the life time of chromium ions is 10
3
sec.
The life time of chromium ions in the Meta stable state is 10
5
times greater than the life
time of chromium ions in higher state.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

construction and working principles of Ruby Laser
Working
Figure:
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

construction and working principles of Ruby Laser
Working
Due to the continuous working of ash lamp, the chromium ions are excited to higher
stateHand returned toMlevel.
After few milli seconds the levelMis more populated than the level G and hence the
desired population inversion is achieved.
The state of population inversion is not a stable one. The process of spontaneous
transition is very high.
When the excited chromium ion passes spontaneously fromHtoMit emits one photon
of wave length 6943A
0
.
The photon reects back and forth by the silver ends and until it stimulates an excited
chromium ion inMstate and it to emit fresh photon in phase with the earlier photon.
The process is repeated again and again until the laser beam intensity is reached to a
sucient value.
When the photon beam becomes sucient intense, it emerges through the partially
silvered end of the rod. The wave length 6943A
0
is in the red region of the visible
spectrum.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

construction and working principles of Ruby Laser
Draw backs of ruby laser
The laser requires high pumping power
The eciency of ruby laser is very small
It is a pulse laser
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

construction and working principles of Ruby Laser
Uses o ruby laser
Ruby lasers are in optical photography
Ruby lasers can be used for measurement of plasma properties such as electron density
and temperature.
Ruby lasers are used to remove the melanin of the skin.
Ruby laser can be used for recording of holograms.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Laser characteristics
Laser diers from the ordinary light with respect to some properties.
Monochromaticity
Directionality
Coherence
Intensity
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Applications of lasers
Due to high intensity, high monocromacity and high directionality of lasers, they are widely
used in various elds like
communication
computers
chemistry
photography
industry
medicine
military
scientic research
communication
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Applications of lasers
communication
In case of optical communication semiconductors laser diodes are used as optical sources
and its band width is

10
14
Hz

is very high compared to the radio and microwave
communications.
More channels can be sent simultaneously
Signal cannot be tapped
As the band width is large, more data can be sent. -
A laser is highly directional and less divergence, hence it has greater potential use in
space crafts and submarines.
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Applications of lasers
Asst. Prof. SHIVANAND B. H (TUNGAL SCHOOL OF BASIC AND APPLIED SCIENCES, JAMKHANDI )Laser Physics May 28, 2024

Laser physics for BSc students and engineering

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