Al Falah School of Engineering and Technology
By Professor (Dr) Anil Kumar
Physics For 1st Semester
Al Falah University
Al Falah School of Engineering and Technology
Physics Notes for Semester I
Professor (Dr) Anil Kumar
Unit 3: Lasers and X-Rays
Lasers Syllabus : Spontaneous and Stimulated emission, Laser action, characteristics of laser beam;
concept of coherence, Spatial and temporal coherence, He-Ne laser, applications
Laser is an acronym for
Light
Amplification by
Stimulated
Emission of
Radiation.
Lasers can be constructed from solids,
liquids, gases, or plasmas. In all the cases, the laser action occurs because photons are emitted as the
system transitions between two energy states.
Spontaneous emission The electrons, atoms or molecules, they occupy certain energy levels. When
an atom or electron spontaneously decays from one energy state E2 to a lower energy state E1, it emits
a photon of the energy
E = h = E2-E1
where h is Planck's constant and  is the frequency of the laser light. This process is called
spontaneous
emission.
(see
Figure). Spontaneous emission does
not occur instantaneously. Instead,
Absorption
2
Spontaneous
Emissions
E2
2
E2
2
Stimulated
Emissions
E2
the electrons/atoms reside in the
upper energy state for a certain
h
h
h
2 h
1
E1
period of time (called life time of
the
energy
level)
before
they
spontaneously come down to the
lower energy state emitting a photon
E1
1
of energy h.
1
E1
Absorption: When a photon of
energy of h interacts with an atom or molecule in lower energy state E1 it absorbs the photon energy
and moves to higher energy state E2 provided the energy of the photon is exactly equal to the energy
difference of two state
E = h = E2 - E1
Unit III
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September 2014
Physics For 1st Semester
Al Falah School of Engineering and Technology
By Professor (Dr) Anil Kumar
Stimulated Emission: Einstein predicted that it was also possible to force a transition from higher
state to lower by means of a photon of energy equal to the energy difference of two states . In other
words, a photon of the energy h can force or stimulate an electron to transfer between states 2 and 1,
yielding another photon of the energy
h = E2 - E1.
This stimulated emission process results in two photons of the energy h. Furthermore, these two
photons will be in phase, of the same polarization, and heading in the same direction
Thus, ideal laser light is formed of groups of photons where all the photons are at exactly the same
frequency (wavelength) and all the photons are in phase.
Einstein coefficients
After Planck theory of radiation and Bohr’s theory of atomics model, Einstein redefined photons and
worked out interaction of photons with different energy states, which is also called radiative transfer
of energy. Einstein was the first to define stimulated emissions along with spontaneous emissions and
absorption of photons. He also worked out the rates and probabilities of these absorption and
emissions
Spontaneous emissions: The rate of spontaneous emissions from energy sate E2 to E1 will depend
only on the number of atoms N2 in higher states E2
 dN 2 
 dt    A21 N 2
The coefficient A21 is called the spontaneous emission probability or "the Einstein A coefficient." N2
atoms per unit volume in the Energy level 2 at any time t.
Absorption: The rate of absorption from energy sate E1 to E2 will depend on the number of atoms N1
in the lower energy states E1
 dN1 
 dt   W12 N1
W12 is absorption probability depends on the intensity or flux of photons F or
W12 =B12 F
The coefficient B12 is called the absorption probability or "the Einstein B coefficient for absorption."
Stimulated Emission: The rate of Stimulated Emission from energy state E2 to E1 will depend on the
number of atoms N2 in the higher energy states E2
 dN 2 
 dt   W21N 2
st
W21 is Stimulated Emission probability depends on the intensity or flux of photons F or
W21 =B21 F
Unit III
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September 2014
Physics For 1st Semester
Al Falah School of Engineering and Technology
By Professor (Dr) Anil Kumar
The coefficient B21 is called the probability of Stimulated Emission or "the Einstein B coefficient for
Stimulated Emission."
Consider an atomic system under equilibrium conditions. The total emission probability per
unit time from level E2 to level E1 (spontaneous + stimulated) is equal to absorption probability
(A21+B21F) N2 = B12 F N1
From this we get photon flux or density F= E()
E() (N1B12 - N2B21) = N2A21
E( ) 
Or
A21
1
B21 N1  B12 

 1
N 2  B21 
At thermal equilibrium, the atomic population N1 and N2 in energy levels E1 and E2 at temperature T
is given by Maxwell-Boltzmann distribution as
N2
 e ( E2  E1 ) / kT  e h / kT
N1
E( ) 
As
h = E2-E1
A21
1
h / kT
B21 e
 B12 

  1
 B21 
Comparing it with Planck's law of radiation
8h 3
1
E ( ) 
3
h / kT
c
e
1
We get
A21 8h 3
B

and 12  1
3
B21
c
B21
The quantities A21, B12, B21 are called Einstein's coefficients.
The ratio of spontaneous and stimulated emission probabilities is proportional to 3. The probability
of spontaneous emission is very high at higher frequencies compared with the probability of
stimulated emission, hence it is very difficult to make lasers in visible blue and ultra violet region, as
compared to the making of lasers in infrared region.
Also B21=B12
The probability of stimulated emission is the same the probability of absorption. It mean in coming
photon hv (=E2-E1) will likely to be absorbed as number of atoms at lower energy N1 is more than N2.
Hence Laser can only be made through stimulated emission if N2>N1 ( Population Inversion
condition)
Laser Action
The laser action, is due to stimulated emission which provides gain to the laser system as it make one
photon in to two photons.
Unit III
Page 3
September 2014
Physics For 1st Semester
Al Falah School of Engineering and Technology
By Professor (Dr) Anil Kumar
To get better Stimulated emission, the higher energy states must have more population of atoms than
lower energy state, which is not common naturally. This situation is known as population Inversion.
Population Inversion
In a case of population inversion, the population in the upper energy state is more than the
population in the lower laser state.
In thermal equilibrium, the population ratio between two states is governed by the Boltzman equation
N2
 e ( E2  E1 ) / kT
N1
where N2 is the population in the upper state, N1 is the population in the lower state, k is Boltzmann’s
constant, and T is the temperature.
However, the Boltzmann equation only describes conditions of thermal equilibrium. Lasers are not
operated in thermal equilibrium. Instead, the upper state is populated by pumping it via some nonequilibrium process. A pulse of light, an electrical spark or a chemical reaction can be used to
populate more in the upper energy state.
Laser media To make laser one must choose laser media like a Gas, a Liquid or a solid state material.
The pumping process is decided depending on the laser gain medium.
For Gas lasers it is generally gas discharge,
For liquid and Solid state lasers it is optical pumping. The optical energy is provided either by flash
lamp or by laser or laser diodes to create population inversion.
Cavity
Pumping
It is another essential item of the laser system which provides selective gain at the wavelength of the
required lasers. It is basically a multi beam Fabry Perot
Interferometer. It is also referred as feedback system like
in any oscillator.
Following three components are required for laser
generation
1.
Laser media
2.
Pumping device
Laser gain media
3.
Feedback system (resonator cavity) to tune lasers.
Resonator cavity with mirrors
Following three mechanisms are responsible for laser
generation
1.
2.
3.
MAJOR COMPONENTS OF LASERS
Pumping to create population inversion
Stimulated emission to get the gain
Feedback system (resonator cavity) to sustain oscillations.
LASER CHARACTERSTICS
The laser is also light but differs from ordinary light due to following properties.
1. MONOCHROMATICITY,
2. COHERENCY,
Unit III
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September 2014
Physics For 1st Semester
Al Falah School of Engineering and Technology
By Professor (Dr) Anil Kumar
3. VERY LOW BEAM DIVERGENCE
4. BRIGHTNESS
5. POLARISATION.
First three qualities come from stimulated emission in laser and next two follows due to first three
qualities of laser. For lasers (like light) wavelength  (in angstroms or nm) is used to define laser over
it’s frequency . But the wavelength  of a laser line could be expressed in terms of frequency . The
property of having a group of photons at exactly one frequency is referred to as monochromaticity.
In actual practice, laser line is not at one wavelength but varies over a very small range of wavelength
due to various broadening process. This range is referred as line width (Δ).
The property of having a group of photons with the same
phase is referred to as coherency. Thus, lasers are often
Monochromatic
termed monochromatic and coherent sources of light.
In reality lasers are neither perfectly
monochromatic nor perfectly coherent (see Figure
below). However, when characterizing a real laser
system, it is generally assumed that the laser beam was
Coherent
initially in phase and the incoherence of the laser arises

only from the lack of monochromaticity of the source.
(This is a reasonable assumption for conventional lasers with feedback, but may not be sufficiently
accurate for unusual laser systems.)
Thus, Coherency and monochromaticity are generally assumed to
Finite line width
measure the same parameter. The monochromaticity of a laser
beam is described by its wavelength line width Δ, (in angstroms
or nm) or its frequency line width  (in Hz). The two quantities
are related as
Δ
  
   1   2  c 2 
 

Finite Coherency
which (assuming that l and 2 are much larger than 2 - 1) can
be approximated by
The fundamental line width for an ideal laser line is extremely small. In practice, various broadening
mechanisms increase this fundamental line width in real lasers. The monochromaticity of a laser beam
can also be described in terms of coherency. Thus, the coherence time  is given by
 = 1/
Coherence is one of the most important concepts in optics and is strongly related to the ability of
light to exhibit interference effects. A light field is called coherent when there is a fixed phase
relationship between the electric field values at different locations or at different times. Partial
coherence means that there is some (although not perfect) correlation between phase values.
Spatial and Temporal Coherence There are two very different aspects of coherence:
Unit III
Page 5
September 2014
Physics For 1st Semester
Al Falah School of Engineering and Technology
By Professor (Dr) Anil Kumar
Spatial coherence means a strong correlation (fixed phase relationship) between the electric
fields at different locations across the beam profile. For
Spatial Coherent
example, within a cross-section
of a beam from a laser with diffraction-limited beam
quality, the electric fields at different positions oscillate
in a totally correlated way, even if the temporal structure
is complicated.
Temporal coherence means a strong correlation
between the electric fields at one location but different
times. For example, the output of a single-frequency
Partial Coherent
laser can exhibit a very high temporal coherence, as the
electric field temporally evolves in a highly predictable fashion: it exhibits a clean sinusoidal
oscillation over extended periods of time.
He Ne Laser

It is a gas laser.

Laser comes from Neon atoms.

Helium is used to help population inversion.

A mixture of Helium and Neon Gases in the ratio of 10: 1 is filled in discharge tube at
pressure of 2-3 torr depending on the size.

The discharge is created by applying high voltage between anode and cathode.

Laser action: In discharge tube He atoms takes energy and go to higher energy states of 23S
and 21S. When Neon atom collide with exited helium atoms, the energy is transferred to Neon
atom and Neon atoms go to exited states of 2S and 3S of Neon.

Exited neon atom leave 3S and 2S level and moves to 2p and 3p and radiate many possible
frequencies of lasers Three main lines of lasers have wavelength 632.8nm (3S2p), 3.39m
(3S3p) and 1.15m(2S2p).

In order to maintain continuous flow the lower level of neon gets depopulated by losing
energy to the wall of discharge tube by wall collisions.
Unit III
Page 6
September 2014
Al Falah School of Engineering and Technology
By Professor (Dr) Anil Kumar
Physics For 1st Semester

To get the laser output the discharge
tube is terminated by lossless Brewster
3S
21S
3.3μ
window and kept in a cavity of mirrors
23S
output one of the mirrors has little
2S
0.63μ
Energy
of very high reflectivity. To get laser
3P
1.15μ
2P
transmission of nearly 1%.

1S
Typical output of the He-Ne Laser is
between 2 – 25 mWatt.

De-excitation with
wall collisions
The laser is very stable and has high
11S
coherence
length
and
very
low
He
Ne
divergence.

Main application of this laser in alignment, scientific studies like interferometers, barcode
reader and in some communication links.
APPLICATIONS OF LASERS
Lasers have found wide applications in all most all walks of life. Lasers depending on wavelength and
powers are used in different applications. Some of them are mentioned below
(i)
Material processing: Laser can cut, drill, weld and remove Metal from surfaces.
(ii)
Communication: Lasers are used as source in fibre optic communication. Laser is also tried
in free space communications.
(iii)
Medicine: laser is used in eye surgery, to burn up brain tumours and remove tattoos. Also
laser is used in acupunctures. Now lasers are being tried to cure Cancer.
(iv)
Applications in Physics and Chemistry: An interesting example is of non-linear Optic with
special mention of harmonic generation and stimulated scattering. In the field of chemistry, lasers are
used both for diagnostic purposes and for producing irreversible chemical change i.e. laser
photochemistry. In diagnostic techniques particularly resonant Raman Scattering and coherent
antistokes
(v)
Applications in Military: laser with high power output can be used for destructive purpose.
It is used for dazzling applications. There are many laser sensor which are used defence such LRF
RLG etc.
(vi)
In entertainment like in Laser shows
(vii)
In construction work for alignment of bridges and tunnels.
__________________________________________________________________________________
Important questions from the topic as they appeared in past exams of MD Univ.
Questions
1. Write note on Population inversion.
2. Explain in brief monochromaticity,
3. What is the principle of laser?
4. Discuss salient characteristics of laser beam. (KU, BT 2005, NITK 2007)
5. What are the main components of laser?
Unit III
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September 2014
Physics For 1st Semester
Al Falah School of Engineering and Technology
By Professor (Dr) Anil Kumar
6.
7.
8.
9.
Write two main requirements' for semiconducting laser material.
Describe various applications of lasers? (MDU,BE 2011)
Write note on He-Ne laser.' (MDU, BE 2002, 2005)
Explain the terms: spontaneous emission, stimulated emission, pumping in lasers and population inversion.
(KU, BT 2005,2007, NITK, 2004. 2008)
10. Explain the characteristics of laser beam. (MDU,BT 2006)
11. Discuss Einstein's coefficients. Derive relation between them. (MDU, BE May 2008),
12. What are gas lasers? Describe the principle, construction and working of He-Ne gas laser. (MDU, 2006)
Unit III
Page 8
September 2014