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Introduction
The term "laser" originated as an acronym for "light amplification by stimulated
emission of radiation".
Laser is a device that generates light by a process called STIMULATED EMISSION.
Laser has become a valuable tool in a variety of fields starting with medicine to
communications.
Laser produces a highly directional and high intensity beam with narrow frequency
range than that available from the common types of light sources. So, laser is a light source
but it is very much different from many traditional sources.
Lasers are more widely used as a high power electromagnetic beam rather than a
light beam.
In 1960, the first laser (Ruby
Laser) was produced – using a ruby
crystal as the amplifier and a flash
lamp as the energy source.
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Quantum Behavior of Light
In 1900, Max Plank proposed that light consists of discrete bundles of energy. The
amount of energy of each bundles is “hv”. These bundles of radiant energy called quanta.
In 1905, Einstein gave the name photon to the quantum of light energy. A photon
represents the minimum energy unit of light. Each photon carries an amount of energy
proportional to the frequency of the light wave, as given by:
E = hv = hc/λ
Where: h is Planck’s constant = 6.62607004×10-34 m2kg/s, v is the frequency, c is the
speed of light and λ is the wavelength.
It is obvious that the higher the frequency of a photon, the more energy it possesses.
The interaction of light with matter is better explained using the concept of the photon
rather than by the wave concept. When light interacts with matter, the energy exchange
can take place only at certain discrete values for which the photon is the minimum energy
unit that light can give or accept.
Photon energy is usually expressed in terms of electron-volts (eV). The photon energy
( in eV) corresponding to light of wavelength λ is given by:
E = 12,400 / λ
Where λ is the wavelength in Angstrom unit (1x10-10 m)
Example 1 The He-Ne laser system is capable of lasing at several different IR wavelengths,
the prominent one being 3.3913μm. Determine the energy difference (in eV) between the
upper and lower levels for this wavelength.
Solution:
Example 2 The CO2 laser is one of the most powerful lasers. The energy difference between
the two laser levels is 0.117 eV. Determine the frequency and wavelength of the radiation.
Solution:
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ENERGY LEVELS
The light energy cannot take arbitrary values but must be multiples of photon energy
hv. It was similarly established that the electrons in an atom cannot have arbitrary amounts
of energy, but they take only discrete energies. This is a consequence of the Bohr’s
postulate of permitted orbits. In each of the permitted (stationary) orbits, the electron has
a specific amount of energy and cannot possess any other energy value.
The energy of electron at a very large distance from the nucleus is purely kinetic
energy and it is assigned a positive value. As the distance between nucleus and electron
decreases, the kinetic energy decreases. The energy levels are schematically represented by
horizontal lines drawn to an energy scale. For example, electron orbits and the
corresponding energy levels of the hydrogen atom are shown in figure below.
Electron orbits and the corresponding energy levels of several types of atoms.
The atom is in its lowest possible energy level when the electron is in the innermost
orbit, closest to the nucleus. Then, the atom is said to be in the ground state. An electron in
this ground state is stable and moves in this orbit continuously without emitting energy. If
electron in ground state absorbs energy in some way, it will go to a higher energy level and
the atom is said to be excited.
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The passing of an electron from one
energy level to another level within the atom
occurs in a jump which is called a quantum
transition. The electron transitions may be
induced by a variety of ways.
Interaction with light photons is one of
the means of supplying energy to orbital
electrons which causes upward electron
transitions and sends the atom into its excited
state.
POPULATION
The atoms of each chemical element have their own characteristic system of energy
levels. The energy difference between the successive energy levels of an atom is of the
order of 1 eV to 5 eV.
The number of atoms per unit volume that occupy a given energy state is called the
population of that energy state. The population N of an energy level E depends on the
temperature T. Thus,
N = e – E/kT ….. Boltzmann’s equation
Where k is known as the Boltzmann constant =1.38064852 × 10-23 m2 kg s-2 K-1
In a material, atoms are distributed differently in different energy states. The atoms
normally tend to be at their lowest possible energy level which need not be the ground
state. At temperatures above 0 K, the atoms always have some thermal energy and
therefore, they are distributed among the available energy levels according to their energy.
At thermal equilibrium, the number of atoms (population) at each energy level
decreases with the increase of energy level.
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ABSORPTION AND EMISSION OF LIGHT
In an atom, an electron in the ground state is stable and moves continuously in that
orbit without radiating energy. When the electron receives an amount of energy equal to
the difference of energy of the ground state and one of the excited states (i.e. outer orbits),
it absorbs energy and jumps to the excited state.
There are a variety of ways in which the energy may be supplied to the electron. One
way is to illuminate the material with light of appropriate frequency ν = (E2 - E1)/h. The
photons of energy hν = (E2 - E1) induce electron transitions from the energy level E1 to the
level E2. Atomic excitation and de-excitation is shown in figures below.
a) Absorbing energy, electron jumps from an
inner orbit to an outer orbit.
b) Energy level representation of excitation and
de-excitation of the atom.
However, the electron cannot stay in the outer orbit (excited state) for longer time.
The Coulomb attraction due to the positive nucleus pulls the electron back to the initial
inner orbit and the electron returns to the ground state. The excited electron has excess
energy equal to (E2 – E1) and it has get rid of this energy in order to come to the lower
energy level. The only mechanism through which the electron can lose its excess energy is
through the emission of a photon. Therefore, the excited electron emits a photon energy hν
= (E2 - E1) and returns to the ground state. This is the visualization of emission of light
according to Bohr’s quantum theory.
When we see light from any source, we actually “see” electrons jumping from
excited states to lower states. This type of emission of light which occurs on its own is
known as spontaneous emission and is responsible for the light coming from candles,
electric bulbs, fire, stars, sun etc. conventional sources of light.
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EINSTEIN’S PREDICTION
Einstein predicted in 1917 that there must be a second emission process to establish
thermodynamic equilibrium. For example, if we illuminate a material with light of suitable
frequency, the atoms in it absorb light and go to higher energy state.
The excited atoms tend to return randomly to the lower energy state. As the
ground state population is very large, more and more atoms are excited under the action of
incident light and it is likely that a stage may be reached where all atoms are excited.
Therefore, Einstein suggested that there could be an additional emission mechanism, by
which the excited atoms can make downward transitions. He predicted that the photons in
the light field induce the excited atoms to fall to lower energy state and give up their
excess energy in the form of photons. He called this second type of emission as stymie on
as stimulated emission.
THE THREE PROCESSES
Let us consider a medium consisting of identical atoms capable of being excited
from the energy level 1 to the energy level 2 by absorption of photons. Let the levels be
denoted by El and E2 and their populations be Nl and N2 respectively. Let the atoms be in
thermal equilibrium. In the equilibrium condition, the number of atomic transitions upward
must be equal to the number or downward transitions. Thus no net photons are generated
or lost. However, when the atoms are subjected to an external light of frequency v, the
following three processes occur in the medium:
(1) Absorption
An atom residing in the lower energy level E1 may absorb the incident photon and
jump to the excited state E2 as depicted in figure below. This transition is known as induced
or stimulated absorption or simply as absorption.
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Corresponding to each absorption transition, one photon disappears from the
incident light field and one atom adds to the population at the excited energy level E2· This
process may be represented as:
A + hν → A*
Where A denotes an atom in the lower state and A* an excited atom.
Absorption process (a) induced absorption (b) Material absorbs photons.
(2) Spontaneous Emission
An excited atom can stay at the excited level for an average lifetime τsp. If it is not
stimulated by any other agent during its short lifetime, the excited atom undergoes a
transition to the lower energy level on its own. During the transition, it gives up the excess
energy in the form of a photon, as shown in figure below.
This process in which an excited atom emits a photon all by itself and without any
external impetus is known as spontaneous emission. The process is represented as:
A* → A + hν
Spontaneous emission process (a) Emission (b) Material emits photons.
Important Features:
1. The process of spontaneous emission is not amenable for control from outside.
2. It is essentially probabilistic in nature.
3. The instant of transition, direction of propagation, the initial phase and the plane of
polarization of each photon are all random. They are different for different photons
emitted by various atoms.
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4. The light is not monochromatic.
5. Because of lack of directionality, the light spreads in all directions around the source.
The light intensity goes on decreasing rapidly with distance from the source.
6. The light is incoherent.
(3) Stimulated Emission
An atom in the excited state need not to “wait” for spontaneous emission to occur.
If a photon with appropriate energy hν = (E2 - E1) interacts with the excited atom, it can
trigger the atom to undergo transition to the lower level and emit another photon, as
shown in figure below.
The process of emission of photons by an excited atom through a forced transition
occurring under the influence of an external agent is called induced or stimulated
emission. The process may be represented as:
A* + hν → A + 2hν
Stimulated emission process (a) Emission (b) Material emits photons in a coordinated manner.
Important Features:
1. The process of stimulated emission is controllable from outside.
2. The photon emitted in this process propagates in the same direction as of the
stimulating photon.
3. The emitted photon has exactly the same frequency, phase and plane of polarization
as those of the incident photon.
4. The light produced in this process is directional, coherent and monochromatic.
5. High Intensity.
6. Light Amplification: The outstanding feature of this process is the multiplication of
photons. For one photon hitting an excited atom there are two photons emerging.
The two photons are in phase and travel along the same direction. These two
photons stimulate two excited atoms in their path and produce a total four photons
which are in phase and travel along the same direction. These four photons can in
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turn stimulate four excited atoms and generate eight photons and so on. The number
of photons builds up in an avalanche like manner, as illustrated in figure below.
POPULATION INVERSION
When an atomic system is in thermal equilibrium, photon absorption and emission
processes take place side by side, but because N1 > N2, absorption dominates. However,
laser operation requires obtaining stimulated emission exclusively. To achieve a high
percentage of stimulated emission, a majority of atoms should be at the higher energy
level than at the lower level. The non equilibrium state in which the population N2 of upper
energy level exceeds to a large extent the population N1 of the lower energy level is known
as the state of population inversion.
Pumping
In order to realize and maintain the state of population inversion, it is necessary
that atoms must be continuously promoted from the lower level to the excited level.
Energy is supplied to the laser medium in order to rise atoms from the lower energy
level to the excited level and maintaining population at the excited level at a value greater
than that of the lower energy.
So, Pumping is the process by which atoms are raised from the lower level to the
upper level of energy.
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Pumping Methods
The most common methods of pumping make use of light and electrons, in order to
create the state of population inversion are:
1- Optical Pumping: Is the use of photon to excite the atoms. Optical pumping is suitable
for any laser medium which is transparent to pump light.
2- Electrical Pumping: This method can be used only in case of laser materials that can
conduct electricity.
Active Medium
An active medium is a medium which, when excited, reaches the state of population
inversion, and eventually causes light amplification. The active medium may be a solid, a
liquid, or a gas.
Metastable States and Pumping Schemes
Longer – lived upper levels from where an excited atom does not return to lower
level at once, but remains excited for a time, are known as metastable state.
(a)
Three level energy diagram
(b) Four level energy diagram.
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