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Module – 4
Quantum Mechanics and lasers
Introduction To Quantum Mechanics
Black body : It is an object which absorbs all radiations incident on it and emit those radiations on
heating. Its absorption coefficient is 100%. Hot filament, SUN etc may be approximated as Blackbody.
Features of Black body spectrum:
For different temperatures of the black body, there are different curves.
At a given temperature the energy is not uniformly distributed the radiation spectrum.
At a given temperature the intensity of radiation increases in wavelength (λmax) its value is
maximum. With further increase in wavelength the intensity of radiation decreases.
The wavelength for which the radiant energy is maximum i.e., λmax decreases as temperature
increases.
Stefans law: Total energy radiated per unit area from a black body is proportional to the fourth power
of its temperature. E = σ T 4
Where σ = 5.67 × 10-8 J/m2/s
Wein’s Displacement Law:
The wavelength of maximum intensity is inversely proportional to the
absolute temperature of the emitting body, because of which the peaks of the energy curves for
different temperatures get displaced towards the lower wavelength side.
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Planck’s radiation law: In 1900, Max Planck developed a structural model for black body radiation
that leads to a theoretical equation for the wavelength distribution that is in complete agreement with
the experimental results at all wavelengths. According to his theory
1. A black body is imagined to be consisting of large number of electrical oscillators which are
vibrating at discrete frequencies.
2. an oscillator emits or absorbs energy in the form of discrete energy packets known as photons
whose energy is an integral multiple of hν where h is the planks constant and ν is the frequency.
3. Energy emitted per unit volume per unit energy range is given by the product of number of modes
of vibration in the given energy range and the energy per mode.
4. Based on these ideas, Planck was able to derive an expression that agreed remarkably well with the
experimental curves. It is given by
Where h is Planck’s constant, c is velocity of light, T is absolute temperature, λ is the wavelength and
k is Boltzmann constant.
Compton Effect: It is an effect which deals with the interaction between X rays and electrons in an
atom. When X rays are incident on an electron, the scattered radiation will have the wavelength equal
to or greater than the incident wavelength.
h
( 1 − cosθ )
m0 c
Here h is Planck’s constant, m0 is rest mass of electron, c is velocity of light & θ is angle of scattering
Change in wavelength
∆λ = λ' – λ=
Physical significance: Compton effect demonstrates the particle nature of electromagnetic waves
(light).
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Debroglie’s theory:By the law of symmetry of nature, a particle exhibits wave properties in addition
to its particle properties.
The wavelength of the group of waves associated with particle of mass m moving with a velocity v is
given by the expression
Properties of matter waves:
1. Matter waves represent the probability density variation in a region.
2. A matter wave in complex form is written as obtained as general solution to Schrodinger’s equation
Ψ = Asin kx(cos ωt + i sin ωt).
3. Matter waves are neither transverse nor longitudinal and their velocity is equal to that of Particle.
4. They propagate as group of waves.
Heisenberg’s Uncertainty Principle: The position and momentum of a particle cannot be
determined accurately
and simultaneously. The product of uncertainty in the measurement of
position (∆x) and momentum (∆p) is always greater than or equal to h/4π
∆x ∆p ≥
h
4π
This uncertainty is not due to discrepancy with the apparatus or with the method of measurement, but
because of the very wave nature of the object. This uncertainty persists as long as matter possesses
wave nature.
Different forms of Heisenberg’s uncertainty principle:
h
4π
h
∆E ∆t ≥
4π
h
∆L ∆θ ≥
4π
∆x ∆p ≥
∆E is uncertainty in energy and ∆t is the uncertainty in time.
∆L is the uncertainty in the angular momentum and ∆θ is the uncertainty in the angular
displacement.
Physical significance of Heisenberg’s uncertainty principle:
1. It introduces the concept of probability.
2. It can be used to find life time of electrons in an excited state.
3. It can be used to show that electrons do not exist inside the nucleus.
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Applications of uncertainty principle - The non-existence of electron inside the nucleus
Let us consider a typical atomic nucleus with diameter of the order of 10 -14m.If the electron is confined
in the nucleus, then the uncertainty in the position is of the order of diameter.
i.e ∆x = 10 -14m
⇒ ∆p =
∆p =
h
4π∆x
6.6 x10−34
4 x π x10−14
∆p = 5.26 x 10 −21 kgm / s
If this is the uncertainty in the momentum, then momentum p must be at least comparable to ∆p.
(p = ∆p)
∴ p = 5.26 x 10 −21 kgm / s
(
2
The equation of energy from theory of relativity is E = p 2 c 2 + m0 c 4
)
1/ 2
m0 c 4 <<< p 2 c 2 as m0 =9.1x10-31kg , c =3x108m/s , m0 c 4 <<<
2
2
E = (p 2 c2)1/2 = p c
∴ E = (5.26x10-21) x (3x108)
= 1.583x10-12J = (1.583x10-12 ) / (1.6x10-19 )
E = 9.9MeV
Thus for electron to exist in nucleus, its energy must exceed 9.9MeV.Experimentally, it is observed
during beta decay that β particle (e- emitted by radioactive nucleus) never have energy exceeding
4MeV, hence we conclude that electron can never exist inside the nucleus.
Wave function:A physical situation in quantum mechanics is represented by a function called wave
function. It is denoted by ‘ψ’. It accounts for the wave like properties of particles. Wave function is
obtained by solving Schrodinger equation. To solve Schrodinger equation it is required to know
1) Potential energy of the particle
2) Initial conditions and
3) Boundary conditions.
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Time independent Schrodinger wave equation: The general differential equation of wave travelling
in x direction with velocity ‘u’ having wave function Ψ given by
d2ψ 1 d2ψ
=
dx 2 u 2 dt 2
------- (1)
The general solution of eq (1) is of form
ψ(x, t) = Aei( kx −ωt )
------- (2)
where A is the constant, k is the wave vector and ω is the angular frequency
Differentiating equation (2) twice w. r .to‘t’ we get
dψ
= Ae i (kx −ωt ) ( − iω)
dt
d 2ψ
= Ae i(kx −ωt) ( −iω) 2
dt 2
d2ψ
= - (ω) 2 ψ
2
dt
(as i2=-1)
-------- (3)
Substitute eq (3) in eq (1)
d2ψ - ω 2
= 2 Ψ
dx 2
u
-------- (4)
We have ω = 2πυ = 2πu/λ where u is velocity of wave and ω is angular frequency
ω 2 4π 2
= 2
u2
λ
-------- (5)
By deBroglie hypothesis λ=h/p
ω 2 4π 2 p 2
=
-------- (6)
u2
h2
The total energy E is sum of kinetic energy and potential energy
1
mv 2 + V
2
1
=
m2v2 + V
2m
∴E =
E=
p2
+V
2m
as p=mv
p2 = 2m [E-V]
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Substitute value of p2 in eq (6)
ω 2 8π 2 m
=
u2
h2
(E − V )
Substitute above eq in (4) we get
d 2 ψ - 8π 2 m
=
dx 2
h2
∴
d 2 ψ(x , t )
(E − V ) ψ
8π 2 m
+
(E - V) ψ = 0
dx 2
h2
This is time –independent Schrödinger’s wave equation in one dimension
Physical significance of wave function: If ψ is the wave function associated with a particle, then | ψ |²
is the probability of finding a particle in unit volume.
The probability of finding a particle in certain elemental volume dτ is given by | ψ |2dτ. Thus | ψ |² is
called probability density. The probability of finding an event is real and positive quantity.
In the case of complex wave functions, the probability density is | ψ |² = ψ * ψ where ψ * is Complex
conjugate of ψ.
Normalization:
The probability of finding a particle having wave function ‘ψ’ in a volume ‘dτ’ is ‘|ψ|²dτ’. If it is certain
that the particle is present in finite volume ‘τ’, then
τ
∫ψ
2
dτ = 1
0
The process of integrating the square of the wave function within a suitable limits and equating it to
unity the value of the constant involved in the wave function is estimated. The constant value is
substituted in the wave function. This process is called as normalization.
Properties of the wave function:
The acceptable wave function has to possess
1. ‘ψ’ is single valued everywhere
2. ‘ψ’ is finite everywhere
3. ‘ψ’ and its first derivatives with respect to its variables are continuous everywhere
4. For bound states ‘ψ’ must vanish at potential boundary and outside. If ‘ψ*’ is a complex
function, then ψ* ψ must also vanish at potential boundary and outside.
The wave function which satisfies the above 4 properties are called Eigen functions.
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Applications of Schrödinger wave equation: Energy Eigen values of a particle in one dimensional,
infinite potential well (potential well of infinite depth) or of a particle in a rigidbox.
Consider a particle of a mass ‘m’ free to move in one dimension along positive x -direction between
x =0 to x =a. The potential energy outside this region is infinite and within the region is zero.
i.e. V(x) = ∞
for x ≤ 0 and x ≥ a
V(x) = 0 for 0<x<a
The particle is in bound state. Such a configuration of potential in space is called infinite potential well.
It is also called particle in a box.
The Schrödinger wave equation for wave like particle is given by
d 2 ψ(x )
dx 2
+
8π 2 m
h2
( E − V )ψ ( x ) = 0
Out side the box (for V=∞), the Schrödinger equation becomes
d 2 ψ( x )
dx 2
+
8π 2 m
h2
(E − ∞)ψ( x ) = 0
so ψ = 0 at the walls and also outside the well i.e ψ = 0 , x ≤ 0 and x ≥ a …..condition 1
Since ψ = 0 , ψ
2
= 0 , probability of finding the particle outside the box is zero.
Inside the box (V=0), the Schrödinger equation
d 2 ψ 8π 2 m
+
Eψ = 0
dx 2
h2
or
where k2=
d2ψ
+ k 2ψ = 0
dx 2
(1)
8π 2 m
E
h2
The solution of equation (1) takes the form
Ψ = A sinkx+B coskx
(2)
Where A and B are constants which can be evaluated by applying boundary conditions
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(i)
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But Ψ=0 at x=0, as per condition 1
∴ equation (2) becomes 0=Asin0+Bcos0 ⇒ B = 0
(ii)
(3)
Ψ=0 at x= a, as per condition 1
equation (2) becomes
0=A sinka+Bcoska
But B = 0 from equation (3)
∴ 0=Asinka
(4)
Here either A=0 or sinka=0
But A≠0 because if A=0 the entire function given by equation (2) will be zero as B=0.
Ψ= 0 leads to no probability of finding the particle, but we are dealing with the particle present in the
potential well. thus equation (4) is satisfied only when
ka= nπ
Q sin nπ = 0 for n= 0,1,2,3………..
n is called quantum number.
∴ k=
nπ
a
∴ Substituting for k and B, equation (2) can be written as
Ψn= Asin
nπ
x
a
(5)
which gives permitted wave functions.
To find out the value of A, normalization of the wave function is to be done.
a
∫ψ
2
dx = 1
0
a
∫A
From eq (5)
0
2
sin 2
nπ
xdx = 1
a
a
⎡1 a
⎤
1
2nπ
A 2 ⎢ ∫ dx − ∫ cos
xdx ⎥ = 1
20
a
⎣2 0
⎦
A2
∴
2
⇒
∴ sin2θ = (1-cos2θ)/2
a
⎡
⎛ 2nπ x ⎞⎤
a
⎟⎟⎥ = 1
sin ⎜⎜
⎢x −
2nπ
⎝ a ⎠⎦ 0
⎣
A2 ⎡
a
⎛ 2nπa ⎞ ⎤
a−
sin ⎜
⎟−0 =1
⎢
2 ⎣
2nπ ⎝ a ⎠ ⎥⎦
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⇒
A2
[a ]= 1
2
∴ A=
Engineering Physics – 18PHY12/ 22
(Qsin 2nπ = 0 )
2
a
Hence the normalized wave functions of a particle in one dimensional infinite potential well is
∴ Ψn =
2
⎛ nπ ⎞
sin ⎜
⎟x
a
⎝ a ⎠
Energy Eigen value:
8π 2 m
n 2π 2
2
and
k
=
E
h2
a2
n 2π 2
8π 2 m
=
E
a2
h2
Using equation k2=
n 2π 2
h2
x
=E
a2
8π 2 m
En =
n2h2
8ma 2
Where n=1,2,3………….
It is clear that the energy of the particle can have only certain values i.e., energy of the particle is
quantized.
E0 =
h2
8ma 2
is called zero point energy or ground state energy for lowest energy value n=1
Below is represented a schematic diagram of wave functions, energy values and probability density Ψ 2
for the first three permitted states.
Case (i) : For n=1
This is the ground state and normally particle is found in this state.
E1 =
h2
8ma 2
and
Ψ1 =
2 ⎛π ⎞
sin ⎜ ⎟ x
a
⎝a⎠
with ψ1 = 0 at x = 0 and x = a
and ψ1 is maximum at x=a/2.
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Case (ii) : For n=2
This is the first excited state.
E2 = 4
h2
= 4 E0
8ma 2
Ψ2 =
2 ⎛ 2π ⎞
sin ⎜ ⎟ x
a ⎝ a ⎠
with ψ2 = 0 at x = 0, (a/2) and
ψ2 reaches maximum values for x=(a/4) and (3a/4.)
Case (iii): For n=3
This is the second excited state.
E3 = 9
h2
= 9 E0
8ma 2
Ψ3 =
2 ⎛ 3π ⎞
sin ⎜ ⎟ x
a
⎝ a ⎠
with ψ3 = 0 at x = 0, (a/3), (2a/3) and
ψ3 reaches maximum for x=(a/6),(a/2) and (5a/6)
Eigen function: It is the physically acceptable solution to Schrodinger’s equation. It represents the
matter wave corresponding to a quantum particle in a specific state.
Ex: For a particle in an infinite potential well, the eigen function is ∴ Ψn =
2
⎛ nπ ⎞
sin ⎜
⎟x
a
⎝ a ⎠
Eigen Value: It represents the energy of a particle incorresponding to its Eigen function.
Eigen value for a particle in an infinite potential well is E n =
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LASERS
LASER is the abbreviation for Light Amplification by Stimulated Emission of Radiation. LASER is a
device which is used to produce a parallel and highly coherent light beam of high intensity. The
production of laser light is a consequence of interaction of radiation with matter. There are three
methods by which the radiation interacts with matter. They are
(1) Induced absorption
(2) Spontaneous emission
(3) Stimulated emission.
Induced Absorption: The process of absorption of incident photon by an atom and hence the excitation
of the atom to the high-energy state is called Induced Absorption.
Spontaneous Emission: The process of emission of a photon of suitable frequency by an atom due to
the transition from a higher energy state to a lower energy state without any supply of external energy is
called spontaneous emission.
Stimulated Emission: The process of emission of a photon by an atom in the excited state due to the
incidence of an identical photon of same energy on the atom and hence the transition of the atom to a
lower energy state is called stimulated emission.
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Population inversion: It is a state in which number of atoms in an excited energy state is more than
the number of atoms in the ground state. N2>N1
Under ordinary conditions the population of any higher energy state is less than the population of its
lower energy states. N1>N2
Expression For Energy Density - Einstein’s Coefficients
Consider two energy levels E1 and E2 of an atomic system such that E2 > E1. Let the population
of E1 and E2 be N1 and N2 respectively. Let radiations of energy density Uν (energy per unit volume of
the frequency range) with frequency ν, be incident on the atomic system.
In case of induced absorption, when this energy is incident on an atom in the energy level E1, it
absorbs the energy and makes a transition to the energy level E2.
The rate of absorption depends on the number of atoms in the lower energy state and the energy density
Uν of the incident radiation.
Rate of absorption α N1Uν
Rate of absorption = B12N1Uν
Where, B12 is called Einstein’s coefficient of induced absorption.
In case of spontaneous emission, an atom in the higher energy level E2 undergoes transition to the
energy state E1, voluntarily by emitting a photon.
The rate of spontaneous emission depends only on number of atoms (N2) in the energy state E2.
Rate of spontaneous emission α N2
Rate of spontaneous emission = A21N2
Where, A21 is called Einstein’s coefficient of spontaneous emission.
If the energy density Uν is incident on an atom in the energy state E2, it undergoes stimulated
emission. The rate of stimulated emission is proportional to the number of atoms (N2) in the energy
state E2, and the incident energy density Uν
Rate of stimulated emission is proportional to N2Uν
Rate of stimulated emission = B21N2Uν
Where, B21 is called Einstein’s coefficient of stimulated emission.
At thermal equilibrium,
Rate of absorption = Rate of spontaneous emission + Rate of stimulated emission
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B12N1Uν = A21N2 + B21N2Uν
B12N1Uν - B21N2Uν = A21N2
Uν (B12N1 - B21N2) = A21N2
Uν = (A21N2) / (B12N1 - B21N2)
Rearranging the terms
From Boltzmann’s law for thermal equilibrium of an atomic system we have
N2/N1 = e-(E2-E1)/kT
But E2-E1 = hγ
N2/N1 = e-(hγ/kT)
N1/N2 = e (hν/kT)
Substituting this result in equation (1) we get
From Planck’s law of energy distribution, the energy density is given by,
Comparing equations (2) and (3), we find
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Conditions For Laser Action: The conditions for atomic systems to have laser action are
1) Presence of metastable states
2)Achieving population inversion
Metastable State:
An intermediate energy state between an excited state and the ground state of the atomic energy
levels, in which the atoms stay for a long period of time the order 10-2 to 10 -3 seconds, is called a
metastable state.
When an atom in ground state absorbs certain amount of energy it transits to higher energy state.
The lifetime of the atom in the excited state is 10-8 seconds. Since the lifetime of the atoms in this state
is very less all the atoms return to the ground state immediately after excitation. Hence population
inversion cannot be achieved in the higher energy states. But if a metastable state exists in an atomic
energy system, then the atoms stay in that state for a period of the order 10-2 to 10 -3 seconds, which is
very large when compared to that of higher energy states. Hence, before the atoms undergo transition to
the ground state from the metastable state, a large number of atoms collect in the metastable state due to
the pumping action. Thus, population inversion can be achieved in the metastable state. The transition
of the atoms from the metastable state to the ground state emits laser light. Thus the presence of
metastable state in the atomic system is essential for the laser action to take place.
Population Inversion:The process in which the number of atoms in a higher energy state of an atomic
system is made more than the number of atoms in any of its lower energy states is called population
inversion.
For achieving population inversion, the atomic energy levels should have a metastable state. The
process of achieving population inversion can be explained in the following way. Consider three energy
levels E1, E2 and E3 of an atomic system, in such a way that E1 < E2 < E3. Let E2 be the metastable state.
Under normal conditions the atoms remain in the lower energy state E1. But when suitable amount of
energy is supplied to them they start undergoing excitation to the state E3.
The excited atoms in the state E3 stay for a period of 10-8 seconds and then undergo nonradiative transition to the metastable state E2, where they stay for a long duration of the order 10-2
seconds. If the pumping of atoms from E1 to E3 is maintained continuously, then the population of E 1
decreases continuously. The atoms excited to the state E3 undergo immediate downward transition to
E2, as a result of which the population of E2 increases more. Due to this process a stage will reach at
which the population of E 2 will be more than that of E1. This stage of operation is known as population
inversion.
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Requisites of a Laser System: The following are the three requisites of a laser system
1) Active medium: A material medium in which the population inversion and hence the lasing action
can be achieved is called active medium.
Ex : a) He-Ne laser and CO2 laser consist of a mixture of gases as the active medium.
b) Semiconductor lasers (Gallium Arsenide) consist of semiconductors as the active medium.
2) Pumping/Energy Source: The process of exciting atoms from a lower energy state to a higher
energy state, by supplying energy from an external source is called pumping
The population inversion in the laser action is achieved by pumping the atoms from the lower energy
state by supplying energy from an external energy source.
Depending on the type of energy source used for pumping, there are four types of pumping as follows
a) Optical pumping: optical energy
b) Electrical pumping: electrical energy
c) Heat pumping: thermal energy
d) Chemical pumping: chemical energy
The energy supplied is used not only for pumping, but also for stimulated emission in some cases.
3) Resonant cavity: An arrangement used in a laser device to increase the emitted photon energy
density is called resonant cavity.
The resonant cavity consists of two mirrors fixed on either side of the length of the active
medium. One of the mirrors is completely silvered and contributes only to the reflection of the emitted
photons. The other is partially silvered and it acts as both a reflector and exit for the laser beam.
Principle of LASER action (Given for a proper understanding, not important from an examination)
Laser action is based on the phenomenon of population inversion and stimulated emission.
When the number of atoms in the metastable state is made more than the number of atoms in any of the
lower energy states a system is said to have achieved population inversion. If light of a suitable
frequency is incident on such a system, then there will be more stimulated emission from the atoms in
the metastable state than induced absorption by atoms in the lower energy states. The photons emitted
by the stimulated emission travel in the same direction with the same phase, and possess same
wavelength. When they are incident on the other atoms, they stimulate them to emit photons, which in
turn cause further stimulated emission. The process repeats and results in the emission of a large
number of coherent photons. This beam of light having large number of photons is said to be amplified.
Thus the process involves amplification of light by stimulated emission. Hence it is abbreviated as
LASER acts as a source which produces a highly intense, coherent and monochromatic beam of light.
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Carbon dioxide (CO2) laser
Carbon dioxide laser was developed by C K N Patel (Chandra Kumar Naranbhai Patel)in the year 1963
A carbon dioxide molecule has two oxygen atoms between which there is a carbon atom. It has 3
different modes of vibration given as follows. The energies associated with each of these vibrations are
quantized in different sets.
i)
Symmetric Stretching mode : In this mode ,the oxygen atom oscillate along the molecular axis
either approaching towards or departing from carbon atoms simultaneously along molecular axis and
carbon atom remain stationary. This state is 100state.
ii)
ASymmetric Stretching mode : In this mode ,all the 3 atoms oscillate along the molecular axis
,but the two oxygen move in one direction while carbon atom moves in opposite direction and vice
versa. This state is 001 state
iii)
Bending mode: In this mode all the 3 atoms oscillate normal to molecular axis .While vibration
the two oxygen atoms pull together in one direction as the carbon atoms is displaced in the opposite
direction. The molecule possess highest energy in this state. This state is 010state
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Construction:Carbon dioxide laser consists of a discharge tube having a diameter of 2.5cm and a
length of about 5m. The discharge tube is filled with a mixture of carbon dioxide, nitrogen and helium
gases in the ratio of 1:2:3 with traces of hydrogen or of water vapour. Brewster’s windows are sealed
to the tube at both of its ends. Two optically plane mirrors, one fully silvered and other one half silvered
are fixed on either side of the tube normal to its axis. There is 100% reflectivity from the fully silvered
mirror and polarised laser light comes out from the half silvered mirror.
Working: When a suitable voltage is applied across the two electrodes a glow discharge of the gasses
is initiated in tube. During the discharge many electrons are set free from gas atoms and move towards
positive electrode at which time they begin to collide with N2and O2 molecules in their path, which
excites N2 molecules to the first vibrational level V=1 which is a metastable state of N2molecule,
therefore molecules remain there for relatively long time which leads to increase of population in V=1
state so that when N2 molecule in the metastable state collides with CO2 molecules in the ground state,
because of matching of energy levels, resonant energy transfer takes place from the N2 to CO2
molecule due to which CO2 molecule get elevated to the (001) state whereas, N2molecule returns to
the ground state .
Thus the population of the (001) or E 5 level of CO2 increases rapidly which leads the population
inversion. Let us denotes ground state, (010), (020), (100) and (001) states as E1, E2, E3, E4 and E5
levels respectively as shown in figure. Once the population inversion is established between E5 level
with respect to the E3 & E4 levels then two laser transition takes place within CO2 gas.
Those transitions are
1) Transition from E5 to E4 which gives the radiation of wavelength 10.6µm, which is comes under far
infrared (IR) region.
2) Another transition from E5 to E3 level which gives rise to radiation of wavelength 9.6µm which is
also comes under far IR region.
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The CO2 molecules in the E2 level undergo collision with He & H2O vapour molecules efficiently &
come down to the ground state.CO2 laser operates with an efficiently of 30% power output of few kilo
watts can be continuously maintained in a medium.
SEMICONDUCTOR LASER (Gallium Arsenide Laser)
Principle: When a diode is forward biased, the holes are injected into the p-side and electrons are
injected into the n-side of the junction. The recombination of holes and electrons takes place within
the junction region resulting radiation. This recombination is actually the transition of electron form
conduction band to the valence band. It is the basic mechanism involved in the emission of radiation.
If the junction current density is large enough, population inversion takes place between the electron
and hole levels resulting to Stimulated emission.
Construction: It a single crystal of GaAs which consists of heavily doped n and p sections.
The n-section is derived by doping GaAs with Tellurium and the p-section by doping GaAs with Zinc.
1) A pair of parallel planes of the crystal is polished at right angles to the p-n layer. These planes
play the role of reflecting mirror. The other two sides perpendicular to the junction are
roughened to suppress reflections of the photons.
2) The end surfaces of the p and n sections parallel to the plane of the junction are provided with
electrodes in order to apply a forward bias voltage.
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Working: The energy band diagram of heavily doped pn-junction is as shown unbiased condition. At
thermal equilibrium, the Fermi level is uniform across the junction. Because of very high doping on nside, Fermi level is pushed into the conduction band and electrons occupy the portion of the conduction
band lying below the Fermi level. On P-side, the Fermi level lies within the valence band and holes
occupy the portion of the valence band that lies above the Fermi level. When the junction is forward
biased electrons and holes are injected into the junction region in high concentrations. At low forward
current, the electron-holes recombination results in spontaneous emission of photons and the junction
acts as a LED. As the forward current is increased gradually and when it reaches a threshold value the
carrier concentration in the junction region there will be large concentrations of electrons within the
band. As a result condition of population inversion is attained in the narrow region. This narrow zone in
which population inversion occurs is called as an active region, at that stage a photon emitted
spontaneously triggers stimulated emission. This stimulated electron-hole recombination produces
coherent radiation.
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Applications of semiconductor diodes:
1) Optical communication
2) Reading devices for compact disc players, CD- ROMs
Properties of Lasers
1. Directionality: Laser emission takes place in only one direction
2. Monochromaticity: Lasers have a high degree of monochromaticity
3. Coherence: Lasers have high spatial and temporal coherence
4. Intensity: Laser beams are highly intense
5. Focussability: Since a laser is highly monochromatic and highly directional, it can be brought
to sharp focus by a lens. Hence it is said to have high focussability.
Applications Of Lasers
1)
Industrial applications: Laser cutting, welding and drilling.
2)
Defence (laser guided missiles)
3)
Storage of information in memory units of computers. Also used in laser printing
4)
Communication (via satellites)
5)
Medical applications: Eye surgery, Endoscopy, Laparoscopy
Laser Welding: Lasers are used for welding metals, by virtue of its ability to focus large power in a
small region.In laser welding, the laser beam is focused to the spot to be welded by means of a lens
and a very high temperature is generated at this spot by virtue of its high intensity.
Due to the heat, the metal used for welding is melted and a strong, homogeneous joint is formed.
Advantages:
a)
It is a contactless process. Therefore, unwanted materials like oxides can be eliminated.
b)
Only the focused region is heated and so it can be used in micro-electronics, where heatsensitive components are involved.
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c)
There is no mechanical stress on the components involved, thus there is no deformation.
d)
It can be used to weld joints where man cannot physically be present, for example, in nuclear
power plants.
Carbon di-oxide lasers are the most popular one in this particular application.
Laser Cutting:A laser beam, assisted by a jet of gas is used for cutting materials. The laser beam is
surrounded by a nozzle into which oxygen gas is fed. The gas helps in combustion and also assists by
blowing out the molten metal. The flowing action increases the depth and also the speed of cutting. The
cutting accuracy is well controlled.
Laser cutting is used in the tailoring industry where large number of layers of cloth is stockpiled. In this
case the laser beam is focussed on the pile and moved along the path, along which the cut is to be made.
Advantages:
a) There is no thermal damage and chemical change in the material
b) There is no wear and tear and no mechanical stress induced
c) There is no need for a coolant while cutting the material
d) The cutting is clean, fast, accurate, and of a high quality
Laser Drilling: Drilling of holes is achieved by subjecting the material to powerful light pulses of order
10 -4 to 10-3 second duration. The intense heat generated over a short duration by pulses evaporates the
material leaving a hole. Very small dimensional holes can be made by using lasers. (of diameter 10µm)
CO2 laser and Nd-YAG laser are used in drilling
Advantages:
a. No wear and tear of tools
b. Drilling can be done at any oblique angle
c. Fine holes of diameter 0.2 to 0.5 mm can also be drilled adjacent to each other
d. Even hard or brittle materials can be drilled as there are no mechanical stresses induced in the
material
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Laser Range Finder
Laser rangefinders have numerous applications such as measuring of rooms and buildings in the
construction sector, to determine the depth of snow in inaccessible areas, Cloud base height for
atmospheric study, air pollutant distribution, attitude characterization of space debris, trajectory of
aircraft, satellites. Laser technology is more cost effective.
The laser rangefinder uses a laser signal is transmitted and returned from a target. The time delay
between transmission and receipt of the signal is used to determine the distance to the target based on
the speed of light. The receiver consists of reflector, photodetector and amplifier.
Lasers In Data Storage
In a compact disc, series of microscopic holes known as pits are formed by burning. Laser light is
reflected from the disc surface and is detected by photodiodes. The amount of light received by the
diodes varies according to the presence or absence of pits.
In a CD, 1s and 0s are recorded in the form of pits along a spiral track on a plastic material with a metal
coating. The total length of the track would be around 6km.Any transition from pit to land or land to
pit is read as 1 while the region completely in the land or pit is read as 0.Seperation between tracks is
1.6µm in CD and 1.1µm in a DVD (DVD DIGITAL VIDEO DISK).The laser beam is focused on the
surface of CD. The reflected beam reaches photodetector and processed. The laser spot should have
minimum size. Holographic storage uses entire volume of the recording medium rather than the surface
and hence stores large data.
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