Lasers and Optical Fiber
Lasers and Optical Fiber
Lasers and Optical Fiber
LASERS
Introduction:
E1 E1
An atom in the lower energy state E 1absorbs the incident photon of energy (E1-E2) and goes to
the excited state E2. This transition is known as absorption. For each transition made by an
atom one photon disappears from the incident beam.
for an atom A,
A + hν A* (excited state)
The number of absorption transitions per second per unit volume occurring in the material at
any instant of time will be proportional to
(i) The Number of atoms in the ground state N1
(ii) Energy density of the incident radiation (Uν)
Rate of induced absorption = B12UνN1
where B12 is proportionality constant which gives the probability of absorptions and it is
called Einstein co-efficient of absorption. Since the number of atoms in the lower energy
state is greater, the material absorbs more number of the incident photons.
Spontaneous Emission:
An atom which is at higher energy state E 2 is unstable, spontaneously returns to the lower
energy state E1 on its own during which a single photon of energy (E2-E1) = hυ is emitted, the
process is known as spontaneous emission.
This spontaneous transition can be expressed as
A* A + hυ
E2
Emitted photon= hν=(E2-E1)
E1
Before After
The number of spontaneous transitions per second, per unit volume depends on the number of
atoms N2 in the excited state.
Therefore, the rate of spontaneous emission = A21N2
Where A21 is proportionality constant which gives the probability of spontaneous
emission and it is called Einstein co-efficient of spontaneous emission of radiation.
The process has no control from outside. The instant of transition, directions of emission of
photons, phases of the photons and their polarization states are random quantities. There will
not be any correlation among the parameters of the innumerable photons emitted
spontaneously by the assembly of atoms in the medium. Therefore the light generated by the
source will be incoherent (ex: light emitted from conventional sources).
Stimulated Emission:
Emission of photons by an atomic system with an external influence is called stimulated
emission. A mechanism of forced emission was first predicted by Einstein in 1916 in which
an atom in the excited state need not wait for the spontaneous emission to take place. A
photon of energy hυ = (E2-E1), can induce the excited atom to make downward transition and
emit light. Thus, the interaction of a photon with an excited atom triggers it to drop down to
the ground state (lower energy) by emitting a photon. The process is known as induced or
stimulated emission of radiation.
A* + hυ A + 2 hυ
E2
Stimulated photon
Stimulating photon
E1
Before After
The number of stimulated transitions per sec per unit volume in the material is proportional to
(i) The Number of atoms in the excited state N2
(ii) Energy density of the incident radiation (Uν)
Rate of stimulated emission= B21UνN2
Where B21 is proportionality constant which gives the probability of stimulated
emissions and it is called Einstein co-efficient of induced (stimulated) emission.
The process of stimulated emission has the following properties.
(i) The emitted photon is identical to the incident photon in all respects. (It has the same
frequency; it will be in phase and will travel in the same direction and will be in the same
state of polarization).
(ii) The process can be controlled externally.
(iii) Stimulated emission is responsible for laser.
It is the material medium composed of atoms or ions or molecules supports the basic
4. Population
It is the number density (the number of atoms per unit volume) of atoms in a given
energy state.
5. Boltzmann factor
It is the ratio between the populations of atoms in the higher energy state to the lower
energy state under thermal equilibrium. If N2 is the number density of atoms in the
energy state E2 and N1 is the number density of atoms in the ground state then
According to Boltzmann condition N1> N2
And
6. Population inversion
It is the condition such that the number of atoms in the higher energy (N 2) state is
greater than the number of atoms in the ground state (N1). i.e, N2> N1
If N2> N1, it is non-equilibrium condition and it is called population inversion.
Consider an atomic system interacting with radiation field of energy density Uγ. Let E1 and E2
be two energy states of atomic system (E2> E1). Let us consider atoms are to be in thermal
equilibrium with radiation field, which means that the energy density U γ is constant in spite of
the interaction that is taking place between itself and the incident radiation. This is possible
only if the number of photons absorbed by the system per second is equal to the number of
photons it emits per second by both the stimulated and spontaneous emission processes.
We know that
The rate of induced absorption = B12UνN1,
The rate of spontaneous emission = A21N2
The rate of stimulated emission = B21UνN2
N1 and N2 are the number of atoms in the energy state E 1 and E2 respectively, B12, A21 and B21
are the Einstein coefficients for induced absorption, spontaneous emission and stimulated
emission respectively.
At thermal equilibrium,
Rate of induced absorption = Rate of spontaneous emission + Rate of stimulated
emission
B12N1Uγ = A21N2 + B21N2Uγ
or Uγ (B12N1 – B21N2) = A21N2
--------- (1)
In a state of thermal equilibrium, the populations of energy levels E 2 and E1 are fixed by the
Boltzmann factor. The population ratio is given by,
According to Planck's law of black body radiation, the equation for U is,
-------(3)
Now comparing the equation (2) and (3) term by term on the basis of positional identity we
have
and or
This implies that the probability of induced absorption is equal to the probability of stimulated
emission. Due to this identity the subscripts could be dropped, and A 21 and B21 can be simply
represented as A and B and equation (3) can be rewritten.
At thermal equilibrium the equation for energy density is
(Think: Even though the probability of induced absorption is equal to the probability of
stimulated emission, the rate of induced absorption is not equal to rate of stimulated emission.
Why?)
21 12
(B /B = 1)
2 1. 2 1
The stimulated emission will be larger than the absorption only when N >N If N >N the
stimulated emission dominates the absorption otherwise the medium will absorb the energy.
2 1
Active medium:
It is the material medium composed of atoms or ions or molecules in which the laser action is
made to take place, which can be a solid or liquid or even a gas. In this, only a few atoms of
the medium (of particular species) are responsible for stimulated emission. They are called
active centers and the remaining medium simply supports the active centers.
Pumping Mechanism:
To achieve the population inversion in the active medium, the atoms are to be raised to the
excited state. It requires energy to be supplied to the system. The process of supplying
energy to the medium with a view to transfer the atoms to higher energy state is called
pumping.
method is adopted in solid state lasers (ex: Ruby laser and Nd:YAG laser).
b)
Electric discharge: In this process an electric field causes ionization in the medium and
+
raises it to the excited state. This technique is used in gas lasers (ex: Ar laser).
c)
Inelastic atom-atom collision :In this method a combination of two types of gases are
used, say A and B. During electric discharge A atoms get excited and they now collide
with B atoms so that B goes to excited state. This technique is used in gas lasers (ex: He-
Ne laser).
d) Direct conversion : In this process electrical energy is directly converted into light
In order to increase stimulated emission it is essential that N 2>N1 i.e., the number of atoms in
the excited state must be greater than the number of atoms in the ground state. Even if the
population is more in the excited state, there will be a competition between stimulated and
spontaneous emission. The possibility of spontaneous emission can be reduced by using
intermediate state where the life time of atom will be little longer (10 -6 to 10-3s ) compared to
excited state (10-9 s). This intermediate state is called metastable state and it depends upon the
nature of atomic species used in the active medium.
Consider three energy levels E1, E2 and E3 of a quantum system of which the level E2 is
metastable state. Let the atoms be excited from E 1 to E3 state by supply of appropriate energy.
Then the atom from the E3 state undergoes downward transition to either E1or E2 states
rapidly. Once the atoms undergo downward transitions to level E 2 they tend to stay, for a long
interval of time, because of which the population of E 2 increases rapidly. Transition from E2 to
E1 being very slow, in a short period of time the number of atoms in the level E 2 is far greater
than the level E1. Thus Population inversion has been achieved betweenE 1 and E2 . The
transition from meta stable state to ground state is the lasing transition. It occurs in between
upper lasing E2 and lower lasing level E1.
E3
Non-radiative transition
Lasing
transition
Optical resonator:
An optical resonator generally consists of two plane mirrors, with the active material
placed in between them. One of the mirrors is semi-transparent while the other one is
100% reflecting. The mirrors are set normal to the axis of the active medium and
parallel to each other.
The optical resonant cavity provides the selectivity of photon states by confining the
possible direction of photon propagation, as a result lasing action occurs in this
direction.
The distance between the mirrors is an important parameter as it chooses the
wavelength of the photons. Suppose a photon is traveling between two reflectors, it
undergoes reflection at the mirror kept at the other end .the reflected wave superposes
on the incident wave and forms stationary wave such that the length L of the cavity is
given by
Hence
The wavelengths satisfying the above condition are only amplified. Hence the cavity is also
called resonant cavity. r
rro
mi
ror ent
mir Active medium par
ing ns
lect
tra
Ref
% mi
100 Se
Working:
When a d.c. voltage (at 1000 V) is applied, the electric field ionizes some atoms of the gas
mixture, due to this the electron are released and are accelerated towards the anode and
helium and neon ions are accelerated towards cathode. Due to the smaller mass electrons
acquire very high velocity. The free electrons while moving towards anode collide with atoms
in their way. Collisions are more with the Helium (as Helium and Neon are in 10:1 ratio) and
helium atoms are excited to the levels 3S and 1S level which are meta stable state of helium.
This is electrical pumping. This collisions are of first kind i.e.,
He + e1 He* + e2
Where He: Helium in ground state, He *: Helium in excited state, e 2 is lesser with
energy less than that of e1
When current is continuously passed through the discharge tube more and more helium atoms
are excited to state 3S and 1S. The energy levels 3S2 (20.66 eV) and 2S2 (19.78 eV) of neon
atoms are very close to the helium levels 1S and 3S.
Collisions of 2nd type takes place between helium and neon atoms. In this process Neon atoms
are excited to 3S2 and 2S2 levels and the Helium atoms come to ground state. This is called
resonance transfer of energy.
He*+ Ne ---------------- He + Ne*
This is the pumping mechanism in the He-Ne laser and Ne atoms are active centers and
population inversion sets with lower energy states.
It is to be noted that there may be a chance of quick transition from 2S 2 state to the ground
state since it is radiatively connected to the ground state. Such case possible when the
probability of decay (2S2 state) to the ground state exceeds that to the 2p 4 levels which occurs
between S and P levels at very low pressures. Since we are applying a high pressure of the
order of a mm Hg, the transitions to the ground state undergo complete resonance trapping
instead of escaping from the gas i.e, every time a photons is emitted is simply absorbed by
another atom in the ground state and ends up in the excited 2S 2 state through resonance
energy transfer. Hence population increases at 2S2 levels through continuous process. This
leads to increase the life time of S levels to ~100 ns when compared to the life time of P 4
levels of the order of 20 ns. Therefore a favorable lifetime ratio for producing the required
population inversion satisfies the lasing action in Ne atoms.
The Infra- red (IR) radiations of 3.39 μm and 1.15 μm are absorbed by quartz window and
632.8 nm component is amplified in the resonance cavity and comes out through the partially
silvered mirror m2.
Directionality:The design of the resonant cavity, especially the orientation of the mirrors
to the cavity axis ensures that laser output is limited to only a specific direction. Since
laser emits photons in a particular direction, the divergence is less when compared the
other ordinary sources.
Monochromacity:The laser beam is characterized by a high degree of mono-
chromaticity (single wavelength or frequency) than any other conventional
monochromatic sources of light. Ordinary light spreads over a wide range of frequencies,
whereas laser contains only one frequency. The spectral bandwidth is comparatively very
less when compared to ordinary light. Hence the degree of mono chromaticity is very
high in lasers.
Coherence: The degree of coherence of a laser beam is very high than the other sources.
The light from laser source consists of wave trains that are in identical in phase. Laser
radiation has high degree of special (with respect to Space) and temporal (with respective
to time) coherence.
High Intensity: The laser beam is highly intense. Since wave trains are added in phase
and hence amplitudes are added. Laser light emits as a narrow beam and its energy is
concentrated in a small region. Since all the energy is concentrated in the particular focus
point, it is highly intense and bright. When laser beam is focused on a surface, the energy
incident is of the order of millions of joules.
Focus ability: Since laser is highly monochromatic, it can be focused very well by a
lens. It is so sharp the diameter of the spot will be close to the wavelength of the focused
light. It can be focused to a very small area 0.7m2. Since even laser is not ideally
monochromatic the spot diameter in actual cases will be 100 to 150 times larger than the
wavelength.
Optical fibres are the light guides used in optical communications as wave-guides. They are
thin, cylindrical, transparent flexible dielectric fibres. They are able to guide visible and
infrared light over long distances. The working structure of optical fibre consists of three
layers. Core- the inner cylindrical layer which is made of glass or plastic.Cladding- which
envelops the inner core. It is made of the same material of the core but of lesser refractive
index than core. The core and the cladding layers are enclosed in a polyurethane jacket called
sheath which safeguards the working structure of fibre against chemical reactions, mechanical
abrasion and crushing etc.
------------(1)
At the point Bon the core and cladding interface, the angle of incidence = 90-θ1
Applying Snell’s law at B
or
-------------------(2)
Therefore,
If θi is the angle of incidence of an incident ray, then the ray will be able to propagate,
If i <0
or if sin i < sin 0
or sin i< NA
=
We have RI change
Or -----------(1)
We know that,
Therefore,
We can see that, the value of NA can be increased by incresing the value of ∆, so as to
receive maximum light into the fibre. However, fibres with large ∆ will not be useful for
optical communication due to the occurrence of a phenomenon inside the fibre called
multipath dispersion or intermodal dispersion. This phenomenon introduces a time delay
factor, in the travel length and may cause distortion of the transmitted optical signal. This
leads to pulse broadening, which in turn limits the communication distance.
Modes of Propagation:
The possible number of paths of light in an optical fibre determines the number of modes
available in it. It also determines the number of independent paths for light that a fibre can
support for its propagation without interference and mixing.
We may have a single mode fibre supporting only one signal at a time or multimode
fibre supporting many rays at a time.
Such number of modes supported for propagation in the fibre is determined by a
parameter called V-number. If the surrounding medium is air then the V- number is given by
or
where d is the core diameter, n 1 is the refractive index of core, n 2 is the refractive index of
the cladding and λ is the wavelength of the light propagating through the fibre.
For single mode fibre, the number of modes supported by step index fibre is ≈
Radial distance
Ray propagation
Cladding
Core
light ray
Radial distance
RI profile
Cladding
Core
RI profile
Radial distance
The total energy loss suffered by the signal due to the transmission of light in the fibre is
called attenuation.
The important factors contributing to the attenuation in optical fibre are
i) Absorption loss ii) Scattering loss iii) Bending loss
iv) Intermodal dispersion loss and v) coupling loss.
Attenuation is measured in terms of attenuation co-efficient and it is the loss per unit length. It
is denoted by symbol . Mathematically attenuation of the fibre is given by,
dB/km
Where Pout and Pin are the power output and power input respectively, and L is the length of
the fibre in km.
Therefore, Loss in the optical fibre = α x L
1. Absorption loss:
There are two types of absorption;
(a) Absorption by impurities.
(b) Intrinsic absorption.
In the case absorption by impurities, the type of impurities is generally transition
metal ions such as iron, chromium, cobalt and copper. During signal propagation when
photons interact with these impurities, the electron absorbs the photons and get excited
to higher energy level. Later these electrons give up their absorbed energy either as
heat energy or light energy. The re-emission of light energy is of no use since it will
usually be in a different wavelength or at least in different phase with respect to the
signal. The other impurity which would cause significant absorption loss is the OH -
(Hydroxyl) ion, which enters into the fibre constitution at the time of fibre fabrication.
In Intrinsic absorption it is the absorption by the fibre itself, or it is the absorption
that takes place in the material assuming that there are no impurities and the material
is free of all in homogeneities and this sets the lowest limit on absorption for a given
material.
2 Scattering loss:
The signal power loss occurs due to the scattering of light energy due to the obstructions
caused by imperfections and defects, which are of molecular size, present in the body of the
fibre itself. The scattering of light by the obstructions is inversely proportional to the fourth
power of the wavelength of the light transmitted through the fibre. Such a scattering is called
Rayleigh scattering. The loss due to the scattering can be minimized by using the optical
source of large wavelength.
4 Coupling losses:
Coupling losses occur when the ends of the fibres are connected. At the junction of coupling,
air film may exist or joint may be inclined or may be mismatched and they can be minimized
by following the technique called splicing.
Point-to-point Communication
The use of optical fibres in the field of communication has revolutionized the modern world.
An optical fibre acts as the channel of communication (like electrical wires), but transmits the
information in the form of optical waves. A simple p to p communication system using optical
fibres is illustrated in the figure.
An optical repeater consists of a receiver and a transmitter arranged adjacently. The receiver
section converts the optical signal into corresponding electrical signal. Further the electrical
signal is amplified and recast in the original form and it is sent into an optical transmitter
section where the electrical signal is again converted back to optical signal and then fed into
an optical fibre.
Finally at the receiving end the optical signal from the fibre is fed into a photo
detector where the signal is converted to pulses of electric current which is then fed to
decoder which converts the sequence of binary data stream into an analog signal which will
be the same information which was there at the transmitting end.
Advantages over conventional communication:
Disadvantages
The disadvantages in the communication systems using optical fibres are
Fibre loss is more at the joints if the joints do not match (the joining of the two ends of
the separate fibres are called splicing)
Attenuation loss is large as the length of the fibre increases.
Repeaters are required at regular interval of lengths to amplify the weak signal in long
distance communication.
Sever bends will increase the loss of the fibre. Hence, the fibre should be laid straight
as far as possible and avoid severe bends.
Note:
Point to Point haul communication system is employed in telephone trunk lines. This
system of communication covers the distances 10 km and more. Long-haul
communication has been employed in telephone connection in the large cities of New
York and Los Angeles. The use of single mode optical fibres has reduced the cost of
installation of telephone lines and maintenance, and increased the data rate.
Local Area Network (LAN) Communication system uses optical fibres to link the
computer-oriented communication within a range of 1 or 2 km.
Community Antenna Television (CATV) makes use of optical fibres for distribution
of signal to the local users by receiving a multichannel signal from a common antenna.
1. Medical application
Endoscopes are used in the medical field for image processing and retrieving the image to
find out the damaged part of the internal organs of the human body. It consists of bundle of
optical fibres of large core diameter whose ends are arranged in the same sequence.
Endoscope is inserted to the inaccessible damaged part of the human body. When light is
passed through the optical bundle the reflected light received by the optical fibres forms the
image of the inaccessible part on the monitor. Hence, the damage caused at that part can be
estimated and also it can be treated.
2. Industry
Optical fibres are used in the design of Boroscopes, which are used to inspect the inaccessible
machinery parts. The working principle of boroscope is same as that of endoscopes.
3. Domestic
Optical fibre bundles are used to illuminate the interior places where the sunlight has no
access to reach. It can also be used to illuminate the interior of the house with the sunlight or
the incandescent bulb by properly coupling the fibre bundles and the source of light. They are
also used in interior decorating articles.
S. No Questions CO
1 Give reason 1
Optical fibres are immune to electromagnetic interference.
Intermodal dispersion is minimum in GRIN compared to MMSI fibre.
Repeaters are used in the path of optical fibres in point to point
communication system.
2 Explain the terms 1
a. Acceptance angle
b. Cone of acceptance
c. Numerical aperture
d. Modes of propagation
e. Attenuation.
3 Explain attenuation losses in optical fibres. 2
4 Write any two advantages of optical fibre communication over normal 2
communication.
5 Explain propagation mechanism in optical fibres. 2
6 Distinguish between step and graded index fibres. 2
, T=330K, λ=?
λ = 632.8nm.
We have
But
== =10-15
3. Calculate on the basis of Einstein’s theory, the number of photons emitted per second
by a He-Ne laser source emitting light of wavelength 6328A o with an optical power of
10mW.
Hence
= 3.182x1016
4. Calculate the numerical aperture, relative RI difference, V- number and number of
modes in an optical fibre of core diameter 50µm. Core and cladding Refractive indices
1.41 and 1.40 at λ= 820nm.
5. An optical fibre has clad of RI 1.50 and NA 0.39. Find the RI of core and the
acceptance angle.
(NA)2 = n12- n22 θo= sin-1 0.39
(0.39)2= n12 - (1.50)2 = 22.96o
n1 = 1.54
6. The NA of an OF is 0.2 when surrounded by air. Determine the RI of its core. Given
The RI of cladding as 1.59. Also find the acceptance angle when it is in a medium of RI
1.33.
(NA)2 = (n12 – n22) θo = 8.64o
n1= 1.60
7. A glass clad fibre is made with core glass of RI 1.5 and cladding is doped to give a
fractional index difference of 0.0005. Determine
a) The cladding index.
b) The critical internal reflection angle.
c) The external critical acceptance angle
d) The numerical aperture
L = 2 : Pout/Pin = 36.3%
L=6 : Pout/Pin = 4.79%
9. Find the attenuation in an optical fibre of length 500m, when a light signal of power
100mW emerges out of the fibre with a power 90mW.
α=
α = 0.915dB/km
10. A semiconductor laser emits green light of 551 nm. Find out the value of its band gap.
Eg = hc/ = 2.25 eV
11. The probability of spontaneous transition is given as 0.08. in a laser action which
results with the radiation of 632.8 nm wavelength. Calculate the probability of
stimulated emission.
(Ans. 1.22x1013)
12. Calculate the critical angle if the refractive indices of optical fibre are 1.5 & 1.48.
(Ans. θc = 80.63o)
13. The optical fibre power after propagating through a fibre of 1.5 km length is reduced
to 25% of its original value. Compute the fibre loss in dB/km.
(Ans. 4 dB/km)