Optical fiber
The optical fiber is a cylindrical waveguide system which can be operated at optical frequencies, i.e.
optical signals can be transmitted through a fiber over long distances. It is playing an important role in
the field of communication to transmit voice, television and digital data signals from one place t other
place. The transmission of light along the thin cylindrical glass fiber by total internal reflection was
first demonstrated by John Tyndal in 1870 and the application of this phenomenon was first tried only
from 1927.
Fiber optic communication become popular due to following reason
(Advantages of fiber optic communication )
1. Higher information carrying capacity
2. Light in weight and small in size
3. Low cost of the cable higher bandwidth
4. Zero interference of electric and magnetic field and cross talk
5. Nominal installation cost
6. Electrical isolation
7. Signal security
8. Low transmission loss
The optical fibers are used as dielectric wave guides for guiding the electromagnetic waves at optical
frequencies through one copper pair only 48 independent speech signals can be sent simultaneously.
But in optical fibers, the transmission of 1500 or more simultaneous telephone conversations is
possible.
Principle of optical fiber:
Optical fiber works based on the total internal reflection phenomenon. The light is guided through
transparent glass fiber by total internal reflection. The structure of the optical fiber is shown in the
figure.
The fiber has a core surrounded with a cladding with refractive index slightly less than that of the core
to satisfy the condition for total internal reflection. To give mechanical protection to the fiber a
protective skin call outer jacket is used. The light launched inside the core through its one end
propagates to the other end due to total internal reflection at the core and cladding interface.
The total internal reflection at the fiber core and cladding interface can occur only if two conditions
are met.
1) The refractive index of the core material n1 is slightly higher than that of the cladding n2
surrounding it.
2) At the core-cladding interface the angle of incidence θ ( between the ray and normal to the
interface ) must be greater than critical angle θc.
n2
Sin θc = n1
Suppose a ray traveling from denser media to rarer media. If the angle of incidence θi is less than θc
then light ray refracted into the rarer media
If θi = θc then the refracted ray grazes the interface between the media.
If θi > θc then the light cannot refract instead it reflected back in the same media and obey the law of
reflection.
If angle of incidence is θi and θc , θr = 90
Let the refractive index of the denser media be n1 and rarer media be n2
We know that
n1 Sin θi = n2 Sin θr
Sin θc =
n2
n1
n2
θc = Sin −1 ( )
n1
The total internal reflection will occur rays whose angle of incidence θi > θc
Acceptance angle: When we launch the light beam into a fiber at its one end using a focusing lens,
The entire light may not pass through the core and propagate only the rays which make the angle of
incidence greater than critical angle at the core cladding interface undergo total internal reflection and
propagate through the core. The other rays are refracted to the cladding and are lost. Hence, it is very
essential to know at what angle called acceptance angle we have to launch the beam at its end to
enable the entire light to pass through the core.
The above figure shows the longitudinal cross section of the fiber with a ray entering it. Let the light
launch from a media of refractive index n0 and the angle of incidence is αi with the fiber axis
(normal). The light ray refracted with an angle of refraction αr and enter into core of refractive index
ni. It then undergoes total internal reflection at B on core wall (interface) at an incidence angle θ. Then
from the figure αr = 90 – θ
Applying snell’s law
n0 Sin α i = n1 Sin α r
n0 Sin α i = n1 Sin (90 – θ)
n0 Sin α i = n1 Sinθ
Sin α i =
n1
Cosθ
n0
If θ is less than critical angle, the ray will be lost by refraction. Therefore limiting value for containing
the beam inside the core by total internal reflection is θc. Let Sin α i(max) be the maximum possible
angle of incidence at the fiber end face at a for which θ is equal to less than θc. If for a ray α i exceeds
α i(max) , then θ will be less than θc hence the ray will be refracted.
At the core cladding interface point B, applying snells law
n1 Sin θc = n2 Sin 90
n2
Sin θc =
n1
Substituting (2) in (1)
Sin α i(max) =
n1
Cosθc
n0
n1
√1 − (Sin θc)2
n0
n1
√1 − (Sin θc)2
=
n0
Sin α i(max) =
Sin α i(max)
Sin α i(max) =
n1
n 2
√1 − ( 2 )
n0
n1
n1 2 − n2 2
Sin α i(max) = √
n0 2
α i(max) = Sin−1
√n1 2 − n2 2
n0
If the light launch at the fiber end within this acceptance cone will be accepted and propagated to the
other end of the fiber by total internal reflection.
Acceptance angle is defined as the maximum value of the incidence at the entrance end of the fiber, at
which the angle of incidence at the core cladding interface is equal to critical angle of the core
medium.
Numerical Aperture :
It is the sin of the maximum acceptance angle is called the numerical aperture of the fiber. It is a
measure of the amount of light rays can be accepted by the fiber. It also represents light collecting
efficiency.
n1 2 − n2 2
NA = Sin α i(max) = √
n0 2
Fractional change in the refractive index :
It is defined as the ratio of difference of refractive index of core and cladding to refractive index of the
core.
n1 − n2
n1
n1 − n2 = ∆n1
∆=
n1 − n2 = ∆n1
Also
(n1 − n2 )(n1 + n2 )
NA = Sin α i(max) = √
n0 2
∵ n1 ≈ n2
2∆ n1 2
NA = Sin α i(max) = √
n0 2
also
NA =
n1 √2∆
n0
Construction of an optical fiber
1. Core of the optical fiber is made up of glass of thickness 9 to 50μm surrounded by cladding.
2. Cladding of a fiber have lower refractive index of diameter 125 to 200μm. It is made up of
glass.
3. Buffer jacket over the optical fiber is made of plastic and protects the fiber from moisture and
abrasion.
4. In order to provide necessary toughness and tensile strength a layer of strength member
(kelver) is arranged surrounding the buffer jacket.
5. Finally the fiber cable is covered by polyurethane outer jacket. This will not damage the core
of the fiber during pulling, bending, stretching or rolling.
Step index fiber:
In step index fiber the refractive fiber the refractive index of the core remain constant from the centre
of core to the core cladding interface and there is an abrupt of step change in refractive index at the
core cladding interface.
Mode refers to the number of paths for the light rays in the fiber. As the name implies, a single mode
fiber sustains only one mode of propagation, where as multimode fibers can contain many modes.
Depends on the no of modes of propagation of light rays through the step index fiber, they are
classified into two types.
1. Single mode fiber
2. Multi mode fiber
1. Single mode step index fiber:
In single mode step index fiber only one mode can propagate through fiber. It has very small core
diameter (10μm) and difference between core and cladding refractive index is very small. Dispersion
of light pulse is very small, Since information transmission capacity in optical fiber is inversely
proportional to dispersion, the single mode fibers are suitable for long distance communication.
Launching of light into single mode fibers and joining of two fibers are very difficult. Fabrication is
very difficult and the fiber is costly. It has very high bandwidth approximately 3GHz. Signal
attenuation is very low. High quality laser source is required for launching light pulse. It has small
acceptance angle due to small size of core. Used in submarine cable system.
2. Multimode step index fiber:
Multimode fiber allows a large number of path or modes for the light rays travelling through it. It has
larger core diameter (50μm to 200μm) and the relative refractive index is larger than single mode step
index fiber. Due to large dispersion and attenuation of the signal the multimode fibers are less suitable
for long distance communication. They are used in LAN. Launching of light into fiber and joining of
two fiber are easy. Fabrication is less difficult and so fiber is not costly. Numerical aperture is large.
Refractive index is constant along the core. The incident light ray suffers multiple reflection. It has
very low bandwidth approximately less than 200MHz. Light propagate through the fiber in a Zig Zag manner and always cross the axis of the core during propagation. This light rays are called
meridional rays.
3. Graded index fiber:
The refractive index of the core decreases from the center to the boundary of the core. Light ray
propagating through the core follow the helical path and never cross the optical fiber axis. This
type of rays are called skew ray. The light ray while travelling through the core suffers multiple
refraction till it totally reflected. It has low dispersion. It has low attenuation loss. The size of the
core diameter is 50μm. It has large bandwidth than multimode step index fiber. It is easy to couple
light source
0.5
𝑟 𝛼
𝑛(𝑟) = 𝑛1 [1 − 2∆ (𝑎) ]
for r > a
𝑛(𝑟) = 𝑛1 [1 − 2∆]0.5 = n2 for r≥a
Where 𝛼 is 0 for single mode fiber and 𝛼 is 2 for graded index fiber
Limitation
It is difficult to fabricate,
Cost of the fiber is more,
Attenuation
Attenuation is the loss of optical power as light travels through the fiber. Attenuation controls the
distance that an optical signal can travel and it is mainly a result of light absorption, scattering and
bending losses. Dispersion spreads the optical pulses at it travels along the fiber. This spreading of the
signal pulse reduces the system bandwidth or the information carrying capacity of the fiber.
𝑃𝑜𝑢𝑡
𝐿𝑜𝑠𝑠 = −10𝑙𝑜𝑔 (
)
𝑃𝑖𝑛
Where 𝑃𝑜𝑢𝑡 is the power coming out of the fiber and 𝑃𝑖𝑛 is the power launched into the fiber. In
optical fiber communications the attenuation is generally expressed in decibels per unit length (i.e.
dB/Km)
10
𝑃𝑜𝑢𝑡
𝑙𝑜𝑔 (
)
𝐿
𝑃𝑖𝑛
Where 𝛼 is the signal attenuation and L is the length fo the fiber.
The basic attenuation mechanisms in the fiber are absorption, scattering and bending (radiative) losses
of the optical energy. Absorption is related to the fiber material, scattering is associated with both the
fiber material and structural imperfections in the fiber. Bending losses occurs when ever the fiber
deviates from its straight line path.
𝛼=−
Absorption
Absorption is caused by three different mechanisms,
1) Absorption by atomic defects in the glass composition
2) Extrinsic absorption by impurity atoms in the glass material
3) Intrinsic absorption by basic constituent atoms of the fiber material
Atomic imperfections or defects such as missing molecules, high density clusters of atom groups, or
oxygen defects in glass structures causes the fiber loss. Usually, absorption loss due to these defects
are negligible compared with other loss mechanisms. The presence of impurities in the fiber material
is major sources of loss in practical fibers. Impurity absorption results from transition metal ions and
OH ions. Metal ion impurities such as Fe, Cu, V, Co, Ni, Mn and Cr absorbs strongly in the region of
interest ( 0.5 to 1.6μm) and must not exceed 1 to 10ppb to cause the losses below 20dB/Km. The loss
mechanism in the metal ions involves incompletely filled inner electron shells. Absorption of light
causes electrons to move from a lower level shell (low energy state) to a higher level 9higher energy
state). This energy is obtained from the incident photon.
The most important impurity to minimize is the OH ion. The OH impurity results from the
oxyhydrogen flame used for the hydrolysis reaction of the SiCl 4, GeCl4, P0Cl3,. The fundamental
absorption peak by molecular vibration (ion resonance) of OH is around is 2.7 μm and its overtones
occur at 1.38 μm, 0.95 μm and 0.725 μm. This absorption can be reduced by reducing the water
content in the fiber below 1ppb.
Intrinsic absorption is associated with basic fiber material (SiO2). Intrinsic absorption results for the
electronic absorption band in the UV region and from the atomic vibration in bands in near infrared
region.
UV loss contribution decays exponentially with increasing the wavelength. The tail of ultraviolet
absorption presents at lower wavelengths near 0.8 μm. At this wavelength l loss is 0.3dB/Km.
The infrared absorption is associated with the characteristic vibration frequency of the particular
chemical bond between the atoms of which the fiber is composed. An interaction between the
vibration bond and the electromagnetic field of the optical signal results the transfer of energy from
the field to the bond there by giving rise the absorption. In pure silica fibers, tail of infrared absorption
Si-O occurs at higher wavelength around 1.4 μm to 1.6 μm. So at operating wavelengths of the fiber
there is no IR absorption.
It is found that in case of pure silica fibers the transmission losses are reduced to a minimum value at
1.55 μm. At 1.3 μm also the losses are minimum but net attenuation is slightly greater compared to
1.55 μm.
Scattering:
Scattering losses in glass arise from microscopic variations in the material density, from the
compositional fluctuations and from the structural inhomogenities of defects occurring during the
manufacturing of the fiber. If the dimensions of these fluctuations are of the order of λ/10 or less, each
irregularity acts as a point source of scattering center. This type of scattering is known is Rayleigh
Scattering. The Rayleigh scattering greatly depends on the wavelength. It varies at 1/ λ 4 and it
becomes important a lower wavelength region. Thus Rayleigh scattering sets a lower limit, on the
wavelength that can be transmitted by a glass fiber at 0.8 μm, below which the scattering is very high.
( at wavelength 1.3μm scattering loss is less than about 0.3dB/km while at a wavelength it is about
5dB/Km)
Bending losses:
Bending (radiative) losses occurs whenever an optical fiber undergoes a bend of finite radius of
curvature. There are two types of bending losses.
Microscopic bending losses: These losses occur when the radius of curvature of bend is greater than
the fiber diameter. The situation arises when a fiber cable turns a corner. When there is a bend, the
part of propagation is maintained. So the mode in the cladding has to travel with a velocity more than
the velocity of light, which is not possible. This leads to loss of energy.
Microscopic bending losses: These losses occur due to random microscopic bends of the fiber axis.
This situation arises when the fibers are incorporated in to cables. The amount of loss depends upon
the length of fiber and the optical power distribution among different modes. Micro bending losses are
proportional to number of modes propagating in the fiber and inversely proportional to wavelength.
Optical fiber communication system
The above diagram shows optical communication system
1. Input : This is a port. We apply analog information signal to this port. In case digital
communication we use an electronic system that converts the analog information signals, such as
voice of a telephone user into binary data called encoder. The binary data consists of a series of
electrical pulses.
2. Amplifier : The analog of digital information signal is fed to the amplifier for amplification.
3. Light source: The output of the amplifier fed the light source. The source of light can either be a
light emitting diode or a semiconductor laser diode. The source converts electrical pulses into a
light pulses. The light source usually radiates near infrared region of electromagnetic spectrum
where the transmission characteristics of optical fibers are best utilized.
4. Source to fiber coupler : It is a special connector that couples the light form the light form the
source to the fiber core. A connector acts as a temporary joint between the fiber and the light
source. Misalignment of the fiber and the source can lead to loss of light energy near the joint.
5. Optical fiber : The optical fiber guides the light pulses making use of the phenomenon of total
internal reflection.
6. Fiber to Detector coupler: It serves the same purpose as the source to fiber connector.
7. Detector: The major component of the detector circuit is either a PIN or avalanche diode. This
diode is biased under reverse bias and the light is allowed to fall on the diode junction. This
increase reverse current and the increase in current is directly proportional to applied light
radiation.
8. Amplifier: The change in current from the detector circuit is fed to the input of the amplifier for
amplification
9. If the applied input signal is analog and is fed to the input circuit of the amplifier then from the
output of the amplifier we get analog signal.
10. But if the applied input signals to the amplifier is digital then the output of the amplifier contain
electrical pulse containing information is fed to an electronic circuit called decoder. Decoder is an
electronic circuit which converts digital information to analog. Thus the decoder converts the
sequence of binary data into analog signal which contain information such as voice which was fed
to the system at the other end.
Application of fiber
Fiber can be used as sensor. These sensors are lighter and occupy lesser volume and low cost. This
sensor can be used to measure the acoustic field, magnetic field , current, rotation, acceleration, strain
l pressure and temperature.
There are two types of sensor
1. Active sensor
2. Passive sensor
1. Active sensor :
The fiber which itself active as transducer called active sensor.
Example: pressure sensor,
Light is allowed to propagate through the fiber and intensity of received light is measured. When
some pressure is applied on the fiber by some pressure element. Bending of the fiber occur. This
produce bending loss of light radiation and decreases the intensity of received light. This change in
intensity of light is directly proportional to pressure applied. Thus pressure measured. It is shown in
the figure.
2. Passive sensor
The fiber which carries light signal to and from the sensor called passive sensor.
Example: Temperature sensor.
The figure shows the intensity modulated temperature sensor based on reflective concept. Here the
bimetallic strip acts as the sensing element. It consists of steel and brass which are welded together to
form a strip. Since the linear expansion of brass is more than the steel the strip bends into an arc when
heated. The metal with higher linear expansion will be outside the arc when the strip is heated.
The strip is attached to a bifurcated refractive fiber optic probe. The fiber optic probe contains a
bundle of passive multimode fibers. The strip is designed to move continuously and its movement is
directly proportional to temperature.
The amount of reflected light is converted into voltage by a photodiode or photo voltaic cell detector.
The amount of light reflected decreases with the increase of temperature. So that, the output of the
photodiode decreases with the increase of temperature.
Endoscope
It is an optical instrument which facilitates visual inspection of internal parts of a human body. It is
shown in the figure. The input end of the endoscope contains a powerful light source such a Xenon
high pressure arc lamp or a suitable laser. The system consists of two bindles of optical fibers. The
outer fibers system conduct light from source to the object under study. It consists of a number of
optical fibers of large numerical aperture. They are bundled together without any particular
arrangement. The light that transmitted through this system illuminates the part with the human body.
The inner system of fibers consists of closely packed optical fibers in a perfect order. A small lens
prism system is fixed to one end of the bundle. The end plane of the fiber is at the focal plane of the
lens. Light reflected from the internal part of the body is brought to focus by the lens at the end plane
of the bundle. Each fiber picks up a small region of the picture. The collection of fibers in the bundle
picks up bits of information and transmits them in order. As a result internal part of the human body
can be seen at the other end of the bundle.
Displacement sensor
It is an intensity of light modulation optical fiber sensor. Two optical fibers are separated by a
distance‘d’. As the distance increases intensity of light received by the receiving fiber and the detector
decreases. The decrease in intensity of radiation is a measure of change in separation between the two
fibers. A sensitivity graph is plotted between output voltage at the detector and the displacement of
the fiber.
Important questions:
1) Draw the block diagram of fiber optic communication system and explain the functions
of each block in the system.
2) Discuss between step index fiber and graded index fiber
3) Describe the various advantages of communication with optical fibers over the
conventional coaxial cables
4) Write notes on attenuation in optical fibers.
5) What is a displacement sensor? Draw its sensitivity curve
6) Derive an expression for numerical aperture of an optical fiber
7) Explain the principle behind the functioning of an optical fibre
8) Write any three applications of optical fibers
9) Discuss the propagation mechanism of light waves in optical fibers
10) A step index fiber has a numerical aperture of 0.16, and core refractive index of 1.45.
Calculate the acceptance angle of the fiber and the refractive index of the cladding.