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Optical fibers
Optical fibers are thin, flexible strands of transparent dielectric material such
as glass or plastic. They are basically used to guide infrared & visible light
waves through curved paths. John Tyndall a British physicist had
demonstrated in 1854 to the Royal society that light could be guided along a
curved stream of water.
Principle of optical fibers:
rarer medium

= C
>C
denser medium
Optical fibers work on the principle of total internal reflection of light.
When a beam of light traveling in an optically denser medium falls on a
surface separating a relatively less denser medium at an angle of incidence
greater than the critical angle (C) for the pair of media, the light undergoes
total internal reflection.
Total internal reflection is the most superior type of reflection. Reflection is
total in the sense that the entire energy is returned to the first medium
through reflection without any loss of energy. Due to this the optical fibers
are able to sustain light signal transmission over very long distances despite
infinite number of reflections.
Construction It consists of a central cylindrical core made of pure glass or
plastic of refractive index n1 surrounded by a cladding made of similar
material but of lower refractive index n2 (n2 < n1). But there is a material
continuity from core to cladding. The cladding is enclosed in a polyurethane
jacket that protects the fiber from external damaging factors such abrasion,
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crushing & chemical reactions. Many such protected fibers are grouped to
form a cable. The diameter of the core varies between 10 to 200 m
depending upon type of the optical fiber & that of the cladding varies
between 50 to 250 m.
Condition for signal propagation through an optical fiber
Consider an optical fiber with refractive index of the material of the core n 1
& cladding n2 placed in a surrounding medium of refractive n0. Let a ray AO
of light enter the core of the fiber at an angle 0. Let this ray after refraction
through an angle  at O strike the interface between the core & the cladding
at the critical angle such that the refracted ray grazes the interface.
sin  0 n1

sin 
n0
Applying snells law of refraction at O, we have,
 sin  0 
n1
sin  ….(1)
n0
Applying snells law of refraction at B
sin (90   )

sin 90
n2
n1
or
cos  
n2
n1
&
sin  
1
n 22
n12
….(2)
substituting for sin  from eqn (2) in eqn (1)
sin  0 
1
n0
n12  n22
If the surrounding medium is air or vacuum, n0 = 1.
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0 is called the acceptance angle or half angle of the acceptance cone. The
acceptance angle is generally about 5 for a single mode fiber & 10 to 15
for multi mode fibers.
n0sin 0 is called the numerical aperture (NA) and it indicates the light
gathering power of the optical fiber.
It is evident that any ray that enters the fiber at an angle less than 0, strikes
the core-cladding interface at angle greater than the critical angle &
undergoes total internal reflection each time it strikes the interface. The
optical fiber sustains the light signal transmission over a long distance.
Fractional index change : is the ratio of the change in the refractive
indices (n1n2) between the core & the cladding to the refractive index n 1 of
the core.  
(n1  n2 )
n1
Relation between NA & 
n12  n 22 = (n1  n2 )(n1  n2 )
NA =
 n1  n2 ,
But (n1n2) = n1  & (n1+n2)  2 n1
 NA = ( n1 ) (2n1 )  n1 2
The light accepting capacity of a fiber can be increased by making  large.
But there are practical limitations to this. Also a very large  may cause
signal distortion.
Types of optical fibers
Based on their refractive index profile, geometry & ability to support the
number of modes for propagation, optical fibers may be broadly classified
into
a) single mode step index optical fibers
b) multi mode step index optical fibers
c) multi mode graded index (GRIN) optical fibers
Number of modes of transmission through an optical fiber
Depending on the launch angle into the fiber, there can be hundreds of ray
apaths or modes by which energy can propagate down the core. An optical
fiber permits a discrete number of modes to propagate through it. Not all the
rays that enter the acceptance cone sustain propagation. Only those modes
that satisfy the coherent phase condition are successfully propagated. The
rays belonging to the same propagating wave front must remain in step
despite the phase changes that occur on reflection & traversing different
optical paths.
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The number of modes supported for propagation through an optical fiber is
determined by a parameter called the V number that is given by
V 
d
n0

where d is the diameter of the core &  is the wavelength
n12  n22
of the light propagated.
If V >>1 then the number of successfully
2
propagated modes is
V
2
Skip distance Ls
Skip distance is the distance between two successive reflections of a ray of
light propagating through the optical fiber. Consider a portion of the optical
fiber through which a light signal is transmitted.
Ls

d
0
From the figure
Ls  d cot   d
Ls  d
cos ec 2  1
n12
1
n02 sin 2  0
 sin  
n0
sin  0
n1
To estimate the number of reflections occurring when the signal traverses a
given distance, consider n0 = 1, n1 = 1.6,  = 15 & d = 50m
Then Ls = 305 m
 no of reflections per meter =
1
= 3278
Ls
Single mode step index optical fiber
n
core diameter 5-10m
0
distance from the axis
Cladding diameter
Refractive index profile
50- 70 m
Geometrical dimensions
core
Mode of propagation
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A single mode optical fiber consists of a core having a uniform refractive
index n1 that abruptly decreases at the core-cladding interface to a lower
value n2 the refractive index of the cladding. The diameter of the core is
narrow (5-10m) generally a few times the wavelength of the light
propagating through it. Only rays nearly parallel to the fiber axis will travel
through. It supports a single mode propagation because of its narrow core.
Single mode optical fibers
1. need laser as the source of light.
2. are less expensive
3. have least signal attenuation & highest transmission speed & are free
from modal dispersion.
4. are the most extensively used constituting about 80% of the total
world manufacture of the fibers.
5. have low information carrying capacity
6. are difficult to splice
Step-Index Multimode fiber
In this case also the refractive index profile is similar to step index fiber i.e.,
fiber consists of a core having a uniform refractive index n1 that abruptly
decreases at the core-cladding interface to a lower value n2 the refractive
index of the cladding. But the diameter of the core is much larger (50200m). The comparatively large central core makes it rugged and easily
infused with light, as well as easily terminated and coupled. It is the least
expensive but also the least effective of the lot, and for long range
applications, it has some serious drawbacks especially intermodal
dispersion. It supports a large number of modes for propagation because of
its large core diameter.
n
core diameter 50-200m
0
distance from the axis
Refractive index profile
Cladding diameter 100- 200m
Geometrical dimensions
Mode of propagation
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Step-index multi mode optical fibers
1 accept either laser or a LED as the source of light.
2 are least expensive of all the three types of fibers
3 are used in data links that have lower band width requirements.
4 not free from modal dispersion.
5 have higher information carrying capacity.
Graded-Index Multimode fiber (GRIN)
It consists of a core whose refractive index decreases gradually from its axis
radially outward & becomes equal to the refractive index of the cladding at
the core-cladding interface. The refractive index of the cladding remains
uniform. Dimensions of the core and cladding are similar to that of step
index multimode fibers. It supports a large number of modes for
propagation because of its large core diameter.
n
0
distance from the axis
Refractive index profile
core diameter 50-200m
Cladding diameter 100- 200 m
Geometrical dimensions
Fig. from E. Hecht
P.No.198
Mode of propagation
Graded-index multi mode optical fibers
1 accept either laser or a LED as the source of light.
2 are the most expensive of all the three types of fibers.
3 are used in telephone trunks between central offices.
4 Have lower modal dispersion.
5 have higher information carrying capacity.
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Attenuation: Attenuation is the loss of power of the light signal that occurs
during its propagation through the optical fiber. The main sources of
attenuation are
1. absorption
2. scattering
3. other losses
Absorption
Absorption of light during propagation occurs due to the impurities present
in the fiber material & also due to the intrinsic nature of the material itself.
Absorption by impurities: Photons from the propagating signal are
absorbed by the impurity atoms.
The impurities generally present are
a) transition metals such as iron,chromium,cobalt, copper etc.
b) the hydroxy ions (OH) that enter into the fiber material at the time of
fabrication due to the reaction between the starting material & the oxy
hydrogen flame.
The photons absorbed by the impurities may be lost as heat or may be
reemitted as light energy of different wavelength & different phase from the
one that is propagated. Hence it results in a loss.
Though in the past, the greatest loss in the fiber optic propagation had been
due to impurity absorption, improved methods of production from time to
time have reduced such losses remarkably.
Intrinsic absorption: Intrinsic absorption occurs by the pure material itself
even if the material is free from impurities & inhomogeneities. These losses
are wavelength dependent. Absorption loss due to a material over a length L
of the fiber can be estimated from I = I0 e   L where,
I is the intensity of the signal after traversing a length L of the fiber,
I0 is the intensity of the signal entering the fiber
&  is the attenuation coefficient for the fiber material.  is a function of
wavelength & also a function of the angle of incidence. The rays that strike
the fiber at smaller angles of incidence travel a lesser distance of the fiber &
thus the absorption is less. Intrinsic absorption though quite less compared
to the loss due to the impurities, it cannot be eliminated.
Attenuation due Scattering
Glass is a heterogenous mixture of oxides of silicon, phosphorus,
germanium etc. Structural inhomogeneities in the core index will set in the
fiber material during solidification of glass from its molten state. It will also
result in a fluctuation of the molecular density. These inhomogeneities act
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as scattering centers. Since their dimensions are smaller than  the
wavelength of the light propagated through the fiber, the energy loss that
occurs due to such scattering resemble Rayleigh scattering that is 
1
4
. An
optical fiber transmitting longer wavelength say 1.3m represents roughly 7
times lesser scattering than transmitting wavelength of 800nm. The losses
due to these scattering cannot be eliminated by any process.
There are other structural inhomogeneities & defects that set in during
fabrication of the fiber that contribute to the loss due to scattering.
Their sources are trapped gas bubbles, unreacted starting materials etc.
However these can be reduced to a great extent by improved methods of
manufacturing.
Other losses
a) Due to dimensional irregularities & imperfections in the fibers (that are
called microscopic bends) the light may not sustain total internal reflection.
The energy will escape from the core.
b) Losses due the restrictions of the fiber numerical aperture, inevitable
reflections at the interface. These are called the Fresnel losses.
c) Radiation pattern & the size of the light source if not well adapted to the
fiber ends reduce the efficiency both at the input & the output ends.
Mismatch of the coupled fiber ends, alignment also lead to losses if not
properly taken care of.
d) Loses due to connectors, couplers & splices which become inevitable
over long distances.
e) Macroscopic bends occur during wrapping the fiber on a spool or
negotiating a curve during cable laying. They have a large radius of
curvature large as compared to the fiber diameter. Fibers can withstand
bends of curvature up to about 10cm without significant loss. For bends
smaller than this the loss increases exponentially up to a critical radius of
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curvature & suddenly increases to a very large value showing the total
absence of the total internal reflection at the bends.
Due to the losses that occur due to various causes during propagation as
explained above an amplification is needed in communication applications at
regular intervals in order to compensate for the losses that occur despite all
precautions. An optical repeater is used to boost the signal.
Applications & Advantages of optical fibers
1. The simplest & the most important use of optical fibers is their use as
flexible light pipes. It can transmit light to otherwise inaccessible areas &
even provide information about such regions by returning images. The
fiberscope, a bundle of fibers end-equipped with objective lens & eye piece
is used by doctors to examine regions of the stomach, lungs, duodenum.
2. The rods & the cones of the human eye function as light pipes
transmitting light as in optical fibers.
3. Voice or video communication & data transmission.
4. Optical fibers are smaller in size & light in weight compared to
conventional metallic cables. Since optical frequencies are much higher than
the conventional electrical signals, replacement of copper coaxial cables by
fiber optic cables offers greater communication capacity in smaller space.
Their maintenance cost is much lower.
5. In contrast with the metallic conduction techniques, communication by
light through optical fibers offers complete electrical isolation, immunity to
electromagnetic interference, radio frequency interference & voltage surge.
Optical fibers are free from signal leakage, electric sparks & fire hazards.
They are useful in laying cables near electronic hardware in industrial
equipment.
6. Communication through optical fibers is especially important &
advantageous where security of information is vital.
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