Module 3: Fibre Optics

Fibre Optics:
It is the branch of science that deals with the transmission of
data, images or voices by the passage of light through thin
transparent fibres.
Definition:
An optical fibre is a cylindrical waveguide made up of
transparent dielectric (glass or clear plastic) which guides light
waves along its length by the phenomenon of total internal
reflection. It is as thin as human hair, approximately on the
order of 70  m or 0.003 inch in diameter.
(A thin strand of metal is called a wire, while a thin strand of
dielectric is called a fibre)
Structure of Optical Fibre:
A practical optical fibre is cylindrical in
shape and has in general three co-axial
regions.
1.Core: The innermost cyindrical region
is the light guiding region known as the
core. In general, the diameter of the
core is of the order of 8.5  m  62.5  m .
2. Cladding: The core is surrounded by a coaxial middle region
known as the cladding. Its diameter is of the order of 125  m.
The refractive index of cladding ( n2 ) is always lower than that
of the core ( n1). Light travelling into the core and striking the
core to cladding interface at an angle greater than the critical
angle will be reflected back into the core. Since the angles of
incidence and reflection are equal, the light will continue to
rebound and propagate through the fibre.
3. Buffer Coating : The outermost region is called the sheath or a
protective buffer coating. It is a plastic coating given to the
cladding for extra protection. This coating is necessary to provide
protection to the fibre from physical damage and environmental
effects.
Necessity of Cladding:
The necessity of cladding in an optical fibre is very important
because of the following reasons:

1. The cladding maintains uniform size of the fibre: It is

necessary that the diameter of an optical fibre remains
constant throughout its length and is surrounded by the
same medium. Any change in the thickness of the fibre or the
medium outside the fibre will cause loss of light energy
through the walls of the fibre.
Necessity of Cladding:
2. The cladding maintains the total internal reflection: A large number of
reflections occur through the fibre and it is necessary that the condition
for total internal reflection is satisfied over the entire length of the fibre.
If there is a scratch on the surface of the glass fibre, the light travelling
through the fibre will get scattered and escapes from the fibre.
3. It prevents the leakage of light energy into another medium: Anytime
the fibre touches something else, the light can leak into the new medium
or be scattered away from the fibre. Even a small amount of dust will
cause a fair amount of leakage of light energy.
4. It adds mechanical strength to the optical fiber: Since optical fibres
are made up of glass or plastics, it is very likely that they might break.
Generally, the fibres are placed beneath ground or submerged in water, it
needs extra mechanical strength which is provided by the cladding.
Propagation of light in an optical fibre:
The propagation of light in an
optical fibre from one of its ends
to the other end is based on the
principle of total internal
reflection. When light enters
from one end of the fibre, it
undergoes successive total
internal reflections from sidewalls and travels down the length of
the fibre along a zigzag path as shown in the figure. A small
fraction of light may escape through sidewalls but a major fraction
emerges out from the exit end of the fibre. Light can travel
through the fibre even it is bent.
Let us discuss its propagation in terms of core-cladding
interface.
As we know, the diameter of an optical fibre is very small and as such
we cannot use bigger light sources for launching light beam into it. Light
emitting diodes (LEDs) and laser diodes are the optical sources used in
fibre optics. Even in case of these small sized sources, a focussing lens
has to be used to concentrate the beam on to the fibre core. Light
propagates as an electromagnetic wave through an optical fibre. As light
enters the fibre, it strikes the core-clad interface at different angles. As
the refractive index of the cladding is less than that of the core, majority
of the rays undergo total internal reflection at the core-clad interface.
Due to the cylindrical symmetry, the rays reflected from an interface on
one side of the fibre will suffer total internal reflection at the interface
on the opposite side also. Thus the rays travel forward through the fibre
and emerge out from the exit of the fibre.
Since each reflection is a total internal reflection, there is no loss of light
energy and light confines itself within the core during the course of
propagation. Because of the negligible loss, optical fibre can carry the
light waves over very long distances. Thus, the optical fibre acts
essentially a wave guide. At the exit end of the fibre, the light is received
by a photodetector.
Condition of propagation of light through an optical fibre:
Light propagates through an optical fibre if the following two conditions
are satisfied.
1. The refractive index of the core material n1 must be slightly greater
than that of the cladding n2 .
2. At the core-cladding interface, the angle of incidence  must be
greater than the critical angle c defined by
n2
sin c 
n1
which means the rays that are incident at smaller angles are refracted
into the cladding and are lost and therefore light cannot propagate
through the optical fibre.
Modes of propagation in Optical Fibres:
In an optical fibre, the light propagates in a similar manner as
electromagnetic waves propagate. Light is described as an
electromagnetic wave that consists of a periodically varying
electric field E and magnetic field H which are oriented at right
angles to each other. Thus, variation of E and H in optical fibre
takes place in a number of distinct modes.

1. Transverse Electric Mode (TE mode):

In this mode, the electric field is perpendicular to the direction
of propagation (i.e. longitudinal component Ez  0 ), but a
component of the magnetic field H is in the direction of
propagation. Here propagation of light is considered along z-
axis.
2. Transverse Magnetic Mode (TM mode):
Here, the magnetic field is perpendicular to the direction of
propagation (i.e. H z  0 ) and a component of the electric field E is
in the direction of propagation.
3. Transverse Electromagnetic Mode (TEM mode):
In this mode, both electric field E and magnetic field H are
perpendicular to the direction of propagation (i.e. both E z , H z are
zero). Although this type of mode occur in metallic conductors,
very few are found in optical fibres.
Angle of Acceptance:

Let us consider an optical fibre into which light is launched at one

end as shown in the figure 1. Let the refractive index of the core be
n1 and the refractive index of the cladding be n2 ( n2  n1 )
. Let n0 be the refractive index of the medium from which light is
launched into the fibre.
Let us consider a light ray which enters the fibre at an angle
 i to the axis of the fibre. The ray refracts at an angle  r and
strikes the core-cladding interface at an angle  . If  is greater
than the critical angle c , the ray undergoes total internal
reflection at the interface. As long as the angle  is greater than c
the light will stay within the fibre.
Applying Snell’s law to the launching face of the fibre, we get
sin  i n1
 (1)
sin  r n0
The maximum value of  i occurs when  c .
From the ABC , it is seen that
sin  r  sin(900   )  cos  (2)

[ Since  r    90  180   r  (90   ) ]

0 0 0

Using eq. (2) in eq. (1), we obtain

n1 n1
sin i  sin  r  cos  (3)
n0 n0
When   c ,
sin i max  1 cos c
n
(4)
n0
But
n2
sin c  (5)
n1
Therefore,
n12  n22
cos c 
n1
(6)  sin 2
c  cos 2 c  1 

Therefore, eq. (4) implies

n12  n22 n12  n22
sin  i max
n1
   (7)
n0 n1 n0
Quite often, the incident ray is launched from air medium for
which n0  1 .
Designating i max  0 , eq. (7) can be written as

sin  0  n12  n22 (8)

Therefore,
0  sin 1 ( n12  n22 ) (9)
The angle  0 is called the angle of acceptance of the fibre.
Acceptance angle is the maximum angle that a light ray can have
relative to the axis of the fibre, where it suffers total internal
reflection at the core-cladding interface and propagate down the
fibre.
Acceptance Cone:

All the light rays contained in the cone having vortex angle 2 max
are accepted and allowed to propagate along the fibre. This cone is
known as the acceptance cone.
Numerical Aperture (NA):
The main function of an optical fibre is to accept and transmit as
much light from the source as possible. The light gathering ability
of a fibre depends on the numerical aperture. The acceptance
angle and the fractional refractive index change determine the
numerical aperture of the fibre.
The numerical aperture (NA) is defined as the sine of the
acceptance angle. Thus,
NA  sin 0 (1)
where  0 is the angle of acceptance.
But
sin  0  n12  n22

 NA  n12  n22 (2)

Now,
n12  n22  (n1  n2 )(n1  n2 )
(n1  n2 ) (n1  n2 )
n n 
2
1
2
2  2n1 (3)
2 n1
n1  n2 n1  n2
Let  n1 , and   therefore eq. (3) gives
2 n1

n12  n22   2n12 (4)

Therefore,
NA  2n12   n1 2 (5)
The numerical aperture is the measure of the amount of light that
can be accepted by a fibre. It is seen from eq. (2), that the
numerical aperture is dependent only on the refractive indices of
the core and cladding materials and does not depend on the
physical dimensions of the fibre. The value of NA ranges from 0.13
to 0.50. A large NA implies that a fibre will accept large amount of
light from the source.
Classification of Optical Fibres:
Optical fibres are differently classified into various types based on
different parameters.
A. Classification based on refractive index (R.I) profile:
Refractive index profile of an optical fibre is the variation of
refractive index of the core with respect to the radial distance
from the fibre optic axis. On the basis of refractive index
profile, optical fibres are classified into
1. Step Index Fibres. 2. Graded Index (GRIN)Fibres
Step index refers to the fact
that the refractive index of
the core is constant along
the radial direction and
abruptly falls to a lower
value at the core-cladding
boundary. In case of GRIN
fibres, the R.I of the core is
not constant but varies
smoothly over the diameter
of the core.
It has a maximum value at the centre and decreases gradually
towards the outer edge of the core. At the core-cladding interface,
the refractive index of the core matches with the refractive index
of the cladding. The refractive index of the cladding is constant.

B. Classification based on the modes of light propagation:

1. Single Mode Fibre (SMF): It has a smaller core diameter and
support only one mode of propagation.
2. Multi Mode Fibre (MMF): It has a larger core diameter and
supports a number of modes.
Thus, on the whole, the optical fibres are classified into three
types:
1. Single Mode Step Index Fibre
2. Multi Mode Step Index Fibre
3. Multi Mode Graded Index Fibre
1. Single Mode Step Index Fibre: A single mode step index fibre has a
very thin core of diameter of 8  12  m and support a single mode
of propagation i.e., it can carry only one wavelength of light across
its length. The wavelength is usually 1310-1550 nm. It has a higher
bandwidth of the order of 1000 M H z . The core is surrounded by a
thick cladding of lower refractive index. The diameter of the cladding
is about 125  m . Here the R.I. changes abruptly at the core-clad
interface, so it is known as step index fibres. Since the bandwidth is
high, therefore these fibres can be used for long distance
communication. Also the loss in the light intensity is very much less
which shows no dispersion effect.
Light travels in SMF along a single path i.e., along the optic
axis. Both  and NA are very small for single mode fibres.
Obviously, low NA means low acceptance angle. Laser diodes are
launched light into the SMF.
 Fig. 1
2. Multimode Step Index Fibre: A multimode step index fibre is very
much similar to single mode fibre except that its core is of larger
diameter of the range 50  100  m , and the wavelength of light in an
MMF are in visible spectrum ranging from 850-1300 nm. The
external diameter of cladding is about 125  400  m .
Multimode step index fibres allow finite number of guided modes.

Fig. 2

Let us consider three rays incident on the face of the fibre. The ray 1
is travelling along the fibre optic axis which is known as the axial ray.
The rays 2 and 3 which suffers repeated total internal reflections at
the core-cladding interface from one end of the fibre to the other
end and propagating through the fibre are called marginal rays.
Therefore, these rays will follow a zigzag path instead of straight line.
In other words, many zigzag paths of propagation are permitted in
MMF. The marginal rays that are travelling along a zigzag path will
travel more distance than the axial rays (linear) and will take more
time to reach the end of the fibre. As a result, both these rays will
reach the fibre end at different times which implies there will be a
time delay in between the two. This time delay in axial and marginal
ray causes distortion in the light pulse. The intensity of the output
pulse will be slightly lower than that of the input pulse. Therefore,
this type of fibres are generally used for short distance
communication.
3. Multimode Graded Index Fibre: A graded index fibre is a
multimode fibre with a core consisting of concentric layers of
different refractive indices. Therefore, the refractive index of the
core varies with distance from the fibre axis. It has a high value at
the centre and gradually falls off with increasing radial distance from
the axis and hence this type of fibre is known as graded index fibre.
The propagation of light in multimode GRIN fibres depend
not only on the total internal reflection but also on the refractive
phenomena as well. The light rays propagating through the fibre
bend continuously and follow a helical path, instead of zigzag path.
The underlying reason behind the helical path can be
understood with the help of the fig 3. As we know, when light enters
from a denser to a rarer medium, it bents away from the normal
from one concentric layer to the other, since the core is made up of
concentric layers. Thus, the refraction phenomena continues and
the process goes on till the condition of total internal reflection is
achieved. Then, the ray travels back towards the core axis, again
being continuously refracted which will result in a helical shape.
Fig. 3

Fig. 4
Comparison of Step Index and Graded Index Fibres:
1. Step index fibres are used for long distance communication,
while Grin fibres are used for short distance communication.
2. Step index fibres shows no dispersion effect and therefore
these are more efficient, while GRIN fibres show dispersion
effects and hence less effective.
3. In step index fibres, fabrication is difficult and complex because
of very small core diameter, while in case of GRIN fibres,
fabrication is easy because of larger core diameter.
Classification based on Materials
Optical fibres are fabricated from glass or plastic which are
transparent to optical frequencies. Fibres are produced in three
common forms.
1. A glass core cladded with a glass having a slightly lower refractive
index.
2. A plastic core cladded with another plastic.
3. A silica glass core cladded with plastic.
Generally, the refractive index is the smallest for all glass fibres, a
little larger for the plastic clad silica (PCS) and the largest for all
plastic construction.
1. All glass fibres: The basic material for fabrication of optical fibres
is silica ( SiO2 ). It has a refractive index of 1.45. Materials having
slightly different refractive index are obtained by doping the basic
silica material with small quantities of various oxides. If silica is
doped with germania ( GeO2 ) or phosphorus pentoxide ( P2O5 ), the
refractive index of the material increases. Such materials are used as
core materials and pure silica is used as cladding material. On the
other hand, when pure silica is doped with boria ( B2O3 ) or flourine,
its refractive index decreases. These materials are used for cladding
and pure silica is used as the core material.
2. All plastic fibres: In these fibres, perspex (PMMA) and polysterene
are used for core. Their refractive indices are 1.49 and 1.59
respectively. A flourocarbon polymer or a silicone resin is used as a
cladding material. Plastic fibres have large NA of the order of 0.6 and
large acceptance angles up to 77 0 . The main advantages of the
plastic fibres are low cost and higher mechanical flexibility.
3.PCS fibres: The plastic clad silica (PCS) fibres are composed of silica
cores surrounded by a low refractive index transparent polymer as
cladding. The core is made up of high quality pure quartz. The
cladding is made up of a silicone resin having a refractive index of
1.405 or of Teflon having a refractive index of 1.338. Plastic claddings
are used for step index fibres only. The PCS fibres are less expensive
but have high losses. Therefore, they are used in short distance
applications.
Losses in Optical Fibres:
As a light signal propagates through an optical fibre, it suffers loss of
amplitude and change in shape. The loss of amplitude is referred to
as attenuation and change in shape is called distortion.
Thus, when an optical signal propagates through a fibre, its
power decreases and the resultant intensity decreases with respect
to the distance travelled. This loss in the intensity of light beam
through a fibre is called attenuation.
The signal attenuation can be defined as the ratio of the
output optical power to the input optical power. Thus
Attenuation  10 log10 Pout Pin  (1)
and the attenuation per unit length (  ) is given by

  10 Llog10 Pout Pin     10 Llog10 Pin Pout  (2)

The unit of attenuation per unit length is dB/km.
Mechanism of Attenuation in Optical Fibres:
The mechanisms responsible for attenuation in optical fibres are
broadly divided into two categories.
(1) Intrinsic Attenuation (2) Extrinsic Attenuation
Intrinsic attenuation is caused by substances inherently present in
the fibre, whereas extrinsic attenuation is caused by external forces
such as bending.
(1) Intrinsic attenuation: Intrinsic attenuation results from materials
inherent to the fibre. It is caused by impurities present in the glass.
During manufacturing, there is no way to eliminate all impurities.
When a light signal hits an impurity in the fibre, it is either scattered
or absorbed. Intrinsic attenuation can be further classified into two
types.
(a) Scattering of light (b) Absorption of light by materials
(a) Scattering of light: In understanding the scattering of light, at first
we have to understand what is the difference between regular
reflection and diffused reflection.
If an incident beam of parallel rays fall on a highly polished
plane glass mirror, then the reflected light beam will also be parallel.
Therefore, the angle of incidence and the angle of reflection are
equal. This type of reflection is called regular reflection. On the
other hand, if the incident parallel beam of light falls on a rough
surface, then the reflected rays are not parallel which means that
the light rays will be reflected at random directions. Hence, the
angle of incidence will not be equal to the angle of reflection. This
type of reflection is called diffused reflection or scattering of light.
(a) Scattering of light:
The propagation of light through the core of an optical fibre
takes place due to the total internal reflection of the light waves. At
molecular level of the glass (microscopic level), it is seen that the
surface of the glass is not smooth or plane as expected, but it has some
irregularities. These irregular or rough surfaces will cause light rays to
be reflected in random directions. This is known as diffused reflection
or light scattering. The variation in the density and the refractive index
always takes place in the manufacturing process of glass fibres and
these variations cause scattering of light in an optical fibre.
This scattering of light in an optical fibre is in accordance with
the “Rayleigh scattering law”, according to which the scattering of light
varies inversely as fourth power of the wavelength, i.e.
Scattering, S  1 4
which means that the scattering loss will be more for light waves of
lower wavelength. It is found that wavelengths below 800 nm show a
very high scattering loss. Thus, one need to send wavelength of light in
an optical fibre less than 800 nm so that the scattering losses can be
minimized.
(b) Absorption of light by materials:
When a light propagates through the core of an optical fibre,
it interacts with the molecular structure of the core materials as well
as the impurities present in it, which causes absorption of light. Even
pure glass core fibre absorbs light in certain wavelengths region
specially in ultraviolet and infrared regions. There are mainly two
types of impurities that causes absorption of light propagating
through the fibres.
(i) Transition metal impurities like cobalt, manganese, chromium,
etc.
(ii) Hydroxyl radical ions (OH  ions)
The loss of light intensity due to transition metal impurities is
very less, but a large amount of loss of light intensity occurs because
of the OH  ions. For this reason, special precautions should be taken
during the manufacturing process to ensure very low percentage
level of OH  ion impurity.
Absorption losses are also caused by atomic defects in glass
composition such as missing molecules in the glass particles. But this
type of absorption losses due to atomic defects are very small as
compared to the impurity losses.
(2) Extrinsic Attenuation or Bending losses:
Extrinsic attenuation is caused by two external mechanisms:
macrobending and microbending. Both of them causes a reduction
of optical power. If a bend is imposed on an optical fibre, strain is
produced on the fibre along the region that is bent. The bending
strain affects the refractive index and the critical angle of the light
ray in that specific area. As a result, the condition for total internal
reflection is no longer satisfied. Hence, light travelling in the core
can refract out from the core-cladding interface and thus losses
occur.
Macrobend:
A macrobend is a large-scale bend that
is visible. To prevent macrobends, the
optical fibre has a minimum bend
radius that should not be exceeded.
There is a restriction on how much a
fibre can withstand before
experiencing problems in optical
performance or mechanical stability.
Microbend:
A microbend is a small-scale distortion
and it not clearly visible with naked
eyes. It is caused by the imperfections
in the cylindrical geometry of the fibre
during the manufacturing process. The
microbend causes some of the light to
escape out of the fibre. The external
factors such as temperature, humidity
greatly affects the micobend losses in an optical fibre.
Skew Rays and Meridional Rays
Meridional Rays:
1. Meridional rays enter the fibre
through the axis of the fibre.
2. These rays cross the optical
fibre axis at each reflection.
3. The paths of these meridional
rays are easy to track as they
lie on a single plane.
Ray path view along the Ray path
Skew Rays: fibre axis view of
plane
1. Skew rays do not enter the fibre normal to
fibre axis
through the axis of the fibre.
2. These rays do not cross the optical fibre axis, rather they follow a
zigzag path and hence cannot be confined on a single plane.
3. The paths of these skew rays are difficult to track as they do not
lie on a single plane.
Fibre Optic Communication System:
A fibre optic communication system is the transmission of
information by propagation of optic signals through optical fibres
over a required distance. The FOCS was first developed in 1970
which has created a revolution in the communication world and
replaced copper wire cables, coaxial cables, etc. by the optical fibres
due to their various advantages. This type of communication can
transmit voice, video through local area networks, computer
networks across long distances.
Block Diagram of Fibre Optic Communication System:
A simplified block diagram of fibre optic communication system is
shown below.

It basically comprises of three main components:

1. Optical transmitter.
2. Optical fibre (Communication Channel).
3. Optical receiver.
1. Optical transmitter: It is an electro-optic device that converts the
electrical signal into optical signal and launch the resulting optical
signal into the optical fibre for transmission.
The optical transmitter consists of a light source supported
by necessary driver circuits that are used to control the intensity of
the light beam. The light source is generally a semiconductor laser
diode or Light Emitting Diodes (LEDs). The LEDs are used for short
distance communication due to their low bandwidth and power
applications, while semiconductor diodes are preferred for long
distance applications and high data rate transmission.
2. Optical fibre: The role of communication channel is to transmit
the optical signal from optical transmitter to optical receiver
without distorting it. Optical fibres are used as communication
channel in FOCS. Optical fibres are long thin strand of pure glass
and works on the principle of total internal reflection. In most of
the optical fibres, the loss of light intensity is very less and hence
the information carried by the optical fibres are mostly accurate.
3. Optical receiver: It is an electro-optic device that accepts optical
signals from the optical fibre and converts them to electrical
signals. It includes the following components.
a. Channel coupler.
b. Photodetector.
c. Demodulator.
a. Channel coupler: It is typically a micro lens that receives the
optical signals from the communication channel and focusses
the signal on to the photodetector with maximum efficiency.
b. Photodetector: It is a key element within the optical receiver
that converts the optical signals into electrical signals. A
photodetector is a semiconductor device.
c. Demodulator: It converts the electrical signal generated by the
photodetector in digital form (0 or 1), so that it can be easily
processed by computers.
In this way, the electrical output signal is achieved with the help of
the fibre optic communication system.