Optical Fibre
(fibre optics)
Fibre optics ( optical fibre ) are long thin strands of very pure glass about the
diameter of human hair , They are arranged in bundles called optical cable. And used
to transmit light signals over long distance .
(1) Core—Thin glass center of fibre where light travels.
(2) Cladding--- Outer optical material surrounding the core that reflect the light
back in to the core.
(3) Butter coating ---- Plastic coating that protects the fibre from damage and
moisture . Hundreds or thousands ( nos.) of these optical fibre are arranged in
bundles in optical cables. The bundles are protected by the cables outer
coating, called Jackets.
Critical angle of propagation--
Index profile
Let us consider a step index fibre into which light is launched at one end . the end at
which light enters the fibre called the launching end . In step index fibre , reference
index changes abruptly from core to cladding. Now consider two rays entering the fibre
at two different angle of incidence.The line shown by broken line is incident at an
angle θ2 w.r. to axis of fibre.This light under goes refraction at point A on surface
between air and core. The refracts into fibre at an angle θ1 (θ1< θ2 ) .
The ray reaches the core cladding interface at point B. at point B refraction takes place
again and ray travels in cladding, finally at point C, ray refracts once again and
energes out of fibre in air , this means that ray does not propagate through fibre . Ray
with solid line ,ray incident at an angle θ undergoes refract at point on interface and
propagates at an angle θc in fibre at point D.the ray under goes total internal
reraction. Since n1 > n . let us assume at angle of incidence at core cladding interface
critical angle
-1
(
n2
)
n1
fibre and propagate
in the fibre, A ray incident at the critical angle is called a critical ray. This ray makes
an angle θc with axis of fibre. It is obvious that ray with propagation angles larger
than θc will not propagate in fibre , θc is known a critical propagation angle, from fig.
ΔADE
AE
 sin
AD
AE
 cos θc
AD
(
cos θc =
n2
)
n1
n2
n
θc = cos-1 (
n2
)
n1
Acceptance angle ------
Consider a step index optical fibre into which light is launched at one end
as shown in fig. let reference index of core be n1 and reference index of cladding be n2 (
n2<n1 ).let no be the ref. index of medium from which light is launched into fibre.
Assume that light ray enter into fibre at an angle θi to axis of fibre .the ray refracts at
than
1>n2,
sin i n1
------------(1)

sin r n0
Applying snell’s law to launching
ray escapes from side
From ABC sin θi = sin ( 90 -
------------(2)
From eqn (1) and (2)
Sin θi =
n1
n2
Sin (θi max) =
n1
n2
----------------(3)
n2
 cos2
n1
– sin2
n 21  n2
=
n 21
-
2
n 21  n 2 2 / n1 --------------------(4)
put (4) in (3)
n1  n 2
n
sin(θi)max. = 1 .
n0
n1
2
for air medium n0 = 1
2
n1  n 2
2
=
n0
2
n22
n 21
θi max. = θ0
sin θ0 =
n1 n2
θ0 = sin-1
2
2
n1  n2
2
2
The angle θ0 is called the acceptance angle of fibre , acceptance angle is
maximum that a light ray can have relative to axis of fibre and propagate down the
fibre.
In 3-D,The light ray contained with in cone having a full angle 2 θ0 are accepted and
transmitted along fibre, therefore the cone is called the acceptance cone.
Fractional
Reference index change --------Δ=
n1  n2
n1
, this parameter is always positive ,n1 must be larger
than n2 ,,
Δ <<1
Numerical aperture--------The main function of an optical fibre is to accept and transmit as
much light from source as possible . the light gathering ability of fibre depends
on two factors namely core size and numerical aperture. The acceptance angle
and the fractional reference index change determine the numerical aperture of
fibre .
Numerical aperture is defined as the sine of acceptance angle thus NA = sin θ0
Sin θ0 =
n1  n 2 2
2
Numerical aperture =
n1  n 2 2
2
n12 – n22 = (n1 +n2 ) ( n1- n2 ) = (
n1  n2
 n1 ( approximately )
2
n1  n2  n1  n 2
) 
2
 n

 x2n1

n1  n2

n
n 21 – n22 = 2n12Δ
N.A . =
2n1  = n1
2
2
N.A determine the light gathering ability of fibre. It is a measure of amount of light
that can be accepted by a fibre. NA is only dependent only on ref. indices of core and
cladding materials and does not depend on any physical dimensions of fibre .the
value of numerical aperture ranges from .13 to 0.50 . large N.A. implies that a fibre
will accept large amount of light from source.
Modes of propagation
When light is launched into an optical fibre wave
having ray direction less than the critical angle θc will be trak with in fibre due to
internal reflection . but all such wave do not propagate along the fibre . in reality only
certain ray directions are allowed to propagate. The allowed directions to correspond to
the mode of fibre. Modes can be visualised as possible number of path of light in an
optical fibre. The paths are all zig-zag pathe excepting the axial direction . as zig-zag
ray gets repeatedly reflected at the walls of fibre. Phase shift occurs. Consequently the
waves travelling along certain zig-zag paths will be in phase and intensified while the
wave coursing along certain other paths will be out of phase and diminish due to
destructive interference. The light rays paths along which the waves are in phase
inside the fibre are known as modes. The number of modes will support depends on
d/λ where d is diameter of core and λ is wave length of wave being transmitted.
The number of modes propagating in an optical fibre can be determine by a parameter
V called horizontal wave number.
 2a 
.NA
  
V= 
Types of fibre -------there are two types of fibre—
(1)
Single mode of fibre ---smallest core diameter can support only
mode of propagation.
(2)
Multi mode of propagation Larger core diameter and support a
number of modes can further also classified on the basis of index
profile.
(i)
Step index fibre
(ii)
Graded index fibre.
(Index profile is a plot of reference index on horizontal axis
versus distance from core axis on vertical axis .)
Single mode step index fibre
A typical single mode fibre has a core diameter of 4 μm which
is of the order of a few wave length of light. The fibre is
surrounding by a opaque protective sheath. The reference
index of a fibre changes abruptly at core cladding boundary .
light travels in single mode fibre along a single path that is
along the axis. It is zero order mode that is supported by single
mode fibre. A single mode step index fibre is designed to have a
normalized frequency between 0 and 2.4, this relatively small
value is obtained by reducing fibre radius and by making Δ (
ref. index change) to be small. Both Δ and NA are very small
for single mode fibres. The low numerical aperture means a low
acceptance angle . therefore light coupling into fibre becomes
slightly difficult.
Intermodal dispersion does not exist in single mode fibre
because only one mode exists with the choice of material
dimensions and wave length , the total dispersion can be made
extremely small. Low dispersion makes the fibre suitable for
use with high data base .
In these fibres parts of light propagate in the cladding ,
therefore the cladding must have a low loss and be relatively
thick. Typically for a core diameter of 10 μm , cladding
diameter is 120 μm . manufacturing and handling is more
difficult and therefore , the fibre is costlier.
Multimode step index fibre
A multi mode index
fibre is much similar to
single mode step index fibre except that core is of larger diameter . A typical fibre has
a core diameter of 100 μm which is very large compared wavelength of light . light
followed the zig-zag paths inside the fibre. Many such zig-zag paths of propagation are
permitted in multi mode fibre. The NA of multi mode fibre is larger as the core
diameter of fibre is large and it is order of 0.3.
Larger NA leads to more modes which also means higher dispersion . higher
dispersion means lower data and less efficient transmission. In multi mode fibre the
dispersion is mostly intermodal. The multi mode step index fibre is relatively easy to
manufacture and is less costly.
Graded index fibre -----------A graded index fibre is a multi mode fibre with a core consisting of concentric layers of different
reference indices. Therefore ref. index of core varies with distance from the fibre axis.
It has a high value at centre and falls of with increasing radial distance from axis.A
profile causes a periodic focusing of light propagating through fibre.
In graded index fibre the acceptance angle and numerical aperture decreases with
radial distance from axis. The number of modes in a graded index fibre is about half
that in a similar multi mode fibre. The lower number of modes, lower dispersion than
multi mode fibre. The size of graded index fibre is about the same as step index fibre .
manufacturing is more complex.
The effective acceptance angle of graded index fibre is less than that of equivalent step
index fibre . it makes coupling of light more difficult.
. Dispersion---( pulse dispersion ) This term dispersion is used to describe the pulse
broadening effect by fibre. The pulse at appears at out put of fibre is wider than that of
input pulse. A signal which pulse of light travel through fibre becomes wider because
of various propagation phenomenon. Dispersion is measured in units of time ( nano
scale, Pico scale) practically dispersion Δt is defined as --Δt =
t p 2  t p1
2
2
tp1 = input pulse width
tp2 = out put pulse width
total dispersion depends on length of fibre , larger length, larger dispersion ,
dispersion usually specified per unit length.
Δt = L x (dispersion per kilometer)
(1)Inter modal dispersion ---- Inter modal dispersion due to the wave
propagate in modes. It is dispersion between modes caused by different in
propagation time.when no. of modes are propagate d in fibre , they travel with
different net velocities w.r.to axis of fibre. Parts of wave arrive at out put before
other parts leading to spreading of input pulse . known as intermodal dispersion.
(2)Intra modal dispersion ----Intramodal dispersion due to the fact that light
consist of a group of wavelength .light waves of different wavelength travel at
different speeds in medium. The short wavelength travel slower than long wave
length. Narrow pulse of light tend to broaden as they travel down the fibre. This is
also known as material dispersion. The spectral width of light source determines
the extent of intramodal dispersion .
(3) Wave guide dispersion ----- wave guide dispersion arises from the properties
of fibre. The effective ref. index number for and mode varies with wave length ,
which causes pulse spreading just like variation in ref. index does. This is known
as wave guide dispersion.
(In fibre large NA more modes exists leading to large dispersion . therefore
dispersion may be restricted by selecting low NA and a narrow specvtral width
source . another solution of this problem to use graded index fibre than single
index fibre. However graded index fibres are more expensive.)
Attenuation
-----------An optical signal propagating through a fibre will get
aggressively attenuated . the signal attenuation is defined as the ratio of the
optical output power from a fibre of length L to the input optical power
α=
10
pi
log
L
po
pi = input power of signal at launching end
po = output power of signal at the other end.
If pi = po attenuation would be zero.
The unit of measurement of attenuation is decibal /kilometer.
Absorption by Material
---------- this includes absorption due to the
light interacting with the molecular structure of materials, as well as loss because
of material impurities. Even a high pure glass absorbs light in specific wave length
regions. Strong electronic absorption occurs at ultra violet wavelength , while
vibrational absorption occurs at infra red wavelength. These absorption losses are
inherent property of glass itself and known as intrinsic absorption.
(
Impurities are a major source of losses in fibre. Hydroxyl radical ions (OH)
,
and transition metals such as ,copper, nickel, chromium, vanadium, and magnese
have electronic absorption in and near visible part of spectrum. Their presence
causes heavy losses. Losses due to impurities can be reduced by better
manufacturing processes. In improved fibres, metal ions are practically negligible.
The largest loss is caused by OH ions. These can not be sufficiently reduced. The
absorption of light either through intrinsic or impurity processes constituent a
transmission loss. Because of that much energy is subtracted from the light
propagating through fibre.)
Scattering
---------- When light scattered by an obstruction the power
loss.the local microscopic density variations glass cause. Local variation in
reference index. These variations which inherent in the manufacturing process and
can not be eliminated act as obstructions and scattered light in all directions.this
is known as Rayleigh scattering. This loss depends on wavelength .it varies as 1/λ 4
And becomes important at lower wavelength. Thus Rayleigh scattering sets a limit
( lower) that can be transmitted by a glass fibre at .8μm, below which scattering
loss is very high.
Wave guide and micro band losses
--------------These are fibre losses
introduced during manufacturing or installation processes, structural variation in
the fibre or fibre deformation cause radiation of light away from the fibre. Micro
bands, very minute disturbance in core size also cause radiation of light.
Optical communication: -----------------
A fibre optic communication
system is very much similar to a traditional communication system and has three
major components. A transmitter converts electrical signal to light signal ,an
optical fibre transmit the signal and a receiver capture the signal at other end. Of
fibre and convert them to electrical signal.
trans
ducer
Transmitter
modu
lator
carri
er
cha
nnel
dete
ctor
fibre optic link
signal
proce
ss
trans
ducer
Reciever
The transmitter consists of light source supported by necessary derived circuits. A
transducer convert s a non-electrical message into an electrical signal and is fed to
a light source.The light source is a miniature source , either a light emitting diode
or a semiconductor laser. In either case light is emitted in the IR range with a
wavelength of 850 mm ( .85μm) , 1300 nm ( 1.3 μm) or 1550 ( 1.55 μm ) . The light
waves are modulated with the signal s. By varying the light beam intensity from
laser diode or LED analog modulation is achieved. By flashing the laser diode or
LED on and off at an extremely fast rate, digital modulation is achieved. A pulse of
light represents the number 1 and the absence of light at specified time represents
zero. A message can be transmit ted by a particular sequence of these O and 1 . If
the receiver is programmed to recognize . Such digital pattern it can reconstruct
the original message. Though the digital modulation requires more complicated
equipment. Such as encoders and decoders and also more band width than
modulation, It allow greater transmission distance with same power . |This is a
greater advantage and hence digital modulation has become more popular and
widely used nowdays.
The transmitter feeds the analog or digitaly modulated light wave to transmission
channel, namely optical fibre link. The optical signal travelling through the fibre
will get attenuated progressively and distorted due to dispersion effects. Therefore
repeaters are to be at specific interval to regenerate the signal. At the end of fibre
an out put coupler direct the light from fibre onto a semiconductor photo
diode.which converts the light signal to electrical signals, The photo detector
convert light wave s into electrical signal which are then amplified and decoded to
obtain message. The out put is fed to a suitable transducer to convert it into an
audio or video form.
Application
----------------- OFC system can be broadly classified into two
group ,
(1)
(2)
Local and intermediate range where distance involved are small.
Long haul system where distance are large.
(1) Local area network ---- LAN is computer oriented communication system
LAN operate over short short distance of about 1 to 2 km . it is a multi user
oriented system.
(2) Long haul communication--------- On of the most important application of
fibre optic communication is long haul communication. This system are
used for long distance 10 km or more. Telephone cables connecting various
coutries come under this category. A rather sophiscated long haul network
is NSFNET .which links six super computer centre’s through out USA.
Principal of Holography
Holography is a two step process . first step is the recording the hologram
where object is transferred into a photography record and second step is
reconstruction in which the hologram is transferred into the image. Unlike
in conventional photography lens is not required in the either of the steps .
A hologram is the result of interference occurring between two waves , an
object beam which is the light scattered from the object and a coherent
background , the reference beam which is the light reaching the
photographic plate directly. In original experiment , the reference beam and
object beam s were co-axial. Later on by lieth and upatrieks used reference
beam at an offset angle. That made possible the recording of holograms of
three dimensional objects.
(1) Recording of the hologram ------- In the off axis arrangement a broad
laser beam is divided into two beams, a reference beam and object beam
by beam splitter. The reference beam goes directly to the photographic
plate and second beam of light directed on to the object to be
photographed. Each point of object scatters the incident light and act as
the source of spherical waves. Part of light ,scattered by object travel
towards the photographic plate. At the photographic plate the no. of
spherical waves from object combine with the plane. Light from reference
beam . The set of light wave are coherent because they are from the
same laser . They interfere and from intereference fringes on the plane of
photographic plate. These fringes are a series of zone. Plate like rings,
but these rings also superimpose , making a complex pattern of lines and
swirls. The developed negative of these interference fringes pattern is
hologram. Thus hologram does not contain a distinct image of object but
carries a record of both. Intensity relative phase of light waves at each
point.
Reconstruction of the image ----------------
For reconstruction of the image the hologram is illuminated by a parallel
beam of light from laser . most of light passes straight through , but the
complex of fine fringes act as an elaborate diffraction grating. Light is
diffracted at a fairly wide angle. The diffracted rays form two images , a
virtual image and a real image. The virtual image appears at location
formly occupied by the object and sometimes called as true image. The
real image is formed in front of hologram . since light rays pass through
the point where the real image is it can be photographed . The virtual
image is only for viewing observer can move to different position and
look around the image to the same extent that he would be able to , were
he looking directly at the real object . this type of hologram is known as
transmission hologram , since the image is seen by looking through it .