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1
Kasigari Prasad
Introduction to Optical Fiber Communications
INTRODUCTION TO OPTICAL FIBER COMMUNICATIONS Chapter III
Kasigari Prasad.
2
Kasigari Prasad
Introduction to Optical Fiber Communications
Chapter-3 Contents
Attenuation
Material Absorption losses in silica Glass
fibers
Linear Scattering losses
Fiber Bend Loss
Dispersion
Chromatic dispersion
Intermodal dispersion
Polarization dispersion
Overall fiber dispersion
“In a day, when you don't come across any problems –
you can be sure that you are travelling in a
wrong path”
―
Swami Vivekananda
3
Kasigari Prasad
Introduction to Optical Fiber Communications
INTRODUCTION
The transmission characteristics are of light inside the optical fiber
is very critical and important to study the performance and the suitability
of optical fibers for communication purposes.
It is known fact that the optical fibers have enormous potential
bandwidth, so with that advantage optical fibers finds huge applications in
many fields such as military, banking and so on. Hence one important
parameter the attenuation is to be taken into account when discussing
about the transmission characteristics.
Careful study about attenuation show us, that the attenuation is
largely due to absorption in the glass, caused by impurities such as iron,
copper, manganese and other transition metals which occur in the third
row of the periodic table. So pure glass is to be used for fabricating optical
fibers.
In early 1970’s when the first fiber was in use, the fibers
produced attenuation nearly 20 dB /km". Since 1970 onwards tremendous
improvements have been made in communication era, that made to produce
silica-based glass fibers which gives losses of less than 0.2 dB/ km" in the
laboratory by the late 1980s. Later on attenuation exhibited by fibers are
gradually reduced.
Next importance characteristic to be considered is the bandwidth
of the fiber. Signal dispersion limits the utilization of bandwidth within
the fiber. Therefore, once the attenuation is reduced to acceptable levels,
then automatically the dispersive properties of fibers also reduce.
The various attenuation mechanisms are
1. Material absorption,
2. Linear scattering,
3. Nonlinear scattering,
4. Fiber bends
Dispersion limits the Bandwidth utilization of an optical fiber. This
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Kasigari Prasad
Introduction to Optical Fiber Communications
Dispersion is of two kinds
1. Intra modal dispersion (or) Chromatic
2. Intermodal dispersion
Let us start our discussion with Attenuation concept.
ATTENUATION:
The attenuation simply can also be called as Transmission loss of
optical fibers. Signal attenuation can also be referred as Fiber loss or
Signal loss .This attenuation in the optical fibers will limit the Information
carrying capacity of an optical fiber. This signal attenuation determines the
maximum unamplified or repeater less separation between transmitter and
receiver. So due to attenuation in optical fibers it is necessary to make use
of amplifiers and repeaters which are expensive to fabricate, install and to
maintain. So there by cost of the optical fiber communication system
becomes higher.
Units of Attenuation: Signal attenuation within optical fibers, is
usually expressed in the logarithmic unit of the decibel. The decibel, which
is used for comparing two power levels, may be defined for a particular
optical wavelength as
“The ratio of the input (transmitted) optical power Pi into a fiber to the
output (received) optical power Po from the fiber as:
Number of decibels (dB) = 10 log10
In optical fiber communications the attenuation is usually expressed in
decibels per unit length (i.e. dB km"1)
Three major spectral windows where fiber attenuation is low The 1st window: 850 nm, attenuation 2 dB/km The 2nd window: 1300 nm, attenuation 0.5 dB/km The 3rd window: 1550 nm, attenuation 0.3 dB/km 1550 nm window is today’s standard long-haul communication wavelengths.
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Kasigari Prasad
Introduction to Optical Fiber Communications
Several mechanisms are responsible for attenuation in optical fibers. These mechanisms are influenced by the material composition, the preparation and purification technique, and the waveguide structure. They are given as
Material absorption,
Material scattering (linear and nonlinear scattering),
Curve and Micro bending losses,
Mode coupling radiation losses and
Losses due to leaky modes.
Apart from attenuation due to distortion pulse broadening takes place which produces errors at receiver while detecting the information which is send from transmitter. So distortion mechanism limits the Information carrying capacity of a fiber.
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Kasigari Prasad
Introduction to Optical Fiber Communications
Consider that light ray when travelling through the fiber its power
decreases exponentially with distance. First of all start understanding with Material absorption.
MATERIAL ABSORPTION IN SILICA GLASS FIBERS
Material absorption is a loss mechanism related to the material
composition and the fabrication process for the fiber, which results in the
dissipation of some of the transmitted optical power as heat in the
waveguide.
The absorption of the light may be
Intrinsic absorption: (caused by the interaction with one
or more of the major components of the glass).
Extrinsic absorption: (caused by impurities within the
glass).
Intrinsic absorption:
An absolutely pure silicate glass has little intrinsic absorption due
to its basic material structure in the near-infrared region.
There are two major intrinsic absorption mechanisms at optical
wavelengths which leave a low intrinsic absorption window over the 0.8
to 1.7 µm wavelength range, as illustrated in Figure, which shows a
possible optical attenuation against wavelength characteristic for
absolutely pure glass.
Ultraviolet region:
It may be observed that there is a fundamental absorption edge, the peaks
of which are centered in the ultraviolet wavelength region.
[1]. This is due to the stimulation of electron transitions within the glass
by higher energy excitations.
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Kasigari Prasad
Introduction to Optical Fiber Communications
The tail of this peak may extend into the window region at the shorter
wavelengths, as illustrated in Figure.
Also in the infrared and far infrared, normally at wavelengths above 7
µm, fundamentals of absorption bands from
[1]. The interaction of photons with molecular vibrations within the
glass occurs.
These give absorption peaks which again extend into the window region.
Figure : Intrinsic loss mechanism
[2]. The strong absorption bands occur due to oscillations of
structural units
such as Si-0 (9.2 µm), P-0 (8.1 µm), B-0 (7.2 µm) and Ge-0 (11.0 µm)
within the glass. Hence, above 1.5 µm the tails of these largely far-
infrared absorption peaks tend to cause most of the pure glass losses.
The effects of both these processes may be minimized by suitable choice of
both core and cladding compositions.
8
Kasigari Prasad
Introduction to Optical Fiber Communications
For instance, in some non oxide glasses such as fluorides and chlorides,
the infrared absorption peaks occur at much longer wavelengths which are
well into the far infrared (up to 50 µm), giving less attenuation to longer
wavelength transmission compared with oxide glasses.
Extrinsic Absorption:
In practical, optical fibers prepared by conventional melting
techniques are major source of signal attenuation which is caused mainly
from transition metal element impurities are called as extrinsic
absorption.
Truly speaking the extrinsic absorption is caused by two
mechanisms namely one by
1) Transition metal impurity and
2) absorption due to water in glass
Some impurities, namely chromium and copper, in their worst valence
state can cause attenuation in excess of 1 dB km in the near-infrared
region.
Transition element contamination may be reduced to acceptable levels by
glass refining techniques such as vapor-phase oxidation which largely
eliminates the effects of these metallic impurities.
Another major extrinsic loss mechanism is caused by absorption due to
water (as the hydroxyl or OH ion) dissolved in the glass. These hydroxyl
groups are bonded into the glass structure and have fundamental
stretching vibrations which occur at wavelengths between 2.7 and 4.2 µm.
The fundamental vibrations give rise to overtones appearing almost
harmonically at 1.38, 0.95 and 0.72 µm, as illustrated in Figure
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Kasigari Prasad
Introduction to Optical Fiber Communications
Figure: Absorption spectrum for Hydroxyl group in silica
Figure: Attenuation s pectrum for Ultra low loss single mode fiber
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Kasigari Prasad
Introduction to Optical Fiber Communications
It may also be observed in Figure that the only significant absorption band
in the region below a wavelength of 1 µm is the second overtone at 0.95
µm which causes attenuation of about 1 dB km1 for one part per million
(ppm) of hydroxyl.
Although in standard, modern single-mode fibers the loss caused by the
primary OH peak at 1.383 µm has been reduced below 1 dB km1, it still
limits operation over significant distances to the lower loss windows at
1.31 and 1.55 µm.
LINEAR SCATTERING
Scattering losses in glass arises from microscopic variations in
material density from compositional fluctuations and from structural in-
homogeneities or from defects occurring during fiber manufacture.
Linear scattering mechanisms cause the transfer of some or all of the
optical power contained within one propagating mode to be transferred
linearly (proportionally to the mode power) into a different mode.
This process tends to result in attenuation of the transmitted light as the
transfer may be to a leaky or radiation mode which does not continue to
propagate within the fiber core, but is radiated from the fiber.
It must be noted that as with all linear processes, there is no change
of frequency on scattering.
Linear scattering may be categorized into two major types:
1. Rayleigh scattering and
2. Mie scattering.
Both result from the non ideal physical properties of the manufactured fiber
which are difficult and, in certain cases, impossible to eradicate at present.
Rayleigh scattering:
Glass is composed of randomly connected molecules. So in glass
materials it is found that it has high molecular density areas, medium
11
Kasigari Prasad
Introduction to Optical Fiber Communications
molecular density areas and low molecular density areas. And also in
general the glass materials consist of oxides of SiO2, GeO2, P2O5 and so on.
The molecular fluctuations of these compounds are responsible for the
variations in relative refractive indices over a distance that is small
when compared to wavelength. This type of refractive index variations
causes Rayleigh type Scattering.
Rayleigh scattering is the dominant intrinsic loss mechanism in the low-
absorption window between the ultraviolet and infrared absorption tails.
It results from in homogeneities of a random nature occurring on a small
scale compared with the wavelength of the light.
These in-homogeneities manifest themselves as refractive index fluctuations
arise from density and compositional variations which are frozen into
the glass lattice on cooling.
The compositional variations may be reduced by improved
fabrication.
The fundamental component of Rayleigh scattering is strongly
reduced by operating at the longest possible wavelength.
The subsequent scattering due to the density fluctuations, which is in
almost all directions, produces an attenuation proportional to
Rayleigh scattering for a single-component glass is given by
Where γR is the Rayleigh scattering coefficient,
λ is the optical wavelength,
n is the refractive index of the medium,
p is the average photo elastic coefficient,
βc is the isothermal compressibility at a fictive temperature TF, and
K is Boltzmann's constant.
The fictive temperature is defined as
“The temperature at which the glass can reach a state of thermal
equilibrium and is closely related to the anneal temperature”.
Transmission loss Factor or Transmissivity of the fiber
12
Kasigari Prasad
Introduction to Optical Fiber Communications
where ‘L’ is the length of the fiber.
Features of Rayleigh scattering:
Rayleigh scattering is the same phenomenon that scatters light
from the sun in the atmosphere there by giving rise to a blue sky.
Mie Scattering:
Linear scattering may also occur at in-homogeneities which are
comparable in size to guided wavelength. These in-homogeneities are
results from the non – perfect cylindrical structure of the wave guide
and may caused by the fiber imperfections such as
Irregularities in core-cladding interface
Core cladding refractive index difference along the fiber length
Diameter fluctuations
Strains and
Bubbles.
The scattering created by such in-homogeneities is mainly in forward
direction and is called Mie scattering.
Depending upon the fiber material, design and manufacture, Mie Scattering
may cause significant losses.
The in homogeneities may be reduced by
Removing imperfections due to the glass manufacturing
process.
Carefully coating the fiber
By increasing relative refractive index differences.
13
Kasigari Prasad
Introduction to Optical Fiber Communications
FIBER BEND LOSSES
Radiation losses:
Optical fibers suffer radiation losses at bends or curves on their
paths. This is due to the energy in the evanescent field at the bend
exceeding the velocity of light in the cladding and hence the guidance
mechanism is removed, which causes light energy to be radiated from the
fiber.
This situation is shown in the following Figure.
Figure: Radiation losses at the fiber bend
The part of the mode (light) which is on the outside of the bend is
required to travel faster than that light mode travelling on the inside the
fiber core, so that a wave front perpendicular to the direction of
propagation is maintained.
Hence, part of the mode in the cladding needs to travel faster
than the velocity of light in that medium. As this is not possible, the
energy associated with this part of the mode is lost through radiation.
The loss can generally be represented by a radiation attenuation
coefficient which has the form
where R is the radius of curvature of the fiber bend and c1, c2 are constants
which are independent of R.
14
Kasigari Prasad
Introduction to Optical Fiber Communications
Generally bending losses are of two kinds
I. Macro bending losses
II. Micro bending losses
Macro Bending Loss or Large bending losses may occur in multimode
fibers at a critical radius of curvature Rc and is given as
So if the bending of the fiber is large then such a fiber have large
radius when compares to normal fiber diameter. They generally occur
when a fiber cable turns a corner. So from the above equation it is
clear that the Macro bending losses may be reduced by:
Designing fibers with large relative refractive index
differences;
Operating at the shortest wavelength possible.
The critical radius of curvature for a single-mode fiber is given as
Rcs = ( 2.478 – 0.996 )-3
Where λc is the cutoff wavelength for the single-mode fiber.
For a specific single-mode fiber that is at a fixed relative index difference
and cutoff wavelength,
The critical wavelength of the radiated light becomes progressively
shorter as the bend radius is decreased.
Micro Bending losses: Micro bends are repetitive small scale fluctuations in the radius of
the curvature of the fiber axis. These are shown in the following figures.
Micro bending losses are caused either by
non uniformities in the manufacturing of the fiber or
By non uniform lateral pressures created during the
cabling of the fiber. This effect is called as CABLING or
PACKAGING LOSSES.
To minimize this micro bending losses Place compressible jacket over
15
Kasigari Prasad
Introduction to Optical Fiber Communications
the fiber. When external forces are applied to such compressible fibers the
jacket may get deformed but the fiber remains to be straight in line.
Figure: Micro bending losses due to small fluctuations.
Figure: Micro bending losses due to small fluctuations.
Figure: Optical fiber with Compressible Jacket to reduce micro bendi ng losses
The micro bending losses αm of a jacketed fiber is reduced from that of an
unjacketed fiber by a factor
F(αm) = [1+π∆2
( )4
] -2
Here Ef and Ej are Young’s module of the jacket and the fiber respectively.
The youngs module ranges from 20 to 500 MPa. The youngs modulus of
fused silica ia about 65GPa.
16
Kasigari Prasad
Introduction to Optical Fiber Communications
INFORMATION CAPACITY DETERMINATION
A light pulse as it travels along an optical fiber the pulse will
broaden. This Pulse broadening will eventually cause a pulse to overlap
with neighboring pulses. After a certain amount of overlap has occurred,
adjacent pulses can no longer be individually distinguished at the receiver
and errors will occur. Thus the dispersive properties determine the limit of
the information capacity of the fiber.
Band width distance product is used to measure the information
capacity of an optical fiber. Its units is MHz. Km
For a step-index fiber the various distortion effects limit the
bandwidth-distance product to about 20 MHz km.
In graded-index fibers the radial refractive-index profile can be
carefully selected so that pulse broadening is minimized.
The pulse broadening phenomenon with respect to distance is shown from
the following figure.
Figure: Pulse broadening mechanism
17
Kasigari Prasad
Introduction to Optical Fiber Communications
A pulse overlaps with other pulses during its transmission to receiver
end; this effect is known as Inter Symbol Interference (ISI). Signal
dispersion alone limits the maximum possible bandwidth attainable with a
particular optical fiber to point where individual symbols can no longer be
distinguished.
In order not to have any overlapping of light pulses inside the fiber
during their travel, the Digital Bit Rate BT must be less than the reciprocal
of the broadened pulse duration (2τ).
So, Bit rate BT ≤
The amount of the pulse broadening is dependent on the distance the pulse
travels within the fiber. In the absence of mode coupling the pulse
broadening increases linearly with fiber length and thus bandwidth is
inversely proportional to distance.
A comparison of the information capacities of different fibers with
capacities are shown in the following figure.
18
Kasigari Prasad
Introduction to Optical Fiber Communications
Group Delay:
Phase and Group Velocity: The plane wave which is propagating in a fiber can be discussed with its phase. Each wave moving in a fiber (ideal case) has some constant phase points. The phase velocity of light propagating in z direction is given as
Phase velocity Vp = =
But in practical such constant phase points does not exist and light energy is generally composed of sum of plane wave components of different frequencies. A group of waves with closely similar frequencies propagate like a Packet. This wave packet does not travel at a phase velocity of the individual wave but is observed to move at a group velocity Vg given by
Vg =
The formations of the wave packet from combining two waves with nearly equal frequencies are shown in the following figure. Group of waves travel at a group velocity Vg.
Figure1.14: Formation of wave packet.
19
Kasigari Prasad
Introduction to Optical Fiber Communications
The propagation constant is given as The phase velocity can also be written as This parameter Ng is known as GROUP INDEX
The light that emitting from optical source follows different modes.
Assume that all the modes are equally excited. So, each mode thus carries
an equal amount of energy through the fiber.
Also consider each mode contains all of their individual spectral
components. The signal may be considered as modulating each of these
spectral components in the same way. As the signal propagates along the
fiber, each spectral component can be assumed to be travel
independently, and to undergo a time delay or Group delay per unit
length in the direction of propagation.
20
Kasigari Prasad
Introduction to Optical Fiber Communications
The time delay or the group delay is given by
fibertheinsidetravelsenergylightwhichatvelocitytheisThis
d
dC
dk
dV
d
dCV
c
fd
dC
c
fd
dC
dk
dCVSo
dk
d
CV
thatknowWe
dk
d
cdC
db
VL
T
dC
d
L
T
cd
d
fd
d
d
d
VL
T
V
LTSo
speed
cedistimethatknowWe
d
dV
gg
g
g
g
gg
g
g
g
g
g
111
11
1
22
22,
11
1
.2
1
.2
.
)2(2
1;
tan
Pulse spreading arises from group delay. If the spectral component width is not too wide then delay difference per unit wave length is given by
d
dTg.
21
Kasigari Prasad
Introduction to Optical Fiber Communications
)δδdλ
βdλ
dλ
dβλ(
πC
LST
d
dTSTasgivenisLcedisaoverTdifferencedelaytotalThe
thenfigureinshownastolengthwavetheCentralbelowand
abovetieswhichandpartaarewhichcomponentspectralaConsider
g
2
222
2
.''tan
2
In terms of Angular Frequency this delay difference can be expressed as
GVDparameterdispensionvelocitygroupisd
dfactorThe
d
dL
V
L
d
d
d
dT
g
g
2
2
2
2
2
This GVD parameter determines how much light pulse broadens as it travels along the fiber. If spectral width of optical source is characterized can be approximated by runs pulse width as.
2222
2
22
2211
22
CC
vgd
d
d
d
LD
asgivenbecanparameterDispersiontheThen
d
d
d
d
C
L
d
gd
g
g
g
From this equation it is clear that dispersion is dependent on
Length of fiber
Group velocity of Light
Group delay and
Group velocity dispersion parameter.
We can see dispersion in the different ways.
1. INTRA MODEL DISPERSION
2. INTER MODEL DISPERSION and a special case
22
Kasigari Prasad
Introduction to Optical Fiber Communications
INTRA MODEL DISPERSION:
Intra model dispersion can also is known as CHROMATIC DISPERSION.
This chromatic dispersion causes within a single mode. The pulse
spreading arises from the finite spectral emission width of an optical
source. This phenomenon is known as group velocity dispersion, since
dispersion is a result of group velocity being function of wave length.
The causes for chromatic dispersion are
a. Material dispersion
b. Wave guide dispersion
Material Dispersion: Material dispersion occurs because of refractive index variation as
variation as a function of wave length. Pulse broadening due to material
dispersion results from the different group velocities of various spectral
components lunched into the fiber from optical source.
It occurs when the phase velocity of a plane wave propagating in the
dielectric medium varies non linearly with wave length and so material is
said to be exhibit the material dispersion.
02
2
d
dnWhen
i.e. From Optical source various spectral components of Different group velocities are launched. This happens because, The dielectric medium used in optical source Makes plane wave (Light) to propagate Non linearly with wave length and so Material dispersion occurs.
23
Kasigari Prasad
Introduction to Optical Fiber Communications
The variation of refractive index as a function of wave length is shown as follow
So, group delay
d
dnn
cd
dg 1
1
The pulse delay τm due to material dispersion for an optical fiber of length L is given as
Now, for a source with rms spectral width and mean wave length ; the rms pulse broadening due to material dispersion m is obtained from TAYLOR SERIES about is
kmnmarePsUnits
d
nd
C
L
So
d
dn
dn
nd
d
dn
C
L
d
nd
C
L
d
mdBut
d
md
d
md
d
md
m
m
m
//
,
1
....2
2
1
2
1
2
1
2
1
2
2
2
2
The material dispersion parameter M variation with respect to wave
length for pure silica is shown as follow.
From the figure it is observed that
Material dispersion parameter M tends to zero in
longer wave length region around 1.3 wave length.
Even in shorter wave lengths the material dispersion
can be minimized if optical source LASER is used
instead of LED.
24
Kasigari Prasad
Introduction to Optical Fiber Communications
Wave Guide Dispersion:
The Wave guiding of the filer may also create intramural dispersion.
This results from the variation in group delay velocity with wave length for
a particular mode.
For a single mode whose propagation constant is β, the fiber
exhibits wave guide dispersion when .02
2
d
d
Multimode fibers are free from wave guide dispersion. Since they
propagate far from cutoff. The effect of wave guide dispersion on pulse
spreading can be approximated by assuring that “the refractive under of
the material is independent of wave length”.
So group delay arising from wave guide dispersion is
)1(dk
d
C
Lg
This group delay can be expressed in terms of normalized
propagation constant ‘b’ as
)2(2
2/1
22
1
222
nn
nkB
v
uab
25
Kasigari Prasad
Introduction to Optical Fiber Communications
When refractive index difference is small
)5()()(
)4()1(
)3(''
)3(/
1
2222
22
2
21
2
21
dk
kbdnn
C
L
dk
bkdnn
C
L
kbnndk
d
C
L
dk
d
C
LT
isdispersionguidewaveforTdelaygroupAgain
bkn
getequationfromforSolving
nn
nkb
thenn
nnThen
kwg
wg
where
db
vbdnn
C
LT
byreplacedbecanegindelaygroupSo
kanvnnkav
asnumbervtorelatedistconsnpropagatioetheNow
wg )6()(
)5(
2
tanmod
22
2
2
2
2
1
dispersionguidewavefromdelayisGroupdb
vbd )(
26
Kasigari Prasad
Introduction to Optical Fiber Communications
27
Kasigari Prasad
Introduction to Optical Fiber Communications
SIGNAL DISTORTION IN SINGLE MODE FIBERS:
For Single mode fiber wave guide dispersion and material
dispersion are of same order in magnitude. The pulse spread due to wave
guide dispersion is given by
24/14
2
22
2222
44
2
2
2
)4(1
)21(1)(
21
2/1
2)41(
)21(
1)(
)(
vvb
getWe
nn
nk
v
ab
binaPut
v
vafactorthe
dispersionguidewaveanalysisTo
dv
vbdV
C
Ln
d
dTV
DLd
dT
y
wg
wg
wg
wg
wg
28
Kasigari Prasad
Introduction to Optical Fiber Communications
INTER MODAL DISPERSION
Inter modal dispersion is a result of different values of the group
delay for each individual mode at a SINGLE FREQUENCY.
The steeper the angle of propagation of the ray, the higher is the mode
number so the group velocity is slower. This variation in the group
velocities of the different modes results in a group delay spread of
intermodal dispersion.
Intermodal dispersion does not appear in single mode fibers but is
important for multi mode fibers.
The maximum pulse broadening arising from intermodal
dispersion is the difference between the travel time Tmax of the higher
order mode and the travel time Tmin of the fundamental mode.
C
LnTTT 1
minmaxmod
This formula applies only for meridional rays but not for Skew rays.
29
Kasigari Prasad
Introduction to Optical Fiber Communications
Sometimes intermodal dispersion is known
Modal dispersion(or)
Mode dispersion
This results from the propagation delay differences between modes
within the multimode fiber.
POLARIZATION MODE DISPERSION:
In a single-mode optical fiber, the optical signal is carried by the
linearly polarized “fundamental mode” LP01, which has two polarization
components that are orthogonal. (in x and y directions)
In a real fiber (i.e. ngx ngy), the two orthogonal polarization modes
propagate at different group velocities, resulting in pulse broadening –
polarization mode dispersion.
Polarization mode dispassion is very critical or important in long distance
very high data rate optical links. This dispersion generally occurs because
of the effect of BIRE FRINGENCE on the polar gates state of an optical
signal.
Birefringence:
The refractive index difference is known as birefringence.
B = nx – ny . There are two independent degenerate propagation modes in
a fiber. These modes are very similar but their polarization planes are
orthogonal i.e one mode is horizontally polarized and another is vertically
polarized.
30
Kasigari Prasad
Introduction to Optical Fiber Communications
Because of imperfections such as asymmetrical lateral stresses. Non
circular cores and variations in refractive index profiles there two
modes propagate with different phase velocities and the difference
between their (modes) effective refractive indices called the fiber
birefringence.
Bf= ny-nx Some external factors such as Bending Twisting or
Pinching of the fiber can also lead to Birefringence.
Polarization:
Orientation of dielectric field of the light along the length of the filer
is known as polarization.
A varying birefringence along the length of the fiber will cause polarization
mode to travel at a slight different velocity and the polarization orientation
will rotate with distance.
The resulting difference in polarization time T between two
orthogonal polarization modes will result in PULSE SPREADING”
This is polarization mode dispersion PMD and is given as
31
Kasigari Prasad
Introduction to Optical Fiber Communications
., lrespectivedirectionsxyinvelocitiesGroupVV
delaytimealdifferentiT
V
L
v
L
gygx
POL
gygx
Tpol
Chromatic dispersion is stable phenomenon but PMD is random. In
terms of mean values of the differential group delay, it is given as
PSPMD
PS
PMDPOl
KMtoisrangeparameterPDMaverageD
KMunits
LDT
0.11.0
:
OVER- ALL DISPERSION Multi mode filers:
The overall description in multi mode fibers comprises both intra
model and inter model dispersion.
The total RMS pulse bordering is given by σT = (σc2 + σ n 2)1/2
Where
σC is intra model or chromatic broadening
σn is inter model broadening caused by delay difference between the
modes.
Wave guide dispersion is negligible in multimodal filters then σC ≈ σm
Single mode fibers:
The pulse broadening in single – mode filters is mainly due to intra
model or chromatic dispersion.
The transits time or specific group delay τg for a light pulse propagating
along a unit length of single mode filter is
Where C I s velocity of light in a vacuum is propagating constant
The total first order dispersion parameter or the chromatic description of
a single mode fibers , is given by DT
32
Kasigari Prasad
Introduction to Optical Fiber Communications
Where the variable Is replaced by ω then the total dispersion is
The fiber exhibits intra model description when varies non linearly with
wave length
may be expressed in terms of relative refractive index difference ∆ and
normalized propagation constant ‘b’
1/2
The total R M S pulse broadening caused by intra model dispersion in a
fiber of length L is given by of group delay with respect to wave length
Total r.m.s pulse broadening = σλ L
= σλ L 2 π/ cλ 2
Where σλ is source rms spectral line width centered at a wave length λ.
The dependency of pulse broadening on the fiber materials properties and
the normalized propagation constant ‘b’ causes three interrelated effects
involving complicated cross product terms and are discussed as follows
1.Material Dispersion Parameter,
Where n=n1 or n2 core or cladding respectively
2.Wave Guide Description Parameter ,
Where V is normalized frequency for the fiber
3.Profile Dispersion Parameter,
However the profile dispersion parameter Dp can be neglected in rough
estimates of total dispersion within single mode fibers , as it will be quite
small at longer wave lengths.
The TOTAL FIRST ORDER DISPERSION can be given as
DT =DM+DW=DP PS/nm/km