chapter 3 oc today

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Kasigari Prasad

Introduction to Optical Fiber Communications

INTRODUCTION TO OPTICAL FIBER COMMUNICATIONS Chapter III

Kasigari Prasad.

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Kasigari Prasad


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

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Kasigari Prasad


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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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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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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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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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.

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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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Figure: Absorption spectrum for Hydroxyl group in silica

Figure: Attenuation s pectrum for Ultra low loss single mode fiber

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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

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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

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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.

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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.

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Kasigari Prasad


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

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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.

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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

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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.

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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.

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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.

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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.

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Kasigari Prasad


)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

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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.

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Kasigari Prasad


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.

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Kasigari Prasad


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

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Kasigari Prasad


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 )(

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Kasigari Prasad


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Kasigari Prasad


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

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Kasigari Prasad


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.

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Kasigari Prasad


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.

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Kasigari Prasad


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

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Kasigari Prasad


., 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

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Kasigari Prasad


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

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