Optical Full Units NOTES

8/12/2019 Optical Full Units NOTES

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OPTICAL FIBER COMMUNICATION

UNITI

OPTICAL FIBERS-STRUCTURE

1.INTRODUCTION:

The communication medium is either wire conductor cable or freespace.

Nowadays a new medium is fiberoptic cable. Fiber is essentially a light pipe that is used to carry a light beam from

one place to another.

The transmitter & receiver operates at low frequency 103HZ , mediumfrequency 10

6HZ & high frequency 10

14HZ, depending upon the

requirement of communication at narrow band, medium band or broad

band frequencies. Optical fiber cables are working at 1300nm,1500nm. In future we will

go to higher wavelengths around 2500nm.

ADVANTAGES:

High speed. Low loss Flexibility Wide channel

Low size & weight Low interruption(interference & crosstalk) Broad bandwidth. Long distance communication.

DISADVANTAGES:

High cost Maintenance is difficult Brittleness.

WDM:

To use multiple sources operating at slightly different wavelengths to

transmit several independent information streams over the same fiber.


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1.1EVOLUTION OF FIBER OPTICS SYSTEMS:

In 1880, Alexander Graham Bell experimented with an apparatus called

Photophone. It was a device constructed from mirror that transmitted sound

waves over a beam of light.

There are three generations in fiber optics:

1.1.1 FIRST GENERATION:

In 1977 ,GTE in Los Angeles & AT & T in Chicago were introduced. Intransmitter side they used LASER, it has high output power, high

frequency of operation, wide bandwidth.

The operating wavelength is 800 to 900nm i.e., around 850nm. Fiber material is GaAS and bit rate is 45 to 140 Mbps and repeater

spacing is 10kms.

1.1.2SECOND GENERATION:

The operating wavelength is around 1300nm. Fiber material is Indium Gallium Arsenide, Phosphorus and bit rate is

155 to 622 Mbps and repeater spacing is 40kms.

Both single mode and multimode fibers are used in LAN, & its bit rateis 10 to 100Mbps.

In 1984, Single mode fibers were used for larger bandwidth.1.1.3 THIRD GENERATION:

The operating wavelength is around 1550nm. Bit rate is 2.5 Gbps and repeater spacing is 90kms. In 1970s start to use WDM to boost the transmission capacity. In

1990s combination of EDFA & WDM was used to boost fiber capacityto even higher levels & to increase the transmission distance.

In 1996 onwards bit rate is increased around 10 Gbps by using highquality lasers.

Introduce the optical amplifier in 1989 gave a major boost to fibertransmission capacity.

GaAlAs was first introduced but successful & widely used devices areErbium Doped Fiber Amplifier(EDFA) ->1500nm and Prascodymium

Doped Fiber Amplifier(PDFA)->1300nm.

The use of WDM offers a further boost in fiber transmission capacity. The basis of WDM is to use multiple sources operating at slightly

different wavelengths to transmit several independent information

streams over the same fiber.Mid-1990s, a combination of EDFAs &


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WDM was used to boost fiber capacity to even higher levels and to

increase the transmission distance.

1.2ELEMENTS OF AN OPTICAL FIBER TRANSMISSION

LINK:

The basic components in the optical fiber communication are lightsource, the light signal transmitter, the optical fiber & photodetecting

receiver.

The other elements include fiber and cable splices and connectors,regenerators, beam splitters and optical amplifiers.

Information source:

The information signal to be transmitted may be voice, video orcomputer data. The first step is to convert the information into a form

compatible with the communications medium.

-

Figure:1.2.1.Major elements of an Optical fiber transmission link


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1.3BASIC LAWS & DEFINITIONS:

1.3.1Refractive Index (or) Index of Refraction:

The ratio of speed of light in free space to the speed of light in medium

n= c/v

n-> 1.00 for air, 1.50 for glass, 1.33 for water, 2.42 for diamond

Figure:1.3.1.Law of reflection

1.3.2.Angle of incidence(1):

The angle at which light strikes a surface with respect to normal iscalled angle of incidence.

The angle of incident light ray determines whether the ray will bereflected or refracted.

1.3.3.Angle of Reflection(2):

The angle at which light is reflected from a surface is called angle of

reflection.The law of reflection is 1= 2

1.3.4.Snells law:

It states that how the light ray reacts when it meets the interface of two

media having different refactive indexes. Mathematically it can be expressed by

n1 sin1=n2 sin 2

n1 = sin 2

n2 sin 1


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Figure:1.3.4. Reflection of a light ray at material boundary

1.3.5.Critical angle:

The value of angle of incidence at which the angle of refraction is 90ois

called critical angle.

1= c, 2 =90o

n1 sinc=n2 sin 90o

sinc = n2

n1

1.3.6.Total Internal Reflection:

When the light ray strikes the interface at an angle greater than the

critical angle,the light ray does not pass through the interface into the glass.Whan this occurs, the angle of reflection 2 is equal to angle of incidence 1.

This action is known as total internal reflection.

Figure:1.3.6.Total internal Reflection


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Condition:

i. n1>n2ii. 1> 2

1.3.7.Numerical aperture:

It is used to describe the light gathering or light collecting ability of an

optical fiber. It is referred as figure of merit commonly used to measure the

magnitude of acceptance angle. The numerical aperture for light entering the

glass fiber from an air medium is described mathematically as

NA=sinin

Where in-> acceptance angle

Acceptance angle is the maximum angle to the fiber axis at which light

may enter the fiber axis in order to be propagated.

in(max)=sin-1(n12-n22)

no

where no is refractive index of air( no=1)

Therefore in (max)=sin-1(n12-n22)

NA = sinin

Therefore NA= (n1

2

-n2

2

)

Hence acceptance angle is in=sin-1(NA

NA=sin in =(n12-n22)

NA= (n1+n2)(n1-n2)

= 2n1(n1-n2) [n1=n2]

Substitute =n1-n2

n1

therefore NA=2n1(n1 )

NA=n12


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1.4.RAY OPTICS:

There are 2 types of rays in fiber.

i. Meridional rays.ii. Skew rays.

1.4.1Meridional rays:

These rays are confined to the meridian planes of fiber, which are theplanes the contain the axis of symmetry of the fiber.

It lies in a single plane , its path is easy to track as it travels along thefiber . It can be classified into

i. Bound rays.ii. Unbound rays.

1.4.1.1.Bound rays:

That are trapped in the core and propagate along the fiber axis accordind

to the laws of geometrical optics.

1.4.1.2.Unbound rays:

That are refracted out of the fiber core.

1.4.2.Skew rays:

These rays are confined to single plane , but instead tend to follow ahelical type path along the fiber.

These rays are more difficult to track as they travel along the fiber ,since do not lie in a single plane.

A greater power loss arises when skew rays are included in analysis, thatare actually leaky rays.These leaky rays are only partially confined to

the core of circular optical fiber and attenuate as light travels along the

optical waveguide.

1.4.3.Meridional rays for Step index fiber:

The light ray enters the fiber core from a medium of refractive index n atan angle o with respect to fiber axis and strikes the core claddinginterface at an normal angle .

If it strikes this interface at such an angle that it is totally internallyreflected, then meridional ray allows a zigzag path along the fiber core.


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Figure:1.4.3.Meridional ray optics representation of the propagation mechanism

in an optical waveguide

From Snells law, the minimum angle min that supports total internal reflectionfor meridional ray is

sinmin = n2

n1

The rays striking the core-cladding interface at angles less then minwill refract out of core and be lost in cladding. By applying Snells lawto the air-fiber face boundary, then the relationship is

nsinomax = n1 sinc =((n12-n22)

omax maximum entrance angle

Where c= -- c2

NA for step-index fiber for meridional rays

NA=nsin omax= (n12-n22) = n12

1.5.MODES:

The number of paths for the light rays in the fiber. The set of

electromagnetic waves propagate inside any wave guide. There are two types of

modes are.

i. Single mode fiber:

Only one signal can propagate inside along the optical fiber parallel to

core axis.


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ii. Multimode fiber:

The light takes many paths through the core. The number of paths

possible for multimode fiber cable depends on frequency of light signal,

refractive index of core and cladding and core diameter.

Index profile:

It is a graphical representation of value of refractive index of core

diameter. According to index profile we can divide the configuration into 3

types of modes.

i. Single mode step index fiber.ii. Multimode step index fiber.iii. Multimode graded index fiber.

Step index:Refractive index of core is uniform throughout & undergoes a abrupt

change at cladding is called step-index fiber.

Graded index:

The core of refractive index is made to vary as a function of radialdistance from the center of fiber.

Advantages of cladding:

Used to reduce the scattering loss. It protects the core from absorbing surface. It adds mechanical strength to the fiber.

Fiber structure:

INDEX PROFILE FIBER CROSS SECTION& RAY OPTICS


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STEP INDEX GRADED INDEX

Refractive index of core isuniform Not uniform & is made to varyas a function of radial distancefrom the center of fiber

Light rays are meridional Light rays are skew rays No distortion for single mode

fiber &signal distortion in

multimode fiber

Distortion is less because ofself focusing effect & light rays

reach the fiber at the same timedue to helical path or light

propagation

Attenuation :Single mode fiberless effect

Multimode fibermore effect

Less attenuation Numerical Aperture:

Single mode fiberless

efficiency

Multimode fiberhighefficiency

Less efficiency

Band width:Single mode fiber > (GHZ)

Multimode fiber 50 MHZ

Theoretically infinitebandwidth

1.6.MODE THEORY OF CIRCULAR WAVE GUIDE:

In optical fiber, the core cladding boundary conditions lead to couplingbetween electric & magnetic field components.

This gives rise to hybrid modes, which makes optical waveguideanalysis more complex than metallic waveguide analysis.

The hybrid modes are HE or EH modes depending on whether thetransverse electric or magnetic field is larger for that mode. The lower

order modes are 11HE and 01TE .

Fibers usually are constructed so that the difference in the core &cladding refractive index is very small, then only four field components

exists(n1-n2


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Each mLP0 mode is derived from mHE1 mode and each mLP1 modecomes from mTE0 , mTM0 and mHE0 modes. Thus the fundamental

01LP mode corresponds to 11HE mode.

1.6.1.OVERVIEW OF MODES:

1. Guided modeswaves should be propagated inside the core.2. Radiated modesunbounded rays.3. Leaky Modesmore amount of power in cladding region.

Figure:1.6.1.1.Electric field Distributions for several of the lower-order

guided modes in a symmetricalslab waveguide

The order of a mode is equal to number of field zeros across the guide. The order of mode is also related to the angle that the ray congruence

corresponding to this mode makes with the plane of waveguide or axis

of fiber.

The plot shows that electric field of guided modes are not completelyconfined to the central dielectric slab i.e., they do not go to zero at core

cladding interface & extends into the cladding. The field vary harmonically in core region of refractive index n1 and

decay exponentially outside of this region of refractive index n2.


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In lower- order modes, the fields are tightly concentrated near the centerof slab or axis of an optical fiber, with little penetration into cladding

region.

In higher-order modes, the fields are distributed more towards the edgeof guide and penetrate further into the cladding region.

Due to this penetration, radiated modes are propagated in claddingregion.

In the leaky modes the fields are confined partially in the fiber core &attenuated as they propagate along the fiber length due to radiation and

tunnel effect.

1.6.1.2.Tunnel effect:

The leaky modes are continuously radiating their power out of the coreas they propagate along the fiber. This power radiation out of the wave

guide results from quantum mechanical phenomenon known as tunnel

effect.

Therefore, in order to mode remains guided, the propagation factor satisfy the condition

n2K < < n1K

Where, n1refractive index of core

n2refractive index of cladding

K propagation constant =

2

The boundary between truly guided modes and leaky modes is defined by cutoff

condition.

1. =n2K cutoff condition2. < Kn2 leaky modes3. > Kn2 guided modes

When becomes smaller than n2K ( < Kn2 )power leaks out of coreinto cladding region.

Leaky modes can carry significant amounts of optical power in shortfibers.

1.7.KEYMODEL CONCEPTS:

An important parameter connected with cutoff condition is V number isV = 2a (n12-n22)1/2


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= 2a

It determines how many modes a fiber can support for the lowest order11HE mode, each mode can exist only for values of V that exceed

certain limiting value.

The modes are cutoff when =n2K . This occurs when V


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A cylindrical co-ordinate system (r,, Z)is defined with Z-axis. The

waveguide equation are ).2..(..........

).1..(..........

2

2

r

EH

rq

jH

r

HE

rq

jE

ZZ

ZZ

The solutions can be obtained in 2 cases.

Case(i):

In metallic wave guide

For TE modes ZE =0

For TM modes ZH =0

Case(ii):

For optical waveguide

Hybrid modes are exist. Both ZE and ZH are non-zero.

Waveguide equation for step-index fiber:

Using separation of variable method , we can find the guided modes in

step-index mode. The general equation for wave equation is

jv

Ztj

Z

eF

etFZF

AtFZFFrAFE

()

)()(

)..().........()()()(

2

)(

43

4321

because of circular symmetry of waveguide each field component must

not change when the co-ordinate is increased by 2.

The fields are harmonically varied in the core region & deceying incladding region.

The solutions are Bessels function of first time of order , for this

For core region


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).(..........).........()(

2&

1

11

22

1

2

IurJVrF

nKKu

For cladding region

).(..........).........()(

2&

1

22

2

2

2

1

2

IIrKVrF

nKK

Sub:all equations in ( A)

For core region

)3....(..........)()( )( ZtjjvZ ejurAJVarE

Similarly for magnetic component

)()( urBJVarHZ )4....(..........)( Ztjjv ej

For cladding region

)5....(..........)()( )( ZtjjvZ ejrCKVarE

)6....(..........)()( )( ZtjjvZ ejrDKVarH

The solution for must be find from boundary conditions E and zE arethe tangential components for inside and outside dielectric.

H and zH are the tangential components for inside and outsidedielectric.

At the inner core cladding boundary

1ZZ EE

When r=a,

)(

1 )(

Ztjjv

Z ejuaAJVE

At the outside of boundary

2ZZ EE

When r=a,


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)(

2 )( ZtjjvZ ejaCKVE

At boundary conditions

021 ZZ EE

)7......(..........0)()(0)()(

)(

aCKVuaAJVaCKVuaAJVee

Ztjjv

Inside the core q2=u

2using equation (3) and (4) sub: in (1) find

1E

]..)(.([..)(.(

]..)(.([..)(.(

..)('

..)(

..)(

..)(

)(')(

22

)(')(

21

)(

)(

)('

)(

ZtjjvZtjjv

ZtjjvZtjjv

ZtjjvZ

ZtjjvZ

ZtjjvZ

ZtjjvZ

eeaJVDejveaKVCa

jE

eueuaJVBejveuaJVAau

jE

eeaDKVr

H

ejveaCKV

E

eueuaBJVr

H

ejveuaAJVE

At boundary condition

021 EE

)8.......(..........0).(.)(.).(.)(. '2

'

2

aKVDaKV

a

jvC

juuaJVBuaJV

a

jvA

u

j


)9......(..........0)(.)(.

.).(.

.).(.

0

)(

2

)(

1

21

aKVDuaJVB

eeaKVDH

eeuaJVBH

HH

Ztjjv

Z

Ztjjv

Z

ZZ



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]..)(.([..)(.(

]..)(.([..)(.(

0

)(')(

22

)(')(

21

21

ZtjjvZtjjv

ZtjjvZtjjv

eeaJVCejveaKVDa

jH

eueuaJVAejveuaJVBau

jH

HH


021 HH

)10.......(..........0).(.)(.).(.)(. '2

'

2

aKVCaKV

a

jvD

juuaJVAuaJV

a

jvB

u

j

Using equation 7,8,9,10. Find the unknown values A,B,C,D using determinant

method

)(.)(.)(.)(.

)(0)(0

)(.)(.)(.)(.

0)(0)(

2

'

2

'

'

2

'

2

aKVa

VaKV

juaJV

au

VuaJV

u

jaKVuaJV

aKVj

aKVa

VuaJV

u

juaJV

au

V

aKVuaJV

=0

Evaluation of this determinant gives the Eigen equation .

)12.(..................................................)(

)('&

)(.

)('

)11......(`....................11

)((

2

22

2

2

2

2

1

aKV

aKVKV

uaJVu

uaJVJV

where

ua

VKVKJVKKVJV

1.9.MODES IN STEP INDEX FIBER:

To describe the modes we should examine the behavior of J type Besselfunction. Bessel function is the harmonic function & its having

oscillatory behavior of JV.

M roots for a given V value. The corresponding modes are TEvm&TMvm, EHvm &HEvm. These are designated by the roots of vm. For a


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dielectric waveguide all modes are hybrid modes except those for which

v=0.

At v=0, substitute in equation 11.( 0) 02202100 KKJKKJ

From this

( 0)00 KJ (or) 0022021 KKJK

Using regression formula in equation 12 substitute v=0 & JV ischanged in terms of J

Therefore,

0)(

)(

)(

)(

0

1

0

1 aK

aK

uauJ

uaJ

Cutoff condition:

v Mode Cutoff condition

0

1

>=2

TE0m,TM0m,

HE1m, HM1m,

EHvm,

0J (ua)=0

0)(1 uaJ

JV(ua)=0

At cutoff condition, the mode is not longer bound to core of fiber. Thenormalized propagation constant is

2

2

2

1

2

2

2

nn

nK

b

The normalized value )(2 NAav

. It determines how many modes a

fiber can support. HE11 mode has not cutoff and stop only core diameter

=0. By choosing appropriately a, n1, n2 value v


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In a step-index the difference between the refractive index of core&cladding is very small that is


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)(

)(

)(

)(. 11

aK

aK

uaJ

uaJu

j

j

j

j

It shows that within the weakly guiding approximation all modescharacterized by common set of j & m satisfy the same characteristic

equation. This means that these modes are degenerate.

Parameters:

1. All linearly polarized modes are degenerate modes.2. If an HEv+1,m is degenerate with an EHv-1,m mode and then combination

of these modes will constitute a guided mode of the fiber.

3. Degenerate modes are also called as linearly polarized modes.4. i. Each LPoMmode is derived from HE1Mmode.

ii.Each LP1M mode comes from TEoM , TMoM , HE2M ,modes.

iii. LPVM , mode(V>=2 )is derived from HEv+1,m & EHv-1,m .

Merits:

1. It provides an ability to visualize a mode quickly and easily.2. It is used to analysize the transmission characteristics of optical fibers.

Demerits:

1. If is not very much less than 1, LP mode has no sense.2. It cant form linearly polarized mode.

1.11.SINGLE MODE FIBER:

For single mode fiber, core diameter of an operating wavelength is 8-12m & its having small index differences between the core & cladding

with V=2.4.

The core cladding difference varies between 0.2 to 1 percent.1.11.1.Mode field diameter:

The fundamental parameter of single mode fiber is mode fielddiameter(MFD) & it can be determined from the mode field distributionof LP01 mode.

The field is Gaussian distribution.


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Figure:1.11.1.Distribution of light in SMF above its cutoff

wavelength

Its distance betweene

1to

2

1

e. therefore MFD=2W0.

The Gaussian distribution is )/exp()( 2020 wrErE rradius, 0Efield at zero radius. 0w width of electric

field distribution.

The MFD width 2 0w of LP01 mode can be defined2

1

0

2

0

23

0

)(

)(.2

22

drrrE

drrEr

W

1.11.2. PROPAGATION MODES IN SMF:

There are 2 independent degenerate modes arei. Horizontal polarization modes.ii. Vertical polarization modes.

These modes are very similar but their polarization planes are orthogonal.

In general , the electric field of light propagating along the fiber is alinear superposition of these two polarization modes & depends on

polarization of light at launching point into the fiber.

In ideal fibers with perfect rotational symmetry, the modes aredegenerate with equal propagation constants yx KK .

Due to fiber imperfectionsyx

KK . The modes propagate with

different phase velocities & difference between their effective indices

is called fiber birefringence.

xyf nnB

The fiber birefringence is defined as


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2

)(

0

0

K

where

nnK xy

Two modes will beat at 2 radius & length over which this beatingoccurs in the fiber is called beat length.

2pL

1.12.GRADED INDEX FIBER:

In Graded index fiber, the core refractive index decreases continuoslywith increasing radial distance r from the fiber axis, but refractive index

for cladding is constant.

The refractive index variation in core is the power law relationship thatis

arfora

rnrn

0.....21)(

21

1

aforrnnn 2121

1 )1()21(

rradial distance, 1n refractive index of core, refractive indexdifference

2n refractive index of cladding , core radius defines the shape of index profile. The index difference for the

graded index fiber is

=1

21

n

nn

For = infinite, n(r)= 1n

Determining NA for GIF is more complex than for SIF. Light incidenton fiber core at position r, will propagate as guide mode only. NA at

that point is defined as

NA(r)= arfor

arforarNAnrn

......................................................0

......1)0()( 2

12

2

2

Where the axial NA is defined as

NA(0)= 21

2

2

2 )0( nn


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2121

2

2

2

1 nnn

NA decreases from NA(0) to zero as r moves from fiber axis to corecladding boundary.

The number of bounded or guided modes in GIF is

)2(....................)2(.

:

)1........(.2

21

.1

2

1

KanV

sub

KanM

Sub :equation 2 in 1

2.

2

2VM

For aparabolic refractive index profile core fiber. Sub =2

4

2VM

UNITII

SIGNAL DEGRADATION OPTICAL FIBERS

2.INTRODUCTION

Signal attenuation also known as fiber loss or signal loss is one of the most

important proprieties of an optical fiber because it largely determines the

maximum unamplified or repeaterless separation between txr and rxr.

2.1.ATTENUATION:

Attenuation of a light signal as it proaogates along a fiber is an

important consideration in design of optical of an optical communication

system, since it playes a major role in determining maximam txn distance

between txr and rxr .


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The basic three mechanisms are:

1. Absorption loss2. Scattering loss3. Radiation loss

Figure: 2.1.1.optical fiber attenuation as a function of wavelangth

Attenuation Units:

At origin Z=0 the parallel power is P(0) after the same distance Z, the

power is P(z).

)(

)0(10)/(

.)(

)0(1

)0()(

zp

pLog

zkmdb

f icientuationcoeff iberatten

neperszp

pLog

z

ePZP

p

p

p

zp


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)343.4( 1 kmp

Pout(db)=10 Log .1

)(

mw

wpout

For First Window:

.4

850

km

dbLoss

nm

For Second Window:

m

dbloss

nm

5.0

1300

Third Window:

km

dbloss

nm

3.0

1550

2.2.Absorption Loss:

It is caused bu 3 different mechanisms.

1. Atomic defects in fiber material.2. Extrinsic absorption.3. Intrinsic absorption.

2.2.1.Atomic defects:

Radiation damages in internal structure fiber. The damage effects depends

on energy of ioniziny particles at rays.

It occurs due to imperfection of atomic structure. For eg. Missing molecules, high- density clusters of atom groups or exygen

defeats in the glass structure.

The total dose a material receives is expressed in rad(si ), which is measure

and relation absorbed in bulk silicon. //this unit is defined by 1 rad

(si)=0.01J/Kg

2.2.2. Extrinsic Absorption loss:


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Due to impurity atoms present in fiber material then this loss will occur Due to transition of metal ions. Impurity absorption occurs either bze of electronic transition between

energy levels or charge transition between ions.

Its also due to Hydroxyl ion. OH impurities result from ox hydrogen frame used for hydrolysis

reaction in fiber fabrication.

It can be reduced by reducing the water content in the fiber 1 to 10PPb(Parts/bullion).

2.2.3Intrinsic Absorption:

Associated with fiber material. It occurs from electronic absorption band in uv region and atomic

vibration band in infrared region.

UV Absorption:

It takes place when a pboton interval with electron in valence bandexcited to higher energy level.

\it decreases exponentially by increasing warelength , the UV edge ofabsorption is calculated by 0.

EE

uv eC C, 0E -

Emperial constant

E-photon energy.

IR Absorption

Above 1.2 m , wave guide loss in determine presence of hydroxyl ions.

An interaction between vibrating band and electro magnetic field opticalsignal results in a transfer of energy from field to the band, there by

giving rise to absorption.

22

48.4811

1081.7 SioforGeoeX xIR

material.

2.3.Scattering loss:

It occurs due to vibration in material density from compositionalfluctuations and from structural in homogeneities or defects during

fiber manufacturing.

Types:

1. Linear Scattering


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2. Non Linear Scattering2.3.1.Linear Scattering

Optical power is transferred from 1 mode to other mode linearly. It is more Predominant in multimode fibers because of compositionalfluctuation and it has higher dopant concentration

It can be classified into

1. Rayleigh Scattering.

2 . MIE Scattering

Rayleigh Scattering:

Rayleigh Scattering is the Phenomenon that Scatters light from the sunin the atmosphere. there by giving rise to blue sky.

It arise due to variation in refractive index that is compositionfluctuation.

It is dominant in UV region and less in IR region and it is inverselyproportional to 4

90% of Scattering loss occur due to Rayleigh Scattering in OFC.

For single component glass. the scattering loss is

128

4

3

3

8 mKTPn fcsoat

n R.I

P Photoetastic coefficient

c Isothermal compressibility

fT fictive temperature

For Multicomponent

nentglasscompoionofiionflutuatconcentratc

p

cn

n

rn

th

i

m

i

icn

i

nflactuatiodensity

)()(

)(3

8

2

1

22

2

22

22

4

3

2

Fictive temperature:Temperature at which the glass reach to state of thermo equality.

MIE:

It arises due to structural inhomogenetis of fiber. It occurs in forward direction only. It is minimized by


28/98

28

1. Proper coaling2. Check the quality of fiber (detect free method )3. Increasing the wave length4. Decreasing R.I value.

2.3.2.Non- linear Scattering:

It occurs at higher energy levels. Frequency shift is associated with thisloss. R.I of core depends upon optical signal intensity.

It is divided into1. SBS(Stimulated Brilliant Seattering )2. SRS(StimulatedRomans Seattering).

SBS:

It is defined as modulation of light signal through thermal molecularvibration within the fiber.

The scattered light contains USB and LSB with incident light frequency. The incident Photon having nonlinear interaction between vibrational

energy or phonon as well as scattered light or photons.

The scattered light is found to be frequency modulator by thermalenergy.

Frequency shift and strength of scattering signal vary as a function ofscattering angle (angle between scattered ray and cladding region).

Frequency shift is maximum in backward direction and forwarddirection is zero.

widthsourceband

changein

waltsdXP dbB

.104.4 223

SRS:

Scattered light consisting of high frequence phonon and a scatrteredphoton.

Scatters occurs in forward and backward direction. Light signal is Predominant in forward direction . Threshold opticalpower is 3 times greater than

SBS.

wattesdXP dbR 22109.5

It is minimized by threshold optical power is launched in a fiber beforeSBS Occur.


29/98

29

2.4.BENDING LOSS;

Bending loss and core and cladding loss under tadiating loss twotypes of bends are;

Macroscopic bends; Fiber bends at corner having radius of curratureis large com[pared to fiber diameter.

Microscopic bends: that can arise when the fibers are incorporatedinto cables.

Figure:2.4.1.A compressible jacket extruded over a fiber reduces microbending

resulting from external forces

Macro:

Large curvature radiation loss is called macro bending loss. For slightbend the loss is small. As the radius of curvature decreases the loss increase

exponentially until at a certain critical becomes observable.

When a fiber is bend at critical distance cx from the center of fiber thefield tail an the far side of centre of curvature must move faster to keep up

with the field in the core for lower order fiber mode. Since this is not

possible the optical energy in the field tail beyond cx Radiates away.

The amount of optimal radiation from a bend fiber depends on thefield strength at cx on the radius of curvature R

Thus the total number of modes that can be supported by curved fiberis less than straight fiber


30/98

30

The effective number of modes effN that are guided by curvedmultimode fiber is expressed by

32

22

32

2

21

KRnR

aNNeff

N Total number of modes in straight fiber

2

12

KaAN n

Micro:

An increase in attenuation results from micro bending because the fibercurvature causes repetitive coupling of energy between guided modes

and leaky modes in the fiber.

Micro bending loss is minimized by extending a compressible cover isthe fiber.

When the external forces are applied to this configuration, the cover willbe deformed but the fiber will tend to stay relatively straight.

For MMGIF having a core radius a outer radius b & index diff themicro bending loss M of a covered fiber is reduced from that of

uncovered fiber by the factor is 2421)(

Ej

E

a

bF

f

M

fE , Ej are youngs moduli of cover & fiber

2.5.Core & Cladding Loss

Core and cladding bare different indices of refraction and havingdifferent attenuation coefficients 21&

For SIF , the loss for the mode of order (V,M )P

P

P

P cladcorevm 21

P

Pclad = 1 -P

Pcore

P

P

P

P cladcladvm 21 1


31/98

31

=P

Pclad112

For GIF both the Attenuation co efficient & model power tend to befunctions of radial coordinate. At a distance r from the core axis the loss

if 222

22

121 )(

)()(

nob

rnob

r

The complexity of multi mode ware guide has presented by correlation

with the model

0

0

rdrrp

drrpr

gi

2.6.SIGNAL DISTORTION IN OPTICAL WAVE GUIDES

Dispersion of txed optical signal causes dispersion for both digital &analog txn along optical fibers.

An optical signal is distorted as it travels along a fiber. This distortion isdue to intra modal d dispersion and intermodal delay effects.

Dispersion means spreading of light pulse as it propagates through fiber. It introduces intersymbol interference (ISI) . It limits the information

carrying capacity of fiber

Dispersion:

Types are

i. Intermodal dispersion

ii. Intramodal dispersion

Intramodal dispersion are

i. Material (or) chromatic dispersion

ii. Wave guide dispersion

iii. Group velocity dispersion


32/98

32

Figure:2.6.1.Broadening and attenuation of two adjacent pulses as they

travel along a fiber

A light pulse will broaden as it travels along the fiber . This pulsebroadening will cause overlap with neighboring pulse.

At certain distance the pulse are not individually distinguished at thereceiver & error will occur.

Information capacity of an optical wave guide is usually specified byBandwidth Distance Product (BLP) IN MHZ-KM. As the length of optical cable increases, the bandwidth decrease in

proportion.

For S.I between distance produced is 20 MHZ.Km & for G.I is 2.5MHZ.Km.

The ICC can be determined by short light pulses propagating along thefiber.

2.6.1.PHASE VELOCITY

As a monochromatic light wares propagates along a fiber in Z-direction. This points of constant phase travel at a velocity.

pV ,

- angular velocity,

- propagation factor

)(2

xyo

pnnk

fV

If the propagation factor in an infinite medium of R.In

cnn

11

2


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33

11

nc

cn

Vp

2.6.2.GROUP VELOCITY

Group of waves with slightly different frequency are propagating alongthe fiber. This elocity is denoted as group velocity

.,1

1

11

1

1

1

1

1

1

g

g

gg

g

g

N

CV

IgroupRNNc

nnc

n

cn

c

cn

V

V


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34

d

dnnNg

d

dnnNg

d

d

d

dnnNg

d

dnnNg

d

d

dc

dcd

c

c

cnn

11

11

11

11

2

11

1

12

12

2

2

2

2.6.3.GROUP DELAY

Group of waves propagate along the fiber with different velocity so itproduces the time delay or group at the rxr side.

.2

12

2

11

2

2

cL

dc

c

cVL

g

g

g

Each modes tares a different amount of time to travel a certain distancedue to this pulse spreading will occur at rxr side.


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35

If the spectrum width of optical source is the delay difference per unitlength is represented by

d

dg

For spectrum components which are X apart and which lie in the2

above and below the central wave length 0 The total delay difference over a distance L

d

d

d

d

c

L

d

d

cL

d

d

d

d g

22

2

2

22

2

Total delay difference in terms of

2

2

2

2

2

d

dwhere

d

dL

d

dL

d

d

d

d g

Group velocity dispersion parameter

.. 2L

The spectrum width of an optical source is characterized by itsRMS value than the puise spreading is approximated by RMS pulse

width is presented by g .

d

d

d

d

c

L

d

dgg

2

2 2

22

The dispersion factor D is


36/98

36

22

2

2

2

2

2

2

2

1

1

11

1

cD

c

d

d

c

d

dD

d

d

d

d

d

d

d

d

d

d

Vd

dD

dbydivideandmultiple

Vd

d

KVd

d

L

d

d

LD

g

g

g

g

It defines the pulse spread spectrum as a function of ware length and it ismeasured in picoseconds / nm .km. The total dispersion = material

dispersion + ware length dispersion

gDmatD=D .

It is calculated by one type of dispersion is in the absence of other.2.7.MATERIAL DISPERSION

It occurs due to variation in R.I as a function of wave length.

The group velocity gV of a mode is a function of R.I the various spectralcomponents of a given mode will travel at different speeds, depending

on the wave length.

To calculate the material dispersion, we consider a plane wavepropagating in an infinitely extended dielectric medium that bas R.I n

)( equal to that of fiber core.


37/98

37

Propagation constant )(2

n

The group deals for material dispersion is

d

dnn

c

Ld

dnn

c

L

d

dnn

c

L

nd

d

c

L

nd

d

c

L

valuesub

d

d

c

L

VL

mat

mat

g

mat

)()(

)()(

)(1)(

1

)(1

)(2

2

2

1

2

2

2

2

2

For a source of spectrum width X and w, L, the VMS pulsebreading due to material dispersion m is given by

.)(1

)(

)()(

)(

)(

)(

)()()(

)(.)(

2

2

2

2

2

2

2

2

2

2

d

d

cD

DLd

d

c

L

DL

alsoand

d

d

c

L

d

d

c

L

d

d

d

d

d

d

c

L

ddXn

cL

dd

d

d

nmat

matn

matmat

nmat

n

nnn

n

mat

mat


38/98

38

Material dispersion can be reduced either by choosing sources withnarrower spectral output widths orm by operating at longer wave

lengths.

2.8.WAVE GUIDE DISPERSION

Its also intramodal dispersion. Due to variation in group velocitywith wavelength for a particular mode , it will occur.

The effect of wave guide dispersion on pulse spreading can beapproximated by assuming that R.I of material is independent of

wave length L.

Group delay can be expressed in terms of normalize propagationconstant b is

2

2

2

1

2

22

2

nn

nkb

For small values of index difference1

21

n

nnD

21

21

21

221

221

221

221

21

2

,1

)(

)(

)(

)(

nkbnk

nn

nbnk

nnnbk

knnnbk

knnnbk

nk

nnb

nn

nkb


39/98

39

Group delay for wave guide dispersion is

.2

.2

)(.

.

.

2

22

21

nKaV

NAKaNAa

V

isfrequencynormalisedThe

dk

bkdnnC

L

nkbnkdk

d

C

L

dk

d

C

LG

For field fiber,

dk

bkdnn

C

LkV

g

)(. 22

First term constant term

Second term group delay due to wave guide dispersion.

The factordv

bvd )( can be expressed by

)()(

)(21)( 2

uaJuaJ

uaJb

dv

bvd

vavH

v

where

radiusfibera

kfactorcoreu

2212

2.9.SIGNAL DISTENTION IN SMF

The pulse spread g occurs over a distance nb of wave length is

obtained from the derivative of group delay with respect to wave length


40/98

40

2

2

2

2

2

2

2

2

2

2

2

2

22

2

)(.)(

)(

.)(

.

)(.

)(.0

)(.

.2

.2

.

&

dvvbdv

cDD

equationbothEquating

DL

v

dv

bvdDn

c

L

dv

bvdDn

c

L

dv

bvdDnc

L

dv

bvdDnn

c

L

d

d

dv

dI

v

d

dv

NAa

d

dv

NAa

d

d

d

dv

d

dv

dv

d

dvbydividemultiply

d

d

ng

gg

g

g

g

g

g

g

Consider the factor (ua) for the lowest order mode in the normalized property

constant

2

41

4

1

41

21

v

uab

vua

Sub (ua) in b

2

41

441

21

vb


41/98


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42

2.11.INTERMODAL DISPERSION:

In multimode fiber, different modes arrive at the receiver at differentthings because of vibration in path & group velocity. It makes pulse

broadening in receiver side. This pulse broadening is called Intermodal

Dispersion.

Figure:2.11.1.Meridional ray optics representation of the propagation

mechanism in an ideal step-index optical waveguide

The time delay at receiver side is

cn

Ln

nc

nn

L

T

nnwhere

nc

L

V

DT

nc

L

V

DT

where

TTT

c

D

2

2

1

1

1

2

max

1

2

1

max

1

min

minmax

sincos,

cos

Therefore minmax TTTD

.

1

1

2

211

2

11

1

2

2

1

c

LnT

n

nn

c

Ln

n

n

c

Lnc

Ln

cn

Ln

D


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43

2.12.MODE COUPLING:

Two modes are coupled with each other is called mode coupling. Atbending or joining, mode coupling will occur.

Due to bending, mode coupling gives rise to conversion of energy fromlower order modes to higher order modes and form the radiated modes.

Due to coupling, power from this lower mode transfer to faster mode &tends to propagate at moderate speed.

It reduces the group delay & intermodal dispersion in transmission link.Group delay for mode coupling is

cn

NAL

2

2

2

)(.

After coupling length Lc, the pulse distortion will change from L to2

1

)( LLc dependence value.

Coupling length Lc is the critical length of fiber at which equilibrium

mode power distribution is reached. For practical Lc=1km.

Due to mode coupling there is an additional loss called coupling lossdenoted byh unit is db/km.

The improvement by pulse spreading is caused by mode coupling overthe distance

Z< Lc, .It is denoted to excess loss L.

chZ c

2

0

0

pulse width increase in absence of mode coupling.

c pulse broadening in presence of strong mode coupling.

hZexcess attenuation.

cdepends upon the fiber profile shape & mode coupling strength

for practical purpose.

For strong mode coupling bandwidth of signal is reduced.2.13.DESIGN OPTIMIZATION OF SM FIBER:

The attributes of SMF are long time, very low attenuation, high qualitysignal transfer due to absence of modal noise.

Largest bandwidth-distance produce. The basis design optimization includes cutoff wavelength, dispersion,

mode field diameter & bending loss.


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44

SMF are used for long distance telecommunication network at 1320nmdispersion is low & attenuation is high & at 1550nm dispersion is high

& attenuation is low.

For long distance communication we should prefer D & A both shouldbe low.

To achieve this, adjust the basic parameters of fiber to zero dispersionfor longer wavelength.

For suitable design of refractive index profile we can get zerodispersion. To achieve zero dispersion to make waveguide

dispersion=material dispersion.

Figure:2.13.1.Typical waveguide dispersions and the common material

dispersion of three different fiber designs & resultant total dispersions


45/98

45

2.13.1.R.I.PROFILE DESIGN:

There are 4 ways of shaping the SMFs.i. 1300nm optimized fiber.ii. Dispersion shifted fiber.iii. Dispersion flattened fiber.iv. Large effective core area fibers.

1.1300nm optimized fiber.

In matched cladding, R.I. of cladding & core region are uniform andmode field diameter MFD=9.5m.

In depressed cladding, R.I. of cladding portion next to core region is lessthan the outer region. MFD=9m..

This is to optimize the waveguide dispersion to get zero dispersion at1300nm.

2. Dispersion Shifted fiber.

At 1550nm, we have to increase the waveguide dispersion=materialdispersion, then we can get zero dispersion at that point.

Waveguide dispersion is function of core radius & value & shape ofrefractive index profile. Adjust the above factor we can get the zero

dispersion at 1550nm.

R.I. profile is shaped with steeper increasing R.I. of core with small coreradius & with large difference R.I. of core & cladding.

For triangular, R.I. profile is designed to get the zero dispersion at1550nm.

3. Dispersion flattened fiber.

The dispersion flattened fiber have minimum dispersion over a range of from 1.3m to 1.55m such that zero dispersion points lies at 1.3mto 1.55m. This fiber only used for WDM network.

R.I. profile is slightly modify from dispersion shifted fiber to get zerodispersion for wide range.

4. Large effective core area fiber.

For distance communication a SMF with large effective core area shouldbe design.

It is used to reduce the system capacity of the fiber & also reduce thenon-linearity in the fiber. Standard SMF have effective core about

55m2. A profile having values greater than 100m

2.


46/98

46

2.13.4.Dispersion Compensating fiber:

For dispersion shifted fiber the cost is high. So we have to usecompensating fiber for same application.

It have negative waveguide dispersion at 1.55m. In optical networkevery 100km replace the 1km length of fiber by 1km conventional

fiber. So we can achieve minimum loss & zero dispersion.

2.13.5.Cutoff wavelength:

The normalized frequency,

405.2.2

.2

VNAa

At

NAa

V

c

Cutoff wavelength of SMF is minimum wavelength from thetransmission takes place. Above cutoff wavelength all the wavelength

can be transmitted. If 405.2V only LP01, HE11 mode is propagated

along the fiber. So generally for SIMMF,

SS

MSV

,

,405.2

Cutoff wavelength of MMF is defined as wavelength at which itbehaves as a SMF.2.14.PULSE BROADENING IN GIF:

In GIF, core R.I. is different according to the radial distance from thecentre of axis. In MMF, due to path difference intermodal dispersion

occurs. But this dispersion is reduced by GIF.

Group delay for GIF:

cLn

g8

2

1

Relationship between GIF, SIF.

sg x8

2


47/98

47

Improvement factor for GIF for theoretical way is 1000, but due todifferent R.I. profile shape we cannot achieve this. The RMS pulse

broadening of GIF for parabolic profile is

sgD

.

s pulse broadening in SIF

g pulse broadening in GIF

Dconstant value & lies between 4 to 10.\

If D=0 & =1, then

sg 1.0

For GIF, core R.I. is optimum then loss is

5

122

opt

g is expressed in terms of 1n , L thenc

Lns

32

1

Therefore,

c

Ln

c

Ln

c

Ln

D

g

g

320

32.

10

32.

21

1

1

Profile Dispersion:

If wavelength propagating along optical fiber cable changed, alpha

value is also changed which leads to pulse broadening.


48/98

48

UNIT- III

OPTICAL SOURCES

3.CHARACTERISTICS OF LIGHT:

High intensity,wavelength, narrow spectrum, less expensive, durable,

flexible, modulation speed should be high.

LEDs:

LEDs are used in optical systems that require bit rates less thanapproximately 100-200 mb/s. It is mostly coupled with multimode fiber.

LEDs require less complex drive circuitry than laser diode since nothermal or optical stabilization circuits are needed.

Principles of Operation:

LEDs must have.

1.High radiance output or brightness

It is a measure of optical power radiated into a unit solid angle per

unit area of emitting surface. Its unit is watts. High radiances are required tocouple sufficiently high optical power levels into a fiber.

2. Fast emission response time:

It is a time delay between the application of a current pulse and onset

of optical emission. This time delay is the factor limiting BW with which the

source can be modulated directly by varying the injected current.

Quantum efficiency:

It is related to fraction of injected electron hole pairs that recombine

radiately.

3.1.LEDS STRUCTURE:

LEDs should provide high radiance and high quantum efficiency, itmust achieve carrier and optical confinement.

Carrier confinement is used to achieve a high level of radiativerecombination in the active region of the device, which yields a highquantum efficiency.

Optical confinement is used for preventing absorption of emittedradiation by material surrounding the pn junction.

Heterojunction structures are used to achieve optical and carrierconfinement.

Heterojunction consists of two adjoining semiconductor materials withdifferent bandgap energies. It is also known as double hetero structure


49/98


50/98

50

A well is etched in a substrate to avoid the heavy absorption of emittedradiation and the fiber is connected to accept the emitted light.

The circular active area in surface emitters is 50m in diameter and upto 2.5m thick. The emission pattern is isotropic with 120 half power

beam width.

Isotropic pattern from a surface emitter is called lambertian pattern.

The source is equally bright when viewed from any direction but powerdiminishes as cos . Where is the angle b/w viewing direction &normal to the surface.

Power is exactly 50 % down of its peak when =600. so that the total half power beam width is 1200

3.1.2.EDGE EMITTING LED.

Figure:3.1.2.Edge-emitting doubleheterojunction LED

EELEDs emit a more directional light pattern than the surface emittingLEDs.

In order to reduce the losses caused by absorption in active layer and tomake the beam more directional the light is collected from the edge of

LED. So it is called EELED.

The EELED has transparent guiding layers with very thin active layer of50 to 100 m in order that the light produced in active layer spreads into


51/98

51

the transparent guiding layers reducing self absorption in the active

layer.

The guiding layers have R.I lower than action region but higher thanouter surrounding material.

This structure forms a waveguide channel that directs the opticalradiation towards the fiber core.

3.2.LASER diodes.

Light amplification by stimulated emission of radiation. For optical fiber systems the laser sources used are almost exclusively

are semiconductor laser diodes. The o/p radiation is highly

monochromatic and light beam is very directional.

Semiconductor laser diodes are performed over LED for the OFCsystems requiring BW > 200 MHZ.

Laser diodes have response time is < 1ns. Optical B.W is 2nm or less.High coupling efficiency.

Principles of Operation:

1. Photon absorption2. Spontaneous emission3. Stimulated emission.

Photon absorption:

When photon with energy E2-E1 is incident on the atom. The atom isinitially in E1. The atom excited into higher energy state e2 through theabsorption of photon. This process is referred to as stimulated

absorption. These dimensions are commonly referred to as longitudinal, lateral and

dimensions of the cavity respectively.

DFB Laser:

In DFB Laser, lasing action is obtained by periodic variations of R.I,which are incorporated into the multiplayer structure along the length of

diode, here optical fiber is not required. The optical radiation within the resonance cavity of laser diode sets up

a pattern of electric and magnetic field lines called modes of cavity. The modes are seperated into two independent sets of TE and TM

modes. Each set of modes can be described in terms of longitudinal,

lateral And traverse modes.

Longitudinal modes.

It is related to length L of cavity and determines the principle structureof frequency of emitted radiation.

Since L is much layer then the lasing W.L of appro 1 um, manylongitudinal modes can exit.

Spontaneous emission:

An atom returns to lower energy state in random manner.


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52

Stimulated emission:

When a photon having equal energy to the difference b/w the two statesinteracts with the atom causing it to the lower state with the creation of

second photon.

Population inversion:

Most photons incident on the system will be absorbed so the stimulatedemission is essentially negligible. Stimulated emission will exceed

absorption onlf if the population of excited states is greater than that of

ground state. This condition is known as population inversion. The

population inversion can be achieved by various pumping techniques.

Fabry- Perot resonator cavity

Lasers are oscillators operations at optical frequency. The oscillator isformed by resonant cavity providing a selective f/b. The cavity is

normally used is fabry-perot resonator.

This cavity is much smaller,250-500 m long, 5.15 m wide, and 0.1-0.2m thick.

Lateral modes.

It lies in the plane of pn junction. These modes depend on the side wallpreparation and width of cavity and determine the shape of lateral

profile of laser beam.

Transverse modes:

It is associated with electromagnetic field and bean profile in thedirection perpendicular to the plane of pn junction.

These modes determine the laser characteristic such as the radiationpattern and threshold current density i.e, the point at which lasing starts.

3.2.1.Lasing conditions and resonant frequency.

The electromagnetic wave propagating in the longitudinal direction is expressed

as

E(z,t)= )()( ZtjeZI

I(z)optical field intensity

- optical radian frequency &

BPropagation constant

Lasing is the condition at which light amplification becomes possiblein layer diode. The condition for lasing is that population inversion be

achieved.


53/98

53

The stimulated emission rate for particular mode is proportional tointensity of radiation in that mode.

The radiation intensity at a photon energy h varies exponentiallywith the distance Z that it transverse along the lasing cavity according to

the relationship.

I(z)=I(0) )()(exp hhg

effective absorption coefficient of material in optical path.

optical field confinement factor or fraction of optical power in activelayer.

ggain coefficient, Zdistance traverses along the lasing cavity,

hphoton energy.

Lasing occurs when the gain of guided modes exceeds above the opticalloss during one round trip through the cavity i.e,z=2L.

If R1,R2 are reflectivities of 2 ends of mirror during 1 round trip thenFresnel reflection coefficient is given by

R=

2

21

21

_

nn

nn

The lasing condition becomes I(2L) is

LRRILL 2exp)0()2( 21 )()( hhg

At threshold condition,For amplitude I(2L)=I(0)

For phase 1 Lje

The condition to reach the lasing threshold is the point at which theoptical gain is equal to total loss t in the cavity.

Total loss present in layer cavity.

endtth

th

th

RRLg

g

g

21

1ln21

end mirror loss in lasing cavity.

For lasing action, the gain g thg . i.e.,threshold gain.


54/98

54

For strong carrier confinement the threshold current density for stimulated

emission Jthcan be related with lasing threshold gain is given by

thth gJ

Figure:3.2.1.Relationship between optical output power & laser diode drive

currents

3.2.2.Laser diode Rate equation:

The relationship b/w optical power & diode drive current can be foundby rate equation.

Total carrier population=carrier injection + Spontaneous recombn +

stimulated emission

Total active region with a carrier confinement region of depth d rateequation is given by

No of photons():

ph

spRCndt

d

= stimulated emission +spontaneous emission+photon loss


55/98

55

No.0f electrons(n):

Cnn

qd

J

dt

dn

sp

=Injection + spontaneous recombination + Stimulated emission

where,

ccoefficient describing the strength of optical absorption &

emission interactions

Rsprate of spontaneous emission into lasing diode

ph photon lifetime

sp spontaneous recombn life time

Jinjection current density

For steady state condition ,0&0 dt

dn

dt

d when n & have non

zero values. Assume Rsp is negligible and nothing thatdt

dmust be

positive when is small. At threshold point sthnn & .therefore,

01

0

01

)2......(....................0

)1....(....................0

ph

ths

ph

ths

sth

sp

th

ph

s

spsth

Cnor

Cn

Cnn

qd

J

RCn

is always positive, so 01 ph

thCn

& s=0.


56/98

56

sp

thth

sp

th

n

qd

J

thresholdAt

n

qd

J

n must exceed threshold value nth then only we can get is positive.Using equation 1 & 2.find the sIn equation 1

ph

sspsth RCn

From equation 2

sthth Cn

qd

J

qd

J0

Substitute thCn :

phspthph

s

sp

th

ph

s

ph

s

sp

th

RJJ

qd

Rqd

JJ

Rqd

J

qd

J

.

0

3.2.3External quantum efficiency:

It is defined as number of photons emitted per radiative electron holepair recombination above threshold.

th

thiex t

g

g

For high quality laser

i =(0.6-0.7)%

ex t =(30-40)%

3.3.MODULATION OF LASER DIODE:

The process of imposing information on a light stream is called

modulation. There are 2 types of modulation.


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57

1.Analog Modulation:

It is carried out when the drive current above the threshold current isdirectly proportional to information signal & there should be linear withi/p and o/p.

2. Digital modulation:

It is affected by photon and carrier lifetime. The photon life time isth

phgC

n

.

Threshold current Ithis the minimum value of direct to start the lasingaction. so in carrier life time

thBp

p

dIII

It

ln.

Where,

IBbias current, I

P=pulse current.

The total current flow in laser cavity isI= IP+ IB

Therefore the frequency of oscillation is

21

21

1..

1.

2

1

thphspI

If

3.3.1.TEMPERATURE EFFECTS IN LASER DIODE:

Threshold current I th(T) of laser diodes is temperature dependent. Ith(T)increases with temperatures in all types of semiconductor laser becauseof various complex temperature dependent factors.

Empirical expression that shows the relationship between I th(T) &temperature is given as

0)( T

T

Zth eITI

T0measure of relative temperature insensitivity.

IZconstant, Tdevice absolute temperature.

Experimental values of T0for 1300nm InGaAsp lasers are typically 60-80k(333-353

0c)

For GaAlAs T0=1200c to 1650c For quantum well laser T0=4370c

Using temperature compensation circuit we get the constant laser o/p.


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3.4.POWER LAUNCHING & COUPLING:

Lensing schemes for coupling improvement.

If the source emitting area is larger than the fiber core area thenmaximum optical power is coupled into the fiber. This is a result offundamental energy & radiance conservation principles. It is also known

as law of brightness. If the emitting area of source is smaller than the core area, miniature

lens may be placed between the source and fiber to improve the powercoupling efficiency.

The function of micro lens is to magnify the emitting area of the sourceto match exactly the core area of fiber end face.

If the emitting area is increased by magnification factorM then thesolid angle within which optical power is coupled to the fiber from LEDsource is also increased by same factor.

General possible lensing schemes are

1. Rounded- end fiber:The fiber itself rounded known as rounded end fiber. Here whole radiation from

LED emitting area is incident falls on the fiber end surface.

2.Non imaging microsphere:

A small glass sphere is contact with both fiber and source.

3. Imaging sphere:

A large spherical lens is used to image the source on the core area of teh source.

4. Cylindrical sphere:

Cylindrical lenses are generally formed from a short section of fiber.

5. Taper- ended fiber.

If the width of taper ended fiber is equal to width of emitting surface ofLED, the maximum coupling efficiency is achieved.

An the above techniques can improve the source to fiber couplingefficiency, they also create additional complexities.

One problem is that tha lens size is similar to source & fiber coredimensions which introduces fabrication and bandling difficulties.

Non Imaging Micro sphere:

Non imaging micro sphere is one of the most efficiency lensing methods.


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The spherical lens has R.I is 2.0 and outer medium is 1.0 and emittingarea is circular.

To collimate the output from LED, the emitting surface should belocated at focal point of lens,the focal point can be found from Gaussian

lens formula

r

nn

q

n

s

n ''

where

S Object distance,Q Image distance

S&Q are measured from lens surface

nR.I of lens

nR.I of outside medium

rradius of curvature if lens surface.

To find the focal point for right hand surface of lens is by some sign

conversions are :

1.Light travels from left to right

2.object distances are measured as +ve to left of vertex and -ve to the

right.

3.Images distances are measured as +ve to right vertex andve to the

left.

4.All convex surfaces encountered by light have +ve radius of curvature

and concave surfaces have -ve radius of curvature.

When s is measured from point B.At q= , r=-RL,n=2.0 & n=1.0.

L

L

Rs

Rs

r

nn

q

n

s

n

2

0.10

0.2

''

Thus the focal point is located in the lens surface at point A. If LED is placed to lens surface,thus results in magnification M of

emitting area .2

2

2

s

L

s

L

r

R

r

RM


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With the lens the optical power PLthat can be coupled into full apertureangle 2 is given by

22

sin.

s

LsL

r

RPP

Where

Pstotal output power from LED without lens.

The maximum coupling efficiency n max is determined by fiber size

NAa

rfor

NAa

rfor

NAr

a

s

s

s

1

)(

2

max

When the radius of emitting area is larger than the fiber radius noimprovement in coupling efficiency is efficiency is possible with a lens.3.5.SOURCE TO FIBER POWER LAUNCHING:

A measure of amount of optical power emitted from a source that can be

coupled into fiber is called coupling efficiency.

s

F

P

P

FPpower coupled into the fiber

sPpower emitted from fiber.

Many source suppliers offer devices with short length of optical fiber(1m or Less) already attached in an optimum power couplingconfiguration .this selection of fiber is referred to as flylead.

3.5.1.Source output pattern:

To determine the optical power accepting capability of fiber the spatialradiation pattern of source must be known.

The spherical coordinate system characterized R,Q, with normal toemitting surface.

The radiance may be function of both & s&also vary from point topoint on emitting surface.

Surface emitting LED s are characterized by their lambertian outputpattern which means the source is equally bright when viewed from any

direction.

The power delivered at an angle measured relative to normal toemitting surface, varies as cos

The emission pattern for lambertial source is


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61

cos.),( 0BB

Where

0B radiance along the normal to radiating surface.

Edge emitting LEDs & laser diodes have more complex emissionpattern. These devices have radiances B(,00) & B(,900) in the planesparallel & normal to emitting junction plane of device.

LT BBB cos

cos

cos

sin

,(

1

0

2

0

2

T & L are transverse & lateral power distribution coefficients.

3.5.2.Power coupling calculations:

To calculate, the maximum optical power coupled into a fiber,considerthe symmetric source of brightness B(As,s) where As& sarethe area & solid emission angle of source.

The coupled power can be found using the relationship

drrsdddB

ABsddAP

rm

f

ss

Af

s

2

0

2

0

max0

00

sin),(

),(.

Here emitting surface is taking as circular. If source radius rs is less thancore radius a, then rm=rs& assume surface emitting LED of radius rslessthan a then

rs

rs

rs

drrsdNAB

drrsdB

drrsddBP

0

2

0

2

0

0

2

0

0

2

0

2

0

max0

0

0

0

..

..maxsin

sincos2

For SIF, the NA is independent of positions s& r on the fiber end.

2

10

22

2

0

22

2

)(,

nBr

NABrPP

s

sstepLED

Consider now the total optical power Psthat is emitted from source ofarea Asinto hemisphere.


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62

arforNAPr

astepP

arforNAPstepP

Br

dBr

ddBAP

ss

s

LED

ssLED

s

s

ss

2

2

2

0

22

2/

0

0

2

2

0

2/

0

)(,

)(,

sincos2

sin),(

For Graded Index Fiber:

a

rnP

a

rnBr

drrnrnBP

s

s

ss

rs

gradedLED

2

212

2212

)(2

2

1

210

22

0

2

2

2

0

2

,

3.5.3.Power launching versus wavelength:

The Optical power launched into fiber does not depend on thewavelength of the source but only on its brightness.

The no of modes that can propagate in GIF of core size a & indexprofile is

2

12

2

anM

twice as many modes propagate in a given fiber at 900nm than at 1300nm

The radiated power per mode,Ps/M ,from a source at a particularwavelength is given by radiance multiplied by the square of nominal

source wavelength.

2

0BM

Ps

Thus twice as much power is launched into a given mode at 1300 nmthan at 900nm.

Hence two identically sized sources operating at different wavelengthsbut having identical radiances will launch equal amounts of optical fiber

power into same fiber.


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3.6.LED COUPLING TO SMF.

LED were considered only for MMF systems. However, around 1985,researchers recognized that edge-emitting LEDs can launch sufficientoptical power into SMF for transmission at data rates up to 560 mb/s

over several kms.

Edge-emitting LEDs are used since they have a larger like o/p pattern inthe direction perpendicular to junction plane.

Coupling analyses of o/p from an edge emitting LED electromagnetictheory are interpreted which involves defining a NA for SMP.

The two cases for coupling isi. Direct coupling of an LED into SMF &ii. Coupling into SMF from multimode fly lead attached to LED.

Edge emitting LEDs have Gaussian near o/p profiles with ye2 full widthof approximately 0.9 & 22 m in the direction perpendicular

&parallel to junction plane.

The x(parallel) & y(perpendicular)directions, & let x & y be the x& y power transmissivities.

We can find the maximum LED to fiber coupling efficiency from therelation

yx

s

in

P

P

inPoptical power launched into the fiber, sPtotal source output power


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UNIT-IV

OPTICAL RECEIVERS

4.1.PIN PHOTODETECTOR:

Figure:4.1.1.Schematic representation of a pin photodiode circuit with an

applied reverse bias

The device consists of p and n regions separated by very lightlyn-doped intrinsic(i) region. A large reverse bias voltage is

applied across the device so that the intrinsic region is fully

depleted of carriers.

When an incident photon has an energy is greater than or equalto bandgap energy, the photon can give up its energy & excite anelectron from valence band to conduction band. This process

generates electron-hole pair is known as photocarriers.

Normally these carriers are generated mainly in depletion regionwhere most of the incident light is absorbed.


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The high electric field present in the depletion region causes thecarriers to separate & be collected across the reverse biased

junction.

This gives rise to current flow in every external circuit, with oneelectron flowing for every carrier pair generated. This current

flow is known as photocurrent.

The charge carriers move a distance Ln or Lp for electrons &holes. This distance is known as diffusion length.

The time it takes for an electron or hole to recombine is knownas carrier lifetime & is represented by n & p . The lifetime &diffusion lengths are related by

2121 & pppnnn DLDL

nD & pD electron & hole diffusion coefficients.

Optical radiation is absorbed in semiconductor materialaccording to exponential law.xsePxP )(01)(

)(s

absorption coefficient at which wavelength .

P0 incident optical power level.

P(x)optical power absorbed in a distance x.

The cutoff wavelength is expressed by)(

24.1)(

evEE

hcm

gg

c

The cutoff wavelength is about 1.06m for Si & 1.6m for Ge .

For longer wavelength, the photon energy is not sufficient to

excite on electron from valence to conduction band.

If the depletion region has a width w, then the total powerabsorbed in the distance w is

wsePwP 1)( 0 The primary photocurrent Ip resulting from power absorption is

given by

)1(10 fwp RePh

qI s

Where, fR reflectivity

two important characteristics of photo detector are

i. Quantum efficiency.

ii. Response speed.


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66

The quantum efficiency is the number of electronhole carrier pairsgenerated per incident photon of energy h & is given by

hP

q

Ip

0

The performance of photodiode is characterized by responsivity R. thisis related to quantum efficiency

h

q

P

IR

p

0

4.2.PHOTODETECTOR NOISE:

powernoiseAmplifierpowernoiseectorphoto

ntphotocurrefrompowersignal

N

S

det

To achieve high SNR

i. Quantum efficiency should be high to generate large signal power.

ii. Photodetector & amplifier noises should be kept as low .

4.2.1.NOISE SOURCES:

Fig:4.2.1.1.Photodetector receiver model Fig:4.2.1.2Equivalent

circuit

The photodiode has series resistance Rs, total capacitance Cd,&bias resistor RL.

The primary photocurrent ip(t) is generated when modulatedsignal optical power P9t) falls on the detector.

)()( tPh

qtiph


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67

For pin photodiode, the mean square signal current is

ianceistii ppinss var)(22

,

2

For Avalanche photodiode,

222

,

2

.)( Mtii pAPDss

Mavalanche multiplication factor.

< >ensemble average

The signal component 2pi > for sinusoid ally varying input signal of

modulation index m is

22

22.

2 ppp I

mi

The noise associated with photodiode that have no internal gain arei. Quantum noise or shot noise.

ii. Dark current noise.

iii. Bulk dark current

iv.Surface dark or surface leakage current noise.

1. Quantum noise.

It arises from statistical nature of production & collection of photo-electrons, when the optical signal is incident on a photodiode.

The quantum noise current has a mean square value in bandwidth Bwhich is proportional to average value of photocurrent Ip.

)(2 222

MFqIpBMI QQ

Where, F(M)noise figure arised with random nature of avalanche

process(for pin P.D M=1)

F(M)=Mx

2. Dark current noise:

The current that flows through the bias circuit when no light is incidenton the diode is known as dark current.

3.Bulk dark current:

It is due to thermally generated electrons & holes in the pn junction ofP.D.The mean square of bulk current is given by

BMFMqII DDBDB ).(2 222


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DI primarly (unmultiplied)detector bulk dark current

4.Surface leakage current:

It is due to surface defects, cleanliness, bias voltage & surface area.

The mean square value

BqII LDSDS 222

The total mean square P.D. noise current is

BqIBMFMIIq

iiii

LDP

DSDBQ

DSDBQNN

2)(2 2

222

22222

Thermal noise(Amplifier noise):

The P.D. load resistor gives thermal noise

L

BTT

R

TKi

422

SNR:

L

BLDP

P

R

TKBqIBMFMIIq

MI

N

S

42)(2 2

22

For sinusoidally modulated signal with m=1 & F(M) approximat4ed by

Mxgives

)(

42

2

DP

L

BL

X

optIIXq

R

TKqI

M

4.3.DETECTOR RESPONSE TIME:

4.3.1.Depletion layer photocurrent:

The electron hole pairs generated due to absorption of incident photonswill be separated by reverse bias voltage induced by electric field.

Under steady-state conditions, the total current density throughdepletion layer is

diffdrtot JJJ

The drift current density is expressed as


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69

wPdr seqA

IJ

10

Aphotodiode area , 0 incident photon flux per unit area

Ah

RP f

100 fR surface reflectivity

The hole diffusion can be determined by one dimensional diffusion

equation

0)(02

2

xG

PP

x

PD

p

nnnp

pD hole diffusion co-efficient, nPhole concentration in n-type material

0nP equlilbrium hole density, p excess hole life time

G(x)electron-hole generation rate & is given by

xs sexG 0)( Therefore the diffusion current density is

P

Pn

w

Ps

Ps

diffL

DqPe

L

LqJ s 00

1

The total current density = diff dr JJ

P

Pn

Ps

w

P

Pn

Ps

w

Ps

w

Ps

w

Ps

P

Pn

w

Ps

Psw

P

Pn

w

Ps

Psw

tot

L

DqPL

eq

L

DqP

L

eLeLeLq

L

DqPe

L

Leq

L

DqPe

L

LqeqJ

s

sss

ss

ss

00

00

00

000

11

1

1

11

11

4.3.2.RESPONSE TIME:

The response time of photodiode are depends on

1. Transit time of photocarriers within the depletion region.


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70

2. Diffusion time of photocarriers outside the depletion region.

3. RC time constant of photodiode & its associated circuit.

1. TRANSIT TIME:

The response speed of photodiode is primarily limited by time taken by

photo generated carriers travel across the depletion region.

d

dv

wt

dv carrier drift velocity, wdepletion layer width

2. DIFFUSION TIME:

i. Rise time:

The rise time r is measured from 10 to 90% of leading edge of outputpulse.

ii. Fall time:

f is measured from 90 to 10% of falling edge of output pulse.

For fully depleted photodiodes the rise time r& fall time f are same. Approximately within 1ns, the fast carriers allow the device output rise

to 50% of its maximum value but slow carriers cause a relatively long

delay before the output reaches its maximum value.

3.RC TIME CONSTANT:

To achieve high quantum efficiency, the depletion layer width mustlarger than

s

1[inverse of absorption coefficient] so that most of light

will be absorbed.

Junction Capacitance:

If the width of depletion region is too thin, the junction capacitance willbecome high & is given by

w

AC sj

s permittivity of semiconductor material = sK0

sK semiconductor dielectric constant, Adiffusion layer area

The detector behaves like a simple RC low pass filter with pass band is

given by


71/98

71

TTCRB

2

1

TR combination of load & amplifier input resistance

TC sum of photodiode & amplifier capacitances.

4.3.3.AVALANCHE MULTIPLICATION NOISE:

Every photogenerated carriers donot undergo the same multiplicationand hence the avalanche process is statistical in nature.

Excess noise factor(F):

tionmultiplicaavalancheofsquare

tionmultiplicaavalancheofsquaremeanF

M

m

m

m

2

22

Mean square gain is greater than average gain i.e., if m denotes thestatiscally varying gain, then

> 2=M2 The noise in avalanche process is relatively high because it depends on

mean square gain

=M

2+x, 0


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72

)1(1

2

)1(1

)1(2

122

221

22111

22111

21111

1111

22

22

2

2

eff

e

effee

eff

e

effeffe

e

eff

e

effeffe

eff

e

eff

effe

e

e

eff

e

eff

eff

ee

e

e

eff

e

eff

eff

ee

e

ee

effe

e

effee

KM

KMF

KM

KKM

M

K

MKKM

KM

KKM

M

M

K

M

KK

MMM

M

K

M

KK

MMM

MMKM

MKMF

For injected holes

effheffeff

h

h

heffheffeffhh

h

heffheffeffhh

h

hheff

h

heffhh

KMKK

M

M

MKMKKMMM

MKMKKMMM

MMKM

MKMF

'

2

'

1

'2

1

'

2

'

1

'

12111

'

2

'

1

'

12111

211

'

111

1

1'

1

11

22

22

2

2


73/98

73

1"12"

1'

112

'

'

11

12

'

'

11

1

'

112

'

'

11

'

22

'

eff

h

effhh

effheff

h

effheff

h

effheffeff

h

heffheffeff

h

KM

KMF

KMK

M

KMK

M

KMKK

M

MKMKK

M

Where,

effK" =effK'1

The effective ionization rate ratios are

2

1

2

2

1

2

2

2

12

'

1

K

K

K

KK

KK

KKK

eff

eff

eff

It shows that Fe as a function of average electron gain Me for variousvalue of effective ionization rate ratio Keff.

If the ionization rates are equal , the excess noise is at its maximum thenFe = Me

Smaller value of Keff gives smaller excessive noise factor. Keff rangesbetween 0.015 to 0.035 for silicon & 0.6 to 1.0 for germanium.

For excess noise factor can be approximated asF=M

x

4.4.FUNDAMENTAL RECEIVER OPERATION

A decision circuit compares the solution in each time slot with a certainreference voltage known as threshold level.

(i) Received signal > Threshold Level = 1

(ii) Received signal < Threshold Level = 0


74/98


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75

This equation is approximated by empirical expression

10)( xMMF x

4.4.2.RECEIVER CONFIGURATION:

The rectangular digital pulse falls on P.D is found by)()( b

n

pn nTthbtP

nb Rec

Optical Full Units NOTES

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