dispersion in optical fiber

7/29/2019 dispersion in optical fiber

1/36

Dispersion in Optical Fiber

Unit 1.2


2/36

Dispersion in Optical Fibers

Dispersion: Any phenomenon in which the velocity of propagation of any

electromagnetic wave is wavelength dependent.

In communication, dispersion is used to describe any process by which anyelectromagnetic signal propagating in a physical medium is degradedbecause the various wave characteristics (i.e., frequencies) of the signalhave different propagation velocities within the physical medium.

Effects the information carrying capacity of the fiber

There are 3 dispersion types in the optical fibers, in general:

1- Inter-modal dispersion

2- Intra-modal dispersion: Material Dispersion andWaveguide Dispersion

3- Polarization-Mode Dispersion


3/36

Dispersion & Inter Symbol Interference (ISI)

Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

A measure of informationcapacity of an optical fiber for

digital transmission is usually

specified by the bandwidth

distance product

in GHz.km.

For multi-mode step index fiberthis quantity is about 20

MHz.km, for graded index fiber

is about 2.5 GHz.km & for single

mode fibers are higher than 10

GHz.km.

LBW

Dispersion limits the maximum pulse rate that can propagate in a fiber of a given length

Dispersion causes distortion in the pulse train in the fiber. Two neighboring pulses may

overlap after some distance and the receiver is no longer able to distinguish between the

two pulses.


4/36

Intermodal DispersionDue to modal delay, each mode travels a different distance in the fiber

Appears only in multimode fiber

Due to each mode having a different group velocity

Intra modal dispersionAlso called Chromatic Dispersion or group velocity dispersion

Pulse spreading in a single mode fiber

Due to the finite spectral width of the optical source, each wavelength travels with a different

velocity

Intra modal dispersion increases with the spectral width of the source. For LED source withcentral wavelength 850 nm the spectral width is of the order of 36 nm. LASER diodes have a

much smaller spectral width (1 to 2 nm)

Main causes of intra modal dispersion

1. Material dispersion: Due to the variation of the refractive index of the core material as a

function of wavelength. Pulse spreading occurs even if each wavelength follows the same

path2. Waveguide dispersion: Due to the different refractive index of the core and cladding. Part

of the optical power propagate in the cladding and therefore travels faster the that

propagating in the core because the refractive index of the cladding is less than that of the

core. Waveguide dispersion can be ignored in a multimode fiber but its effect is significant

in single mode fiber


5/36

Material and Waveguide Dispersion

t

Spread,

t0

Spectrum,

12o

Intensity Intensity Intensity

Cladding

CoreEmitter

Very short

light pulse

vg(2)

vg(

1)

Input

Output

All excitation sources are inherently non-monochromatic and emit within aspectrum, , of wavelengths. Waves in the guide with different free spacewavelengths travel at different group velocities due to the wavelength dependenceofn1. The waves arrive at the end of the fiber at different times and hence result in

a broadened output pulse.

1999 S.O. Kasap,Optoelectronics(Prentice Hall)


6/36

Polarization mode dispersion

Due to difference in the refractive

index along the vertical and the

horizontal axis

The two components of the wave

(Horizontal and Vertical) will thentravel with different velocities

This result in the change in the

polarization of the wave as well as

dispersion and pulse spreading

Core

z

n1x

// x

n1y

// y

Ey

Ex

Ex

Ey

E

= Pulse spread

Input light pulse

Output light pu lse

t

t

Intensity

Suppose that the core refractive index has different values along two orthogonaldirections corresponding to electric field oscillation direction (polarizations). We cantake x andy axes along these directions. An input light will travel along the fiber with ExandEy polarizations having different group velocities and hence arrive at the output at

different times

1999 S.O. Kasap, Optoelectronics(Prentice Hall)


7/36

Multipath Dispersion On The Basis Of Ray Model

Consider two rays one axial and the other corresponding to the angle of incidence very

nearly equal but greater to the critical angle c

mL/Cosm

Cladding

m

m

c L

Core

The axial ray travels a distance Lwithin the core of refractive index

n1 with velocity v = c/n1 in time

t1 = L/v = L n1 /c

The most oblique ray which

corresponds to = m Will cover

the same axial length (actual lengthL/Cosm ) in time

t2 = (L/Cosm ) /v

= L n1 /(c Cosm )

= L n1 /(c Sin c )= L n1 /(c (n2 /n1 ))

= Ln12 /cn2

Because Sin c = n2 /n1

The two rays are launched at the

same time but will separated by a

time interval t after travelling the

length L

t = t2 - t1 = Ln12 /cn2 - L n1 /c

t = (Ln1

/c)((n 1 - n2 )/n2 ))= (Ln1

2 /cn2)

Thus the light rays within the cone of angle within

= 0 and = m will be broadened as they

propagate down the fiber.

Pulse broadening per unit length ist/L = (n1

/ n2 )((n 1 - n2 )/c ))

This is referred to as the multipath

time dispersion


8/36

The capacity of the fiber is defined in terms ofbit-rate distance BL. In order that

the neighboring signal pulse to be distinguishable at the reciever the pulse spread

should be < 1/B (1/B = width of the bit period

For a high performance link the requirement is t 0.1/B, however in general it is

taken as t < 1/B

The bit rate distance product is then given by

BL = (n2 /n12 )(c/ )

Example:

n1 = 1.480, n2 = 1.465 and = 0.01t = 50 ns/Km which means that the pulse broadens by 50 ns after travelling a

distance of 1 Km in the fiber.

The bit-rate distance product is BL = 20 Mb/s-Km

For a graded index fiber the bit-rate distance product can be 1Gb/s-Km

Alternately:

Let us say that the system allows a spread of 25%Bit rate is 10Mb/s, that is one pulse every 100 ns and allowable spread is 25ns

The permissible transmission length of the fiber then is 500 m

If the bit rate is increased to 100 Mb/s That is one pulse every 10 ns and allowable

spread of 2.5 ns

Then the permissible transmission length of the fiber will now be only 50 m


9/36

Wave Velocities: Group Velocity

Plane wave velocity: For a plane wave propagating alongz-axis in an

unbounded homogeneous region of refractive index , which isrepresented by , the velocity of constant phase plane is:

Modal wave phase velocity: For a modal wave propagating alongz-axisrepresented by , the velocity of constant phase plane is:

For transmission system operation the most important & useful type of

velocity is the group velocity, . This is the actual velocity which thesignal information & energy is traveling down the fiber. It is always lessthan the speed of light in the medium. The observable delay experiences bythe optical signal waveform & energy, when traveling a length ofl alongthe fiber is commonly referred to as group delay.

1n)exp( 1zjktj

11 n

c

kv

)exp( zjtj

pv

gV

How to characterize dispersion?


10/36

Group Velocity & Group Delay The group velocity is given by:

The group delay is given by:

It is important to note that all above quantities depend both on frequency

& the propagation mode.

d

dVg

d

dlV

l

g

g


11/36

Group delay per unit length can be defined as:

Group delay per unit length = 1/Vg Vg =c(dk/d)=d/d, Vg is the velocity at which the energy in a pulse travels along a fiber.

If the spectral width of the optical source is not too wide, then the delay

difference per unit wavelength along the propagation path is approximately

For spectral components which are apart, symmetrical around center

wavelength, the total delay difference over a distanceL is:

d

d

cdk

d

cd

d

L

g

2

1

2

d

d g

2

2

2

22

22

d

dL

V

L

d

d

d

d

d

d

d

d

c

L

d

d

g

g

L- distance travelled

propagation constant

k=2/

= ck

d-1 = - -2 d

As the signal propagate along the fiber each spectral component

can assumed to travel independently and to undergo a time delay

or group delay per unit length g /L in the direction of propagation

In terms of the angular frequency

this is written as


12/36

The factor is called GVD parameter (Group velocity delay), andshows how much a light pulse broadens as it travels along an optical fiber. Themore common parameter is called Dispersion, and can be defined as the delaydifference per unit length per unit wavelength as follows:

In the case of optical pulse, if the spectral width of the optical source ischaracterized by its rms value of the Gaussian pulse , the pulse spreadingover the length of L, can be well approximated by:

The factor D

Is designated as dispersion, D has a typical unit of [ps/(nm.km)]. It is a resultof material dispersion and the waveguide dispersion

D = Dmat + Dwg The material dispersion and the waveguide dispersion are intricately

related as the in both cases the basic dispersive property is the refractiveindex of the medium

2

2

2

d

d

22

211

c

Vd

d

d

d

L

Dg

g

g

d

d2

2 2

22

d

d

c

L

d

d g

g


13/36

Material Dispersion The refractive index of the material varies as a

function of wavelength,

Material-induced dispersion for a planewave propagation in homogeneous medium of

refractive index n: here = 2n()/and k = 2 /

The pulse spread due to material dispersion

is therefore:

)(n

d

dnn

c

L

nd

dL

cd

dL

cd

dL

mat

)(2

22

22

)(2

2

mat

matg DL

d

nd

c

L

d

d

)(matD is material dispersion


14/36

A plot of material dispersion

ps/nm-Km verses wavelength is as

shown for two different fibers puresilica fiber and fiber made of 86.5

silica and 13.5 germanium dioxide.

Material dispersion can be reduced

by1. Choosing a source of narrower

spectral width 2. Using higher operating

wavelength

It is seen that for a given fiber

the material dispersion is zero at

a particular wavelength

Material Dispersion


15/36

In this case we assume that the refractive index is constant and is independent of

wavelength. The group delay i.e. the time required for a mode to travel along the fiber of

length L

dk

kbdnn

c

Lwg

)(22

The normalized propagation constant b can be expressed as

21

2

2

2

2

1

2

2

22//

nn

nk

nn

nkb

For n1 n2 andsmall value of

index difference = (n1 - n2 )/n1

And therefore

= n2 k(b + 1) therefore

In terms of normalized frequency parameter

Delay time due to waveguide dispersion can then be expressed as:

2)( 22/12

2

2

1 kannnkaV

dV

Vbdnn

c

Lwg

)(22

Waveguide Dispersion


16/36

Waveguide Dispersion Delay time due to waveguide dispersion

dV

VbdnncLwg )(22


The first term is a constant and second term

represent the group delay arising from the

waveguide dispersion.

Plot shows the wave guide dispersion for thevarious modes of a step index fiber as a

function of V

It shows that the group delay is different for

every guided mode.

Thus these modes arrive at the fiber end at

different times depending on their groupdelay resulting in the spread of the pulse

For a multimode fiber the waveguide

dispersion is very small as compared to the

material dispersion and therefore can be

neglected


17/36

Waveguide dispersion in single mode fibers

For single mode fibers, waveguide dispersion is in the same order of material

dispersion. The pulse spread wg over the distribution of wavelength can be

well approximated as:

Where Dwg is the waveguide dispersion

The figure shows the magnitude of the

material and waveguide dispersion for

fused silica core SM fiber with V = 2.4

The two dispersion cancel and give a

zero dispersion at 1320 nm

2

2

2 )()(dV

VbdV

c

LnDL

d

dwg

wg

wg

[3-25]



18/36

Polarization Mode dispersion

The effects of fiber-birefringence on the polarization states of an optical are

another source of pulse broadening. Polarization mode dispersion (PMD)is due to slightly different velocity for each polarization mode because of

the lack of perfectly symmetric & anisotropicity of the fiber. If the group

velocities of two orthogonal polarization modes are then the

differential time delay between these two polarization over a

distanceL is

The rms value of the differential group delay can be approximated as:

gygx vv and

pol

gygx

polv

L

v

L [3-26]

LDPMDpol [3-27]


19/36

Optimum single mode fiber & distortion/attenuation

characteristics

Fact 1) Minimum distortion at wavelength about 1300 nm for single mode

silica fiber.

Fact 2) Minimum attenuation is at 1550 nm for sinlge mode silica fiber.

Strategy: shifting the zero-dispersion to longer wavelength for minimum

attenuation and dispersion by Modifying waveguide dispersion by

changing from a simple step-index core profile to more complicated

profiles. There are four major categories to do that:1- 1300 nm optimized single mode step-fibers: matched cladding (mode

diameter 9.6 micrometer) and depressed-cladding (mode diameter about 9

micrometer)

2- Dispersion shifted fibers.

3- Dispersion-flattened fibers.4- Large-effective area (LEA) fibers (less nonlinearities for fiber optical

amplifier applications, effective cross section areas are typically greater

than 100 ).2m


20/36


21/36

Chromatic & Total Dispersion

Chromatic dispersion includes the material & waveguide dispersions.

Total dispersion is the sum of chromatic , polarization dispersion and other

dispersion types and the total rms pulse spreading can be approximately

written as:

LD

DDD

chch

wgmatch

)(

)(

[3-28]

LDDDD

totaltotal

polchtotal

... [3-29]

Si l d fib di i


22/36


Single mode fiber dispersion


23/36


Single mode fiber dispersion


24/36

Single mode Cut-off wavelength & Dispersion

Fundamental mode is with V=2.405 and

Dispersion:

For non-dispersion-shifted fibers (1270 nm 1340 nm)

For dispersion shifted fibers (1500 nm- 1600 nm)

0111 LPorHE2

2

2

1

2 nnVa

c

[3-30]

LD

DD

d

dD wgmat

)(

)()()(

[3-31]

[3-32]


25/36

Dispersion for non-dispersion-shifted fibers

(1270 nm 1340 nm)

is relative delay minimum at the zero-dispersion wavelength , and

is the value of the dispersion slope in .

2

2

000 )(

8)(

S

0 0 0S.km)ps/(nm2

0

)( 00

d

dDSS

[3-33]

[3-34]

400 )(14

)( SD [3-35]


26/36

Dispersion for dispersion shifted fibers (1500

nm- 1600 nm)

2

00

0 )(2

)( S

00 )()( SD

[3-36]

[3-37]


27/36


Example of dispersion

Performance curve for

Set of SM-fiber


28/36


Example of BW vs wavelength for various optical sources for

SM-fiber.


29/36

MFD



30/36

Bending Loss



31/36

Bending effects on loss vs MFD



32/36

Bend loss versus bend radius


07.0;1056.3

m60;m6.3

2

233

n

nn

ba


33/36

Kerr effect

Innn 20 Kerr nonlinearity in fiber, where I is the intensity ofOptical wave.

Temporal changes in a narrow optical pulse that is subjected to Kerr nonlinearity inA dispersive medium with positive GVD.


34/36

First-order Soliton

Temporal changes in a medium with Kerr nonlinearity and negative GVD. Since dispersion tends to broaden the pulse, Kerr

Nonlinearity tends to squeeze the pulse, resulting in a formation ofoptical soliton.

BENDING LOSS B di th fib l tt ti B di l i l ifi d di t th


35/36

BENDING LOSS. - Bending the fiber also causes attenuation. Bending loss is classified according to the

bend radius of curvature: microbend loss or macrobend loss. Microbends are small microscopic bends of

the fiber axis that occur mainly when a fiber is cabled. Macrobends are bends having a large radius of

curvature relative to the fiber diameter. Microbend and macrobend losses are very important loss

mechanisms. Fiber loss caused by microbending can still occur even if the fiber is cabled correctly. During

installation, if fibers are bent too sharply, macrobend losses will occur.

Microbend losses are caused by small discontinuities or imperfections in the fiber. Uneven coating

applications and improper cabling procedures increase microbend loss. External forces are also a source of

microbends. An external force deforms the cabled jacket surrounding the fiber but causes only a small

bend in the fiber. Microbends change the path that propagating modes take, as shown in figure 2-23.

Microbend loss increases attenuation because low-order modes become coupled with high-order modes

that are naturally lossy.

Figure 2-23. - Microbend loss.Macrobend losses are observed when a fiber bend's radius of curvature is large compared to the fiber

diameter. These bends become a great source of loss when the radius of curvature is less than several

centimeters. Light propagating at the inner side of the bend travels a shorter distance than that on the

outer side. To maintain the phase of the light wave, the mode phase velocity must increase. When the

fiber bend is less than some critical radius, the mode phase velocity must increase to a speed greater than

the speed of light. However, it is impossible to exceed the speed of light. This condition causes some of

the light within the fiber to be converted to high-order modes. These high-order modes are then lost or

radiated out of the fiber.

Fiber sensitivity to bending losses can be reduced. If the refractive index of the core is increased, then

fiber sensitivity decreases. Sensitivity also decreases as the diameter of the overall fiber increases.

However, increases in the fiber core diameter increase fiber sensitivity. Fibers with larger core size

propagate more modes. These additional modes tend to be more lossy.


36/36

Date post:	04-Apr-2018
Category:	Documents
Upload:	sonakshi-gupta
View:	229 times
Download:	1 times

dispersion in optical fiber

Documents