Chapter 2c

n1

21

3

n

n2

OO' O''

n2

23

GRIN fibre does not have a constant refractive index in the core but decreases from n1 at the centre, as a power law, to n2 at the cladding.

Graded index (GRIN) fibre

2n

21

1 21

a

rn ; r < a

; r = a

n(r)

∆ = relative refractive index difference, (n1-n2)/n1

g = profile parameter

n1

n2

21

3

nO

n1

21

3

n

n2

OO' O''

n2

(a) Multimode stepindex fiber. Ray pathsare different so thatrays arrive at differenttimes.

(b) Graded index fiber.Ray paths are differentbut so are the velocitiesalong the paths so thatall the rays arrive at thesame time.

23

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

Dispersion in GRIN fibre

• In the GRIN fibre, the index changes continuously, which is analogous to having ray travel from layer to layer almost immediately.– After many refractions, the angle eventually satisfies the

critical angle to have TIR.– The ray paths in the graded index core are therefore curved

trajectories as shown in Fig.17• The intermodal dispersion is minimum wheng = (4+2D)/(2+3D) 2(1 – D)If D is small so that g ~ 2 (parabolic). This is optima profile

index• With this optima profile index, the rms dispersion

sintermode/L n1D2/(203 c)

n decreases step by step from one layerto next upper layer; very thin layers.

Continuous decrease in n gives a raypath changing continuously.

TIR TIR

(a) A ray in thinly stratifed medium becomes refracted as it passes from onelayer to the next upper layer with lower n and eventually its angle satisfies TIR.(b) In a medium where n decreases continuously the path of the ray bendscontinuously.

(a) (b)


Fig. 17:

The Decibel• The decibel unit is used to express gain or loss in a system or

component. It is used to compare the power entering a system, circuit or component to the power leaving it.

• A useful figure to remember is 3dB, which represents a loss of one half of the power.

• Decibel expressing loss is a negative unit.• dBm means “decibels referenced to a milliwatt”

dBP

PGain

in

out

10log10

mW

PdBm

1log10 10

dBP

PLoss

out

in

10log10

Attenuation in Optical Fibres

• Suppose that the input optical power into a fibre of length L is Pin and the output power is Pout and power anywhere in the fibre at a distance x from the input is P.

• The attenuation coefficient a is defined as the fractional decrease in the optical power per unit distance

LPPP

P

L

dPP

dx

dx

dP

P

inoutout

in

P

P

L out

in

expln1

1

1

0

Attenuation in dB/length

34410ln

10

log101

dB/length,in t coefficienn Attenuatio

km.per dB typicallydB/length, of in term

expressed ispower opticalan in n attenuatiopower general,In

.

P

P

L

dB

out

indB

Attenuation in optical fiber (glass or silica fiber)

Absorption Scattering Geometrical effects

Intrinsic

UV IR

Extrinsic

Metal ions

OH- ions

Rayleigh

Mie

Raman

Brillouin

Attenuation

• Attenuation is a major factor to be considered in the design of any communication systems due to the fact that receivers require minimum level of power.– It determines the maximum length possible before the power

levels drop below its minimum level.

• In a particular optical link, beside the fiber attenuation, losses can occur at the input/output couplers, splices and connectors.– The attenuation is usually expressed in dB/km

Medium

kAttenuation of light in thedirection of propagation.


z

E

Absorption

• Optical energy lost when passes through any medium is called absorption.

• Different material will absorb different amount of light and a material will absorb different amount of light at different wavelengths.

• The absorbed light is usually converted into heat energy within the absorbing material. – The absorption is the dissipation of some optical power as

heat in the optical fiber.

z

A solid with ions

Light direction

k

Ex

Lattice absorption through a crystal. The field in the waveoscillates the ions which consequently generate "mechanical"waves in the crystal; energy is thereby transferred from the waveto lattice vibrations.


Intrinsic Absorption

• This is a natural property of glass.• It is strong in the short wavelength ultraviolet (UV)

region in the electromagnetic spectrum. – It is unimportant because the communication wavelength

is far from the UV region.• Another intrinsic peak occurs in the Infrared region

between 7µm-12µm for typical glass composition.– Although it is still far from the key wavelengths, the edges of

IR absorption extends toward the key wavelength region.

Optical fiber attenuation as a function of wavelength yields nominal values of 0.5 dB/km at 1300 nm and 0.3 dB/km at 1550 nm for standard single mode fiber. The attenuation peak was shown at 1440 nm

Extrinsic absorption

• It is due to impurities present in the glass. They are Hydroxyl ion (OH-) and metal ions.

• The most significant OH losses occur at 1.38µm, 0.95µm and 0.72µm.

• The purity has been achieved for silica fibres nowadays.

Scattering losses

• Linear scattering: Rayleigh scattering, Mie scattering.• Non-linear scattering: Brillouin scattering, Raman

scattering.• Mie Scattering:

– It is caused by imperfections such as irregularities in the core cladding interface, core cladding refractive index differences along the fiber length, diameter fluctuations, strains and bubbles.

Rayleigh scattering

• It occurs due to the random distribution of individual molecules within the medium.

• Molecules moves randomly in molten state are frozen into solid state in the making of fiber.

• This will result in a localized variation of the refractive index throughout the glass due to clumping of the molecules.

• Rayleigh scattering is inversely proportional to the wavelength.

Scattered waves

Incident wave Through wave

A dielectric particle smaller than wavelength

Rayleigh scattering involves the polarization of a small dielectricparticle or a region that is much smaller than the light wavelength.The field forces dipole oscillations in the particle (by polarizing it)which leads to the emission of EM waves in "many" directions sothat a portion of the light energy is directed away from the incidentbeam.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

The attenuation due to Rayleigh scattering in dB/km:

FBcR TkPn 28

4

3

3

8

l = optical wavelength, n = refractive index of the medium,P = average photoelastic coefficient,

bc = isothermal compressibility at temp TF

kB =Boltzman’s constant (1.381×10-23JK-1)

)/exp(

1log10 10

L

nAttenuatio

R

The Rayleigh scattering coefficient is:

Stimulated Brillouin Scattering (SBS)

)(104.4 223 wattsBdP dBB

• SBS is due to modulation of light through thermal vibration within the fiber. The scattered light appears as upper and lower sideband which are separated from the incident light by the modulation frequency.

• The threshold power, PB above which Brillouin scattering occurs is given as:

– d=fibre core diameter in µm, l=operating wavelength in µm, adB=fibre attenuation in dB/km, B=source bandwidth in GHz

– From this formula, the maximum power which can be launched into a SMF before SBS occurs can be calculated.

*SMF : single mode fibre

Stimulated Raman Scattering (SRS)

)(109.5 222 wattsBdP dBR

• SRS is similar to SBS but occurs at higher threshold power, PR:

• SBS and SRS are usually seen in SMF since the MMF with higher core size allows higher power to be traveling in the waveguide.

*SMF: Single Mode Fibre MMF: Multi Mode Fibre

Geometrical Effect – Bend losses

• Bending the fiber causes attenuation. – 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 inhibited, which

causes light energy to be radiated from the fiber.• Macroscopic bending losses due to small changes in

the refractive index of the fiber due to induced strains when it is bent during its use. – It is a large scale bending loss like wrapping fiber on a spool

or pulling (laying) fiber around a corner.• Microscopic bending can occur during the cabling

process due to stress.

Escaping wave

c

Microbending

R

Cladding

Core

Field distribution

Sharp bends change the local waveguide geometry that can lead to wavesescaping. The zigzagging ray suddenly finds itself with an incidenceangle that gives rise to either a transmitted wave, or to a greatercladding penetration; the field reaches the outside medium and some lightenergy is lost.


Fundamental mode field in a curved optical waveguide

Small scale fluctuations in the radius of curvature of the fiber axis leads to micro bending losses. Microbends can shed higher order modes can cause power from low order modes to couple to high order modes.

Bend radius for macroscopic bending losses

• For multimode fibers, the minimum bend radius or the critical radius for curvature is:

• For single mode fiber, it is given by:

where lc=[2 p an1(2∆)1/2]/2.405

232

221

21 )(4/)3( nnnRc

323

21 )/996.0748.2]()/(20[ ccs nnR

Science

Chapter 2c