Intermode Dispersion (MMF)

Low order modeHigh order mode

Cladding

Core

Light pulse

t0 t

Spread,

Broadenedlight pulse

IntensityIntensity

Axial

Lvgmin

L

vgmax

vgmin c/n1. (Fundamental)

vgmax c/n2. (Highest order mode)

L

n1 n2

c/L - 50 ns / km

Depends on length!

Group Delay = L / vg

Intramode Dispersion (SMF)

Group Delay = L / vg

Group velocity vg depends on

Refractive index = n() Material Dispersion

V-number= n() Waveguide Dispersion

= (n1 n2)/n1 = () Profile Dispersion

t

Spread, ²

t0

Spectrum, ²

1 2o

Intensity Intensity Intensity

Cladding

CoreEmitter

Very shortlight pulse

vg(2)

vg(1)Input

Output

Dispersion in the fundamental mode

Material Dispersion

All excitation sources are inherently non-monochromatic and emit within a spectrum ∆ of wavelengths. Waves in the guide with different free space wavelengths travel at different group velocities due to the wavelength dependence of n1. The waves arrive at the end of the fiber at different times and hence result in a broadened output pulse.

t

Spread, ²

t0

Spectrum, ²

12o

Intensity Intensity Intensity

Cladding

CoreEmitter

Very shortlight pulse

vg(2)

vg(1)Input

Output

L

Dm Dm = material dispersion coefficient, ps nm-1 km-1

Waveguide Dispersion

Waveguide dispersion: The group velocity vg(01) of the fundamental mode depends on the V-number which itself depends on the source wavelength even if n1 and n2 were constant. Even if n1 and n2 were wavelength independent (no material dispersion), we will still have waveguide dispersion by virtue of vg(01) depending on V and V depending inversely on . Waveguide dispersion arises as a result of the guiding properties of the waveguide which imposes a nonlinear -lm relationship.

t

Spread, ²

t0

Spectrum, ²

12o

Intensity Intensity Intensity

Cladding

CoreEmitter

Very shortlight pulse

vg(2)

vg(1)Input

Output

L

DwDw = waveguide dispersion coefficient

Dw depends on the waveguide structure, ps nm-1 km-1

0

1.2 1.3 1.4 1.5 1.61.1-30

20

30

10

-20

-10

(m)

Dm

Dm + Dw

Dw0

Dispersion coefficient (ps km-1 nm-1)

Chromatic Dispersion

Material dispersion coefficient (Dm) for the core material (taken as SiO2), waveguide dispersion coefficient (Dw) (a = 4.2 m) and the total or chromatic dispersion coefficient Dch (= Dm + Dw) as a function of free space wavelength,

L

(Dm Dw)

Chromatic = Material + Waveguide

Material and waveguide dispersion coefficients in anoptical fiber with a core SiO2-13.5%GeO2 for a = 2.5to 4 m.

0

–10

10

20

1.2 1.3 1.4 1.5 1.6–20

(m)

Dm

Dw

SiO2-13.5%GeO2

2.5

3.03.54.0a (m)

Dispersion coefficient (ps km-1 nm-1)

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

Core

z

n1x

// x

n1y

// y

Ey

Ex

Ex

Ey

E

= Pulse spread

Input light pulse

Output light pulset

t

Intensity

Polarization Dispersion

n different in different directions due to induced strains in fiber in manufacturing, handling and cabling. n/n 10-6

Dpol L Dpol = polarization dispersion coefficient

Typically Dpol = 0.1 - 0.5 ps nm-1 km-1/2

Self-Phase Modulation Dispersion : Nonlinear Effect

At sufficiently high light intensities, the refractive index of glass n is

n = n + CI

where C is a constant and I is the light intensity. The intensity of light modulates its own phase.

Light intensity

A Gaussian light intensity spectrum and variation ofrefractive index due to self-phase modulation.

nn

n

I

n

Imax

Imin

For 1 ps km-1

Imax 3 W cm-2.

n is 310-7.

2a 10 m,

A 7.8510-7 cm2.

Optical power 23.5 W in the core

Zero Dispersion Shifted Fiber

Total dispersion is zero in the Er-optical amplifier band around 1.55 m

01.2 m 1.4 m

1.6 m

Zero at 1.55 m

MaterialDispersion

Total Dispersion

Dispersion

Waveguide Dispersion

Zero-dispersion shifted fiber

Disadvantage: Cross talk (4 wave mixing)

Outer Core

Outer Cladding

Inner Core

Inner Cladding

End View of Fiber(Not to Scale)

Fiber AxisRefractive

Index

Nonzero Dispersion Shifted Fiber

For Wavelength Division Multiplexing (WDM) avoid 4 wave mixing: cross talk.

We need dispersion not zero but very small in Er-amplifer band (1525-1620 nm)

Dch = 0.1 - 6 ps nm-1 km-1.

Nonzero dispersion shifted fibers

Wavelength (nm)

+10

-10

1300 1400

1500

1600

Dispersion (ps/nm-km) Standard single mode

Nonzero dispersion-shifted

Reduced Slope

Nonzero dispersion-shifted

Zero dispersion-shifted

Nonzero Dispersion Shifted Fiber

Wavelength (nm)

+10

-10

1300 1400

1500

1600

Dispersion (ps/nm-km) Standard single mode

Nonzero dispersion-shifted

Reduced Slope

Nonzero dispersion-shifted

Zero dispersion-shifted 1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

-0.1-25 -15 -5 15 2550

Radius (m)

Refractive Index change (%)

Nonzero dispersion shifted fiber (Corning)

0.6%

0.4%

Fiber with flattened dispersion slope

20

-10

-20

-30

10

1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

30

(m)

Dm

Dw

Dch = Dm + Dw

1

Dispersion coefficient (ps km-1 nm-1)

2

n

r

Thin layer of claddingwith a depressed index

Dispersion Flattened Fiber

Dispersion flattened fiber example. The material dispersion coefficient (Dm) for the core material and waveguide dispersion coefficient (Dw) for the doubly clad fiber result in a flattened small chromatic dispersion between 1 and 2.

t0

Emitter

Very shortlight pulses

Input Output

Fiber

PhotodetectorDigital signal

Information Information

t0

~2² T

t

Output IntensityInput Intensity

²

Dispersion and Maximum Bit Rate

B 0.51/ 2

Return-to-zero (RTZ) bit rate or data rate.

Nonreturn to zero (NRZ) bit rate = 2 RTZ bitrate

t

Output optical power

T = 41

0.50.61

A Gaussian output light pulse and some tolerable intersymbolinterference between two consecutive output light pulses (y-axis inrelative units). At time t = from the pulse center, the relativemagnitude is e-1/2 = 0.607 and full width root mean square (rms)spread isrms = 2.

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

Dispersion and Maximum Bit Rate

B 0.25

0.591/2

1/2

LDch1/2

Maximum Bit Rate Dispersion

BL 0.25L

0.25

Dch

0.59Dch 1/2

Bit Rate = constant

inversely proportional to dispersion

inversely proportional to line width of laser

(single frequency lasers!)

t0

Pi = Input light power

Emitter

OpticalInput

OpticalOutput

Fiber

PhotodetectorSinusoidal signal

Sinusoidal electrical signalt

t0

f1 kHz 1 MHz 1 GHz

Po / Pi

fop

0.1

0.05

f = Modulation frequency

An optical fiber link for transmitting analog signals and the effect of dispersion in thefiber on the bandwidth, fop.

Po = Output light power

Electrical signal (photocurrent)

fel

10.707

f1 kHz 1 MHz 1 GHz

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

Example: Bit rate and dispersion

Consider an optical fiber with a chromatic dispersion coefficient 8 ps km -1 nm-1 at an operating

wavelength of 1.5 m. Calculate the bit rate distance product (BL), and the optical and electrical bandwidths for a10 km fiber if a laser diode source with a FWHP linewidth 1/2 of 2 nm is used.

Solution

For FWHP dispersion,

1/2/L = |Dch|1/2 = (8 ps km-1 nm-1)(2 nm) = 16 ps km-1

Assuming a Gaussian light pulse shape, the RTZ bit rate distance product (BL) is

BL = 0.59L/t1/2 = 0.59/(16 ps km-1) = 36.9 Gb s-1 km.

The optical and electrical bandwidths for a 10 km distance is

fop = 0.75B = 0.75(36.9 Gb s-1 km) / (10 km) = 2.8 GHz.

fel = 0.70fop = 1.9 GHz.

Dispersed pulse shape 1/2 =FWHM width

B(RZ)

B(NRZ)

fop fel

Gaussian with rmsdeviation

= 0.4251/2 0.25/ 0.5/ 0.75B = 0.19/ 0.71fop = 0.13/

Rectangular with fullwidth T

= 0.29T =0.291/2

0.25/ 0.5/ 0.69B = 0.17/ 0.73fop = 0.13/

Relationships between dispersion parameters, maximum bit rates and bandwidths. RZ = Return to zero pulses. NRZ = Nonreturn to zero pulses. B is the maximum bit rate for NRZ pulses.

Combining intermodal and intramodal dispersionsConsider a graded index fiber with a core diameter of 30 m and a refractive index of 1.474 at the center of the core and a cladding refractive index of 1.453. Suppose that we use a laser diode emitter with a spectral linewidth of 3 nm to transmit along this fiber at a wavelength of 1300 nm. Calculate, the total dispersion and estimate the bit-rate distance product of the fiber. The material dispersion coefficient Dm at 1300 nm is 7.5 ps nm-1 km-1. How does this compare with the performance of a multimode fiber with the same core radius, and n1 and n2?

Solution

The normalized refractive index difference = (n1n2)/n1 = (1.4741.453)/1.474 = 0.01425. Modal dispersion for 1 km is

intermode = Ln12/[(20)(31/2)c] = 2.910-11 s 1 or 0.029 ns.

The material dispersion is

1/2 = LDm 1/2 = (1 km)(7.5 ps nm-1 km-1)(3 nm) = 0.0225 ns

Assuming a Gaussian output light pulse shaper,

intramode = 0.4251/2 = (0.425)(0.0225 ns) = 0.0096 ns

Total dispersion is

rms intermode2 intramode

2 0.0292 0.00962 0.030 ns

B = 0.25/rms = 8.2 Gb

Property Multimode step-indexfiber

Single-mode step-index Graded Index

= (n1 n2)/n1 0.02 0.003 0.015Core diameter (m) 100 8.3 (MFD = 9.3 m) 62.5Cladding diameter (m) 140 125 125NA 0.3 0.1 0.26Bandwidth distance orDispersion

20 - 100 MHzkm. < 3.5 ps km-1 nm-1 at 1.3 m> 100 Gb s-1 km in commonuse

300 MHz km - 3 GHz kmat 1.3 m

Attenuation of light 4 - 6 dB km-1 at 850 nm0.7 - 1 dB km-1 at 1.3 m

1.8 dB km-1 at 850 nm0.34 dB km-1 at 1.3 m0.2 dB km-1 at 1.55 m

3 dB km-1 at 850 nm0.6 - 1 dB km-1 at 1.3 m0.3 dB km-1 at 1.55 m

Typical light source Light emitting diode(LED)

Lasers, single modeinjection lasers

LED, lasers

Typical applications Short haul or subscriberlocal networkcommunications

Long haul communications Local and wide-areanetworks. Medium haulcommunications

Comparison of typical characteristics of multimode step-index, single-mode step-index, and graded-index fibers. (Typical values combined from various sources; 1997

Dispersion Compensation

Very shortlight pulse

Input OutputLt

Transmission Fiber

² DtLt

Lt

Dispersion CompensatingFiber

Input Output

² DtLt + DcLc

Dt

Dc

Transmission Fiber Dispersion Compnesating Fiber

Total dispersion = DtLt + DcLc = (10 ps nm-1 km-1)(1000 km) +

(100 ps nm-1 km-1)(80 km)

= 2000 ps/nm for 1080 km or 1.9 ps nm-1 km-1

Dispersion Compensation and Management

Compensating fiber has higher attenuation. Doped core. Need shorter length

More susceptible to nonlinear effects.Use at the receiver end.

Different cross sections. Splicing/coupling losses.

Compensation depends on the temperature.

Manufacturers provide transmission fiber spliced to inverse dispersion fiber for a well defined D vs.

Dispersion Managed Fiber

The inverse dispersion slope of dispersion managed fiber cancels the detrimental effect of dispersion across the a wide spectrum of wavelength. More DWDM channels expected in ultralong haul transmission. (Courtesy of OFS Division of Furukawa.)

Attenuation

Medium

kAttenuation of light in thedirection of propagation.z

E

Attenuation = Absorption + Scattering

Attenuation coefficient is defined as the fractional decrease in the optical power per unit distance. is in m-1.

Pout = Pinexp(L)

dB 1L

10logPin

Pout

dB 10

ln(10) 4.34

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.

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

Lattice Absorption (Reststrahlen Absorption)

Rayleigh Scattering

Scattered waves

Incident wave Through wave

A dielectric particle smaller than wavelength

Rayleigh scattering involves the polarization of a small dielectric particle 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 so that a portion of the light energy is directed away from the incident beam.

R 8 3

34 n2 1 2TkBTf

= isothermal compressibility (at Tf)

Tf = fictive temperature (roughly the softening temperature of glass) where the liquid structure during the cooling of the fiber is frozen to become the glass structure

Example: Rayleigh scattering limit

What is the attenuation due to Rayleigh scattering at around the = 1.55 m window given that pure silica (SiO2) has the following properties: Tf = 1730°C (softening temperature); T = 710-11 m2 N-1 (at high temperatures); n = 1.4446 at 1.5 m.

Solution

We simply calculate the Rayleigh scattering attenuation using

R 8 3

34 (n2 1)2TkBTf

R 8 3

3(1.5510 6)4 (1.44462 1)2(710 11)(1.3810 23)(1730 273)

R = 3.27610-5 m-1 or 3.27610-2 km-1

Attenuation in dB per km is

dB = 4.34R = (4.34)(3.73510-2 km-1) = 0.142 dB km-1

This represents the lowest possible attenuation for a silica glass core fiber at 1.55 m.

0.05

0.1

0.5

1.0

5

10

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Latticeabsorption

Rayleighscattering

Wavelength (µm)

Illustration of a typical attenuation vs. wavelength characteristicsof a silica based optical fiber. There are two communicationschannels at 1310 nm and 1550 nm.

OH-absorption peaks

1310 nm

1550 nm

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

Corning low-water-peak fiber has no OH- peak

E-band is available for communications with this fiber

[Photonics Spectra, April 2002 p.69]

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.

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

Bending Loss

0 2 4 6 8 10 12 14 16 18

Radius of curvature (mm)

B (m-1) for 10 cm of bend

= 633 nm= 790 nmV 2.08

V 1.67

Measured microbending loss for a 10 cm fiber bent by different amounts of radius ofcurvature R. Single mode fiber with a core diameter of 3.9 m, cladding radius 48 m,= 0.00275, NA = 0.10, V 1.67 and 2.08 (Data extracted and replotted from A.J.Harris and P.F. Castle, IEEE J. Light Wave Technology, Vol. LT14, pp. 34-40, 1986; seeoriginal article for discussion of peaks in B vs. R at 790 nm).

exp RRc

exp

R

3/ 2

Microbending Loss

Example: Microbending loss It is found that for a single mode fiber with a cut-off wavelength c = 1180 nm, operating at 1300 nm, the microbending loss reaches 1 dB m-1 when the radius of curvature of the bend is roughly 6 mm for = 0.00825, 12 mm for = 0.00550 and 35 mm for = 0.00275. Explain these findings?

Solution: Maybe later?

Bending loss for three different fibers. The cut-off wavelength is 1.2 m. All three are operating at = 1.5 m.

WDM Illustration

Modulator

Modulator

Non-linear fiber and amplifiers introduce Intermodulation

Modulator

Modulator

Eight Carriers 100 GHz Spacing

Number of carriers and power level must be limited and this reduces range.