chapter 2 dielectric waveguides and optical...

From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA 65

JF, SCO 1617


JF, SCO 1617

Chapter 2 Dielectric Waveguides and Optical Fibers

Charles Kao, Nobel Laureate (2009)Courtesy of the Chinese University of Hong Kong

Propagation losses in optical fibers

S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education© 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is prote cted by Copyright and written permission should be obtained from the

publisher prior to any prohibited reproduction, sto rage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photo copying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearso n Education, Inc., Upper Saddle River, NJ 07458.

21-Fev-2017


JF, SCO 1617


JF, SCO 1617

Light Attenuation

Attenuation = Absorption + Scattering

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

Pout = Pinexp(−αL)

=

out

indB log10

1

P

P

Lα ααα 34.4

)10ln(

10dB ==

The attenuation of light in a medium

21-Fev-2017


JF, SCO 1617


JF, SCO 1617

Attenuation in Optical Fibers

Attenuation vs. wavelength for a standard silica based fiber.


JF, SCO 1617


JF, SCO 1617

Lattice Absorption (Reststrahlen Absorption)

EM Wave oscillations are coupled to lattice vibrations (phonons), vibrations of the ions in the lattice. Energy is transferred from the EM wave to these lattice vibrations.

This corresponds to “Fundamental Infrared Absorption” in glasses


JF, SCO 1617


JF, SCO 1617 Rayleigh Scattering

Rayleigh scattering involves the polarization of a small dielectric particle or a regionthat is much smaller than the light wavelength. The field forces dipole oscillations inthe 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.

αR ≈ 8π 3

3λ4 n2 −1( )2βTkBTf

βΤ = isothermal compressibility (at Tf)

Tf = fictive temperature (roughly thesoftening temperature of glass) wherethe liquid structure during the coolingof the fiber is frozen to become theglass structure


JF, SCO 1617


JF, SCO 1617

Attenuation in Optical Fibers

Attenuation vs. wavelength for a standard silica based fiber.


JF, SCO 1617


JF, SCO 1617

Low-water-peak fiber has no OH- peak

E-band is available for communications with this fiber


JF, SCO 1617


JF, SCO 1617



Dispersion in optical fibers



21-Fev-2017


JF, SCO 1617


JF, SCO 1617

(a) A sine wave is perfectly coherent and contains a well-defined frequency υo. (b) A finite wave train lasts for a duration ∆t and has a length l. Its frequency spectrum extends over ∆υ = 2/∆t. It has a coherence time ∆t and a coherence length λ. (c) White light exhibits practically no coherence.

Spectral width Pulse duration(Temporal and Spatial Coherence)

21-Fev-2017


JF, SCO 1617


JF, SCO 1617 Spectral width Pulse duration(Temporal and Spatial Coherence)

t∆≈∆ 1υ FWHM spreads


JF, SCO 1617



(a) Two waves can only interfere over the time interval ∆t. (b) Spatial coherence involves comparing the coherence of waves emitted from different locations on the source. (c) An incoherent beam

c

(a)

Time

(b)

A

B

∆ tInterference No interferenceNo interference

Space

c

P

Q

Source

Spatially coherent source

An incoherent beam(c)


JF, SCO 1617



∆t = coherence time

l = c∆t = coherence length

For a Gaussian light pulse

Spectral width Pulse duration

t∆≈∆ 1υ


JF, SCO 1617


JF, SCO 1617

Temporal and Spatial Coherence

∆t = coherence time

l = c∆t = coherence lengthNa lamp, orange radiation at 589 nm has spectral width ∆υ ≈5´1011 Hz.

∆t ≈ 1/ ∆υ = 2´10-12 s or 2 ps,

and its coherence length l = c∆t,

l = 6´10-4 m or 0.60 mm.

He-Ne laseroperating in multimode has a spectral width around 1.5´109 Hz, ∆t ≈ 1/∆υ = 1/1.5´109 s or 0.67 ns

l = c∆t = 0.20 m or 200 mm.

t∆≈∆ 1υ


JF, SCO 1617


JF, SCO 1617

Intermode Dispersion (MMF)

∆τL

≈ n1 − n2

c

Group Delay τ = L / vg

(Since n1 and n2 are only slightly different)


JF, SCO 1617


JF, SCO 1617 Intermode Dispersion (MMF)

maxmin gg vvLL −=∆τ

∆τL

≈ n1 − n2

c∆τ/L ≈ 10 − 50 ns / km

Depends on length!

=≈

1

2

11min sin

n

n

n

c

n

ccθgv

−=∆

2

121 )(

n

n

c

nn

L

τ

θc θcTE0

TEhighest

1max n

c≈gv


JF, SCO 1617


JF, SCO 1617 Intramode Dispersion (SMF)

Group Delay τ = L / vg

Group velocity vg depends on

Refractive index = n(λ) Material Dispersion

V-number = V(λ) Waveguide Dispersion

∆ = (n1 − n2)/n1 = ∆(λ) Profile Dispersion

Dispersion in the fundamental mode


JF, SCO 1617


JF, SCO 1617

Material Dispersion

Emitter emits a spectrum∆λ of wavelengths.

Waves in the guide with different free space wavelengths travel at different groupvelocities due to the wavelength dependence ofn1. The waves arrive at the end of thefiber at different times and hence result in a broadened output pulse.

∆τL

= Dm∆λ Dm = Material dispersion coefficient, ps nm-1 km-1


JF, SCO 1617


JF, SCO 1617 Intramode Dispersion (SMF)Chromatic dispersion in the fundamental mode

λ1

vg1

vg2

∆λ = λ2 − λ1

λ2 τg1 τg2

τ

∆λ

δ(t)

∆τ

∆τ = τg1 − τg2

λτ

Ld

dD =

DispersionChromatic spread

Definition of Dispersion Coefficient

λτ

∆∆=

LD

OR

λτ ∆=∆ DLOutput pulse

dispersed


JF, SCO 1617


JF, SCO 1617

Material Dispersion

∆τL

= Dm∆λ

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

Cladding

CoreEmitter

Very shortlight pulse

vg(λ1)Input

Outputvg(λ2)

vg = c / Ng

Depends on the wavelengthGroup velocity

−≈

2

2

λλ

d

nd

cDm


JF, SCO 1617


JF, SCO 1617

b = (β /k)2 − n22

n12 − n2

2

Wave guide dispersion

b hence β depend on V and hence on λ

Normalized propagation constant

k = 2π/λ

2996.0

1428.1

−≈V

b( ) 2/122

21

2nn

aV −=

λπ


JF, SCO 1617


JF, SCO 1617

Waveguide Dispersion

Waveguide dispersionThe group velocity vg(01) of the fundamental mode depends on the V-number, which itself depends on the source wavelength λ, 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 Vdepending inversely on λ. Waveguide dispersion arises as a result of the guiding properties of the waveguide which imposes a nonlinear ω vs. βlm relationship.

∆τL

= Dw∆λ Dw = waveguide dispersion coefficient

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


JF, SCO 1617


JF, SCO 1617

Chromatic Dispersion

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

∆τL

= (Dm + Dw)∆λ

Chromatic = Material + Waveguide


JF, SCO 1617


JF, SCO 1617 What do Negative and Positive Dm mean?

λ1

12

λ2

t

λ1 vg1

vg2λ2

t

∆λ = λ2 − λ1

1 2

λ1 λ2

Positive Dm

Ng2 > Ng1

∆τ = Positive

t

λ1vg1

vg2λ2

t

Negative Dm

Ng2 < Ng1

∆τ = Negative

Negative Dm

Positive Dm

Dm

λτ

∆∆=

LDm

Silica glass ∆τ


JF, SCO 1617


JF, SCO 1617

∆=2

22 )(

dV

bVdV

c

nDw λ

Waveguide Dimension and Chromatic Dispersion

22

025.0

cnaDw

λ−≈

22

11

)]µm([

)µm(76.83)kmnmps(

naDw

λ−≈−−

Waveguide dispersion depends on the guide properties


JF, SCO 1617


JF, SCO 1617

Profile Dispersion

Group velocity vg(01) of the fundamental mode depends on ∆, refractive index difference.

∆ may not be constant over a range of wavelengths: ∆ = ∆(λ)

∆τL

= Dp∆λ Dp = Profile dispersion coefficient

Dp < 0.1 ps nm-1 km-1

Can generally be ignored

NOTE

Total intramode (chromatic) dispersion coefficient Dch

Dch = Dm + Dw + Dp

where Dm, Dw, Dp are material, waveguide and profile dispersion coefficients respectively


JF, SCO 1617


JF, SCO 1617

Chromatic Dispersion

λτ ∆=∆chD

L

−=4

00 14 λ

λλSDch

Dch = Dm + Dw + Dp

S0 = Chromatic dispersion slope at λ0

Chromatic dispersion is zero at λ = λ0


JF, SCO 1617


JF, SCO 1617

L+∆

+∆

=−=∆ 22

2

0 )(!2

1)()()(

00

λλτλ

λτλτλττ

λλ d

d

d

d

Is dispersion really zero at λ0?

The cause of ∆τ is the wavelength spread ∆λ at the input

∆τ = f(∆λ)

chDLd

d =∆λτ

( )( ) ps01.1nm2kmnmps090.02

km1)(

221-2-2

0 ==∆=∆ λτ SL

0Sd

dDch =λ

20 )(

2

1)]([

0

λλτ

λλλτ

λ

∆

+∆=∆d

d

d

dLDch

= 0


JF, SCO 1617


JF, SCO 1617

Polarization Dispersion

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

LDPMD=∆τDPMD = Polarization dispersion coefficient

Typically DPMD = 0.1 − 0.5 ps nm-1 km-1/2


JF, SCO 1617


JF, SCO 1617

Self-Phase Modulation Dispersion : Nonlinear EffectAt 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.

What is the optical power that will give ∆τ/L ≈ 0.1 ps km-1?

Take C = 10-14 cm2 W-1

∴ ∆I ≈ (c/C)(∆τ/L) = 3×106 W cm-2

or ∆n ≈ 3×10-6

Given 2a ≈ 10 µm, A ≈ 7.85×10-7 cm2

∴ Optical power ≈ 2.35 W in the core

c

IC

L

∆≈∆τ

In many cases, this dispersion will be less than other dispersion mechanisms


JF, SCO 1617


JF, SCO 1617 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

Various fibers named after their dispersion

characteristics. The range 1500 - 1600 nm is only

approximate and depends on the particular

application of the fiber.


JF, SCO 1617


JF, SCO 1617 Dispersion Flattened Fiber

Dispersion flattened fiber example. The material dispersion coefficient (Dm) for thecore material and waveguide dispersion coefficient (Dw) for the doubly clad fiberresult in a flattened small chromatic dispersion between λ1 and λ2.


JF, SCO 1617


JF, SCO 1617 Nonzero Dispersion Shifted Fiber: More Examples

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 (µm)

Refractive Index change (%)

Nonzero dispersion shifted fiber (Corning)

Fiber with flattened dispersion slope

(schematic)

0.6%

0.4%


JF, SCO 1617

Commercial Fibers for Optical Communications

Fiber Dch

ps nm-1 km-1

S0

ps nm-2 km-1

DPMD

ps km-1/2

Some attributes

Standard single mode, ITU-T G.652

17

(1550 nm)

≤ 0.093 < 0.5

(cabled)

Dch = 0 at λ0 ≈ 1312 nm, MFD = 8.6 - 9.5 µm at 1310 nm. λc ≤1260 nm.

Non-zero dispersion shifted fiber, ITU-T G.655

0.1 − 6

(1530 nm)

< 0.05 at 1550 nm

< 0.5

(cabled)

For 1500 - 1600 nm range. WDM application

MFD = 8 − 11 µm.

Non-zero dispersion shifted fiber, ITU-T G.656

2 − 14 < 0.045 at 1550 nm

< 0.20

(cabled)

For 1460 - 1625 nm range. DWDM application. MFD = 7 − 11 µm (at 1550 nm). Positive Dch. λc

<1310 nmCorning SMF28e+

(Standard SMF)

18

(1550 nm)

0.088 < 0.1 Satisfies G.652. λ0 ≈ 1317 nm, MFD = 9.2 µm (at 1310 nm), 10.4 µm (at 1550 nm); λc ≤ 1260 nm.

OFS TrueWave RS Fiber 2.6 - 8.9 0.045 0.02 Satisfies G.655. Optimized for 1530 nm - 1625nm. MFD = 8.4 µm (at 1550 nm); λc ≤1260 nm.

OFS REACH Fiber 5.5 -8.9 0.045 0.02 Higher performance than G.655 specification. Satisfies G.656. For DWDM from 1460 to 1625 nm. λ0 ≤ 1405 nm. MFD = 8.6 µm (at 1550 nm)


JF, SCO 1617


JF, SCO 1617 Single Mode Fibers: Selected Examples


JF, SCO 1617


JF, SCO 1617

Dispersion Compensation

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

Deffective = 1.9 ps nm-1 km-1


JF, SCO 1617


JF, SCO 1617

Dispersion Compensation

Dispersion D vs. wavelength characteristics involved in dispersion compensation. Inverse dispersion

fiber enables the dispersion to be reduced and maintained flat over the communication

wavelengths.


JF, SCO 1617


JF, SCO 1617

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. λ


JF, SCO 1617


JF, SCO 1617

Dispersion and Maximum Bit Rate

B ≈ 0.5∆τ1/ 2

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

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


JF, SCO 1617

NRZ and RTZ

1 0 1 1 0 1 0 0 1

NRZ

RZ

Information

T


JF, SCO 1617


JF, SCO 1617

Maximum Bit Rate B

A Gaussian output light pulse and some tolerable intersymbol interference

between two consecutive output light pulses (y-axis in relative units). At time t

= σ from the pulse center, the relative magnitude is e−1/2 = 0.607 and full

width root mean square (rms) spread is ∆τrms = 2σ. (The RTZ case)


JF, SCO 1617


JF, SCO 1617 Dispersion and Maximum Bit Rate

2/1

59.025.0

τσ ∆=≈B 2/1

2/1 λτ ∆=∆chD

L

Maximum Bit Rate Dispersion

2/12/1

59.059.0

λτ ∆=

∆≈

chDBL

Bit Rate × Distance is

inversely proportional to dispersion

inversely proportional to line width of laser

(so, we need single frequency lasers!)


JF, SCO 1617


JF, SCO 1617

Dispersion and Maximum Bit Rate

B ≈ 0.25σ

= 0.59∆τ1/2

Maximum Bit Rate

2intramodal

2intermodal σσσ +=2

2intramodal2/1

2intermodal2/1

22/1 )()()( τττ ∆+∆=∆


JF, SCO 1617


JF, SCO 1617

Optical Bandwidth

An optical fiber link for transmitting analog signals and the effect of dispersion in the

fiber on the bandwidth, fop.


JF, SCO 1617

Pulse Shape and Maximum Bit Rate


JF, SCO 1617


JF, SCO 1617

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 µm. Calculate the bit rate distance product (BL), and the optical and electrical bandwidths for a 10 km fiber if a laser diode source with a FWHP linewidth ∆λ1/2 of 2 nm is used.

Solution

For FWHP dispersion,

∆τ1/2/L = |Dch|∆λ1/2 = (8 ps nm-1 km-1)(2 nm) = 16 ps km-1

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

BL = 0.59L/∆τ1/2 = 0.59/(16 ps km-1) = 36.9 Gb s-1 km

The optical and electrical bandwidths for a 10 km fiber are

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

fel = 0.70fop = 1.9 GHz


JF, SCO 1617


JF, SCO 1617



Graded Index (GRIN) Fibers



21-Fev-2017

chapter 2 dielectric waveguides and optical...

Documents