Power Considerations in Optical Power Considerations in Optical Transmission Systems in Presence of Transmission Systems in Presence of

Nonlinear Phase Noise Nonlinear Phase Noise

Alan Pak Tao Lau

Department of Electrical Engineering,Stanford UniversityMay 26, 2006

OutlineOutline

Kerr nonlinearity induced nonlinear phase Kerr nonlinearity induced nonlinear phase noise in coherent communication systemsnoise in coherent communication systems

Optimal and practical power profile design Optimal and practical power profile design for variance minimization for variance minimization

Power profile design in WDM systemsPower profile design in WDM systems

Kerr NonlinearityKerr Nonlinearity

)( 3)3(2)2()1(0 EEE P

AEEnnnK

kk /)||2|(|

2

22120

Centro-symmetric materials Centro-symmetric materials 0)4()2( induced intensity dependent refractive index induced intensity dependent refractive index )3(

Nonlinear effects in coherent Nonlinear effects in coherent communications systemscommunications systems

Kerr induced nonlinear phase shiftKerr induced nonlinear phase shift

where where

)||2|(|)||2|(|2

221eff

2

221eff

eff

02NL

K

kk

K

kk EELEEL

A

kn

Self Phase Modulation (SPM)Self Phase Modulation (SPM) Cross Phase Modulation (XPM)Cross Phase Modulation (XPM) Typical ranges of : 1~5 /(W km)Typical ranges of : 1~5 /(W km)

LeL

1eff

Nonlinear phase noiseNonlinear phase noise

ASE from inline amplifiers ASE from inline amplifiers generate Gaussian noisegenerate Gaussian noise

Random power of signal Random power of signal plus noise produce plus noise produce random nonlinear phase random nonlinear phase shift -- Gordon-shift -- Gordon-Mollenauer effectMollenauer effect

overall length L with N spans

Opt. Amp.Fiber

L=3000 km, N=30, = 0dBmkm/1.5,0.25dB/km W

2|| E

Phase Noise for coherent systemsPhase Noise for coherent systems

Linear Phase NoiseLinear Phase Noise

)arg( 21L NnnnE

Optical Amp.

Fiber

Optical Amp.

Fiber

Optical Amp.

Fiber

Nonlinear Phase NoiseNonlinear Phase Noise

21

221

21

effNL||

||||

NnnE

nnEnEL

)1()1(),,0(~ˆ22 ilα

ioptspiii ebGnhINn

System design for variance System design for variance minimizationminimization

Total variance of phase noiseTotal variance of phase noise

Last time, looked at how we can design Last time, looked at how we can design the gain and spacings of inline amplifiers the gain and spacings of inline amplifiers to minimize variance of phase noiseto minimize variance of phase noise

We’ll look at how signal power at different We’ll look at how signal power at different points in the system affects points in the system affects

2NL

2L

2

2

Factors affecting Power Levels Factors affecting Power Levels DesignDesign

High power – Nonlinear phase noise, amplifier High power – Nonlinear phase noise, amplifier gain saturationgain saturation

Low power – Linear phase noise, input coupling Low power – Linear phase noise, input coupling loss, shot noise and thermal noise, quantum loss, shot noise and thermal noise, quantum effectseffects

Allowable Range of Power levelsAllowable Range of Power levels

dBmPPdBm recin 10,20

Optimal Operating PowerOptimal Operating Power

P

eNb

ePbNNN

ebNNNN

eP

N

L

N

L

N

L

N

L

)1(

)1(3

)12)(1(2

)1(3

)1)(1(2)1(

)(

2222

2

222/2

22

8

3

)12)(1()1(4

30

LNNeP

PN

NLopt

Transmitted Power = Received Power = P

Optimal Operating PowerOptimal Operating Power

Mean nonlinear phase shiftMean nonlinear phase shift Corresponds with literature findingsCorresponds with literature findings

rad 866.0 NL

Unequal Input and Received PowerUnequal Input and Received Power

Amplifiers over or under compensate the Amplifiers over or under compensate the signal loss along the linksignal loss along the link

Study a linearly increasing/decreasing Study a linearly increasing/decreasing power profile along the link.power profile along the link.

Unequal Input and Received PowerUnequal Input and Received Power

)ˆ()ˆ()ˆ(2

3

2222

2

)ˆ()ˆ(2

22

)ˆ(2

21)ˆ(

12

)ˆ(2

1

)ˆ(

ˆ8

)ˆ(

12

)ˆ(

1ˆ4

)ˆ(2

)1(ˆ

LLLLLL

LLLL

in

in

LL

eLL

e

LL

e

LL

LbL

LLe

LL

eLbPL

LLP

eLb

)/ln(ˆ , inrec

recin

PPLLPP

Linear Power ProfileLinear Power Profile

Good to have a drop in received power Good to have a drop in received power

Optimal Power ProfileOptimal Power Profile Power profilePower profile Let Let

Phase noise variancePhase noise variance

Euler Characteristic EquationEuler Characteristic Equation

)(lP

L

l

inrec PTPLTdllPlT )0( and )()()(

LL

dlTTTFbdlTT

TTb

00

222 ),,(2/14/

02

2

T

F

dl

d

T

F

dl

d

T

F

Optimal Power ProfileOptimal Power Profile

Power profile design in WDM Power profile design in WDM systemssystems

Cross-phase modulation (XPM)Cross-phase modulation (XPM) Difference in group velocity -- Walk Off EffectDifference in group velocity -- Walk Off Effect

Pulse waveform distortion negligible compared Pulse waveform distortion negligible compared to walk off in modeling to walk off in modeling

2

XPM induced nonlinear phase noiseXPM induced nonlinear phase noise

Assumptions: Flat gain amplifiers and noise spectrumAssumptions: Flat gain amplifiers and noise spectrum Typical spacing: 10Gb/s, 50 GHz, D=4 ps/(km-nm) --> Typical spacing: 10Gb/s, 50 GHz, D=4 ps/(km-nm) -->

Lw=62.5 kmLw=62.5 km

)1)(1(

)1)(1(4

)(2

2

sW

sW

LL

LL

SPM

WXPM

ee

eeL

Power Profile Design in WDM systemsPower Profile Design in WDM systems

Power Profile Design in WDM systemsPower Profile Design in WDM systems

ObjectiveObjective)(max min 2

,2

,2

,

kj

jXPMkSPMkLk

Power drop profile requires less pump Power drop profile requires less pump energyenergy

Future WorkFuture Work

Real systems aren’t point to pointReal systems aren’t point to point Signal path routed by RODAMSignal path routed by RODAM Power drop profile should still provide benefitsPower drop profile should still provide benefits

Power Profile Design in WDM systemsPower Profile Design in WDM systems

AcknowledgementsAcknowledgements

Prof. KahnProf. Kahn Dany, Ezra and Rahul =)Dany, Ezra and Rahul =)

Thank you !Thank you !