The Marriage of Photonics and Communication Theory for 100 Gb/s Long-Haul and Ethernet Fiber-Optic Transmissions The Marriage of Photonics and Communication

The Marriage of Photonics and Communication The Marriage of Photonics and Communication Theory for 100 Gb/s Long-Haul and Ethernet Theory for 100 Gb/s Long-Haul and Ethernet

Fiber-Optic TransmissionsFiber-Optic Transmissions

Ph.D. Candidate,

Department of Electrical EngineeringStanford University

Alan Pak Tao Lau

22

Part I – 100 Gb/s long-haulPart I – 100 Gb/s long-haul

Long-haul fiber-optic communication systemsLong-haul fiber-optic communication systems Coherent detection, DSP, communication theoryCoherent detection, DSP, communication theory Kerr nonlinearity induced system impairmentsKerr nonlinearity induced system impairments

Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN)Nonlinear Phase Noise (NLPN) WDM effects and optical OFDMWDM effects and optical OFDM

SummarySummary

33

Long-haul fiber-optic Long-haul fiber-optic communication systemscommunication systems

Terrestrial link (1500 ~ 3000 km)Submarine link (5000 ~ 10000 km)

44

Tech. Evolution: Optical amplifiers, Tech. Evolution: Optical amplifiers, Wavelength Division Multiplexing (WDM),Wavelength Division Multiplexing (WDM), Forward Error Correction (FEC)Forward Error Correction (FEC)

Long-haul fiber-optic Long-haul fiber-optic communication systemscommunication systems

TAT-8: 280 Mb/s, (1988)TAT-8: 280 Mb/s, (1988)

TAT-12/13: 5 Gb/s, (1996)TAT-12/13: 5 Gb/s, (1996)

TAT-14: 64 x 10 Gb/s, (2001)TAT-14: 64 x 10 Gb/s, (2001)

TPC5: 5Gb/s (1996)TPC5: 5Gb/s (1996)

Bit Rate: 2.5 Gb/s ->10 Gb/s -> 40 Gb/s -> 100/160Gb/sBit Rate: 2.5 Gb/s ->10 Gb/s -> 40 Gb/s -> 100/160Gb/s

Spectral Efficiency: 0.0005 b/s/Hz -> 0.2 b/s/Hz -> 0.8 b/s/Hz Spectral Efficiency: 0.0005 b/s/Hz -> 0.2 b/s/Hz -> 0.8 b/s/Hz

Next technological breakthrough: Electronic signal processing!Next technological breakthrough: Electronic signal processing!

55

Coherent detectionCoherent detection Traditionally in fiber-optics, information encoded in pulse energy – On-Traditionally in fiber-optics, information encoded in pulse energy – On-

Off Keying (OOK)Off Keying (OOK) Differentially coherent detection – information encoded in phase Differentially coherent detection – information encoded in phase

difference between neighboring symbols: DPSK, DQPSKdifference between neighboring symbols: DPSK, DQPSK Coherent detection – information encoded in both phase and Coherent detection – information encoded in both phase and

amplitude: QPSK, 16-QAM amplitude: QPSK, 16-QAM Currently, most interested in QPSK, DQPSK for 100 Gb/s. 16-QAM Currently, most interested in QPSK, DQPSK for 100 Gb/s. 16-QAM

modulation format in future. modulation format in future.

tELOLO

tE )(Re tEi

tEtE LO2

1

tEtE LO2

1

3-dB coupler

BPSKMPSK/QAM

90°

LO tELO

tE

)(Re tEiI

)(Im tEiQ

D-MPSK

tE T

T

90°

)()(Re * TtEtE

)()(Im * TtEtE

Delay

Receiver

tEI

90°

MZ

MZ tEQ

Transmitter

Laser

tVI

tVQ

tE

MZ– Mach Zehnder Modulator

66

Digital Signal Processing Digital Signal Processing Currently available: 40 Gb/s FEC encoder/decoderCurrently available: 40 Gb/s FEC encoder/decoder 40 Gb/s clock/data recovery40 Gb/s clock/data recovery 10 Gb/s MLSD10 Gb/s MLSD Arbitrary signal generation/detection, arbitrary signal Arbitrary signal generation/detection, arbitrary signal

processing processing

Communication theory / signal processing Communication theory / signal processing techniques becomes practicallytechniques becomes practically relevant and important !!relevant and important !!

Information theory is also getting more attentionInformation theory is also getting more attention Fiber-optic channel is different from wireless / wireline Fiber-optic channel is different from wireless / wireline

communicationscommunications

77

Signal propagation in optical fibersSignal propagation in optical fibers

Erbium Doped Fiber Amplifiers (EDFA)Erbium Doped Fiber Amplifiers (EDFA)

)(

0

P

EH

BE

B

D

j

j

))((),(),(),,,( tzjx etzEyxFtzyx E

z1n

2n

EEjEt

Ej

z

E 22

22 ||

22

Nonlinear Schrödinger Equation (NLSE)Nonlinear Schrödinger Equation (NLSE)

Mode

Pulse envelope

Carrier frequency

(~193 THz or 1550 nm)

Japan USA

E

Dispersion Compensating Fibers (DCF)Dispersion Compensating Fibers (DCF)

amplifieramplifier amplifier

Attenuation

t

)0,(tE

t

),( ztE

Chromatic

Dispersion

SMFSMF SMFDCF DCFDCF

Kerr

nonlinearity

x

y

Kerr nonlinearity – not a LTI effectKerr nonlinearity – not a LTI effect Dominant transmission impairment in long-haul systems!Dominant transmission impairment in long-haul systems!

88

Kerr Nonlinearity in optical fibersKerr Nonlinearity in optical fibers

)( 3)3()1(0 EE P

effA

E

nnn

2

0

)3(

0

||

8

)Re(3

induced intensity dependent refractive index induced intensity dependent refractive index )3(

Electric Polarization of moleculesElectric Polarization of molecules

effAn0

)3(

8

)Re(32

(NLSE) ||22

22

22 EEjE

t

Ej

z

E

Kerr induced nonlinear phase shiftKerr induced nonlinear phase shift

Linear Regime

EI

EQ

E

Nonlinear Regime

EI

EQ

E2

ELeffNL

99

Impairments in long-haul systems Impairments in long-haul systems with coherent detectionwith coherent detection

Noise limits communication system performanceNoise limits communication system performance BPSK / QPSK / DQPSK – phase noiseBPSK / QPSK / DQPSK – phase noise

Laser phase noiseLaser phase noise Amplified Spontaneous Emission (ASE) noise from inline Amplified Spontaneous Emission (ASE) noise from inline

amplifiersamplifiers Receiver shot/thermal noiseReceiver shot/thermal noise Noise and inter-symbol interference (ISI) resulting from Kerr

nonlinearity and its interaction with amplifier noise and other propagation effects

Amplitude noise and phase noise are generally Amplitude noise and phase noise are generally differentdifferent

1010

Part I – 100 Gb/s Long-haulPart I – 100 Gb/s Long-haul

Long-haul fiber-optic communication systemsLong-haul fiber-optic communication systems Coherent detection, DSP, communication theoryCoherent detection, DSP, communication theory Kerr nonlinearity induced phase noise

Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN)Nonlinear Phase Noise (NLPN) WDM effects and optical OFDMWDM effects and optical OFDM

SummarySummary

1111


Long-haul fiber-optic communication systemsLong-haul fiber-optic communication systems Coherent detection, DSP, communication theoryCoherent detection, DSP, communication theory Kerr nonlinearity induced phase noiseKerr nonlinearity induced phase noise

Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN)Nonlinear Phase Noise (NLPN) WDM effects and optical OFDMWDM effects and optical OFDM

SummarySummary

1212

A form of inter-symbol interference (ISI) due to A form of inter-symbol interference (ISI) due to the term the term

Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM)

SMF DCF

amplifier

EEj 2||

(NLSE) ||22

22

22 EEjE

t

Ej

z

E

t

)(tE

t

)(tE

t

)(tE

1313

Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM)

Pulse trainsPulse trains , ),(),( k

kkk

k UxkTtzUxtzE

pml

pmlpml UUUxxxj,,

**

kkk uuU

pml

pmlpmlkkk uuuxxxju

t

uj

z

u

,,

**2

22

22

First-order perturbation theoryFirst-order perturbation theory

Linear solution to NLSE

IFWM: not FWM!IFWM: not FWM! pmlk )( pmlk

Nonlinear perturbation

Pulse shape

Phase modulated info

IFWM is ISI caused by interaction of dispersion and Kerr nonlinearityIFWM is ISI caused by interaction of dispersion and Kerr nonlinearity

Et

Ej

z

E

22 2

22

EEj 2|| (NLSE)(NLSE)

1414

IFWM - induced phase noiseIFWM - induced phase noise

IFWM-induced phase noise on time slot 0IFWM-induced phase noise on time slot 0

ml

mlmlml tCxxxxt,

2,*0

*0 ),,,(Im)(

Highly nonlinear ISIHighly nonlinear ISI Each term in summation is a triple product of info. symbolsEach term in summation is a triple product of info. symbols Triple product comes from future and past symbols combined in a strange way Triple product comes from future and past symbols combined in a strange way

Too complicated to be fully exploited (at present)Too complicated to be fully exploited (at present) Considered noise most of the timeConsidered noise most of the time

1515

ProbabilityProbability distribution ofdistribution of

Need to know the probability Need to know the probability distribution of to distribution of to analytically characterize analytically characterize system bit error ratio (BER)system bit error ratio (BER)

Empirical distribution of Empirical distribution of only. BER obtained by only. BER obtained by numerical methodsnumerical methods

Is it possible to at least Is it possible to at least approximate the probability approximate the probability distribution ? distribution ?

ml

mlmlml Cxxxx,

,*0

*0 Im

0

Ho, PTL vol. 17, no. 4, Apr. 2005, pp. 789-791)(

0p

0

1616

ml mlmlml Cxxxxt

, ,*0

*0 Im)( Insight: terms in are Insight: terms in are

pairwise independent. For example, pairwise independent. For example,

are independentare independent

31

21

xxz

xxy

i.i.d. iixm ,1,,1

zxxzyz ppp 21||

41

02

2

3

A consequence of modulo addition in phase ofA consequence of modulo addition in phase of Not jointly independent Not jointly independent

mx

ml

mlp,

, )()()(00

)(0pApproximate probability distributionApproximate probability distribution

Approximation:Approximation:

2,1*0

*3211,1

*0

*211 ImIm CxxxxCxxxx ,

1717

for QPSK/DQPSK systemsfor QPSK/DQPSK systems

QPSK DQPSK

DQPSK: Group terms from that are correlated with DQPSK: Group terms from that are correlated with each other each other

10 ,

)(0p

1818

Tail Probability of Tail Probability of

QPSK DQPSK

)(Q

)(0p

1919

areare correlatedcorrelated

Exploiting Correlation structure of Exploiting Correlation structure of

Wei and Liu, Optics Letters, Vol. 28, no. 23, pp. 2300-2302, 2003

k

10 ,

No analytical knowledge of correlation structure of IFWM-induced No analytical knowledge of correlation structure of IFWM-induced phase noisephase noise

2020

Correlation Correlation ][)( 0 kEkR

ccCCxxxxxxxxE

CCxxxxxxxxEkR

kqkpmlkkqpqpmlml

ml qpkqkpmlkkqpqpmlml

.][

][4

1)(

,*,

**0

**

, ,,,

***0

*

0]|||||||[| when 0][ 2222 EMbxE ba

m

kmkmm

kmmmkm CCCCkR ,,*

,, Re2

1Re

2

1)(

mkmkm

mkmmmkm

mkmkm

mkmmmkm

CCCC

CCCCkR

*,,,,

,,*

,,

Re2

1Re

2

1

Re2

1Re

2

1)(

MPSKMPSK

BPSKBPSK

2121

)(kR for 40 GSym/s QPSK systemsfor 40 GSym/s QPSK systems

L (km)L (km)

SMFSMF 8080 .25.25 1717 1.21.2

DCFDCF 1616 .6.6 -85-85 5.35.3

(dB/km) km)-(ps/nm2 km)(/W

0 )( pst5.2 5

Sampling points

SMF DCF

Pulse shape: 33% RZ Pulse shape: 33% RZ Gaussian Gaussian

2222

Exploiting Exploiting )(kR Optimal linear prediction of Optimal linear prediction of

11111 , xx

1i

ikikkk ax

,)3(

)2(

)1(

1

3

2

1

R

R

R

Ra

a

a

topelitz

1.8 dB improvement when dominates1.8 dB improvement when dominates 0.8-1.2 dB improvement in presence of amplifier noise0.8-1.2 dB improvement in presence of amplifier noise

k

)(),( jiRjiRtopelitz

k

2323

IFWM-induced phase noise and IFWM-induced phase noise and amplitude noiseamplitude noise

ml

mlmlml Cxxxx,

,*0

*0 Im

ml

mlmlml Cxxxxr,

,*0

*0 Re

MPSK0

BPSK2/}Im{][

2,

00mlC

rE

Received amplitude uncorrelated with phase Received amplitude uncorrelated with phase noise for QPSK/DQPSK systemsnoise for QPSK/DQPSK systems

0

0r

A.P.T. Lau, S. Rabbani and J.M. Kahn, subm. OSA/IEEE JLT Sept. 2007

2424


Long-haul fiber-optic communication systemsLong-haul fiber-optic communication systems Coherent detection, DSP, communication theoryCoherent detection, DSP, communication theory Kerr nonlinearity induced phase noiseKerr nonlinearity induced phase noise

Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM)Nonlinear Phase Noise (NLPN) WDM effects and optical OFDMWDM effects and optical OFDM

SummarySummary

2525

Nonlinear phase noise (NLPN)Nonlinear phase noise (NLPN)

2effNL || nEL

Kerr nonlinearity induced nonlinear phase shift:Kerr nonlinearity induced nonlinear phase shift:

corrupted by Amplified Spontaneous Emission (ASE) noise from corrupted by Amplified Spontaneous Emission (ASE) noise from inline amplifiersinline amplifiersE

EI

EQ

Linear Regime

EI

EQ

Nonlinear Regime

EI

EQ

Linear Regime

En

Etot

Nonlinear Regime

EI

EQ

Etot

NL|Etot|2

),0(~ , 2InnE N

Nonlinear phase noise or Gordon-Mollenauer effectNonlinear phase noise or Gordon-Mollenauer effect

2626

Joint probability distribution (PDF) Joint probability distribution (PDF) of received amplitude and phaseof received amplitude and phase

,/Er

1

)(, )(

1)(),(

m

jmmRice

o

oserCerfrf

)2(1

)( 0)( 2

sr

Rice rIrerf s

K.P. Ho “K.P. Ho “Phase modulated Optical Communication SystemsPhase modulated Optical Communication Systems,” Springer 2005,” Springer 2005

,2/1

s

PLx

jmxsm sec )2/(tan jmxjmxsm

jmxm

sejmx tan sec

m

mm

s

r

m

mm s

rIe

s

rrC m

m 2

22

)(

Transmitted signal with power , phase Transmitted signal with power , phase s 0

2727

PDF and maximum likelihood (ML) decision PDF and maximum likelihood (ML) decision boundaries for 40G Sym/s QPSK Signalsboundaries for 40G Sym/s QPSK Signals

L=5000 km, P=-4 dBm, L=5000 km, P=-4 dBm, km,/1.2,0.25dB/km WdB 5.4nF

2828

Maximum Likelihood (ML) DetectionMaximum Likelihood (ML) Detection

To implement ML To implement ML detection, need to know detection, need to know the ML boundariesthe ML boundaries

Need to knowNeed to know With ,can either de-With ,can either de-

rotate the received phase rotate the received phase or use a lookup tableor use a lookup table

rc rc

4

rc

4

rc

rc

2929

With approximations With approximations ML decision boundaryML decision boundary rc

zezIzzzzzz zm 2/)( ,3/tan ,3/sin 33

it can be shown that it can be shown that )(arg)(arg 1 rCmrCm

0)()(argsin4

sin|)(| 11

rrCmm

rC cm

m

xx

xxx

rCrc

2cos2cosh

2sinh2sin

2

)(arg)(

1

2r

xx

xxxxxs

2cos2cosh

2/sinh2/cos2/cosh2/sin

24

r )(xh

2/1

s

PLx

3030

Received phase rotation by Received phase rotation by

Before rotationBefore rotation After rotationAfter rotation

Straight line ML decision boundaries after rotationStraight line ML decision boundaries after rotation

rc

3131

Symbol Error Rate (SER) for MPSK SystemsSymbol Error Rate (SER) for MPSK Systems

)(4

)(;1,

2

2

)1()(2

)2(5.0)(

!

))(()(

21

2

11

1 0)2(5.01

xa

xm

kmF

mxa

kmx

k

xjgxse

M

MSER

m

m

m kkm

mm

mm

km

m

Numerical results Analytical

3232

SER for D-MPSK Systems SER for D-MPSK Systems

1

2 sinc 21

mm M

mD

NM

MSER

0

)( drrCD mm

3333

16-QAM modulation formats16-QAM modulation formats

High spectral efficiency. High spectral efficiency. Together with coding, Together with coding, approach information-approach information-theoretic limits.theoretic limits.

For a given bit rate, For a given bit rate, reduce inter-symbol reduce inter-symbol interference compared interference compared to 2-PSK or 4-PSK.to 2-PSK or 4-PSK.

3434

16-QAM transmitter16-QAM transmitterLaser

3535

Maximum likelihood detection for 16-Maximum likelihood detection for 16-QAM systems in presence of NLPN QAM systems in presence of NLPN

No analytical formula for ML No analytical formula for ML decision boundaries for 16-decision boundaries for 16-QAM system as power of QAM system as power of signal points not constantsignal points not constant

Boundaries distorted from Boundaries distorted from straight linesstraight lines

Can we design/process the signals at the transmitter Can we design/process the signals at the transmitter and/or receiver such that ML detection can be better and/or receiver such that ML detection can be better approximated by straight lines?approximated by straight lines?

3636

16-QAM signal phase pre-compensation16-QAM signal phase pre-compensation

With phase pre- comp.With phase pre- comp.Without phase pre-comp.Without phase pre-comp.

Pavg= -2.5 dBm

inNL LP

Modes of conditional probability distribution corresponding to each Modes of conditional probability distribution corresponding to each signal point do not form a square constellationsignal point do not form a square constellation

Pre-rotate phase by the negative of mean nonlinear phase shiftPre-rotate phase by the negative of mean nonlinear phase shift

3737

NLPN post-compensationNLPN post-compensation Rotate the received phase by proportional to received Rotate the received phase by proportional to received

intensity for phase noise variance minimizationintensity for phase noise variance minimization

2/recLP

With phase pre- comp. onlyWith phase pre- comp. only Phase pre- comp. with NLPN Phase pre- comp. with NLPN post-comp.post-comp.

Ho and Kahn, JLT vol.22 no. 3, Mar. 2004 Ly-Gagnon and Kikuchi, Paper 14C3-3, OECC 2004

3838

Performance of phase rotation Performance of phase rotation methods in 16-QAM systemsmethods in 16-QAM systems

(No phase comp.)

A.P.T. Lau and J.M. Kahn, OSA/IEEE JLT, pp. 3008-3016, Oct 2007

3939

Comparison of various phase Comparison of various phase noises in long-haul systemsnoises in long-haul systems

ASE induced ASE induced phase noisephase noise

IFWM-induced IFWM-induced phase noisephase noise

Nonlinear Nonlinear Phase NoisePhase Noise

Signal Signal PowerPower

Amplifier Amplifier noise powernoise power

System System LengthLength

RemarksRemarks Dominant in Dominant in terrestrial linksterrestrial links

Dominant in Dominant in Submarine linksSubmarine links

sP

12

sP sP

2n 2

n~L 2L 3L

4040


Long-haul fiber-optic communication systemsLong-haul fiber-optic communication systems Coherent detection, DSP, communication theoryCoherent detection, DSP, communication theory Kerr nonlinearity induced perturbationsKerr nonlinearity induced perturbations

Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN)Nonlinear Phase Noise (NLPN)WDM effects and optical OFDM

SummarySummary

4141

Summary – 100Gb/s Long-HaulSummary – 100Gb/s Long-Haul Coherent detection and DSP technologies results in the Coherent detection and DSP technologies results in the

relevance and importance of communication theory in long-relevance and importance of communication theory in long-haul system design for 100 Gb/s transmissionhaul system design for 100 Gb/s transmission

Performance of long-haul systems limited by Kerr Performance of long-haul systems limited by Kerr nonlinearity induced system impairments such as IFWM, nonlinearity induced system impairments such as IFWM, NLPNNLPN

System BER characterizationSystem BER characterization Appropriate signal processing techniques for performance Appropriate signal processing techniques for performance

improvementsimprovements Much more work remains to understand/improve long-haul Much more work remains to understand/improve long-haul

system performance!system performance!

4242

Part II – 100Gb/s Ethernet using Part II – 100Gb/s Ethernet using multimode fibermultimode fiber

Motivation and backgroundMotivation and backgroundPrincipal Modes and adaptive optics using Principal Modes and adaptive optics using

spatial light modulatorspatial light modulatorSystem optimization framework and System optimization framework and

experimental resultsexperimental results

4343

Ethernet RoadmapEthernet Roadmap

Who needs 100G Ethernet?Who needs 100G Ethernet? Not me (individual user) ~Not me (individual user) ~ Data centers (e.g. Google) and other large enterprise/core switchesData centers (e.g. Google) and other large enterprise/core switches

Multimode Fiber (MMF) widely deployed. Want to reuse Multimode Fiber (MMF) widely deployed. Want to reuse it for cost effectiveness (just like DSL)it for cost effectiveness (just like DSL)

4444

100 Gb/s Ethernet100 Gb/s Ethernet IEEE Higher Speed Study Group formed July ‘06IEEE Higher Speed Study Group formed July ‘06 Standards expected to be finalized by 2010Standards expected to be finalized by 2010 100Gb/s transmission over 100 m of multi-mode fiber100Gb/s transmission over 100 m of multi-mode fiber

4545

Multimode Fibers (MMF)Multimode Fibers (MMF)

m125

m5.62/50

m125

m9

MMFSMF

M

n

tzjnnx

netzEyxFtzyx1

))((),(),(),,,( E

Ideal ModesIdeal Modes Spatially orthogonal (typical MMF has Spatially orthogonal (typical MMF has

100 modes) having well-defined propagation speeds100 modes) having well-defined propagation speeds Propagate without cross-coupling in Propagate without cross-coupling in idealideal fiber fiber Significant mode coupling in real installed fibersSignificant mode coupling in real installed fibers

Mode

Pulse envelope

pqqp dxdyFF *

4646

Different modes have different – different speedDifferent modes have different – different speed Single pulse in – many pulses out (modal dispersion or ISI).Single pulse in – many pulses out (modal dispersion or ISI). Linear ISI – identical to ISI in wireless/wirelineLinear ISI – identical to ISI in wireless/wireline

t t

Modal Dispersion in MMFModal Dispersion in MMF

EEjEt

Ej

z

E 22

22 ||

22

n

tzjnnx

n

etzEyxFtzyx )( )(

),(),(),,,( E

)(n

MMFTx

)(tPin )(tPout

)()( tPtI out

MMF systems – OOK with direct detectionMMF systems – OOK with direct detection

4747

Motivation and backgroundMotivation and backgroundPrincipal Modes and adaptive optics using

spatial light modulatorSystem optimization framework and System optimization framework and

experimental resultsexperimental results


4848

Principal Modes in Multimode FiberPrincipal Modes in Multimode Fiber

Principal Modes (PM) – linear combinations of ideal modesPrincipal Modes (PM) – linear combinations of ideal modes Single pulse in – single pulse out (well defined group delay )Single pulse in – single pulse out (well defined group delay ) Insight – input electric field design to excite single PM!Insight – input electric field design to excite single PM!

S. Fan and J. M. Kahn, Optics Letters, vol. 30, no. 2, pp. 135-137, 2005

n

nn yxFayx ),()(),,( inE

inoutin A AA )(,21 Uaaa TM

PMPM AA

UU

j

Propagation matrix that captures mode coupling

Input electric fieldInput electric field

UU

j

Group delay operatorGroup delay operator

4949

Spatial Light Modulator (SLM)Spatial Light Modulator (SLM)

kx

ky

x

y

SLM

MMF

2-D array of mirrors with the reflectance of each mirror (2-D array of mirrors with the reflectance of each mirror (vvii) ) can be controlled.can be controlled.

Sort of a 2-D spatial filterSort of a 2-D spatial filter

Collimating lens

Laser

n

nn yxFa ),(

nyxnn kkFa ),(

~

n

yxnn kkFva ),)(~

(

nnn yxFva ),)((

5050

Adaptive Transmission SchemeAdaptive Transmission Scheme

Spatial LightModulator

Multimode Fiber

OOKModulator

AdaptiveAlgorithm

Fourier Lens

Iin(t)

Trans.Data

Transmitter

Low-Rate Feedback Channel

Photo-Detector

Clock & DataRecovery

ISIEstimation

Rec.Data

ISI ObjectiveFunction

Receiver

Iout(t)

Impulse response Eye opening

0.80.3-0.1-0.4

5151

Motivation and backgroundMotivation and backgroundPrincipal Modes and adaptive optics using

spatial light modulatorSystem optimization framework and

experimental results


5252

Optimization ProblemOptimization Problem

M

iiiPMin tqdxdyzyxHyxEtg

2

1

2

, ˆ,,

The pulse response is given by

vuuv

M

ii

Hii

H tq2

1

The ISI is given by

01

0

0

zz

nTggyn

minimizesubject to

ISI (or modal dispersion)

z1z0

g(t)

0 T 2T 3T 4T 5T 6Tt

q(t)

,2,11 jv j

Let be the spatial light modulator (SLM) settingsv

5353

Optimization ProblemOptimization Problem

2

21 vPvp2 HH

Niv ,,1 12

i

maximize

subject to

2

21 vPvp2 HH

Niv ,,1 12

i

maximize

subject to

Not in any standard form. For example, not convex.Not in any standard form. For example, not convex.

y

Niv ,,1 12

i

maximize

subject to tyH 2xx

tH vp1

xvP H2

y

Niv ,,1 12

i

maximize

subject to tyH 2xx

tH vp1

xvP H2

Convex! (Second order cone program)Convex! (Second order cone program)

NC1p )1(2

NNCPNCv

and

is the SLM setting (optimization variable)

NC1p )1(2

NNCPNC1p )1(2

NNCPNCv

andand (not explicitly known in experiment)

5454

Adaptive algorithms to achieve globally minimal Adaptive algorithms to achieve globally minimal ISI – efficient, robust in presence of noise and ISI – efficient, robust in presence of noise and no need to know system parameters.no need to know system parameters.

Sequential Coordinate Ascent (SCA) Sequential Coordinate Ascent (SCA)

Adaptive AlgorithmsAdaptive Algorithms

Amplitude-and-Phase SCA (APSCA):Amplitude-and-Phase SCA (APSCA):

1)1) Pick the Pick the iithth SLM block SLM block

2)2) Optimize amplitude and phase of Optimize amplitude and phase of vvii

3)3) go to next SLM blockgo to next SLM block

4)4) RepeatRepeat

2v

1v

cvbvay ii *2Re

5555

Experimental SetupExperimental Setup

PM SMFNA = 0.11

f = 10.4 mm

f = 10.4 mm

50 m GRIN MMFNA = 0.19

45-45

LinearPolarizer

NematicLiquid Crystal

SLMPhase-Only 256 256

/2plate

/4plate

Two-AxisTranslation Stage

SLM DriveSignal

PM SMFNA = 0.11

f = 10.4 mm

f = 10.4 mm

50 m GRIN MMFNA = 0.19

45-45

LinearPolarizer

NematicLiquid Crystal

SLMPhase-Only 256 256

/2plate

/4plate

Two-AxisTranslation Stage

SLM DriveSignal

kx

ky

NA = 0.19

NA = 0.11

kx

ky

NA = 0.19

NA = 0.11

5656

Transmission SchemeTransmission Scheme

5757

Experimental Results: 10 Gb/s over 2 kmExperimental Results: 10 Gb/s over 2 km

Before Before adaptationadaptation

After After adaptationadaptation

4 um offset patch cord

2 kmLight from SLM

5858Before AdaptationAfter Adaptation


2 kmLight from SLM


59590 1 2 3 4 5 6 7 8 9 10

10-10

10-8

10-6

10-4

10-2

100

Attenuation (dB)

BE

R

Before

2PSCA4PSCA

CPSCA


2 kmLight from SLM


Before

After

6060

50 55 60 6510

-10

10-8

10-6

10-4

10-2

100

Channel number

BE

R

Channel spacing is 50 GHz with channels 54-59 error free – 300 GHz of usable bandwidth!


2 kmLight from SLM


R. A. Panicker, R. A. Panicker, A.P.T. LauA.P.T. Lau, J.P. Wilde and J. M. Kahn, submitted to IEEE JLT, Nov 2007, J.P. Wilde and J. M. Kahn, submitted to IEEE JLT, Nov 2007

6161


Multimode Fiber

AdaptiveAlgorithm

Fourier Lens

OOKModulator

Trans.Data 1

Transmitter


Photo-detector


ISIEstimation

Rec.Data 1


Receiver

f

OOKModulator

Trans.Data M

…

Single-ModeMultiplexer

I1,in(t)

IM,in(t)Single- or Multi-

Mode Demultiplexer

…

I1,out(t)

IM,out(t)Photo-

detectorClock & Data

RecoveryRec.

Data M


Multimode Fiber

AdaptiveAlgorithmAdaptiveAlgorithm

Fourier Lens

OOKModulator

OOKModulator

Trans.Data 1

Transmitter


Photo-detector



ISIEstimation

ISIEstimation

Rec.Data 1


Receiver

ff

OOKModulator

OOKModulator

Trans.Data M

…

Single-ModeMultiplexer

I1,in(t)

IM,in(t)Single- or Multi-

Mode Demultiplexer

…

I1,out(t)

IM,out(t)Photo-

detectorClock & Data

RecoveryClock & Data

RecoveryRec.

Data M

Experimental Results: 100 Gb/s, 2.2 kmExperimental Results: 100 Gb/s, 2.2 km

6262

Experimental Results: 100 Gb/s, 2.2 kmExperimental Results: 100 Gb/s, 2.2 kmP

ow

er i

n 0

.2 n

m B

W (

dB

m)

Wavelength (nm)

5

10

15

20

25

1545 1549 1553 1557 1561 1565

0 1 2 3 4 5 6 7 8 9 10

FE

C D

eco

der

Inp

ut

BE

RAttenuator Setting (dB)

100

102

104

106

108

1010

FECThreshold

R. A. Panicker et al., IEEE PTL , Aug. 2007.

6363

Experimental Results: 100 Gb/s, 2.2 kmExperimental Results: 100 Gb/s, 2.2 km

0 1 2 3 4 5 6 7 8 9 10

FE

C D

eco

der

Inp

ut

BE

RAttenuator Setting (dB)

100

102

104

106

108

1010

FECThreshold

Po

wer

in

0.2

nm

BW

(d

Bm

)

Wavelength (nm)

5

10

15

20

25

1545 1549 1553 1557 1561 1565

Error-free transmission after Forward Error Correction !Error-free transmission after Forward Error Correction !

6464

Principal Modes in Multimode Fiber Principal Modes in Multimode Fiber

A.P.T. Lau, J.P. Wilde and J. M. Kahn, “Principal modes in multimode fibers,” in preparation

0 1 2 3 4

-0.1

-0.05

0

Chn 56

0 1 2 3 4

-0.1

-0.05

0

Chn 57

0 1 2 3 4

-0.1

-0.05

0

Chn 58

0 1 2 3 4

-0.1

-0.05

0

Chn 59

0 1 2 3 4

-0.1

-0.05

0

Chn 60

0 1 2 3 4

-0.1

-0.05

0

Chn 61

0 1 2 3 4

-0.1

-0.05

0

Chn 62

0 1 2 3 4

-0.1

-0.05

0

Chn 63

0 1 2 3 4

-0.1

-0.05

0

Chn 64

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 56

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 57

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 58

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 59

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 60

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 61

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 62

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 63

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 64

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 56

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 57

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 58

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 59

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 60

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 61

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 62

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 63

0 1 2 3 4-0.2

-0.15

-0.1

-0.05

0

0.05Chn 64

0 1 2 3 4

-0.2

-0.1

0

Chn 56

0 1 2 3 4

-0.2

-0.1

0

Chn 57

0 1 2 3 4

-0.2

-0.1

0

Chn 58

0 1 2 3 4

-0.2

-0.1

0

Chn 59

0 1 2 3 4

-0.2

-0.1

0

Chn 60

0 1 2 3 4

-0.2

-0.1

0

Chn 61

0 1 2 3 4

-0.2

-0.1

0

Chn 62

0 1 2 3 4

-0.2

-0.1

0

Chn 63

0 1 2 3 4

-0.2

-0.1

0

Chn 64

Chn 56 Chn 57 Chn 58












Chn. 59 Chn. 60 Chn. 61

PulseResponse

ModeIntensityProfile

Ability to excite best Principal Modes for any particular channelAbility to excite best Principal Modes for any particular channel Potentially mode division multiplexing !Potentially mode division multiplexing !

6565

Comparison between Optical and Comparison between Optical and Electrical EqualizationElectrical Equalization

Optical Optical ElectricalElectrical

ComplexityComplexity Independent of Independent of BxLBxL Linear (FFE/DFE) and Linear (FFE/DFE) and exponential (MLSD) in exponential (MLSD) in BxLBxL

Noise enhancementNoise enhancement NoNo FFE/DFE have noise FFE/DFE have noise enhancementenhancement

Multi-channelMulti-channel

equalizationequalization

One SLM setting equalizes One SLM setting equalizes multiple channelsmultiple channels

Per channel equalization Per channel equalization requiredrequired

Power consumptionPower consumption No power consumption No power consumption after adaptationafter adaptation

Steady power consumptionSteady power consumption

PerformancePerformance Comparable to MLSDComparable to MLSD

Lastly, they can be simultaneously implemented!Lastly, they can be simultaneously implemented!

0 T T2 T3 T4 T5

0 T T2 T3 T4 T5

Electrical equalization: get the best out of a ‘dirty’ channel

Optical equalization: Clean up the channel

6666

Summary – 100 Gb/s EthernetSummary – 100 Gb/s Ethernet Principal Modes – a new understanding in modal Principal Modes – a new understanding in modal

dispersion and ISI in multi-mode fiber transmissiondispersion and ISI in multi-mode fiber transmission Modal dispersion (or ISI) mitigation through spatial light Modal dispersion (or ISI) mitigation through spatial light

modulator that modifies spatial profile of input electric modulator that modifies spatial profile of input electric fieldfield

Adaptive algorithms to achieve optimal performanceAdaptive algorithms to achieve optimal performance Experimentally demonstrated 10 Gb/s and 100 Gb/s Experimentally demonstrated 10 Gb/s and 100 Gb/s

transmission over multiple kilometers of multi-mode transmission over multiple kilometers of multi-mode fibers with real world impairmentsfibers with real world impairments

Comparable or outperform the best known electrical Comparable or outperform the best known electrical equalization technique from communication theoryequalization technique from communication theory

6767

Research OutlookResearch Outlook

Advances in photonic/electronic devices allows Advances in photonic/electronic devices allows one to start a research problem in fiber-optic one to start a research problem in fiber-optic communications bycommunications by

Underlying physics of signal transmission yet to Underlying physics of signal transmission yet to be fully understoodbe fully understood

Fiber-optic communications will be even more Fiber-optic communications will be even more interdisciplinary in the future! interdisciplinary in the future!

““Consider an arbitrarily modulated signal x(t)...”Consider an arbitrarily modulated signal x(t)...”

6868

Thank you!Thank you!

Documents

The Marriage of Photonics and Communication Theory for 100 Gb/s Long-Haul and Ethernet Fiber-Optic Transmissions The Marriage of Photonics and Communication