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New Approaches to Modeling Optical Fiber Transmission Systems

Presented by

C. R. MenyukWith

R.M. Mu, D. Wang, T. Yu, and V. S. Grigoryan

University of Maryland Baltimore CountyComputer Science and Electrical Engineering Department

Baltimore, MD 21250

UMBC

New Approaches to Modeling Optical Fiber Transmission Systems

Presented by

V. S. GrigoryanWith

R.M. Mu, D. Wang, T. Yu, and C. R. Menyuk

University of Maryland Baltimore CountyComputer Science and Electrical Engineering Department

Baltimore, MD 21250

UMBC

Professors

Gary Garter Curtis Menyuk

Associates

Vladimir Grigoryan Edem Ibragimov Pranay Sinha

Students

Ronald Holzlöhner Ivan Lima, Jr. Ruomei Mu Yu Sun Ding Wang Tao Yu

Current research group

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A Decade Ago

System with Electronic Repeaters

• 500 Mb/s looked achievable; 100 Mb/s was achieved

• Only attenuation mattered in fibers

– fibers were a transparent pipe

• Repeaters had limited bandwidth (WDM and upgrading impossible)

– Cost and complexity rose dramatically with data rate

– spacings of 20 km were required

R R R

20 km

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Today

System with Erbium-doped amplifiers

• 1 Tbit/s looks achievable; 200 Gbits/s achieved

• Wavelength division multiplexing (WDM) is possible

and becoming widely used (200 Gb/s = 80 channels 2.5 Gb/s)

• Fiber dispersion, nonlinearity, and polarization effects all accumulate!

• Fiber impairments set the limits on what is achievable

– nonlinearity is strong and hard to model properly.

50 km or more

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What formats should be used?

1 1 0 1 0 0 1

Non-return to zero (NRZ)

(close to zero dispersion)

Solitons

(anomalous dispersion)

vs.

11 0 1 00 1

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Approaches are converging!

Solitons and NRZ resemble each other

– solitons dispersion-managed solitons

– NRZ phase- and amplitude-modulated pulses

01110 01110 01110 01110

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What formats should be used?Time-division multiplexed (TDM)

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

I

t

channels

Wavelength-division multiplexed (WDM)

channels

1 2 3 4 5 6 7 8

I

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Fiber impairments

Chromatic Dispersion Polarization Effects Nonlinearity ASE noise

Four Horsemen of the Apocalypse

Albrecht Dürer

Four Horsemen of Optical Fiber Transmission

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Modeling approaches

Multiple scale length methods— for establishing equations

Split-step modeling— often too slow (especially with WDM)

Reduced methods— dealing with many channels, long-term effects, networks

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Modeling approaches

Monte Carlo— often too slow

Ito’s method— often does not work

Linearization

Randomly varying effects

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Multiple Scale Lengths methods

Light wavelength1 m

10 m

100 m

1 mm

10 mm

100 mm

1 m

100 m

10 m

1 km

100 km

10 km

1 Mm

10 Mm

100 Mm

Core diameter

Pulsedurations

Polarizationbeat length

Attenuation length

Nonlinearlength

Fiber correlationlength

Dispersionlength

FLAG

trans-Atlantic

Manakov-PMDapproximation

Slowly varyingenvelopeapproximation

Maxwell’s equations

land link

Optical systems have a wide spread in length scales!

Scale lengths in fiber transmission

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Coupled Nonlinear Schrödinger Equation

Maxwell’s Equations

Coupled Nonlinear Schrödinger Equation

Manakov-PMD Equation

Averaging over the Poincaré sphere

Using the slowly varying envelope approximation

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Linearization approach

Monte Carlo:

Linearization (with small noise):

signal noise complicated mix

signal noise Gaussian statistics

(nonlinear) (linear)

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Comparison of theory & experiment

0

1

2

0 10000 20000

Tim

ing

jitte

r (p

s)

Distance (km)

experimentMonte Carlo simulationour approach

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Average Power Approximation

With N channels, scaling reduces from N 2 to better than N!

Useful for point-to-point systems(Yu, Reimer, and Menyuk; Wang and Menyuk)

Critical for network simulations(Bellcore: R. Wagner, I. Roudas, & colleagues)

target channelcomplete channelaveraged channel

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With polarizationS

toke

s ve

ctor

distance (km)

simulation simulationtheory

Evolution of the Stokes vector

–0.5

0

0.2

0 10000–0.5

0

0.2

0 10000–0.5

0

0.2

0 10000

S 1 S3

S2

(a)

S 1 S3

S2

(b)

S 1 S3

S2

(c)

realistic dispersion large dispersion

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Reduced Polarization Model

PDL effects calculated — one year ago

Verification of model effectiveness with chromatic dispersion and

nonlinearity — now

Inclusion of PMD, PDL, and PDG — in one year

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Experimental Applications

D

LNormal

AnomalousAverage

1.2 nmFilter

AO

Switch60/40 Coupler

Input To Receiver

PC

EDFANormalAnomalous

Dispersion-managed soliton experiments

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Theory and experimentDynamic Evolution in One Round Trip

Amplitude Margin

0 bit

1 bit

⎫⎬⎭experimental

theoretical

experimental

theoretical

0 30000Amplidute Margin (mV)

Distance (km)0200

–200

0510152025

FWHM (ps) Normal Anomalous2550751003.57.0Distance

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Normal dispersion solitons:

A

B

0

10

20

0 0.2

D=110D=100D=90D=80D=70D=60

Pul

se e

nerg

y

Average dispersion

— Solitons exist in the normal dispersion regime— These solutions are stable

Inte

nsity

0

Time– 5

5

10000

0

5000

1

0.001

At point B:

Distance

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World record experiment

20 Gbit/s: BER < 1×10−9@ 20 Mm

20 Gbit/s input 10 Gbit/s Demux output (20 Mm)

experimental

theoretical}

1 Bit 0 Bit

}

0

0.2

0 250T (ps) 0 250

0.8

0

– 0.4

T (ps)

0

300

0 25000

Amplitude Margin (mV)

Z (km)

sliding no sliding

– 100

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Conclusions

Optical fiber transmission systems are rapidly changing

Good modeling has become critical

Enormous strides have been made