1

Statistical properties of DGD distribution in a long-haul recirculating loop system

Hai Xu1, Brian S. Marks1, John Zweck2, Li Yan1, Curtis R. Menyuk1, Gary M. Carter1

1. Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County2. Department of Mathematics and Statistics, University of Maryland Baltimore County

March 15, 2005

2

Focus

• Polarization mode dispersion (PMD) degrades system performance [1]

• Polarization properties drift over time [2]

– This leads to time-varying system performance

• We determine time scale of drift and its impact

3

Context

Previous theoretical work assumes uncorrelated drift [3]• Good model for aerial fiber [4]; Not good for other systems [5], [6]

Our contributions• We develop a theoretical model that properly accounts for time correlations

• We validate the model by comparison to experiments

4

PMD effects

• Waveform is distorted due to PMD-induced differential group delay (DGD)

Fiber

Transmitter Receiver

Long-term DGD distribution [7]–[9]

− Maxwellian in a straight line system

− Bessel-shape in a recirculating loop

0 20 (ps)

0.1

0

pdf

Short-term DGD distribution

− Correlated and non-Maxwellian / non-Bessel

− Varies from time window to time window

0 25 0 25 (ps) (ps)

− Hour 51−53− Hour 171−173

− Day 1−2− Day 5−6

− straight line− 107 km loop

Long-term5000 km

3 hour5000 km, loop

2 days 5000 km, loop

0 200Time (ps) 0 200Time (ps)

5

Quantification of DGD distribution

• : Standard deviation of DGD in a time window

• (T): Average of over all windows of time T

1

1 L

mm

TL

1 2 3 L

T T T T

time

We use (T) to quantify the statistical properties of the DGD distribution

6

Experimental setup: 107 km recirculating loop [10]

TX: RX:AOSW:PS:SMF: DSF:OBF:►:

TX RX

OBF

PS

LiNbO3

AOSW2

AOSW1 3 dB

DSFSMF

107 km

DSF DSF

DSFSMF

We repeatedly measure DGD at 5, 000 km (50 round trips) every 10 seconds for 10 days

DGD at 5, 000 km depends on:

• 107 km fiber — drifts over time

• PS — randomly varied in each DGD measurement (10 sec.)

TransmitterDGD measurement at ReceiverAcousto-optic switchLoop-syn. polarization scrambler [11]Standard single-mode fiber (3.5 km)Dispersion shifted fiber (25 km)Optical band-pass filterErbium-doped fiber amplifier

7

Simulation (I) — Loop system

• Coarse-step method to model 107 km fiber [12]

• RPS(i), PS-induced polarization rotation after ith round trip

ˆ ˆ : birefringence vector of th section

: fixed by 0.62 ps of 107 km fiber [12]

ˆ : perturbed to model fiber drift

n n

n

n

r

r

1̂r

2r̂3̂r

75r̂

RPS(1) RPS(2)

Round trip 1 Round trip 2

RPS(50)

Round trip 50

RXTX

ˆnrDGD of the whole system is determined by RPS(i) and

Birefringent fiber, length z = 107/75 km

107 km fiber

8

Simulation (II) — Fiber drift models

ˆnr

ˆnr

• Statistical properties of DGD distribution are only determined by fiber drift models

• Uncorrelated model: Brownian, parameterized by drift rate

• Correlated model: Quasi-deterministic, parameterized by drift rate and correlation

• We try 3 different parameter settings in each model: Brownian 1–3; QD 1–3

• We perturb 6 million times for each parameter setting

in Brownian model in quasi-deterministic modelˆnr

9

Brownian model

10−2 105T (hours)

2.5

1.5

(ps)

• Simple — insensitive to parameter settings– All three settings yield almost the same results

• Accurate when T > 25 minutes

ˆ ˆ ΔACF Δ

ˆ ˆPolarization dispersion vector of one round trip,

d

t

d t d t tt

dt dt

0 180t (min)

AC

F d(t

) (p

s2 /m

in2 )

10−3

0 • differential time of 2 minutes• differential time of 4 minutes

× Experiment − Brownian 1− Brownian 2− Brownian 3 • Correlation time (t0) is 25 minutes

Why 25 minutes ?

10

Quasi-deterministic model

Agrees with experiment for almost all Ts• By properly accounting for time correlation (in parameter setting QD 2)

2.5

1.75

(

ps)

10−2 104T (hours)

× Experiment − QD 1− QD 2− QD 3

Two characteristic times

• 25 minutes: Uncorrelated region

• 1000 hours: Long-term region

11

Conclusion

• Two characteristic times in our 107 km loop system– 25 minutes: fiber drift becomes uncorrelated

– 1000 hours: DGD distribution converges

• Our approach can be applied to straight line systems– Correlation time must be determined

– Uncorrelated region: Simple uncorrelated model

– Correlated region: Proper correlated model

We give an approach for characterizing the statistical properties of the DGD distribution

12

References

1. H. Kogelnik, R. M. Jopson, and L. E. Nelson, “Polarization-mode dispersion,” in Optical Fiber Telecommunications, I. P. Kaminow and T. Li, Eds. San Diego, CA: Academic, 2002 Vol. IVB, Ch. 15, pp. 725–861.

2. P. Kaminow, “Polarization in optical fibers”, IEEE J. Quantum Electron., vol. QE-17, pp. 15–22, 1981.

3. M. Karlsson, J. Brentel, and P. A. Andrekson, “Long-term measurement of PMD and polarization drift in installed fiber,” J. Lightwave Technol., vol. 18, pp. 941–951, 2000.

4. D. S. Waddy, L. Chen, and X. Bao, “Theoretical and experimental study of the dynamics of polarization-mode dispersion,” IEEE Photon. Technol. Lett., vol. 14, pp. 468–470, 2002.

5. M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, “Field PMD measurements through a commercial, Raman amplified ULH transmission system,” Proc. LEOS PMD Summer Topical Meeting 2003, 2003, MB3.3.

6. C. D. Angelis, A. Galtarossa, G. Gianello, F. Matera, and M. Schiano, “Time evolution of polarization drift in installed fiber,” J. Lightwave Technol., vol. 10, pp. 552–555, 1992.

7. F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Statistical treatment of the evolution of the principle states of polarization in single-mode fiber,” J. Lightwave Technol., vol. 8, pp. 1162–1165, 1990.

8. E. Corbel, “Concerns about emulation of polarization effects in a recirculating loop,” in Proc. ECOC 2003, 2003, Mo3.7.4.

9. H. Xu, B. S. Marks, J. Zweck, L. Yan, C. R. Menyuk, and G. M. Carter, “The long-term distribution of differential group delay in a recirculating loop,” in Symposium on Optical Fiber Measurements 2004, 2004, pp. 95–98.

10. J. M. Jacob and G. M. Carter, “Error-free transmission of dispersion-managed solitons at 10 Gbit/s over 24500 km without frequency sliding,” Electron. Lett., vol. 33, pp. 1128–1129, 1997.

11. Q. Yu, L. S. Yan, S. Lee, Y. Xie, and A. E. Willner, “Loop-synchronous polarization scrambling for simulating polarization effects using recirculating fiber loops,” J. Lightwave Technol., vol. 21, pp. 1593–1600, 2003.

12. D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol., vol. 15, pp. 1735–1746, 1997.