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1 Statistical properties of DGD distribution in a long-haul recirculating loop system Hai Xu 1, Brian S. Marks 1, John Zweck 2, Li Yan 1, Curtis R. Menyuk 1, Gary M. Carter 1 1.Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County 2.Department of Mathematics and Statistics, University of Maryland Baltimore County March 15, 2005

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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

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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

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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 (ps) Hour 51 53 Hour 171 173 Day 1 2 Day 5 6 straight line 107 km loop Long-term 5000 km 3 hour 5000 km, loop 2 days 5000 km, loop 0 200Time (ps)0 200Time (ps)

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5 Quantification of DGD distribution : Standard deviation of DGD in a time window (T): Average of over all windows of time T 1 2 3 L T T T T time We use (T) to quantify the statistical properties of the DGD distribution

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6 Experimental setup: 107 km recirculating loop [10] TX: RX: AOSW: PS: SMF: DSF: OBF: : TX RX OBF PS LiNbO 3 AOSW2 AOSW1 3 dB DSF SMF 107 km DSF SMF 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.) Transmitter DGD measurement at Receiver Acousto-optic switch Loop-syn. polarization scrambler [11] Standard single-mode fiber (3.5 km) Dispersion shifted fiber (25 km) Optical band-pass filter Erbium-doped fiber amplifier

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7 Simulation (I) Loop system Coarse-step method to model 107 km fiber [12] R PS (i), PS-induced polarization rotation after ith round trip R PS (1) R PS (2) Round trip 1 Round trip 2 R PS (50) Round trip 50 RX TX DGD of the whole system is determined by R PS (i) and Birefringent fiber, length z = 107/75 km 107 km fiber

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8 Simulation (II) Fiber drift models 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 modelin quasi-deterministic model

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9 Brownian model 10 2 10 5 T (hours) 2.5 1.5 ( ps) Simple insensitive to parameter settings –All three settings yield almost the same results Accurate when T > 25 minutes 0 180 t (min) ACF d ( t) (ps 2 /min 2 ) 10 3 0 differential time of 2 minutes differential time of 4 minutes × Experiment Brownian 1 Brownian 2 Brownian 3 Correlation time ( t 0 ) is 25 minutes Why 25 minutes ?

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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 10 4 T (hours) × Experiment QD 1 QD 2 QD 3 Two characteristic times 25 minutes: Uncorrelated region 1000 hours: Long-term region

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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

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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.

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