Presentation on theme: "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."— Presentation transcript:
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
2 Focus Polarization mode dispersion (PMD) degrades system performance  Polarization properties drift over time  –This leads to time-varying system performance We determine time scale of drift and its impact
3 Context Previous theoretical work assumes uncorrelated drift  Good model for aerial fiber ; Not good for other systems ,  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 – Maxwellian in a straight line system Bessel-shape in a recirculating loop 0 20 (ps) pdf Short-term DGD distribution Correlated and non-Maxwellian / non-Bessel Varies from time window to time window 0 25 (ps) Hour Hour 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)
5 Quantification of DGD distribution : Standard deviation of DGD in a time window (T): Average of over all windows of time T 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  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  Standard single-mode fiber (3.5 km) Dispersion shifted fiber (25 km) Optical band-pass filter Erbium-doped fiber amplifier
7 Simulation (I) Loop system Coarse-step method to model 107 km fiber  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
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
9 Brownian model T (hours) ( ps) Simple insensitive to parameter settings –All three settings yield almost the same results Accurate when T > 25 minutes t (min) ACF d ( t) (ps 2 /min 2 ) 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 ?
10 Quasi-deterministic model Agrees with experiment for almost all Ts By properly accounting for time correlation (in parameter setting QD 2) (ps) T (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
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