Abstract

We demonstrate multistage polarization-mode dispersion (PMD) compensation numerically and experimentally by using a particle-swarm optimization (PSO) algorithm in the searching process and an adaptive dithering algorithm in the tracking process. PMD compensation in a 40-Gb/s nonreturn-to-zero (NRZ) system based on the algorithm with a global neighborhood structure in one channel and in two channels is explored numerically. The numerical results show that the PSO algorithm is very efficient for multiple-degree-of-freedom PMD compensation systems. For high-PMD compensation the algorithm with a local neighborhood structure is more efficient than that with a global neighborhood structure. We also investigate the performance of PSO in an experiment, where 4-degree-of-freedom PMD compensation is demonstrated in 10-Gb/s NRZ and return-to-zero (RZ) systems. The total search time with the PSO algorithm is several hundred milliseconds, and the response time for the compensator to recover from a sudden disturbance is less than 20 ms.

© 2005 Optical Society of America

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  1. M. Karlsson, C. Xie, H. Sunnerud, and P. A. Andrekson, "Higher-order polarization-mode dispersion compensator with three degrees of freedom," in Optical Fiber Communications , Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper MO1-1.
  2. Q. Yu, L. S. Yan, Y. Xie, M. Hauer, and A. E. Willner, "Higher-order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay," IEEE Photonics Technol. Lett. 13, 863-865 (2001).
    [CrossRef]
  3. Y. Zheng, B. J. Yang, and X. G. Zhang, "Three-stage polarization-mode dispersion compensator capable of compensating second-order polarization-mode dispersion," IEEE Photonics Technol. Lett. 14, 1412-1414 (2002).
    [CrossRef]
  4. L. Möller, "Filter synthesis for broadband PMD compensation in WDM systems," IEEE Photonics Technol. Lett. 12, 1253-1255 (2000).
  5. K. Yamada, T. Kudou, and T. Ozeki, "Simultaneous multichannel PMD equalization for WDM systems," Optical Fiber Communications Conference (OFC) , Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), Paper TuP2-2.
  6. A. Eyal and A. Yariv, "Design of broadband PMD compensation filters," IEEE Photonics Technol. Lett. 14, 1088-1090 (2002).
    [CrossRef]
  7. R. Fletcher, Practical Methods of Optimization , 2nd ed. (Wiley, New York, 1987).
  8. R. Khosravani, S. A. Havstad, Y. W. Song, P. Ebrahimi, and A. E. Willner, "Polarization-mode dispersion compensation in WDM systems," IEEE Photonics Technol. Lett. 13, 1370-1372 (2001).
    [CrossRef]
  9. R. Eberhart and J. Kennedy, "A new optimizer using particle swarm theory," Proceedings of the Sixth International Symposium on Micro Machine and Human Science (Institute of Electrical and Electronics Engineers, New York, 1995).
  10. E. C. Laskari, K. E. Parsopoulos, and M. N. Vrahatis, "Particle-swarm optimization for minimax problems," Proceedings of the 2002 Congress on Evolutionary Computation, 2 (2002), pp. 1576-1581.
  11. J. Kennedy and R. Mendes, "Population structure and particle swarm performance," Proceedings of the 2002 Congress on Evolutionary Computation (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 1671-1676.
  12. A. Carlisle and G. Dozier, "An off-the-shelf PSO," in Proceedings of the 2001 Workshop on Particle Swarm Optimization (Indiana University - Purdue University of Indianapolis, Indianapolis, Ind., 2001), pp. 1-6.
  13. Y. Zheng, Y. Liu, B. Yang, and X. Zhang, "Study of the statistical characteristics of second-order polarization mode dispersion by Jones transfer matrix method," Chin. J. Lasers 30, 45-48 (2003).
  14. K. E. Parsopoulos and M. N. Vrahatis, "Particle swarm optimizer in noisy and continuously changing environments," in Artificial Intelligence and Soft Computing (International Association of Science and Technology for Development and ACTA, Zurich, 2001), pp. 289-294.
  15. J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization-mode dispersion in optical fibers," Proc. Natl. Acad. Sci. U.S.A. 97, 4541-4550 (2001).
    [CrossRef]
  16. Y. Zheng, X. G. Zhang, L. Chen, and B. J. Yang, "Analysis of degree of polarization ellipsoid as feedback signal for polarization mode dispersion compensation in NRZ, RZ and CS-RZ systems," Opt. Commun. 234, 107-117 (2004).
    [CrossRef]
  17. F. Roy, C. Francia, F. Bruyere, and D. Penninckx, "A simple dynamic polarization mode dispersion compensator," in Optical Fiber Commications Conference , 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper TuS4-1.

2004

Y. Zheng, X. G. Zhang, L. Chen, and B. J. Yang, "Analysis of degree of polarization ellipsoid as feedback signal for polarization mode dispersion compensation in NRZ, RZ and CS-RZ systems," Opt. Commun. 234, 107-117 (2004).
[CrossRef]

2003

Y. Zheng, Y. Liu, B. Yang, and X. Zhang, "Study of the statistical characteristics of second-order polarization mode dispersion by Jones transfer matrix method," Chin. J. Lasers 30, 45-48 (2003).

2002

Y. Zheng, B. J. Yang, and X. G. Zhang, "Three-stage polarization-mode dispersion compensator capable of compensating second-order polarization-mode dispersion," IEEE Photonics Technol. Lett. 14, 1412-1414 (2002).
[CrossRef]

A. Eyal and A. Yariv, "Design of broadband PMD compensation filters," IEEE Photonics Technol. Lett. 14, 1088-1090 (2002).
[CrossRef]

2001

R. Khosravani, S. A. Havstad, Y. W. Song, P. Ebrahimi, and A. E. Willner, "Polarization-mode dispersion compensation in WDM systems," IEEE Photonics Technol. Lett. 13, 1370-1372 (2001).
[CrossRef]

J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization-mode dispersion in optical fibers," Proc. Natl. Acad. Sci. U.S.A. 97, 4541-4550 (2001).
[CrossRef]

Q. Yu, L. S. Yan, Y. Xie, M. Hauer, and A. E. Willner, "Higher-order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay," IEEE Photonics Technol. Lett. 13, 863-865 (2001).
[CrossRef]

2000

L. Möller, "Filter synthesis for broadband PMD compensation in WDM systems," IEEE Photonics Technol. Lett. 12, 1253-1255 (2000).

Chen, L.

Y. Zheng, X. G. Zhang, L. Chen, and B. J. Yang, "Analysis of degree of polarization ellipsoid as feedback signal for polarization mode dispersion compensation in NRZ, RZ and CS-RZ systems," Opt. Commun. 234, 107-117 (2004).
[CrossRef]

Ebrahimi, P.

R. Khosravani, S. A. Havstad, Y. W. Song, P. Ebrahimi, and A. E. Willner, "Polarization-mode dispersion compensation in WDM systems," IEEE Photonics Technol. Lett. 13, 1370-1372 (2001).
[CrossRef]

Eyal , A.

A. Eyal and A. Yariv, "Design of broadband PMD compensation filters," IEEE Photonics Technol. Lett. 14, 1088-1090 (2002).
[CrossRef]

Gordon , J. P.

J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization-mode dispersion in optical fibers," Proc. Natl. Acad. Sci. U.S.A. 97, 4541-4550 (2001).
[CrossRef]

Hauer, M.

Q. Yu, L. S. Yan, Y. Xie, M. Hauer, and A. E. Willner, "Higher-order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay," IEEE Photonics Technol. Lett. 13, 863-865 (2001).
[CrossRef]

Havstad, S. A.

R. Khosravani, S. A. Havstad, Y. W. Song, P. Ebrahimi, and A. E. Willner, "Polarization-mode dispersion compensation in WDM systems," IEEE Photonics Technol. Lett. 13, 1370-1372 (2001).
[CrossRef]

Khosravani, R.

R. Khosravani, S. A. Havstad, Y. W. Song, P. Ebrahimi, and A. E. Willner, "Polarization-mode dispersion compensation in WDM systems," IEEE Photonics Technol. Lett. 13, 1370-1372 (2001).
[CrossRef]

Kogelnik, H.

J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization-mode dispersion in optical fibers," Proc. Natl. Acad. Sci. U.S.A. 97, 4541-4550 (2001).
[CrossRef]

Liu, Y.

Y. Zheng, Y. Liu, B. Yang, and X. Zhang, "Study of the statistical characteristics of second-order polarization mode dispersion by Jones transfer matrix method," Chin. J. Lasers 30, 45-48 (2003).

Möller, L.

L. Möller, "Filter synthesis for broadband PMD compensation in WDM systems," IEEE Photonics Technol. Lett. 12, 1253-1255 (2000).

Song, Y. W.

R. Khosravani, S. A. Havstad, Y. W. Song, P. Ebrahimi, and A. E. Willner, "Polarization-mode dispersion compensation in WDM systems," IEEE Photonics Technol. Lett. 13, 1370-1372 (2001).
[CrossRef]

Willner, A. E.

R. Khosravani, S. A. Havstad, Y. W. Song, P. Ebrahimi, and A. E. Willner, "Polarization-mode dispersion compensation in WDM systems," IEEE Photonics Technol. Lett. 13, 1370-1372 (2001).
[CrossRef]

Q. Yu, L. S. Yan, Y. Xie, M. Hauer, and A. E. Willner, "Higher-order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay," IEEE Photonics Technol. Lett. 13, 863-865 (2001).
[CrossRef]

Xie, Y.

Q. Yu, L. S. Yan, Y. Xie, M. Hauer, and A. E. Willner, "Higher-order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay," IEEE Photonics Technol. Lett. 13, 863-865 (2001).
[CrossRef]

Yan, L. S.

Q. Yu, L. S. Yan, Y. Xie, M. Hauer, and A. E. Willner, "Higher-order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay," IEEE Photonics Technol. Lett. 13, 863-865 (2001).
[CrossRef]

Yang, B.

Y. Zheng, Y. Liu, B. Yang, and X. Zhang, "Study of the statistical characteristics of second-order polarization mode dispersion by Jones transfer matrix method," Chin. J. Lasers 30, 45-48 (2003).

Yang, B. J.

Y. Zheng, X. G. Zhang, L. Chen, and B. J. Yang, "Analysis of degree of polarization ellipsoid as feedback signal for polarization mode dispersion compensation in NRZ, RZ and CS-RZ systems," Opt. Commun. 234, 107-117 (2004).
[CrossRef]

Y. Zheng, B. J. Yang, and X. G. Zhang, "Three-stage polarization-mode dispersion compensator capable of compensating second-order polarization-mode dispersion," IEEE Photonics Technol. Lett. 14, 1412-1414 (2002).
[CrossRef]

Yariv, A.

A. Eyal and A. Yariv, "Design of broadband PMD compensation filters," IEEE Photonics Technol. Lett. 14, 1088-1090 (2002).
[CrossRef]

Yu, Q.

Q. Yu, L. S. Yan, Y. Xie, M. Hauer, and A. E. Willner, "Higher-order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay," IEEE Photonics Technol. Lett. 13, 863-865 (2001).
[CrossRef]

Zhang, X.

Y. Zheng, Y. Liu, B. Yang, and X. Zhang, "Study of the statistical characteristics of second-order polarization mode dispersion by Jones transfer matrix method," Chin. J. Lasers 30, 45-48 (2003).

Zhang, X. G.

Y. Zheng, X. G. Zhang, L. Chen, and B. J. Yang, "Analysis of degree of polarization ellipsoid as feedback signal for polarization mode dispersion compensation in NRZ, RZ and CS-RZ systems," Opt. Commun. 234, 107-117 (2004).
[CrossRef]

Y. Zheng, B. J. Yang, and X. G. Zhang, "Three-stage polarization-mode dispersion compensator capable of compensating second-order polarization-mode dispersion," IEEE Photonics Technol. Lett. 14, 1412-1414 (2002).
[CrossRef]

Zheng, Y.

Y. Zheng, X. G. Zhang, L. Chen, and B. J. Yang, "Analysis of degree of polarization ellipsoid as feedback signal for polarization mode dispersion compensation in NRZ, RZ and CS-RZ systems," Opt. Commun. 234, 107-117 (2004).
[CrossRef]

Y. Zheng, Y. Liu, B. Yang, and X. Zhang, "Study of the statistical characteristics of second-order polarization mode dispersion by Jones transfer matrix method," Chin. J. Lasers 30, 45-48 (2003).

Y. Zheng, B. J. Yang, and X. G. Zhang, "Three-stage polarization-mode dispersion compensator capable of compensating second-order polarization-mode dispersion," IEEE Photonics Technol. Lett. 14, 1412-1414 (2002).
[CrossRef]

Chin. J. Lasers

Y. Zheng, Y. Liu, B. Yang, and X. Zhang, "Study of the statistical characteristics of second-order polarization mode dispersion by Jones transfer matrix method," Chin. J. Lasers 30, 45-48 (2003).

IEEE Photonics Technol. Lett.

A. Eyal and A. Yariv, "Design of broadband PMD compensation filters," IEEE Photonics Technol. Lett. 14, 1088-1090 (2002).
[CrossRef]

Q. Yu, L. S. Yan, Y. Xie, M. Hauer, and A. E. Willner, "Higher-order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay," IEEE Photonics Technol. Lett. 13, 863-865 (2001).
[CrossRef]

Y. Zheng, B. J. Yang, and X. G. Zhang, "Three-stage polarization-mode dispersion compensator capable of compensating second-order polarization-mode dispersion," IEEE Photonics Technol. Lett. 14, 1412-1414 (2002).
[CrossRef]

L. Möller, "Filter synthesis for broadband PMD compensation in WDM systems," IEEE Photonics Technol. Lett. 12, 1253-1255 (2000).

R. Khosravani, S. A. Havstad, Y. W. Song, P. Ebrahimi, and A. E. Willner, "Polarization-mode dispersion compensation in WDM systems," IEEE Photonics Technol. Lett. 13, 1370-1372 (2001).
[CrossRef]

Opt. Commun.

Y. Zheng, X. G. Zhang, L. Chen, and B. J. Yang, "Analysis of degree of polarization ellipsoid as feedback signal for polarization mode dispersion compensation in NRZ, RZ and CS-RZ systems," Opt. Commun. 234, 107-117 (2004).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization-mode dispersion in optical fibers," Proc. Natl. Acad. Sci. U.S.A. 97, 4541-4550 (2001).
[CrossRef]

Other

M. Karlsson, C. Xie, H. Sunnerud, and P. A. Andrekson, "Higher-order polarization-mode dispersion compensator with three degrees of freedom," in Optical Fiber Communications , Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper MO1-1.

F. Roy, C. Francia, F. Bruyere, and D. Penninckx, "A simple dynamic polarization mode dispersion compensator," in Optical Fiber Commications Conference , 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper TuS4-1.

R. Fletcher, Practical Methods of Optimization , 2nd ed. (Wiley, New York, 1987).

K. E. Parsopoulos and M. N. Vrahatis, "Particle swarm optimizer in noisy and continuously changing environments," in Artificial Intelligence and Soft Computing (International Association of Science and Technology for Development and ACTA, Zurich, 2001), pp. 289-294.

R. Eberhart and J. Kennedy, "A new optimizer using particle swarm theory," Proceedings of the Sixth International Symposium on Micro Machine and Human Science (Institute of Electrical and Electronics Engineers, New York, 1995).

E. C. Laskari, K. E. Parsopoulos, and M. N. Vrahatis, "Particle-swarm optimization for minimax problems," Proceedings of the 2002 Congress on Evolutionary Computation, 2 (2002), pp. 1576-1581.

J. Kennedy and R. Mendes, "Population structure and particle swarm performance," Proceedings of the 2002 Congress on Evolutionary Computation (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 1671-1676.

A. Carlisle and G. Dozier, "An off-the-shelf PSO," in Proceedings of the 2001 Workshop on Particle Swarm Optimization (Indiana University - Purdue University of Indianapolis, Indianapolis, Ind., 2001), pp. 1-6.

K. Yamada, T. Kudou, and T. Ozeki, "Simultaneous multichannel PMD equalization for WDM systems," Optical Fiber Communications Conference (OFC) , Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), Paper TuP2-2.

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Figures (17)

Fig. 1
Fig. 1

Scheme of PSO algorithm used for multistage PMD compensation.

Fig. 2
Fig. 2

Outage probability of multistage compensators controlled by the PSO algorithm.

Fig. 3
Fig. 3

Number of iterations for higher-order PMD compensation. In one case the weight factor decreases bilinearly. The results are shown as (a) averaged DGD=17.8 ps; (b) averaged DGD=21.3 ps. In the other case the weight factor decreases linearly. The results are shown as (c) averaged DGD=17.8 ps; (d) averaged DGD=21.3 ps.

Fig. 4
Fig. 4

Number of iterations for two-channel PMD compensation. (a), (b) A five-stage compensator is employed. The results are shown as (a) average DGD=8.8 ps; (b) average DGD=11.3 ps. (c), (d) A 10-stage compensator is also considered. The results are shown as (c) average DGD=8.8 ps; (d) average DGD=11.3 ps.

Fig. 5
Fig. 5

Comparison between global and local neighborhood structures; averaged DGD is (a) 20.1 ps and (b) 21.3 ps.

Fig. 6
Fig. 6

Number of iterations when averaged DGD is (a) 20.1 ps and (b) 21.3 ps.

Fig. 7
Fig. 7

Experiment setup for PMD compensation. Tx, Transmitter; LN-Mod, LiNbO3 modulator; PCi (i=1, 2, 3, 4), ith polarization controller; PMFi (i=1, 2, 3, 4), ith polarization maintaining fiber; EDFA, erbium-doped fiber amplifier; OBPF, optical band-pass filter; ELPF, electrical low-pass filter; A/D, analog to digital converter; D/A, digital to analog converter.

Fig. 8
Fig. 8

Effectiveness of the two filters.

Fig. 9
Fig. 9

DOP versus DGD.

Fig. 10
Fig. 10

Relationship between BER and DOP.

Fig. 11
Fig. 11

DOP map of (a) NRZ and (b) RZ formats.

Fig. 12
Fig. 12

Best DOP versus number of iterations.

Fig. 13
Fig. 13

Distribution of optima found for each iteration number.

Fig. 14
Fig. 14

Eye diagrams (left) before and (right) after the searching process; (a) NRZ, (b) RZ.

Fig. 15
Fig. 15

Performance of the tracking algorithm for the NRZ format (a) with and (b) without a sudden disturbance.

Fig. 16
Fig. 16

Short-term performance of the tracking algorithm for the RZ format (a) with and (b) without a sudden disturbance.

Fig. 17
Fig. 17

Long-term performance of the tracking algorithm for NRZ and RZ formats.

Tables (1)

Tables Icon

Table 1 Local Neighborhood Structure

Equations (8)

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MAXparameters(function),
MAXparametersMINj(functionj),
vid=K{ωvid+φ1[rand()](pid-xid)
+φ2[rand()](pgd-xid)}, Xmin<xid<Xmax,
vid=0,otherwise
xid=xid+vid,Xmin<xid+vid<Xmax,
xid=Xmax,xid+vidXmax,
xid=Xmin,xid+vidXmin,

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