Abstract

We study the fluctuations of the bit-error-rate in optical communication systems by taking into account the polarization mode dispersion. We demonstrate analytically and numerically that the probability distribution function of bit-error-rate possesses an extended algebraic tail in the presence of weak birefringent disorder in the fiber. The characteristics of the probability distribution function also depend on the electrical filter temporal width. For weak birefringent disorder, our numerical simulations show that the probability distribution function contains a longer algebraic regime if the smaller size of electrical filter temporal width is used.

©2004 Optical Society of America

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References

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  1. C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibres”, Electron. Lett. 22, 1029–1030, (1986).
    [Crossref]
  2. C. D. Poole, “Statistical treatment of polarization dispersion in single-mode fiber,” Opt. Lett.13, 687, (1988); 14, 523–525, (1989).
    [Crossref] [PubMed]
  3. C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Techn. 6, 1185–1190, (1988).
    [Crossref]
  4. C. D. Poole, J. H. Winters, and J. A. Nagel, Opt. Lett. 16, 372–374, (1991).
    [Crossref] [PubMed]
  5. H. Bülow, “System outage probability due to first- and second-order PMD,” IEEE Photo. Tech. Lett. 10, 696–698, (1998).
    [Crossref]
  6. H. Kogelnik, L. E. Nelson, J. P. Gordon, and R. M. Jopson, “Jones matrix for second-order polarization mode dispersion,” Opt. Lett. 25, 19–21, (2000).
    [Crossref]
  7. A. Eyal, Y. Li, W. K. Marshall, A. Yariv, and M. Tur, “Statistical determination of the length dependence of high-order polarization mode dispersion,” Opt. Lett. 25, 875–877, (2000).
    [Crossref]
  8. S. C. Rashleigh and R. Ulrich, “Polarization mode dispersion in single-mode fibers,” Opt. Lett. 3, 60–63, (1978).
    [Crossref] [PubMed]
  9. S. Machida, I. Sakai, and T. Kimura, “Polarization conservation in single-mode fibres,” Electron. Lett. 17, 494–495, (1981).
    [Crossref]
  10. N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multilongitudinal mode lasers,” J. Lightwave Techn. LT-5, 1618–1622, (1987).
    [Crossref]
  11. D. Andresciani, F. Curti, F. Matera, and B. Daino, “Measurements of the group velocity difference between the principal states of polarization on a low-birefringence terrestrial fiber cable,” Opt. Lett. 12, 844–846, (1987).
    [Crossref] [PubMed]
  12. C. D. Poole and J. A. Nagelin Optical Fiber Telecommunications eds.I. P. Kaminow and T. L. Koch, Academic San Diego, IIIA, pp. 114, (1997).
  13. R. M. Jopson, L. E. Nelson, G. J. Pendlock, and A. H. Gnauck, “Polarization mode dispersion impairment in return to zero and non-return-to zero systems,” in Tech. Digest Optical Fiber Communication Conf., OFC 1999, 1999, Paper WE3.
    [Crossref]
  14. V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Probability of anomalously large Bit-Error-Rate in long haul optical transmission,” Phys. Rev. E. 68, 066619 (2003).
    [Crossref]
  15. V. Chernyak and M. Chertkov, “Extreme outages caused by polarization mode dispersion,” Opt. Lett. 28, 2159–2161, (2003).
    [Crossref] [PubMed]
  16. V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Compensation for extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Opt. Express 11, 1607–1612, (2003).
    [Crossref] [PubMed]
  17. V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Periodic and quasi-periodic compensation strategies of extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Pis’ma v ZhETF. 78(4), 234–237 (2003).
  18. V. Chernyak, M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, “PMD induced fluctuations of bit-error-rate in optical fiber systems,” J. Lightwave Technnol. 22, 1155–1168, (2004).
    [Crossref]
  19. E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks, (JohnWiley & Sons, Inc., New York, 1998).
  20. S. D. Personick, “Receiver design for digital fibre optic communications systems I and II,” Bell Syst. Technol. J. 52, 843–886, (1973).
  21. D. Marcuse, “Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,” J. Lightwave Techon. 8, 1816–1823, (1990).
    [Crossref]
  22. P. A. Humblet and M. Azizoglu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technnol. 9, 1576–1582, (1991).
    [Crossref]
  23. N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier systems,” IEEE Photo. Tech. Lett. 5, 304–306, (1993).
    [Crossref]
  24. R. Ulrich and A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt.,  18, 2241–2251, (1979).
    [Crossref] [PubMed]
  25. I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron.,  QE-17, 15–22, (1981).
    [Crossref]
  26. G. P. Agrawal, Nonlinear Fiber Optics, (Acad. Press, 1989).
  27. C. Xie, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Polarization-Mode dispersion-induced outages in soliton transmission systems,” IEEE Photo. Technol. Lett.13, 1079–1081, (2001).
    [Crossref]
  28. U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
    [Crossref]
  29. G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion: Techniques and Applications,” J. Lightwave Technnol. 22, 1201–1215, (2004).
    [Crossref]

2004 (3)

V. Chernyak, M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, “PMD induced fluctuations of bit-error-rate in optical fiber systems,” J. Lightwave Technnol. 22, 1155–1168, (2004).
[Crossref]

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion: Techniques and Applications,” J. Lightwave Technnol. 22, 1201–1215, (2004).
[Crossref]

2003 (4)

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Probability of anomalously large Bit-Error-Rate in long haul optical transmission,” Phys. Rev. E. 68, 066619 (2003).
[Crossref]

V. Chernyak and M. Chertkov, “Extreme outages caused by polarization mode dispersion,” Opt. Lett. 28, 2159–2161, (2003).
[Crossref] [PubMed]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Compensation for extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Opt. Express 11, 1607–1612, (2003).
[Crossref] [PubMed]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Periodic and quasi-periodic compensation strategies of extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Pis’ma v ZhETF. 78(4), 234–237 (2003).

2000 (2)

1998 (1)

H. Bülow, “System outage probability due to first- and second-order PMD,” IEEE Photo. Tech. Lett. 10, 696–698, (1998).
[Crossref]

1993 (1)

N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier systems,” IEEE Photo. Tech. Lett. 5, 304–306, (1993).
[Crossref]

1991 (2)

P. A. Humblet and M. Azizoglu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technnol. 9, 1576–1582, (1991).
[Crossref]

C. D. Poole, J. H. Winters, and J. A. Nagel, Opt. Lett. 16, 372–374, (1991).
[Crossref] [PubMed]

1990 (1)

D. Marcuse, “Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,” J. Lightwave Techon. 8, 1816–1823, (1990).
[Crossref]

1988 (1)

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Techn. 6, 1185–1190, (1988).
[Crossref]

1987 (2)

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multilongitudinal mode lasers,” J. Lightwave Techn. LT-5, 1618–1622, (1987).
[Crossref]

D. Andresciani, F. Curti, F. Matera, and B. Daino, “Measurements of the group velocity difference between the principal states of polarization on a low-birefringence terrestrial fiber cable,” Opt. Lett. 12, 844–846, (1987).
[Crossref] [PubMed]

1986 (1)

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibres”, Electron. Lett. 22, 1029–1030, (1986).
[Crossref]

1981 (2)

S. Machida, I. Sakai, and T. Kimura, “Polarization conservation in single-mode fibres,” Electron. Lett. 17, 494–495, (1981).
[Crossref]

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron.,  QE-17, 15–22, (1981).
[Crossref]

1979 (1)

1978 (1)

1973 (1)

S. D. Personick, “Receiver design for digital fibre optic communications systems I and II,” Bell Syst. Technol. J. 52, 843–886, (1973).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, (Acad. Press, 1989).

Anderegg, M.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Andrekson, P. A.

C. Xie, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Polarization-Mode dispersion-induced outages in soliton transmission systems,” IEEE Photo. Technol. Lett.13, 1079–1081, (2001).
[Crossref]

Andresciani, D.

Azizoglu, M.

P. A. Humblet and M. Azizoglu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technnol. 9, 1576–1582, (1991).
[Crossref]

Bergano, N. S.

N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier systems,” IEEE Photo. Tech. Lett. 5, 304–306, (1993).
[Crossref]

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Techn. 6, 1185–1190, (1988).
[Crossref]

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multilongitudinal mode lasers,” J. Lightwave Techn. LT-5, 1618–1622, (1987).
[Crossref]

Biondini, G.

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion: Techniques and Applications,” J. Lightwave Technnol. 22, 1201–1215, (2004).
[Crossref]

Bülow, H.

H. Bülow, “System outage probability due to first- and second-order PMD,” IEEE Photo. Tech. Lett. 10, 696–698, (1998).
[Crossref]

Chernyak, V.

V. Chernyak, M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, “PMD induced fluctuations of bit-error-rate in optical fiber systems,” J. Lightwave Technnol. 22, 1155–1168, (2004).
[Crossref]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Periodic and quasi-periodic compensation strategies of extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Pis’ma v ZhETF. 78(4), 234–237 (2003).

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Probability of anomalously large Bit-Error-Rate in long haul optical transmission,” Phys. Rev. E. 68, 066619 (2003).
[Crossref]

V. Chernyak and M. Chertkov, “Extreme outages caused by polarization mode dispersion,” Opt. Lett. 28, 2159–2161, (2003).
[Crossref] [PubMed]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Compensation for extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Opt. Express 11, 1607–1612, (2003).
[Crossref] [PubMed]

Chertkov, M.

V. Chernyak, M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, “PMD induced fluctuations of bit-error-rate in optical fiber systems,” J. Lightwave Technnol. 22, 1155–1168, (2004).
[Crossref]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Periodic and quasi-periodic compensation strategies of extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Pis’ma v ZhETF. 78(4), 234–237 (2003).

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Compensation for extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Opt. Express 11, 1607–1612, (2003).
[Crossref] [PubMed]

V. Chernyak and M. Chertkov, “Extreme outages caused by polarization mode dispersion,” Opt. Lett. 28, 2159–2161, (2003).
[Crossref] [PubMed]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Probability of anomalously large Bit-Error-Rate in long haul optical transmission,” Phys. Rev. E. 68, 066619 (2003).
[Crossref]

Curti, F.

Dailey, M.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Daino, B.

Davidson, C. R.

N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier systems,” IEEE Photo. Tech. Lett. 5, 304–306, (1993).
[Crossref]

Drewnowski, C.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Eyal, A.

Gabitov, I.

V. Chernyak, M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, “PMD induced fluctuations of bit-error-rate in optical fiber systems,” J. Lightwave Technnol. 22, 1155–1168, (2004).
[Crossref]

Gnauck, A. H.

R. M. Jopson, L. E. Nelson, G. J. Pendlock, and A. H. Gnauck, “Polarization mode dispersion impairment in return to zero and non-return-to zero systems,” in Tech. Digest Optical Fiber Communication Conf., OFC 1999, 1999, Paper WE3.
[Crossref]

Gordon, J. P.

Hempstead, M.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Hoyt, R.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Humblet, P. A.

P. A. Humblet and M. Azizoglu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technnol. 9, 1576–1582, (1991).
[Crossref]

Iannone, E.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks, (JohnWiley & Sons, Inc., New York, 1998).

Jopson, R. M.

H. Kogelnik, L. E. Nelson, J. P. Gordon, and R. M. Jopson, “Jones matrix for second-order polarization mode dispersion,” Opt. Lett. 25, 19–21, (2000).
[Crossref]

R. M. Jopson, L. E. Nelson, G. J. Pendlock, and A. H. Gnauck, “Polarization mode dispersion impairment in return to zero and non-return-to zero systems,” in Tech. Digest Optical Fiber Communication Conf., OFC 1999, 1999, Paper WE3.
[Crossref]

Kaminow, I. P.

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron.,  QE-17, 15–22, (1981).
[Crossref]

Karlsson, M.

C. Xie, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Polarization-Mode dispersion-induced outages in soliton transmission systems,” IEEE Photo. Technol. Lett.13, 1079–1081, (2001).
[Crossref]

Kath, W. L.

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion: Techniques and Applications,” J. Lightwave Technnol. 22, 1201–1215, (2004).
[Crossref]

Kerfoot, F. W.

N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier systems,” IEEE Photo. Tech. Lett. 5, 304–306, (1993).
[Crossref]

Kimura, T.

S. Machida, I. Sakai, and T. Kimura, “Polarization conservation in single-mode fibres,” Electron. Lett. 17, 494–495, (1981).
[Crossref]

Kogelnik, H.

Kolokolov, I.

V. Chernyak, M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, “PMD induced fluctuations of bit-error-rate in optical fiber systems,” J. Lightwave Technnol. 22, 1155–1168, (2004).
[Crossref]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Periodic and quasi-periodic compensation strategies of extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Pis’ma v ZhETF. 78(4), 234–237 (2003).

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Probability of anomalously large Bit-Error-Rate in long haul optical transmission,” Phys. Rev. E. 68, 066619 (2003).
[Crossref]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Compensation for extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Opt. Express 11, 1607–1612, (2003).
[Crossref] [PubMed]

Lebedev, V.

V. Chernyak, M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, “PMD induced fluctuations of bit-error-rate in optical fiber systems,” J. Lightwave Technnol. 22, 1155–1168, (2004).
[Crossref]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Periodic and quasi-periodic compensation strategies of extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Pis’ma v ZhETF. 78(4), 234–237 (2003).

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Compensation for extreme outages caused by Polarization Mode Dispersion and amplifier noise,” Opt. Express 11, 1607–1612, (2003).
[Crossref] [PubMed]

V. Chernyak, M. Chertkov, I. Kolokolov, and V. Lebedev, “Probability of anomalously large Bit-Error-Rate in long haul optical transmission,” Phys. Rev. E. 68, 066619 (2003).
[Crossref]

Li, Y.

Machida, S.

S. Machida, I. Sakai, and T. Kimura, “Polarization conservation in single-mode fibres,” Electron. Lett. 17, 494–495, (1981).
[Crossref]

Marcuse, D.

D. Marcuse, “Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,” J. Lightwave Techon. 8, 1816–1823, (1990).
[Crossref]

Marshall, W. K.

Matera, F.

Mauro, Y.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Mecozzi, A.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks, (JohnWiley & Sons, Inc., New York, 1998).

Menyuk, C. R.

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion: Techniques and Applications,” J. Lightwave Technnol. 22, 1201–1215, (2004).
[Crossref]

Mlejnek, M.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Nagel, J. A.

C. D. Poole, J. H. Winters, and J. A. Nagel, Opt. Lett. 16, 372–374, (1991).
[Crossref] [PubMed]

C. D. Poole and J. A. Nagelin Optical Fiber Telecommunications eds.I. P. Kaminow and T. L. Koch, Academic San Diego, IIIA, pp. 114, (1997).

Nelson, L. E.

H. Kogelnik, L. E. Nelson, J. P. Gordon, and R. M. Jopson, “Jones matrix for second-order polarization mode dispersion,” Opt. Lett. 25, 19–21, (2000).
[Crossref]

R. M. Jopson, L. E. Nelson, G. J. Pendlock, and A. H. Gnauck, “Polarization mode dispersion impairment in return to zero and non-return-to zero systems,” in Tech. Digest Optical Fiber Communication Conf., OFC 1999, 1999, Paper WE3.
[Crossref]

Neukirch, U.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Pendlock, G. J.

R. M. Jopson, L. E. Nelson, G. J. Pendlock, and A. H. Gnauck, “Polarization mode dispersion impairment in return to zero and non-return-to zero systems,” in Tech. Digest Optical Fiber Communication Conf., OFC 1999, 1999, Paper WE3.
[Crossref]

Personick, S. D.

S. D. Personick, “Receiver design for digital fibre optic communications systems I and II,” Bell Syst. Technol. J. 52, 843–886, (1973).

Piech, G.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Pikula, D.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Poole, C. D.

C. D. Poole, J. H. Winters, and J. A. Nagel, Opt. Lett. 16, 372–374, (1991).
[Crossref] [PubMed]

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Techn. 6, 1185–1190, (1988).
[Crossref]

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multilongitudinal mode lasers,” J. Lightwave Techn. LT-5, 1618–1622, (1987).
[Crossref]

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibres”, Electron. Lett. 22, 1029–1030, (1986).
[Crossref]

C. D. Poole, “Statistical treatment of polarization dispersion in single-mode fiber,” Opt. Lett.13, 687, (1988); 14, 523–525, (1989).
[Crossref] [PubMed]

C. D. Poole and J. A. Nagelin Optical Fiber Telecommunications eds.I. P. Kaminow and T. L. Koch, Academic San Diego, IIIA, pp. 114, (1997).

Rashleigh, S. C.

Sakai, I.

S. Machida, I. Sakai, and T. Kimura, “Polarization conservation in single-mode fibres,” Electron. Lett. 17, 494–495, (1981).
[Crossref]

Schulte, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Techn. 6, 1185–1190, (1988).
[Crossref]

Settembre, M.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks, (JohnWiley & Sons, Inc., New York, 1998).

Simon, A.

Soulliere, M.J.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Sunnerud, H.

C. Xie, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Polarization-Mode dispersion-induced outages in soliton transmission systems,” IEEE Photo. Technol. Lett.13, 1079–1081, (2001).
[Crossref]

Tur, M.

Ulrich, R.

Wagner, R. E.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Techn. 6, 1185–1190, (1988).
[Crossref]

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multilongitudinal mode lasers,” J. Lightwave Techn. LT-5, 1618–1622, (1987).
[Crossref]

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibres”, Electron. Lett. 22, 1029–1030, (1986).
[Crossref]

Wang, F.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Webb, M.

U. Neukirch, M. Hempstead, G. Piech, Y. Mauro, M. Mlejnek, M.J. Soulliere, M. Webb, D. Pikula, R. Hoyt, M. Anderegg, M. Dailey, F. Wang, and C. Drewnowski, “Time-resolved performance analysis of a second-order PMD compensator,” J. Lightwave Technnol. 22, 1189–1200, (2004).
[Crossref]

Winters, J. H.

Xie, C.

C. Xie, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Polarization-Mode dispersion-induced outages in soliton transmission systems,” IEEE Photo. Technol. Lett.13, 1079–1081, (2001).
[Crossref]

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C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibres”, Electron. Lett. 22, 1029–1030, (1986).
[Crossref]

S. Machida, I. Sakai, and T. Kimura, “Polarization conservation in single-mode fibres,” Electron. Lett. 17, 494–495, (1981).
[Crossref]

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[Crossref]

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[Crossref]

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multilongitudinal mode lasers,” J. Lightwave Techn. LT-5, 1618–1622, (1987).
[Crossref]

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[Crossref]

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[Crossref]

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Other (6)

C. D. Poole, “Statistical treatment of polarization dispersion in single-mode fiber,” Opt. Lett.13, 687, (1988); 14, 523–525, (1989).
[Crossref] [PubMed]

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks, (JohnWiley & Sons, Inc., New York, 1998).

G. P. Agrawal, Nonlinear Fiber Optics, (Acad. Press, 1989).

C. Xie, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Polarization-Mode dispersion-induced outages in soliton transmission systems,” IEEE Photo. Technol. Lett.13, 1079–1081, (2001).
[Crossref]

C. D. Poole and J. A. Nagelin Optical Fiber Telecommunications eds.I. P. Kaminow and T. L. Koch, Academic San Diego, IIIA, pp. 114, (1997).

R. M. Jopson, L. E. Nelson, G. J. Pendlock, and A. H. Gnauck, “Polarization mode dispersion impairment in return to zero and non-return-to zero systems,” in Tech. Digest Optical Fiber Communication Conf., OFC 1999, 1999, Paper WE3.
[Crossref]

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Figures (2)

Fig. 1.
Fig. 1. The logarithm of the probability density vs. the logarithm of BER. From the blue to the black curve (leftmost to rightmost), each curve is the PDF of BER corresponding to Dm =0.2,0.25,0.3,0.35,0.4,0.45,0.5, respectively. Figures (a)-(d) represent the PDFs for detection window size, T=3.3…2.2, respectively. As the guide to the eye, the thick solid lines indicate the algebraic behavior of the PDF of BER.
Fig. 2.
Fig. 2. The ratio of algebraic tail slopes (αm1 /αm2 ) vs. the ratio of corresponding disorder intensities (Dm1 /Dm2 ). The -+- (blue) line is for the theoretical prediction. The rest of the curves are obtained from numerical simulations for different sizes of detection window.

Equations (25)

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z Ψ m ̂ ( z ) t Ψ i d ( z ) t 2 Ψ = ξ ( z , t ) ,
Ψ = φ + ϕ , φ = W ̂ ( z ) Ψ 0 ( t ) ,
ϕ = 0 z d z W ̂ ( z ) W ̂ 1 ( z ) ξ ( z , t ) ,
W ̂ ( z ) = exp [ i 0 z d z d ( z ) t 2 ] U ̂ ( z ) ,
U ̂ ( z ) = T exp [ 0 z d z m ̂ ( z ) t ] ,
h i ( z 1 ) h j ( z 2 ) = D m δ ij δ ( z 1 z 2 ) .
ϕ α ( Z , t 1 ) ϕ β ( Z , t 2 ) = D ξ Z δ α β δ ( t 1 t 2 ) .
B 1 0 = 0 I d d I P 1 ( I ) , B 0 1 = I d d I P 0 ( I ) .
I = d t G ( t ) K Ψ ( Z , t ) 2
G ( t ) = { 1 for t T , 0 otherwise .
ln [ P 1 ( I ) ] ~ ( d t G ( t ) φ 2 I ) 2 D ξ Z , ln [ P 0 ( I ) ] ~ 1 D ξ Z ,
B 1 0 ~ P 1 ( I d ) , B 0 1 ~ P 0 ( I d ) .
I d ~ d t G ( t ) φ 2 4 .
B ~ exp [ I d D ξ Z ] ~ exp [ d t G ( t ) φ 2 4 D ξ Z ] .
φ ( t ; Z ) = T exp [ 0 z d z h ( z ) σ ̂ t ] ( 1 0 ) Ψ 0 ( t ) .
φ ( t ; Z ) = ( 1 0 ) Ψ 0 ( t ) + ( H 3 H 1 + i H 2 ) t Ψ 0 ( t ) + ( H 2 / 2 + i H 12 H 13 + i H 23 ) t 2 Ψ 0 ( t ) + O ( h 3 ) ,
H i 0 z d z h i ( z ) , H = H 1 + H 2 + H 3 , H ij 0 z d z 0 z d z [ h i ( z ) h j ( z ) h j ( z ) h i ( z ) ] .
T / 2 T / 2 d t φ ( t ; Z ) 2 = T / 2 T / 2 dt Ψ 0 ( t ) 2 + 2 H 3 T / 2 T / 2 d t Re [ Ψ 0 * ( t ) t Ψ 0 ( t ) ]
+ 2 T / 2 T / 2 d t Re [ Ψ 0 * ( t ) t 2 Ψ 0 ( t ) ( H 2 / 2 + i H 12 ) ] + T / 2 T / 2 dt t Ψ 0 2 H 2 + O ( h 3 ) .
T / 2 T / 2 dt Ψ 0 ( t ) 2 + 2 Ψ 0 ( T / 2 ) t Ψ 0 ( T / 2 ) H 2 + O ( h 3 ) .
B = B 0 exp ( Γ ( h ) 4 D ξ Z ) , B 0 = exp ( I 0 4 D ξ Z ) ,
P ( l n B ) = B 0 α B α 4 D ξ Z μ , α = 2 D ξ / ( μ D m ) .
B = exp [ C J 2 / ( D ξ Z ) ] ,
P ( J ) exp ( F ( J ) D m Z ) ,
ln P ( B ) C 1 D m Z + C 2 D ξ D m 2 Z ln 1 B ,

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