Abstract

An exact analytical method for evaluating the outage probability due to second-order polarization mode dispersion in a system with first-order compensation is presented. In an uncompensated system the outage is mainly due to the mean differential group delay, whereas higher order effects have low impact. It is shown that in a compensated system all orders contribute to the outage probability, whereas accounting for exact second-order only gives a slight overestimate. Approximate second-order models leaving residual higher order effects may lead to very different outage probabilities.

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  1. C. D. Poole and R. E. Wagner, "Phenomenological approach to polarization dispersion in long single-mode fibers", Electron. Lett., vol. 22, no. 19, pp. 1029-1030, 1986.
  2. G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers", J. Lightwave Technol., vol. 9, pp. 1439-1456, Nov. 1991.
  3. H. Kogelnik, L. E. Nelson and J. P. Gordon, "Emulation and inversion of polarization-mode dispersion", J. Lightwave Technol., vol. 21, no. 2, pp. 482-495, Feb. 2003.
  4. A. Vannucci and A. Bononi, "Statistical characterization of the Jones matrix of long fibers affected by polarization mode dispersion (PMD)", J. Lightwave Technol., vol. 20, pp. 811-821, May 2002.
  5. H. Bülow, "System outage probability due to first-and second-order PMD", IEEE Photon. Technol. Lett., vol. 10, pp. 696-698, May 1998.
  6. E. Forestieri, "A fast and accurate method for evaluating joint second-order PMD statistics", J. Lightwave Technol., vol. 21, pp. 2492-2952, Nov. 2003.
  7. L. M. Gleeson, E. S. R. Sikora and M. J. O. Mahoney, "Experimental and numerical investigation into the penalties induced by second order polarization mode dispersion at 10 Gb/s", in Proc. ECOC'97, vol. 1, 1997, pp. 15- 18.
  8. D. Penninckx and F. Bruyère, "Impact of the statistics of second-order polarization-mode dispersion on systems performance", in Proc. OFC'98 Tech. Dig., 1998, Paper ThR2,. pp. 340-342.
  9. A. Eyal, W. K. Marshall, M. Tur and A. Yariv, "Representation of second-order polarization mode dispersion", Electron. Lett., vol. 35, no. 19, pp. 1658-1659, 1999.
  10. H. Kogelnik, L. E. Nelson, J. P. Gordon and R. M. Jopson, "Jones matrix for second-order polarization mode dispersion", Opt. Lett., vol. 25, no. 1, pp. 19-21, 2000.
  11. E. Forestieri and L. Vincetti, "Exact evaluation of the Jones matrix of a fiber in the presence of polarization mode dispersion of any order", J. Lightwave Technol., vol. 17, pp. 1898-1909, Dec. 2001 .
  12. G. J. Foschini, R. M. Jopson, L. E. Nelson and H. Kogelnik, "The statistics of PMD-induced chromatic fiber dispersion", J. Lightwave Technol., vol. 17, pp. 1560-1565, Sept. 1999.
  13. E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre-and post-detection filtering", J. Lightwave Technol., vol. 18, pp. 1493-1503, Nov. 2000 .
  14. G. J. Foschini, L. E. Nelson, R. M. Jopson and H. Kogelnik, "Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion", IEEE Photon. Technol. Lett., vol. 12, pp. 293 -295, Mar. 2000.
  15. C. D. Poole, R. W. Tkach, A. R. Chraplyvy and D. A. Fishman, "Fading in lightwave systems due to polarization-mode dispersion", IEEE Photon. Technol. Lett., vol. 3, pp. 68-70, Jan. 1991.
  16. C. D. Poole and J. Nagel, "Polarization effects in lightwave systems," in Optical Fiber Telecommunications IIIA, I. P. Kaminov, and T. L. Koch, Eds. New York: Academic, 1997.
  17. P. J. Winzer, H. Kogelnik, C. H. Kim, H. Kim, R. M. Jopson and L. E. Nelson, "Effect of receiver design on PMD outage for RZ and NRZ", in Proc. OFC'02, 2002, Paper TuI1,. pp. 46-48.
  18. P. A. Humblet and M. Azizoglu, "On the bit error rate of lightwave systems with optical amplifiers", J. Lightwave Technol., vol. 9, pp. 1576-1582, Nov. 1991.
  19. A. Orlandini and L. Vincetti, "Comparison of the Jones matrix analytical models applied to optical system affected by high-order PMD", J. Lightwave Technol., vol. 21, pp. 1456-1464, June 2003.
  20. C. Xie, L. Moller, H. Haunstein and S. Hunsche, "Polarization mode dispersion induced impairments in different modulation format systems", in Proc. OFC 2003, Mar. 2003, Paper TuO1,. pp. 258-259.
  21. A. O. Lima, I. T. Lima, T. Adali and C. R. Menyuk, "Comparison of power penalties due to first-and all-order PMD distortions", presented at the ECOC'02, Paper 7.1.2, 2002.
  22. G. Shtengel, E. Ibragimov, M. Rivera and S. Suh, "Statistical dependence between first and second-order pmd", presented at the OFC'01, MO-3, 2001.
  23. M. Karlsson and J. Brentel, "Autocorrelation function of the polarization-mode dispersion vector", Opt. Lett., vol. 24, no. 14, pp. 939-941, 1999 .
  24. M. Shtaif, A. Mecozzi and J. A. Nagel, "Mean-square magnitude of all orders of polarization mode dispersion and the relation with the bandwidth of the principal states", IEEE Photon. Technol. Lett., vol. 12, pp. 696-698, Jan. 2000.

J. Lightwave Technol. (8)

G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers", J. Lightwave Technol., vol. 9, pp. 1439-1456, Nov. 1991.

A. Vannucci and A. Bononi, "Statistical characterization of the Jones matrix of long fibers affected by polarization mode dispersion (PMD)", J. Lightwave Technol., vol. 20, pp. 811-821, May 2002.

E. Forestieri, "A fast and accurate method for evaluating joint second-order PMD statistics", J. Lightwave Technol., vol. 21, pp. 2492-2952, Nov. 2003.

E. Forestieri and L. Vincetti, "Exact evaluation of the Jones matrix of a fiber in the presence of polarization mode dispersion of any order", J. Lightwave Technol., vol. 17, pp. 1898-1909, Dec. 2001 .

G. J. Foschini, R. M. Jopson, L. E. Nelson and H. Kogelnik, "The statistics of PMD-induced chromatic fiber dispersion", J. Lightwave Technol., vol. 17, pp. 1560-1565, Sept. 1999.

E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre-and post-detection filtering", J. Lightwave Technol., vol. 18, pp. 1493-1503, Nov. 2000 .

P. A. Humblet and M. Azizoglu, "On the bit error rate of lightwave systems with optical amplifiers", J. Lightwave Technol., vol. 9, pp. 1576-1582, Nov. 1991.

A. Orlandini and L. Vincetti, "Comparison of the Jones matrix analytical models applied to optical system affected by high-order PMD", J. Lightwave Technol., vol. 21, pp. 1456-1464, June 2003.

Other (16)

C. Xie, L. Moller, H. Haunstein and S. Hunsche, "Polarization mode dispersion induced impairments in different modulation format systems", in Proc. OFC 2003, Mar. 2003, Paper TuO1,. pp. 258-259.

A. O. Lima, I. T. Lima, T. Adali and C. R. Menyuk, "Comparison of power penalties due to first-and all-order PMD distortions", presented at the ECOC'02, Paper 7.1.2, 2002.

G. Shtengel, E. Ibragimov, M. Rivera and S. Suh, "Statistical dependence between first and second-order pmd", presented at the OFC'01, MO-3, 2001.

M. Karlsson and J. Brentel, "Autocorrelation function of the polarization-mode dispersion vector", Opt. Lett., vol. 24, no. 14, pp. 939-941, 1999 .

M. Shtaif, A. Mecozzi and J. A. Nagel, "Mean-square magnitude of all orders of polarization mode dispersion and the relation with the bandwidth of the principal states", IEEE Photon. Technol. Lett., vol. 12, pp. 696-698, Jan. 2000.

G. J. Foschini, L. E. Nelson, R. M. Jopson and H. Kogelnik, "Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion", IEEE Photon. Technol. Lett., vol. 12, pp. 293 -295, Mar. 2000.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy and D. A. Fishman, "Fading in lightwave systems due to polarization-mode dispersion", IEEE Photon. Technol. Lett., vol. 3, pp. 68-70, Jan. 1991.

C. D. Poole and J. Nagel, "Polarization effects in lightwave systems," in Optical Fiber Telecommunications IIIA, I. P. Kaminov, and T. L. Koch, Eds. New York: Academic, 1997.

P. J. Winzer, H. Kogelnik, C. H. Kim, H. Kim, R. M. Jopson and L. E. Nelson, "Effect of receiver design on PMD outage for RZ and NRZ", in Proc. OFC'02, 2002, Paper TuI1,. pp. 46-48.

L. M. Gleeson, E. S. R. Sikora and M. J. O. Mahoney, "Experimental and numerical investigation into the penalties induced by second order polarization mode dispersion at 10 Gb/s", in Proc. ECOC'97, vol. 1, 1997, pp. 15- 18.

D. Penninckx and F. Bruyère, "Impact of the statistics of second-order polarization-mode dispersion on systems performance", in Proc. OFC'98 Tech. Dig., 1998, Paper ThR2,. pp. 340-342.

A. Eyal, W. K. Marshall, M. Tur and A. Yariv, "Representation of second-order polarization mode dispersion", Electron. Lett., vol. 35, no. 19, pp. 1658-1659, 1999.

H. Kogelnik, L. E. Nelson, J. P. Gordon and R. M. Jopson, "Jones matrix for second-order polarization mode dispersion", Opt. Lett., vol. 25, no. 1, pp. 19-21, 2000.

H. Bülow, "System outage probability due to first-and second-order PMD", IEEE Photon. Technol. Lett., vol. 10, pp. 696-698, May 1998.

H. Kogelnik, L. E. Nelson and J. P. Gordon, "Emulation and inversion of polarization-mode dispersion", J. Lightwave Technol., vol. 21, no. 2, pp. 482-495, Feb. 2003.

C. D. Poole and R. E. Wagner, "Phenomenological approach to polarization dispersion in long single-mode fibers", Electron. Lett., vol. 22, no. 19, pp. 1029-1030, 1986.

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