Abstract

The authors investigate the artificial frequency correlation induced by polarization scrambled statistical polarization-mode-dispersion emulators. A simple model is derived that accurately predicts the average frequency correlation when the scrambling is symmetric. It is shown that the nature of the symmetry affects the emulator performance, and that increasingly, isotropic scrambling gives lower correlation. The derived model shows a good agreement with Monte Carlo simulation and experiment.

© 2006 IEEE

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  1. D. Breuer, H.-J. Tessmann, A. Gladisch, H. Foisel, G. Neumann, H. Reiner, H. Cremer, "Measurements of PMD in the installed fiber plant of Deutsche Telekom," Digest of Holey Fibers and Photonic Crystals/Polarization Mode Dispersion/Photonics Time/Frequency Measurement and Control, LEOS Summer Topical Meetings, Vancouver, BC, Canada, 2003, Paper MB2.1.
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  3. J. N. Damask, "Methods to construct programmable PMD sources—Part I: Technology and theory," J. Lightw. Technol. 22, 997-1005 (2004).
  4. M. C. Hauer, Q. Yu, A. E. Willner, E. R. Lyons, C. H. Lin, A. A. Au, H. P. Lee, "Compact, all-fiber PMD emulator using an integrated series of thin-film micro-heaters," Optical Fiber Communication Conf. and Exhibit, Anaheim, CA, 2002, Paper ThA3.
  5. R. Khosravani, I. T. Lima, Jr.P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
  6. Y. K. Lize, L. Palmer, N. Godbout, S. Lacroix, R. Kashyap, "Scalable polarization-mode dispersion emulator with proper first- and second-order statistics," IEEE Photon. Technol. Lett. 17, 2451-2453 (2005).
  7. M. Shtaif, "The Brownian-bridge method for simulating polarization mode dispersion in optical communications systems," IEEE Photon. Technol. Lett. 15, 51-53 (2003).
  8. M. Karlsson, J. Brentel, "Autocorrelation function of the polarization-mode dispersion vector," Opt. Lett. 24, 939-941 (1999).
  9. Q. Lin, G. Agrawal, "Correlation theory of polarization mode dispersion in optical fibers," J. Opt. Soc. Amer. B, Opt. Phys. 20, 292-301 (2003).
  10. M. Shtaif, A. Mecozzi, "Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion," Opt. Lett. 25, 707-709 (2000).
  11. B. S. Marks, I. T. J. Lima, C. R. Menyuk, "Autocorrelation function for polarization mode dispersion emulators with rotators," Opt. Lett. 27, 1150-1152 (2002).
  12. L. Palmer, S. D. Dods, P. M. Farrell, "Broad-band concatenated section PMD emulator design for low-interchannel correlation," IEEE Photon. Technol. Lett. 17, 1019-1021 (2005).
  13. P. B. Phua, E. B. Ippen, "Combinatorial polarization scramblers for many-segment pmd emulator," IEEE Photon. Technol. Lett. 17, 405-407 (2005).
  14. L. Yan, Q. Yu, A. E. Willner, "Uniformly distributed states of polarization on the Poincaré sphere using an improved polarization scrambling scheme," Opt. Commun. 249, 43-50 (2005).
  15. T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).
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  17. J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Nat. Acad. Sci. 97, 4541-4550 (2000).
  18. G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Harcourt/Academic, 2001).
  19. M. Karlsson, J. Brentel, P. A. Andrekson, "Long-term measurement of PMD and polarization drift in installed fibers," J. Lightw. Technol. 18, 941-951 (2000).
  20. A. Leon-Garcia, Probability and Random Processes for Electrical Engineering (Addison-Wesley, 1994).
  21. J. P. Marques de Sá, Applied Statistics Using SPSS, STATISTICA and MATLAB (Springer-Verlag, 2003).
  22. B. L. Heffner, "Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis," IEEE Photon. Technol. Lett. 4, 1066-1069 (1992).
  23. G. A. F. Seber, C. J. Wild, Nonlinear Regression (Wiley, 1989).
  24. L. Yan, M. C. Hauer, Y. Shi, X. S. Yao, P. Ebrahimi, Y. Wang, A. E. Willner, W. L. Kath, "Polarization-mode-dispersion emulator using variable differential-group-delay (DGD) elements and its use for experimental importance sampling," J. Lightw. Technol. 22, 1051-1058 (2004).
  25. J. H. Lee, M. S. Kim, Y. C. Chung, "Statistical PMD emulator using variable dgd elements," IEEE Photon. Technol. Lett. 15, 54-56 (2003).
  26. M. Karlsson, "Probability density functions of the differential group delay in optical fiber communication systems," J. Lightw. Technol. 19, 324-331 (2001).

2005 (5)

L. Palmer, S. D. Dods, P. M. Farrell, "Broad-band concatenated section PMD emulator design for low-interchannel correlation," IEEE Photon. Technol. Lett. 17, 1019-1021 (2005).

P. B. Phua, E. B. Ippen, "Combinatorial polarization scramblers for many-segment pmd emulator," IEEE Photon. Technol. Lett. 17, 405-407 (2005).

L. Yan, Q. Yu, A. E. Willner, "Uniformly distributed states of polarization on the Poincaré sphere using an improved polarization scrambling scheme," Opt. Commun. 249, 43-50 (2005).

T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).

Y. K. Lize, L. Palmer, N. Godbout, S. Lacroix, R. Kashyap, "Scalable polarization-mode dispersion emulator with proper first- and second-order statistics," IEEE Photon. Technol. Lett. 17, 2451-2453 (2005).

2004 (2)

J. N. Damask, "Methods to construct programmable PMD sources—Part I: Technology and theory," J. Lightw. Technol. 22, 997-1005 (2004).

L. Yan, M. C. Hauer, Y. Shi, X. S. Yao, P. Ebrahimi, Y. Wang, A. E. Willner, W. L. Kath, "Polarization-mode-dispersion emulator using variable differential-group-delay (DGD) elements and its use for experimental importance sampling," J. Lightw. Technol. 22, 1051-1058 (2004).

2003 (3)

J. H. Lee, M. S. Kim, Y. C. Chung, "Statistical PMD emulator using variable dgd elements," IEEE Photon. Technol. Lett. 15, 54-56 (2003).

M. Shtaif, "The Brownian-bridge method for simulating polarization mode dispersion in optical communications systems," IEEE Photon. Technol. Lett. 15, 51-53 (2003).

Q. Lin, G. Agrawal, "Correlation theory of polarization mode dispersion in optical fibers," J. Opt. Soc. Amer. B, Opt. Phys. 20, 292-301 (2003).

2002 (1)

2001 (3)

R. Khosravani, I. T. Lima, Jr.P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).

M. Karlsson, "Probability density functions of the differential group delay in optical fiber communication systems," J. Lightw. Technol. 19, 324-331 (2001).

J. Lima, I. T. R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightw. Technol. 19, 1872-1881 (2001).

2000 (3)

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Nat. Acad. Sci. 97, 4541-4550 (2000).

M. Karlsson, J. Brentel, P. A. Andrekson, "Long-term measurement of PMD and polarization drift in installed fibers," J. Lightw. Technol. 18, 941-951 (2000).

M. Shtaif, A. Mecozzi, "Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion," Opt. Lett. 25, 707-709 (2000).

1999 (1)

1992 (1)

B. L. Heffner, "Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis," IEEE Photon. Technol. Lett. 4, 1066-1069 (1992).

1991 (1)

G. J. Foschini, C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightw. Technol. 9, 1439-1456 (1991).

IEEE Photon. Technol. Lett. (8)

R. Khosravani, I. T. Lima, Jr.P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).

Y. K. Lize, L. Palmer, N. Godbout, S. Lacroix, R. Kashyap, "Scalable polarization-mode dispersion emulator with proper first- and second-order statistics," IEEE Photon. Technol. Lett. 17, 2451-2453 (2005).

M. Shtaif, "The Brownian-bridge method for simulating polarization mode dispersion in optical communications systems," IEEE Photon. Technol. Lett. 15, 51-53 (2003).

T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).

L. Palmer, S. D. Dods, P. M. Farrell, "Broad-band concatenated section PMD emulator design for low-interchannel correlation," IEEE Photon. Technol. Lett. 17, 1019-1021 (2005).

P. B. Phua, E. B. Ippen, "Combinatorial polarization scramblers for many-segment pmd emulator," IEEE Photon. Technol. Lett. 17, 405-407 (2005).

B. L. Heffner, "Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis," IEEE Photon. Technol. Lett. 4, 1066-1069 (1992).

J. H. Lee, M. S. Kim, Y. C. Chung, "Statistical PMD emulator using variable dgd elements," IEEE Photon. Technol. Lett. 15, 54-56 (2003).

J. Lightw. Technol. (6)

M. Karlsson, "Probability density functions of the differential group delay in optical fiber communication systems," J. Lightw. Technol. 19, 324-331 (2001).

L. Yan, M. C. Hauer, Y. Shi, X. S. Yao, P. Ebrahimi, Y. Wang, A. E. Willner, W. L. Kath, "Polarization-mode-dispersion emulator using variable differential-group-delay (DGD) elements and its use for experimental importance sampling," J. Lightw. Technol. 22, 1051-1058 (2004).

M. Karlsson, J. Brentel, P. A. Andrekson, "Long-term measurement of PMD and polarization drift in installed fibers," J. Lightw. Technol. 18, 941-951 (2000).

G. J. Foschini, C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightw. Technol. 9, 1439-1456 (1991).

J. Lima, I. T. R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightw. Technol. 19, 1872-1881 (2001).

J. N. Damask, "Methods to construct programmable PMD sources—Part I: Technology and theory," J. Lightw. Technol. 22, 997-1005 (2004).

J. Opt. Soc. Amer. B, Opt. Phys. (1)

Q. Lin, G. Agrawal, "Correlation theory of polarization mode dispersion in optical fibers," J. Opt. Soc. Amer. B, Opt. Phys. 20, 292-301 (2003).

Opt. Commun. (1)

L. Yan, Q. Yu, A. E. Willner, "Uniformly distributed states of polarization on the Poincaré sphere using an improved polarization scrambling scheme," Opt. Commun. 249, 43-50 (2005).

Opt. Lett. (3)

Proc. Nat. Acad. Sci. (1)

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Nat. Acad. Sci. 97, 4541-4550 (2000).

Other (6)

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Harcourt/Academic, 2001).

A. Leon-Garcia, Probability and Random Processes for Electrical Engineering (Addison-Wesley, 1994).

J. P. Marques de Sá, Applied Statistics Using SPSS, STATISTICA and MATLAB (Springer-Verlag, 2003).

M. C. Hauer, Q. Yu, A. E. Willner, E. R. Lyons, C. H. Lin, A. A. Au, H. P. Lee, "Compact, all-fiber PMD emulator using an integrated series of thin-film micro-heaters," Optical Fiber Communication Conf. and Exhibit, Anaheim, CA, 2002, Paper ThA3.

D. Breuer, H.-J. Tessmann, A. Gladisch, H. Foisel, G. Neumann, H. Reiner, H. Cremer, "Measurements of PMD in the installed fiber plant of Deutsche Telekom," Digest of Holey Fibers and Photonic Crystals/Polarization Mode Dispersion/Photonics Time/Frequency Measurement and Control, LEOS Summer Topical Meetings, Vancouver, BC, Canada, 2003, Paper MB2.1.

G. A. F. Seber, C. J. Wild, Nonlinear Regression (Wiley, 1989).

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