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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 19, Iss. 5 — May. 1, 2002
  • pp: 992–1000

Transient evolution of the polarization-dispersion vector’s probability distribution

Yu Tan, Jianke Yang, William L. Kath, and Curtis M. Menyuk  »View Author Affiliations


JOSA B, Vol. 19, Issue 5, pp. 992-1000 (2002)
http://dx.doi.org/10.1364/JOSAB.19.000992


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Abstract

We determine the transient evolution of the probability distribution of the polarization dispersion vector both analytically and numerically, using a physically reasonable model of the fiber birefringence. We show that, for all practical birefringence parameters, the distribution of the differential group delay (DGD), which is the magnitude of the polarization dispersion vector, becomes Maxwellian in just a few kilometers, except in the tail region, where the DGD is large. In this limit, the approach to a Maxwellian distribution takes much longer, of the order of tens of kilometers. In addition, we show that in the transient regime the DGD distribution is very different from Maxwellian. We also find that the probability-distribution function for the polarization-dispersion vector at the output of the fiber depends upon the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.

© 2002 Optical Society of America

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(260.5430) Physical optics : Polarization

Citation
Yu Tan, Jianke Yang, William L. Kath, and Curtis M. Menyuk, "Transient evolution of the polarization-dispersion vector's probability distribution," J. Opt. Soc. Am. B 19, 992-1000 (2002)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-5-992


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References

  1. G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991). [CrossRef]
  2. J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization-mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000). [CrossRef]
  3. N. Gisin, “Solutions of the dynamic equation for polarization dispersion,” Opt. Commun. 86, 371–373 (1991). [CrossRef]
  4. F. Curti, B. Daino, G. D. Marchis, and F. Matera, “Statistical treatment of the evolution of the principal states of polarization in single-mode fibers,” J. Lightwave Technol. 8, 1162–1170 (1990). [CrossRef]
  5. N. Gisin, J.-P. Von der Weid, and J.-P. Pellaux, “Polarization mode dispersion of short and long single-mode fibers,” J. Lightwave Technol. 9, 821–827 (1991). [CrossRef]
  6. P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996). [CrossRef]
  7. N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, “Definition of polarization mode dispersion and first results of the COST 241 round-robin measurements,” Pure Appl. Opt. 4, 511–522 (1995). [CrossRef]
  8. I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981). [CrossRef]
  9. R. E. Schuh, X. Shan, and A. S. Siddiqui, “Polarization mode dispersion in spun fibers with different linear birefringence and spinning parameters,” J. Lightwave Technol. 16, 1583–1588 (1998). [CrossRef]
  10. J. Botineau and R. H. Stolen, “Effect of polarization on spectral broadening in optical fibers,” J. Opt. Soc. Am. 72, 1592–1596 (1982). [CrossRef]
  11. M. N. Islam, “Ultrafast all-optical logic gates based on soliton trapping in fibers,” Opt. Lett. 14, 1257–1259 (1989). [CrossRef] [PubMed]
  12. A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso, “Statistical characterization of fiber random birefringence,” Opt. Lett. 25, 1322–1324 (2000). [CrossRef]
  13. C. D. Poole, J. H. Winters, and J. A. Nagel, “Dynamical equation for polarization dispersion,” Opt. Lett. 16, 372–374 (1991). [CrossRef] [PubMed]
  14. L. Arnold, Stochastic Differential Equations, Theory and Applications (Wiley, New York, 1974).
  15. J. W. Zhang, P. K. A. Wai, W. L. Kath, and C. R. Menyuk, “Nonlinear polarization-mode dispersion in optical fibers with randomly varying birefringence,” J. Opt. Soc. Am. B 16, 2967–2979 (1997).
  16. A. H. Nayfeh, Perturbation Methods (Wiley, New York, 1973).
  17. G. Strang, “On the construction and comparison of difference schemes,” SIAM J. Numer. Anal. 5, 506–517 (1968). [CrossRef]
  18. D. R. Durran, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics (Springer-Verlag, New York, 1999).
  19. H. Ritchie, C. Temperton, A. Simmons, M. Hortal, T. Davies, D. Dent, and M. Hamrud, “Implementation of the semi-Lagrangian method in a high-resolution version of the ECMWF model,” Mon. Weather Rev. 123, 489–514 (1995). [CrossRef]
  20. A. J. Barlow, D. N. Payne, M. R. Hadley, and R. J. Mansfield, “Production of single-mode fibers with negligible intrinsic birefringence and polarization mode dispersion,” Electron. Lett. 17, 725–726 (1981). [CrossRef]
  21. A. J. Barlow and J. J. Ramskov-Ha, “Birefringence and polarization mode-dispersion in spun single-mode fibers,” Appl. Opt. 20, 2962–2968 (1981). [CrossRef] [PubMed]
  22. M. J. Li and D. A. Nolan, “Fiber spin-profile designs for producing fibers with low polarization mode dispersion,” Opt. Lett. 23, 1659–1662 (1998). [CrossRef]
  23. R. E. Schuh, X. Shan, and A. S. Siddiqui, “Polarization mode dispersion in spun fibers with different linear birefringence and spinning parameters,” J. Lightwave Technol. 16, 1583–1588 (1998). [CrossRef]
  24. T. Ueda and W. L. Kath, “Dynamics of optical pulses in randomly birefringent fibers,” Physica D 55, 166–181 (1992). [CrossRef]

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