Abstract

The unitary transfer matrix of a fiber affected by polarization mode dispersion (PMD) is analyzed using the Stokes representation of its eigenmodes and its retardation angle, or equivalently through its Pauli coordinates. We develop a statistical theory applied to these parameters and relate it to the extensive existing literature on the statistics of the PMD vector Ωo (ω). Dynamical equations are established for the Pauli coordinates. Assuming a standard"white Gaussian"model for the local birefringence, and using the tools of stochastic calculus,we derive the distributions of the eigenmodes, the retardation angle, the Pauli coordinates, and of the frequency derivatives of all these parameters. The evolution in space of the Pauli coordinates is also characterized as a standard Brownian motion on the unit sphere in Re4. An expression for the frequency autocorrelation function of the Pauli coordinates, the eigenmodes and the retardation angle is derived and their coherence bandwidth is compared to that of the PMD vector. All theoretical results are supported by simulation over an ensemble of 10 000 fibers,using the standard retarder plate model.

[IEEE ]

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  1. 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 .
  2. P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. P. Von der Weid, F. Prieto and C. W. Zimmer, "Second-order polarization mode dispersion: Impact on analog and digital transmission", J. Lightwave Technol., vol. 16, pp. 757-771, May 1998.
  3. P. K. A. Wai and C. R. Menyuk, "Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence", J. Lightwave Technol., vol. 14, pp. 148-157, Feb. 1996.
  4. M. Karlsson, "Polarization mode dispersion-induced pulse broadening in optical fibers", Opt. Lett., vol. 23, pp. 688-690, May 1998.
  5. M. O. van Deventer, "Probability density functions of optical polarization states: Theory and applications", J. Lightwave Technol., vol. 12, pp. 2147-2151, Dec. 1994.
  6. D. Marcuse, C. R. Menyuk and P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence", J. Lightwave Technol., vol. 15, pp. 1735-1745, Sept. 1997 .
  7. M. Karlsson and J. Brentel, "Autocorrelation function of the polarization-mode dispersion vector", Opt. Lett., vol. 24, pp. 939-941, July 1999.
  8. M. Shtaif and A. Mecozzi, "Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion", Opt. Lett., vol. 25, pp. 707-709, May 2000.

J. Lightwave Technol. (5)

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 .

P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. P. Von der Weid, F. Prieto and C. W. Zimmer, "Second-order polarization mode dispersion: Impact on analog and digital transmission", J. Lightwave Technol., vol. 16, pp. 757-771, May 1998.

P. K. A. Wai and C. R. Menyuk, "Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence", J. Lightwave Technol., vol. 14, pp. 148-157, Feb. 1996.

M. O. van Deventer, "Probability density functions of optical polarization states: Theory and applications", J. Lightwave Technol., vol. 12, pp. 2147-2151, Dec. 1994.

D. Marcuse, C. R. Menyuk and P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence", J. Lightwave Technol., vol. 15, pp. 1735-1745, Sept. 1997 .

Opt. Lett. (3)

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