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

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 polarizationdispersion vector at the output of the fiber depends upon the angle between it and the local birefringence vector

[1]  Tomasz R. Wolinski,et al.  POLARIZATION IN OPTICAL FIBERS , 1999 .

[2]  W. Kath,et al.  Nonlinear polarization mode dispersion in optical fibers with randomly varying birefringence , 1996, Summaries of papers presented at the Conference on Lasers and Electro-Optics.

[3]  Benedetto Daino,et al.  Statistical treatment of the evolution of the principal states of polarization in single-mode fibers , 1990 .

[4]  D. Nolan,et al.  Fiber spin-profile designs for producing fibers with low polarization mode dispersion. , 1998, Optics letters.

[5]  J. Nagel,et al.  Dynamical equation for polarization dispersion. , 1991, Optics letters.

[6]  Nicolas Gisin,et al.  Solutions of the dynamical equation for polarization dispersion , 1991 .

[7]  J. Botineau,et al.  Effect of polarization on spectral broadening in optical fibers , 1982 .

[8]  H. Kogelnik,et al.  PMD fundamentals: polarization mode dispersion in optical fibers. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[9]  S. Shreve,et al.  Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[10]  D N Payne,et al.  Birefringence and polarization mode-dispersion in spun single-mode fibers. , 1981, Applied Optics.

[11]  Nicolas Gisin,et al.  Definition of polarization mode dispersion and first results of the COST 241 round-robin measurements , 1995 .

[12]  G. Foschini,et al.  Statistical theory of polarization dispersion in single mode fibers , 1991 .

[13]  William L. Kath,et al.  Dynamics of optical pulses in randomly birefringent fibers , 1992 .

[14]  David N. Payne,et al.  Production of single-mode fibres with negligible intrinsic birefringence and polarisation mode dispersion , 1981 .

[15]  M. Islam,et al.  Ultrafast all-optical logic gates based on soliton trapping in fibers. , 1989, Optics letters.

[16]  Vimal Singh,et al.  Perturbation methods , 1991 .

[17]  W. Kath,et al.  Nonlinear polarization-mode dispersion in optical fibers with randomly varying birefringence , 1997 .

[18]  D. Durran.  Numerical methods for wave equations in geophysical fluid dynamics , 1999 .

[19]  R. E. Schuh,et al.  Polarization mode dispersion in spun fibers with different linear birefringence and spinning parameters , 1998 .

[20]  G. Strang.  On the Construction and Comparison of Difference Schemes , 1968 .

[21]  T Tambosso,et al.  Statistical characterization of fiber random birefringence. , 2000, Optics letters.

[22]  L. Arnold.  Stochastic Differential Equations: Theory and Applications , 1992 .

[23]  A. Simmons,et al.  Implementation of the Semi-Lagrangian Method in a High-Resolution Version of the ECMWF Forecast Model , 1995 .

[24]  P. Wai,et al.  Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence , 1996 .

[25]  J. P. von der Weid,et al.  Polarization mode dispersion of short and long single-mode fibers , 1991 .