Solutions to the dynamical equation of polarization-mode dispersion and polarization-dependent losses

We study the evolution of optical signals in single-mode optical fibers in the presence of polarization-mode dispersion and polarization-dependent losses. Two geometric vectors on the Poincare sphere are defined to characterize the effects of polarization-mode dispersion and polarization-dependent losses on the optical field in the fiber. By solving the dynamical equation for these two vectors, several general statistical results are obtained. The practically important weak polarization-dependent-loss situation is discussed in detail.