Solutions of the dynamical equation for polarization dispersion

We model the local briefringence of a standard fiber by representing each component of the modal birefringence vector as colored noise (Ornstein-Uhlenbeck stochastic processes). For this statistical model we consider the dynamical equation for polarization dispersion and derive the distribution of the group delays between the principal states. We then compare statistical ensembles at a fixed wavelength ensembles with a fixed local birefringence. We show that under reasonable assumptions the average over both ensembles coincide. We conclude thus that the use of a large spectrum source, like a LED, permits measuring the rms deviation in a single run.