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An analytical characterization of polarization dispersion measurements is presented. The authors report the solution of Poole's stochastic dynamical equation for the evolution of the polarization dispersion vector with fiber length. The authors extend this to a more complete description by considering small, second-order dispersion effects through the frequency derivative of the dispersion vector. The complete analytical solution is seen to accord with what were originally empirically derived features of the joint probability distribution of the polarization dispersion vector and its frequency derivatives. Among the analytically determined properties are the Gaussian probability densities of the three components of the dispersion vector, and the hyperbolic secant (soliton shaped) probability densities of the components of the derivative of the dispersion vector.>
Foschini et al. (Tue,) studied this question.