Statistics of the Jones Matrix of fibers affected by Polarization Mode Dispersion

We carry out a statistical characterization of Jones matrix eigenvalues and eigenmodes to gain deeper insight into recently proposed fiber models based on Jones matrix spectral decomposition. A set of linear dynamic equations for the Pauli coordinates of the Jones matrix is established. Using stochastic calculus, we determine the joint distribution of the retardation angle of the eigenmodes and, indirectly, their autocorrelation function. The correlation bandwidth of the eigenmodes is found to be sqrt(2/3) that of the polarization mode dispersion vector. The results agree well with simulations performed with the standard retarded plate model.