Jones Transfer Matrix for Polarization Mode Dispersion Fibers

With the advent of long distance high bit rate optical systems, polarization mode dispersion (PMD) has become an important source of limitation for the system performance. In a first order approximation, PMD, that is described by a differential group delay (DGD) between two orthogonal states of polarization (PSPs), causes an undesired output pulse broadening; the frequency dependence of DGD and PSPs produces other distorting effects, considered as higher order PMD effects. A useful theoretical means of predicting the overall distortion of the transmitted signal is the evaluation of the Jones transfer matrix of the fiber but, unfortunately, the statistics of its coefficients are not available up to now. On the other hand, the statistical behavior of the three-dimensional dispersion vector, that characterizes the PMD of the fiber in the Stokes space and can be measured, is known up to a second order PMD approximation. Consequently, finding the analytical relationship between the PMD vector and the coefficients of the Jones matrix is mandatory. In the work, the tight methodology of calculating the Jones matrix, starting from the knowledge of the PMD vector, is shown. This new method is used to determine the output temporal pulse expression in a second order PMD approximation and it is applied to evaluate the performance of a system affected by PMD. The results obtained with the present model are compared to the performance evaluated by numerical simulations, where all order PMD effects are taken into account; our model gives a performance curve that is more accurate in the approximation of all order PMD effects