Improved Numerical Model for the Average Transfer Matrix of First- and Second-Order PMD

An improved model for the average transfer matrix of first- and second-order polarization-mode dispersion (F&SO-PMD) in optical fibers is derived from numerical simulations of the frequency dependence of the differential phase shifts and cross coupling between signal components that are transmitted in two principal states of polarization (PSPs). The mean differential phase shifts and cross-coupling phases are calculated for various given values of the differential group delay (DGD) and the second-order PMD parameter that characterizes the coupling between PSPs. It is found that the mean differential phase delays are equal to the DGDs only over a narrow optical bandwidth, beyond which they decrease with increasing frequency offset and in some cases even reverse sign. Similarly, the mean cross-coupling phases increase less rapidly with frequency than assumed in other popular models and always approach an asymptotic value, at which half of the optical power is coupled from one PSP to the other. Moreover, it is shown that these mean differential phase shifts and cross-coupling phases define a transfer matrix for F&SO-PMD that nicely predicts the average eye-opening penalties in return-to-zero-formatted digital optical signals that are transmitted in one of the two PSPs. These predictions are particularly accurate when the average polarization-dependent chromatic dispersion (PCD) is included in the PSP phases. Additional simulations of F&SO-PMD compensation reveal that the signal impairments caused by PCD, on average, are substantially smaller than those introduced by the cross coupling between PSPs