This paper numerically investigated the evolution of the degree of polarization of individual channels and their Stokes parameters in a wavelength division multiplexed (WDM) system in which Kerr nonlinearity and chromatic dispersion are taken into account but in which polarization mode dispersion as well as polarization-dependent loss and gain are neglected. We compared the results to a mean field model which assumes that the channels are strongly dispersion-managed so that each channel is only affected by the Stokes parameters of the others. This model predicts no change in the degree of polarization of each of the channels so that an initially polarization-scrambled channel does not repolarize. The full simulations showed that the repolarization of a polarization-scrambled signal is small for parameters corresponding to realistic communication systems, validating the use of the mean field model. However, we also found that the repolarization can become significant for low data rates and a small number of channels in a dispersion-managed system with a short length map, thus setting limits on the model's validity and indicating operating regimes that should be avoided in real communication systems.
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