Analytical Formulation of Fiber Nonlinear Noise Statistics in the Presence of Polarization Dependent Loss

Fiber nonlinearity has been considered as one of the main burdens to further boost the system capacity. In polarization multiplexing (Pol-Mux) systems, fiber nonlinearity induced noise is significantly affected by the polarization dependent loss (PDL), which is random and modelled via the time-consuming Monte Carlo simulations. A statistical study is carried out for this phenomenon based on a stochastic differential equation (SDE) approach. Ordinary differential equations (ODEs) are derived for the average values of the random terms, which significantly reduces the computational efforts. The average nonlinear noise power, the power variance, the correlation between the noise terms and the correlation variance are computed by the model and comparison is conducted with the results by the Monte Carlo simulation in combined with the GN model and the SSFM algorithm. Excellent agreement between the results is observed.