Fiber-optic transmissions in nonlinear regime: analysis of the numerical error in split-step simulations and modeling of polarization dependent loss

One of the main problems in nowadays fiber optical communications is to correctly asses the impact the nonlinearity of the fiber, which is one of the main impairments limiting the signal-to-noise ratio (SNR) of the communication. Over the years the problem has been tackled by means of analytical modeling, experimental investigations, and numerical simulations based on the split-step Fourier method (SSFM). Such approaches present advantages and disadvantages depending on the application. Numerical simulations are a general and precise way to estimate the impact of the nonlinearity since they can be applied to any link configuration. Although a simulation cannot account for all the physical effects occurring in an experiment, it has the advantage to abstract the investigation by isolating the interactions of interest. Such prominent advantages, however, come at the expense of the computational effort to run the algorithm, which could be excessively long in applications where the complexity is an issue. On the contrary, analytical modeling can provide results in faster computational times, but lacks the generality of the numerical simulation due to their inherent simplificative assumptions. In this thesis work, we address such methodologies by facing two different problems arising in nowadays optical systems. First, we study the accuracy of the SSFM in wideband signal transmissions, showing that the numerical error introduced by the algorithm on the SNR in dB is power-independent and it scales quadratically with the signal bandwidth, in contrast with two common rules used in the literature to set the accuracy of the simulation. We propose a new rule to set the first step of the simulation yielding a constant error on the received SNR in dB for a wide range of signal powers, bandwidths, and fiber dispersions. It can thus be used as a universal method to simulate wideband signal propagations at constant accuracy. The scaling of the computational effort of the SSFM by increasing the signal bandwidth over the C-band is also discussed. Second, we address the problem of modeling the nonlinearity in presence of random polarization dependent loss (PDL). We show by numerical investigations that the PDL-nonlinearity interaction may change the statistical distribution of the SNR at the receiver in a different way than what expected by current semi-analytical models developed for the linear transmission regime. We then propose for the first time an extension of the Gaussian noise model to estimate nonlinear interference variance with PDL. The new model showed an excellent accuracy in estimating the such interaction with a much smaller complexity overhead compared to SSFM-based simulations.