On the Accuracy of Split-Step Fourier Simulations for Wideband Nonlinear Optical Communications

We investigate the accuracy of wideband split-step Fourier method (SSFM) simulations by treating SSFM numerical noise as an additive distributed noise source, much like amplified spontaneous emission and nonlinear interference. In this framework, we emphasize that the step size of a numerical simulation targeting a given error on the received signal-to-noise ratio (SNR) should be launch-power independent, and should scale inversely with the square of the signal bandwidth. From this we conclude that the commonly used nonlinear phase criterion for the step update along the distance is not optimal due to its power dependence and its unawareness of signal bandwidth. We propose a general criterion, based on four-wave mixing control, to set the first step of a series of exponentially increasing steps at the desired received SNR accuracy. Finally, we discuss the behavior of the SSFM accuracy versus step-size showing that at practical accuracies of interest the well-known arguments based on the Baker-Campbell-Hausdorff formula may not hold, and explain how to set up a correct SSFM simulation to target an acceptable SNR error.