Optimization of the Split-step Fourier Method in Modeling Optical Fiber Communications Systems

We studied the efficiency of different implementations of the split-step Fourier method for solving the nonlinear Schrödinger equation that employ different step size selection criteria. We compared the performance of the different implementations for a variety of pulse formats and systems including higher-order solitons, collisions of soliton pulses, a single-channel periodically-stationary dispersion-managed soliton system, and chirped return to zero systems with single and multiple channels. We introduce a globally third-order accurate split-step scheme, in which a bound on the local error is used to select the step size. In many cases, this method is the most efficient when compared with commonly-used step size selection criteria, and it is robust for a wide range of systems providing a system-independent rule for choosing the step sizes. We find that a step-size selection method based on limiting the nonlinear phase rotation of each step is not efficient for many optical fiber transmission systems, although it