Menyuk, “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 for-mats 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 1 works well for solitons. We also tested a method that uses a logarithmic step size distribu-tion to bound the amount of spurious four-wave mixing. This method is as efficient as other second-order schemes in the single-channel dispersion-managed soliton system, while it is not efficient in other cases including multi-channel simulations. We find that in most cases the simple approach in which the step size is held constant is least efficient of all the methods. Fi-nally, we implemented a method in which the step size is inversely proportional to the largest group velocity difference between channels. This scheme performs best in multi-channel opti-cal communications systems for the values of accuracy typically required in most transmission simulations