Optimization of the split-step fourier method in modeling optical-fiber communications systems

TLDR

The authors propose a globally third‑order accurate split‑step Fourier scheme that adapts step size based on a local error bound, and a variant that scales step size inversely with the maximum group‑velocity difference among channels. The study evaluates multiple split‑step Fourier implementations—varying step‑size selection rules, including a logarithmic distribution and a group‑velocity‑based scaling—across diverse pulse formats and system configurations to benchmark computational efficiency. The globally third‑order scheme outperforms standard step‑size rules and remains robust across systems; the nonlinear‑phase‑rotation limiter is inefficient except for solitons; logarithmic step‑size matches second‑order methods only in single‑channel dispersion‑managed solitons; constant step size is the least efficient; and the group‑velocity‑based scaling yields the best performance in multichannel optical communications.

Abstract

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 works well for solitons. We also tested a method that uses a logarithmic step-size distribution 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 multichannel simulations. We find that in most cases, the simple approach in which the step size is held constant is the least efficient of all the methods. Finally, 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 multichannel optical communications systems for the values of accuracy typically required in most transmission simulations.