Comparison of Split-Step Fourier Schemes for Simulating Fiber Optic Communication Systems

This paper mainly focuses on efficient schemes for simulating propagation in optical fibers. Various schemes based on split-step Fourier techniques to solve the nonlinear Schrödinger equation (NLSE), which describes the propagation in optical fibers, are compared. In general, the schemes in which the loss operator is combined with nonlinearity operator are found to be more computationally efficient than the schemes in which the loss is combined with dispersion. When the global error is large, the schemes with variable step size outperform the ones with uniform step size. The schemes based on local error and/or minimum area mismatch (MAM) further improve the computational efficiency. In this scheme, by minimizing the area mismatch between the exponential profile and its stepwise approximation, an optimal step size distribution is found. The optimization problem is solved by the steepest descent algorithm. The number of steps to get the desired accuracy is determined by the local error method. The proposed scheme is found to have higher computational efficiency than the other schemes studied in this paper. For QPSK systems, when the global error is 10^-8, the number of fast Fourier transforms (FFTs) needed for the conventional scheme (loss combined with dispersion and uniform step size) is 5.8 times that of the proposed scheme. When the global error is 10^-6, the number of FFTs needed for the conventional scheme is 3.7 times that of the proposed scheme.