Abstract
Many numerical approximations are introduced in solving the general nonlinear Schrdinger equation （GNLSE） using the split-step Fourier method （SSFM）. In addition, careful consideration of the spatial and the temporal step sizes and the temporal window is needed to ensure the numerical precision. Supercontinuum generation in photonic crystal fiber is analyzed to show the improvement and precision control. The nonlinear term is treated directly by an integral instead of any mathematical approximation. Then the integral term can be transformed to a convolution to be solved by the Fourier transform, which facilitates the accurate numerical computation of the nonlinear term. High precision is ensured since no factitious approximation is introduced. Computation precision with respect to the step size choice is analyzed. Criteria are proposed as follows. The temporal and spatial step sizes can be appropriately chosen from the spectrogram, and the temporal figure provides a criterion for the temporal step size. These conclusions present direct criteria for the difficuet job of step size choice in solving the GNLSE.
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