Open AccessImprovement and precision analysis of the split-step Fourier method in solving the general nonlinear Schr?dinger equation
Author(s) -
Zhao Lei,
Shiping Zhan,
Qi Zhu,
Ying Zhang,
Yanlei Zuo
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.4731
Subject(s) - nonlinear system , computation , fourier transform , supercontinuum , convolution (computer science) , split step method , computer science , numerical analysis , mathematics , algorithm , partial differential equation , mathematical analysis , physics , photonic crystal fiber , optical fiber , telecommunications , quantum mechanics , artificial neural network , machine learning
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.