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Solving Coupled Nonlinear Schrödinger Equations Based on the Discrete Split-Step Multi-Wavelet Method
Q. Tao, F-G. Luo, Z-W. Wan, Q-L. Liang, X-M. Song and X-C. Liu

In this paper the discrete split-step multi-wavelet method (DSSMWM) is proposed to solve the coupled nonlinear Schrödinger equations (CNLSE) for researching the switching characteristics of a silicon-on-insulator (SOI) nonlinear directional coupler. Three kinds of effective refractive index are obtained for the rectangular waveguide. For each refractive index the relative transmission efficiency errors and relative amplitude errors are calculated by the splitstep Fourier method (SSFM) and the DSSMWM, respectively. Although output pulses display a little broadening and losses, all Dij were less than 0.1% and all hi were below 0.25%. Although these changes had a little influence on the switching characteristics, the time of solving the coupling equations was sharply reduced showing that this method is obviously effective.

Keywords: Coupled nonlinear Schrödinger equations (CNLSE), discrete split-step multi-wavelet method (DSSMWM), silicon-on-insulator (SOI), vector finite element, refractive index

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