Split-step wavelet method for numerical simulation of optical pulse propagation

Abstract

The multi-scale wavelet decomposition and orthogonal wavelet transform are outli ned and applied to the representation of optical pulses. The nonlinear Schrdin ger(NSL) equation, which describes the pulse propagation in optical media, is us ed to represent the split-step operator form in wavelet domain. The iterative eq uation of the split-step wavelet algorithm for the solution of the NLS equation is presented. The expression of the linear operator in wavelet domain is given a nd the framework of the derivative operator is discussed. As an example, the linear and nonlinear propagations of ultrashort Gaussian pulse through optical fibers are numerically simulated by using the split-step wavelet method (SSWM), and compared with that by using the analytic solution and the split-step Fourier met hod. The results show that SSWM is an accurate and effective numerical method fo r the study of the pulses propagation through optical media.