Abstract

In this thesis, general nonlinear Schrödinger equation is solved in very detailed numerical process by using Symmetrized Split-Step Fourier Method (S-SSFM), Higher-Order Symmetrized Split-Step Fourier Method (HO-S-SSFM) and Predictor-Corrector Symmetrized Split-Step Fourier Method (PC-S-SSFM). We simulated the SC generations in the PCF by using HO-S-SSFM and PC-S-SSFM respectively. To our knowledge, this is the first time the PC-S-SSFM is used in simulations of SC generation. Typical physical parameters of a PCF are chosen in our simulations. Based on the same condition, the simulation results of the HO-S-SSFM and the PC-S-SSFM are compared with the results from a published paper, and the comparison proves that our simulations are correct and accurate. Then, the time used by the HO-S-SSFM and the PC-S-SSFM in our simulations are compared at different points of propagation along the PCF and at the end of the PCF with different step sizes. The comparison results show that the PC-S-SSFM can save almost one third time used by the HO-S-SSFM under the same accuracy.