快速数值差分递推改进算法在超宽连续谱模拟中的应用研究

对快速数值差分递推公式进行了改进,使之能够求解带有脉冲自陡峭项和脉冲内喇曼散射项的非线性薛定谔方程.通过与传统孤子解析结果及分步傅里叶方法数值结果的对比分析表明,快速数值差分递推改进算法是一种快速而准确的数值计算方法,它不仅能够同步考虑光学媒质中的群速色散作用和非线性克尔作用,而且将所有高阶非线性项对光脉冲传输的影响也...

Modified Rapid Numerical Difference Recurrence Algorithm and Its Application in the Simulation of Supercontinuum

A new modified form of the rapid numerical difference recurrence formula has been proposed to calculate the nonlinear Shr?dinger equation (NLSE) , in which the last two terms are responsible for the effects of the pulse self-steepening and the intrapulse Raman scattering in this paper. It shows that the modified rapid numerical difference recurrence algorithm, compared with the traditional analytical results of solitons and the solutions of Split-step Fourier method (SSFM), is a fast and precise numerical method, in which it has been taken into account simultaneously that not only the effects of the chromatic dispersion and the nonlinear Kerr effect together along each fiber segment, but also the effects of all the higher-order nonlinear items of the optical medium. By using this method, it has been validated successfully to simulate the Supercontinuum generated as a result of the optical fiber nonlinear effects and the group velocity dispersion (GVD) effects together. The formula has been proved that it can provide some new ideas of research for the simulation of the other nonlinear phenomena in the optical medium.