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  

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

作　　者：邱桥飞[1] 张冠茂[1] 张晓萍[1] 

机构地区：[1]兰州大学信息科学与工程学院现代通信技术研究所,兰州730000

出　　处：《光子学报》2011年第1期29-35,共7页Acta Photonica Sinica

基　　金：教育部"新世纪优秀人才支持计划"基金(No.NCET-04-0981);兰州大学交叉学科青年创新研究基金(No.LZU200514)资助

摘　　要：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考虑了进去.运用该算法模拟了由于光纤非线性效应和群速色散效应共同作用所产生的超宽连续谱现象,为光学媒质中一系列非线性现象的模拟提供了新的研究思路.A new modified form of the rapid numerical difference recurrence formula was proposed to calculate the nonlinear Shrdinger equation,with ites of the pulse self-steepening and the intrapulse Raman scattering.Compared with the traditional analytical results of solitons and the solutions of Split-step Fourier method,the results show that the modified rapid numerical difference recurrence algorithm is a fast and precise numerical method,which takes into account simultaneously both the effects of the chromatic dispersion and the nonlinear Kerr effect together along each fiber segment,and the effects of all the higher-order nonlinear items of the optical medium.By using this method,it was validated successfully to simulate the supercontinuum generated as a result of the optical fiber nonlinear effects and the group velocity dispersion effects together.The formula was proved that it can provide some new ideas of research for the simulation of the other nonlinear phenomena in the optical medium.

关 键 词：快速数值差分递推改进算法 非线性薛定谔方程 超宽连续谱 脉冲自陡峭效应 脉冲内喇曼散射效应 

分 类 号：TN929.1[电子电信—通信与信息系统]