光脉冲传输数值模拟的分步小波方法  

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

作　　者：陈宏平[1] 王箭[1] 何国光[1] 

机构地区：[1]浙江大学物理系,杭州310027

出　　处：《物理学报》2005年第6期2779-2783,共5页Acta Physica Sinica

基　　金：浙江省自然科学基金(批准号:601137)资助的课题.~~

摘　　要：从信号的多尺度小波分解和正交小波变换出发,将描述光学介质中脉冲传输的非线性薛定谔方程(NLSE)表示为小波域中的分步算符形式,给出了分步小波算法的迭代公式,导出了线性算符在小波域中的具体表式,并讨论微分算符的矩阵结构.作为一个例子,用分步小波方法(SSWM)解NLSE,给出了超短高斯脉冲在光纤中线性和非线性传输的波形演化,并与解析解和分步傅里叶方法的结果作了比较.结果表明,分步小波方法是研究脉冲在光学介质中传输的一种有效的数值计算方法.The multi-scale wavelet decomposition and orthogonal wavelet transform are outlined and applied to the representation of optical pulses. The nonlinear Schrodinger(NSL) equation, which describes the pulse propagation in optical media, is used to represent the split-step operator form in wavelet domain. The iterative equation 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 and 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 method. The results show that SSWM is an accurate and effective numerical method for the study of the pulses propagation through optical media.

关 键 词：分步小波方法 光脉冲传输 非线性薛定谔方程 多尺度小波分解 

分 类 号：O411.1[理学—理论物理]