不同形式非线性薛定谔方程及其分步傅里叶法求解

Different Forms of Nonlinear Schrödinger Equation and Solutions Using Split Step Fourier Method

摘要: 讨论光通信中脉冲的准单色光光场的正负频表示,正负频形式的傅里叶变换,正负频形式的非线性薛定谔方程及它们之间的关系.尤其在脉冲频谱的求解问题中,如果采用负频形式的非线性薛定谔方程则必须选取负频形式的傅里叶变换;如果采用正频形式的非线性薛定谔方程则必须选取正频形式的傅里叶变换.采用分步傅里叶法对具体实例进行数值求解,验证了讨论结果.

Abstract: The positive and negative frequency expressions of quasi-monochromatic optical fields of a pulse in fiber-optic communication and the positive and negative frequency forms of Fourier transformations and nonlinear Schrödinger(NLS) equations are discussed.Especially,in the solution of pulse spectrum,the negative frequency form of NLS equation should be solved by the negative frequency form of Fourier transformation,while the positive frequency form of NLS equation is solved by the positive frequency form of Fourier transformation.An example is given using split step Fourier method.