非线性薛定谔方程数值解法中傅立叶正逆变换选取的讨论
Discussion on the Choice of the Fourier Transformation Form in Numerical Solutions of Nonlinear Schrödinger Equation
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摘要: 讨论了光波场正负频表示与正逆傅立叶变换形式的选取及非线性薛定谔方程的形式密切相关,指出了现在熟知的非线性薛定谔方程形式是选取负频表示的结果,因此正逆傅立叶变换形式的选取就不是任意的.在采用基于傅立叶变换数值方法解非线性薛定谔方程时,要注意所用编程语言中快速傅立叶变换正逆变换的形式.而在大多数编程语言中其快速傅立叶变换正逆变换形式是与非线性光学中应采用的傅立叶变换正逆形式恰好相反,因此时而出现一些错误的计算结果.分析了这些错误的原因,并给出了正确结果.Abstract: Relationships between the choice of the positive and negative frequency expression of optical waves, adoption of Fourier transformation form and form of nonlinear Schrödinger equation are discussed. The generally accepted form of nonlinear Schrödinger equation is the result of choosing the negative frequency expression. In accord with the negative frequency expression, the form of Fourier transformation cannot be chosen at will. When the nonlinear Schrödinger equation is solved using numerical methods based on Fourier transformation, the form of fast Fourier transformation must be paid attention in the programming languages used. In most programming languages, the adopted forms of fast Fourier transformation and inverse transformation are opposite to the forms adopted in nonlinear optics. It is also pointed out that some related numerical errors existed in some references.