摘要
利用分步傅里叶算法求解广义非线性薛定谔方程时对非线性项的处理往往采取了较多的数值近似,而且需要特别小心选择空间和时间的步长以及窗口尺寸,以保证精度要求.以描述光子晶体光纤中超连续谱产生的广义非线性薛定谔方程为例,利用分步傅里叶方法求解时对非线性项直接采用积分处理,而不采取任何数学近似,数值计算时又将积分变成卷积利用傅里叶变换求解,从而方便而又精确地完成了非线性项的计算.整个过程没有任何人为的近似,从而保证了计算模型的精确度.同时,还对因步长选择引起的计算精度进行了分析,提出了从频谱图上判断空间、时间步长选取合理性,从时域图上判断时间窗口合理性的方法,从而为广义非线性薛定谔方程求解过程中的步长选择等问题提供了直观参考标准.
Many numerical approximations are introduced in solving the general nonlinear Schrodinger equation （GNLSE） using the split-step Fourier method （SSFM）. In addition, careful consideration of the spatial and the temporal step sizes and the temporal window is needed to ensure the numerical precision. Supercontinuum generation in photonic crystal fiber is analyzed to show the improvement and precision control. The nonlinear term is treated directly by an integral instead of any mathematical approximation. Then the integral term can be transformed to a convolution to be solved by the Fourier transform, which facilitates the accurate numerical computation of the nonlinear term. High precision is ensured since no factitious approximation is introduced. Computation precision with respect to the step size choice is analyzed. Criteria are proposed as follows. The temporal and spatial step sizes can be appropriately chosen from the spectrogram, and the temporal figure provides a criterion for the temporal step size. These conclusions present direct criteria for the difficuet job of step size choice in solving the GNLSE.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2009年第7期4731-4737,共7页
Acta Physica Sinica
基金
高温高密度等离子体物理国防科技重点实验室基金(批准号:9140C6803010803)
中国工程物理研究院科学技术发展基金(批准号:2008A0401017)资助的课题~~
关键词
非线性光学
广义非线性薛定谔方程
分步傅里叶方法
超连续谱产生
nonlinear optics, general nonlinear Schrodinger equation, split-step Fourier method, supercontinuum generation
