光脉冲传输模拟的快速数值差分递推算法及其应用研究

Study on the rapid numerical difference recurrence algorithm for the simulation of optical pulse propagation and its applications

利用零邻域的马克劳林展开对归一化非线性薛定谔方程的频域差分形式进行分析,得出一个能够同时考虑光学媒质的色散作用以及非线性克尔作用的时域快速数值差分递推公式.选取若干算例,将运用该公式的数值计算结果与已知的解析结果和传统分步傅里叶方法所得的计算结果做了相应的比较,结果表明这种快速数值差分递推公式不但拥有相当快的计算速度,也有很高的计算精度,而且在物理上符合光脉冲在光学媒质中传输时色散和非线性作用同时施加影响的客观实际,这说明它是研究非线性光学媒质中光脉冲传输的一种科学、合理而快速有效的数值计算方法.

Maclaurin expansion near zero domain is applied to analysis the difference form of the normalized nonlinear Schrfidinger equation in frequency domain, and a rapid numerical difference recurrence formula is deduced in time domain, which considers the nonlinear Kerr effect as well as the effect of chromatic dispersion in optical medium simultaneously. Through some examples, a comparison is made between the results using the algorithm of this paper and the known analytical results, including the results of SSFM method. The calculated results show that this method has not only fairly fast calculation speed, but also very high calculation precision, and is more suitable to the actual situation of light pulse propagation affected by the dispersion and nonlinearity at the same time through optical medium. All the above results show that it is a well founded, fast and effective numerical calculation method to study light pulse propagation in optical medium.