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Numerical computation of the nonlinear Schrödinger equation with higher order group velocity dispersion and frequency-dependent gain using the differential method
Optical Review ( IF 1.2 ) Pub Date : 2021-07-16 , DOI: 10.1007/s10043-021-00680-6
Yasushi Ishii 1
Affiliation  

The response of light in a nonlinear dispersive medium is governed by the nonlinear Schrödinger equation (NLSE). In general, for higher order group velocity dispersion (GVD) with frequency-dependent gain or absorption, NLSE is numerically solved using the split-step Fourier method. Extended NLSEs including the effects of higher order GVD, frequency-dependent gain and frequency-dependent absorption comprise higher order derivative terms. In this paper, an algorithm to solve partial differential equations with any higher order derivative term is described. A program based on this algorithm was used to solve optical pulse propagation equations in a nonlinear medium with higher order GVD, frequency-dependent gain and saturable absorption.



中文翻译:

使用微分方法对具有高阶群速度色散和频率相关增益的非线性薛定谔方程进行数值计算

非线性色散介质中的光响应由非线性薛定谔方程 (NLSE) 控制。通常,对于具有频率相关增益或吸收的高阶群速度色散 (GVD),NLSE 使用分步傅立叶方法进行数值求解。扩展的 NLSE 包括高阶 GVD、频率相关增益和频率相关吸收的影响,包括高阶导数项。在本文中,描述了一种求解具有任何高阶导数项的偏微分方程的算法。使用基于该算法的程序来求解具有高阶 GVD、频率相关增益和可饱和吸收的非线性介质中的光脉冲传播方程。

更新日期:2021-07-16
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