An efficient numerical approach to nonlinear propagation in waveguides based on an approximation of the overlap integrals’ frequency dependence is proposed. Two test cases are studied: a weakly guiding step-index fiber and a weakly guiding parabolic-index fiber, where the approximation is compared to the standard approach of neglecting the frequency dependence and calculating the overlaps at a center wavelength ${\lambda _0}$, and benchmarked against a Gaussian quadrature approach, whose accuracy can be increased systematically. We believe that the combined accuracy and efficiency of the proposed approximation make it superior to the other two approaches in few-mode simulations.

中文翻译：

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广义非线性薛定谔方程中模式分布色散的近似优于弱导光纤的恒定重叠方法

提出了一种基于重叠积分频率依赖性近似的波导非线性传播的有效数值方法。研究了两个测试案例：弱引导阶跃折射率光纤和弱引导抛物线折射率光纤，其中将近似值与忽略频率相关性并计算中心波长处重叠的标准方法进行比较${\lambda_0} $，并以高斯正交方法为基准，其准确性可以系统地提高。我们相信，所提出的近似的综合精度和效率使其在少数模式模拟中优于其他两种方法。