稳健的分步傅里叶方法用于模拟单模和双模光纤中超短脉冲的传播
Robust split-step Fourier methods for simulating the propagation of ultra-short pulses in single- and two-mode optical communication fibers
AI总结：
本文提出稳健的分步傅里叶方法，用于模拟单模和双模光纤中飞秒脉冲的传播，通过改进的算子分裂方法处理非线性项，并在单模和双模情况下验证了方法的可靠性和鲁棒性。
摘要：
针对Schrödinger型脉冲传播方程，本文扩展了分步傅里叶方法（SSFM），用于模拟单模和双模光纤中飞秒脉冲的传播。核心思想是采用算子分裂方法，将非线性子算子（包括克尔非线性、自陡峭和受激拉曼散射项）通过Madelung变换转化为信号强度和相位的准线性一阶系统。在单模情况下，推导了二阶精度的上游数值方法；该方法被直接扩展用于近似由所选双模模型非线性引起的四维系统。在理想化的单模和双模光纤中，通过基准SSFM计算验证了所提方法在均匀和交替色散参数以及高非线性情况下的可靠收敛性和鲁棒性。
英文摘要：
Extensions of the split-step Fourier method (SSFM) for Schrödinger-type pulse propagation equations for simulating femto-second pulses in single- and two-mode optical communication fibers are developed and tested for Gaussian pulses. The core idea of the proposed numerical methods is to adopt an operator splitting approach, in which the nonlinear sub-operator, consisting of Kerr nonlinearity, the self-steepening and stimulated Raman scattering terms, is reformulated using Madelung transformation into a quasilinear first-order system of signal intensity and phase. A second-order accurate upwind numerical method is derived rigorously for the resulting system in the single-mode case; a straightforward extension of this method is used to approximate the four-dimensional system resulting from the nonlinearities of the chosen two-mode model. Benchmark SSFM computations of prototypical ultra-fast communication pulses in idealized single- and two-mode fibers with homogeneous and alternating dispersion parameters and also high nonlinearity demonstrate the reliable convergence behavior and robustness of the proposed approach.
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