A Reliable Split-Step Fourier Method for the Propagation Equation of Ultra-Fast Pulses in Single-Mode Optical Fibers
A Reliable Split-Step Fourier Method for the Propagation Equation of Ultra-Fast Pulses in Single-Mode Optical Fibers
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DOI：
10.1109/jlt.2013.2262654
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发表时间：
2013-06-15
影响因子：
4.7
通讯作者：
Poole, Stephen
中科院分区：
文献类型：
--
作者：
Deiterding, Ralf;Glowinski, Roland;Poole, Stephen
本文提出的对薛定谔型脉冲传播方程的分步傅立叶方法（SSFM）的扩展是在设计时考虑到单模通信光纤中飞秒波段脉冲的精确模拟。我们证明了通过适当的算子分裂方案，克尔非线性和自陡变和受激拉曼散射项可以组合成一个由实值量强度和相位的非齐次拟线性一阶双曲系统组成的单个子步骤。针对这一非线性子步骤，已经开发了一阶和二阶精确的迎风激波捕获方案，使信号在拉曼散射和SSFM极端自陡峭影响下的精确和无振荡模拟成为可能。对具有强非线性的光纤中超快高斯脉冲的基准计算表明，该方法具有良好的近似性能。
The extension to the split-step Fourier method (SSFM) for Schrodinger-type pulse propagation equations that we propose in this article is designed with the accurate simulation of pulses in the femto-second regime in single-mode communication fibers in mind. We show that via an appropriate operator splitting scheme, Kerr nonlinearity and the self-steepening and stimulated Raman scattering terms can be combined into a single sub-step consisting of an inhomogeneous quasilinear first-order hyperbolic system for the real-valued quantities intensity and phase. First- and second-order accurate shock-capturing upwind schemes have been developed specifically for this nonlinear sub-step, which enables the accurate and oscillation-free simulation of signals under the influence of Raman scattering and extreme self-steepening with the SSFM. Benchmark computations of ultra-fast Gaussian pulses in fibers with strong nonlinearity demonstrate the superior approximation properties of the proposed approach.