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Analysis of solving multimode-coupled equations and its improvement for modulated fiber Bragg gratings

机译：调制光纤布拉格光栅求解多模耦合方程的分析及其改进

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摘要

An efficient numerical method to solve multimode-coupled equations with two point boundary conditions is improved. Our method [Abrishamian et al., Opt. Fiber Technol. 13, 32-38 (2007)] based on theoretical matrix integration of coupled differential equations and then solving the system of equations by use of initial or final conditions would be straightforward and thus beneficial in comparison with previously used fundamental matrix methods that depend strongly on the initial guess. However, we found that the new analysis depends on how accurately the integrals of the matrix element are calculated. For accuracy in the matrix integration it is required to divide the system of equations into a large number of subsections. Then, the reflectivity calculated is found to be comparable to experimental data reported so far. The present method is highly applicable for simulation of any type of fiber Bragg gratings modulated by long period gratings.
机译：改进了求解具有两点边界条件的多模耦合方程的有效数值方法。我们的方法[Abrishamian et al。，Opt。纤维技术。 13，13，32-38（2007）]基于耦合微分方程的理论矩阵积分，然后通过使用初始或最终条件求解方程组将非常简单，因此与以前强烈依赖于基本矩阵的方法相比，这是有益的最初的猜测。但是，我们发现新的分析取决于矩阵元素的积分计算得如何准确。为了保证矩阵积分的准确性，需要将方程组划分为大量小节。然后，发现计算出的反射率与迄今为止报道的实验数据相当。本方法非常适用于模拟由长周期光栅调制的任何类型的光纤布拉格光栅。

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