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首页> 外文期刊>Optics Letters >Arbitrary truncation order three-point finite difference method for optical waveguides with stepwise refractive index discontinuities
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Arbitrary truncation order three-point finite difference method for optical waveguides with stepwise refractive index discontinuities

机译：折射率不连续的光波导的任意截断阶三点有限差分法

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摘要

An exact finite difference (FD) representation of the second-order derivative on three nodes is presented and used to obtain an FD algorithm that allows achieving an arbitrary truncation order. The FD weights are calculated analytically using the series that expresses the field value at a given FD node in terms of the field value and its derivatives at a neighboring node, when a stepwise discontinuity in the refractive index distribution is present between the nodes. The results obtained confirm that the proposed algorithm is accurate, efficient, and achieves the predicted improved performance.
机译：给出了三个节点上二阶导数的精确有限差分（FD）表示，并将其用于获得允许实现任意截断顺序的FD算法。当节点之间存在逐步的折射率分布不连续时，可使用表示在给定FD节点处的场值及其相邻节点上的场导数的级数来分析计算FD权重。获得的结果证实了所提出的算法是准确，高效的，并且达到了预期的改进性能。

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