Multiscale Modeling &Simulation, Volume 18, Issue 1, Page 44-78, January 2020.
We present an analysis of wave propagation in a two step-index, parallel waveguide system. The goal is to quantify the effect of scattering at randomly perturbed interfaces between the guiding layers of high index of refraction and the host medium. The analysis is based on the expansion of the solution of the wave equation in a complete set of guided, radiation, and evanescent modes with amplitudes that are random fields, due to scattering. We obtain a detailed characterization of these amplitudes and thus quantify the transfer of power between the two waveguides in terms of their separation distance. The results show that, no matter how small the fluctuations of the interfaces are, they have a significant effect at a sufficiently large distance of propagation, which manifests in two ways: The first effect is well known and consists of power leakage from the guided modes to the radiation ones. The second effect consists of blurring of the periodic transfer of power between the waveguides and the eventual equipartition of power. Its quantification is the main practical result of the paper.

中文翻译：

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随机扰动的弱耦合波导中的波传播

多尺度建模与仿真，第18卷，第1期，第44-78页，2020年1月。
我们提出了在两步指数，平行波导系统中的波传播分析。目的是量化在高折射率的引导层和主体介质之间的随机扰动界面处的散射效果。该分析基于波动方程在一组完整的导波，辐射和e逝模式下的扩展，这些模式由于散射而具有随机场的振幅。我们获得了这些幅度的详细描述，从而根据两个波导的分离距离来量化功率的传递。结果表明，无论界面的波动多么小，它们在足够大的传播距离处都具有显着的影响，这表现为两种方式：第一个效果是众所周知的，包括从引导模式到辐射模式的功率泄漏。第二个效果包括模糊波导之间的周期性功率传输以及最终的功率均分。其量化是本文的主要实践结果。