粗糙波导中的传播：正问题与反问题
Propagation in rough waveguides: Forward and inverse problems
AI总结：
针对粗糙内表面波导中的多重散射难题，本文采用 L-R 算子分裂计算二维与三维散射场，并提出由轴向场测量恢复表面轮廓的推广算法。
摘要：
我们在此讨论具有粗糙内表面和任意平均形状的波导中波传播的正问题和反问题。波导内部高度的多重散射给正向计算和表面轮廓恢复都带来了重大挑战，并引发了关于散射截面的重要问题。本文分为与这些问题相对应的两个部分。我们首先应用 Left-Right（L-R，左-右）算子分裂来计算二维和三维波导中的散射场。利用这一方法，我们展示了散射场以及表面粗糙度的影响。在第二部分中，我们构建了一种根据沿波导轴的场测量恢复表面的算法，该算法推广了近期关于二维表面的工作。该方法实际上利用了前向散射假设，即在未知表面场中构建一个积分方程，并将其视为表面的函数。尽管讨论是在波导背景下进行的，但所给出公式的形式适用于多种几何结构，其系数将取决于并由每个具体应用确定。
英文摘要：
We discuss here the direct and inverse problems for wave propagation in a waveguide with rough internal surface and arbitrary mean shape. The high degree of multiple scattering inside the waveguide poses significant challenges both for the forward computation and for the recovery of the surface profile, and raises important questions about scattering cross-sections. This paper falls into two parts corresponding to these issues. We first apply Left-Right (L-R) operator splitting to calculate the scattered fields in 2- and 3-dimensional waveguides. Using this we illustrate the scattered fields and the effect of surface roughness. In the second part we formulate an algorithm for surface recovery from field measurements along the waveguide axis, which generalises recent work on surfaces in 2 dimensions. This method utilizes forward scattering assumptions in effect by formulating an integral equation in the unknown surface field, treated as a function of the surface. Although discussed in the context of waveguides, the formulae are given in a form applicable to a variety of geometries, with coefficients which will depend on and be determined by each specific application.
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