Daniele V G, Lombardi G
Department of Electronics and Communications, Politecnico di Torino, 10129 Torino, Italy.
Proc Math Phys Eng Sci. 2021 Aug;477(2252):20210040. doi: 10.1098/rspa.2021.0040. Epub 2021 Aug 25.
In this work, we introduce a general method to deduce spectral functional equations and, thus, the generalized Wiener-Hopf equations (GWHEs) for wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity with application to electromagnetics. The functional equations are obtained by solving vector differential equations of first order that model the problem. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper shows the general theory and the validity of GWHEs in the context of electromagnetic applications with respect to the current literature. Extension to scattering problems by wedges in arbitrarily linear media in different physics will be presented in future works.
在这项工作中，我们介绍了一种推导谱函数方程的通用方法，进而得到用于任意线性均匀介质填充的角域中波动的广义维纳 - 霍普夫方程（GWHEs），这些波动由位于无穷远处的源照射，应用于电磁学领域。通过求解对该问题进行建模的一阶矢量微分方程来获得函数方程。将边界条件应用于函数方程可得到实际问题的GWHEs。本文展示了GWHEs在电磁应用背景下相对于当前文献的一般理论和有效性。未来的工作将介绍在不同物理环境中任意线性介质中楔形物散射问题的扩展。
