Spectral Analysis of Electromagnetic Diffraction Phenomena in Angular Regions Filled by Arbitrary Linear Media

A general theory for solving electromagnetic diffraction problems with impenetrable/penetrable wedges immersed in/made of an arbitrary linear (bianistropic) medium is presented. This novel and general spectral theory handles complex scattering problems by using transverse equations for layered planar and angular structures, the characteristic Green function procedure, the Wiener–Hopf technique, and a new methodology for solving GWHEs. The technique has been proven effective for analyzing problems involving wedges immersed in isotropic media; in this study, we extend the theory to more general cases while providing all necessary mathematical tools and corresponding validations. We obtain generalized Wiener–Hopf equations (GWHEs) from spectral functional equations in angular regions filled by arbitrary linear media. The equations can be interpreted with a network formalism for a systematic view. We recall that spectral methods (such as the Sommerfeld–Malyuzhinets (SM) method, the Kontorovich–Lebedev (KL) transform method, and the Wiener–Hopf (WH) method) are well-consolidated, fundamental, and effective tools for the correct and precise analysis of electromagnetic diffraction problems constituted by abrupt discontinuities immersed in media with one propagation constant, although they are not immediately applicable to multiple-propagation-constant problems. To the best of our knowledge, the proposed mathematical technique is the first extension of spectral analysis to electromagnetic problems in the presence of angular regions filled by complex arbitrary linear media, thereby providing novel mathematical tools. Validation through fundamental examples is proposed.