The Wiener-Hopf Formulation of the Penetrable Wedge Problem: Part II

Abstract

Solutions of the generalized Wiener-Hopf equations obtained in the companion article (Daniele, 2010) do not provide the global spectra of the unknowns but only some of their analytical elements. It means that this solution is not sufficient to evaluate the dielectric wedge field. To obtain the global spectra, a process of analytical continuation is required. In this article, this is accomplished by using some properties of the Wiener-Hopf equations of the problem. After obtaining the global spectra of the Wiener-Hopf unknowns, the article presents Laplace transform expressions for arbitrary observation direction. In order to evaluate the far field, the Sommerfeld technique is briefly recalled. This technique permits one to separate, recognize, and understand the different components of the dielectric wedge field: reflected and refracted plane waves, surface waves, lateral waves, and diffraction coefficients.