Exact geometrical optics scattering by an isorefractive wedge structure

Summary form only given. Some exact solutions to plane wave scattering by penetrable wedge structures with a common edge have been obtained previously by geometrical optics, utilizing either refraction at the Brewster angle or a combination of Brewster angle refraction and lateral waves between isorefractive materials. All structures thus examined consist of four wedge regions, and the solutions obtained are valid for a specific direction of incidence and a specific polarization. A new structure is examined, consisting of four right-angled regions with a common edge. The media in the four regions are isorefractive to one another, i.e. the product of electric permittivity and magnetic permeability has the same value in all four regions, so that refractive index and phase velocity are the same everywhere, while the intrinsic impedances of the four regions are different from one another. Under the restriction that the product of intrinsic impedances of two opposite wedge regions (i.e. regions with no interface in common) be the same for the two coupler of opposite wedge regions, it can be proven that under plane wave incidence, geometrical optics provides the exact solution to the boundary value problem, and the edge does not scatter. The electromagnetic field in each of the four wedge regions is the superposition of one or two plane waves. This solution is valid for an arbitrary direction of incidence and for an arbitrary polarization of the primary plane wave.