Penetration, radiation, and scattering for a cavity-backed gap in a corner

A partially covered cavity, or trench, located along the edge of two intersecting metallic walls perpendicular to each other is considered. The cross-section of the cavity is a quarter ellipse and is slotted along the interfocal distance. The cavity is filled with a material isorefractive to that occupying the quarter-space between the walls. This two-dimensional boundary-value problem is solved exactly, when the primary field is either a plane wave of arbitrary polarization and direction of incidence or an electric or magnetic line source. Numerical results are given and discussed.