Electromagnetic radiation and scattering for a gap in a corner backed by a cavity filled with DNG metamaterial

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 double-negative (DNG) metamaterial that is isoimpedance to the material filling the half-space above the trench. This two-dimensional boundary value problem is solved exactly, in the frequency domain, 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 exhibited and discussed.