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Exact penetration, radiation, and scattering for a slotted semielliptical channel filled with isorefractive material

A semielliptical channel flush-mounted under a metal plane and slotted along the interfocal distance of its cross-section is considered. The channel is filled with a material isorefractive to the medium that occupies the half-space above the metal plane. The boundary-value problem is solved exactly in terms of Mathieu functions, when the primary source is a plane wave with arbitrary direction of incidence and polarization, or an electric or magnetic line source parallel to the channel and located either above the channel or inside it.