Exact 2-D scattering from a slot in a ground plane backed by a semielliptical cavity and covered with a multilayer isorefractive diaphragm

A semielliptical channel flush-mounted under a metal plane and slotted along the interfocal distance of its cross section is separated from the half-space above by a multilayer diaphragm. The cavity, the diaphragm, and the half-space are all isorefractive to each other. Both the cavity and the multilayer diaphragm are filled with materials isorefractive to the medium in the half-space above. This is a two-dimensional geometry where the source is invariant with respect to the axial variable. The resulting electromagnetic boundary-value problem is solved exactly in terms of Mathieu functions, when the excitation source is either a plane wave or a line source. For plane wave incidence, the polarization is with either the electric or the magnetic field parallel to the axis of the structure and the direction of incidence is arbitrary in a plane perpendicular to the axis. For line source excitation, the polarization is with either the electric or the magnetic field parallel to the axis of the structure and the source is arbitrarily located. Numerical results are also provided.