Regularized solution of 2d scattering from impedance-loaded cavities

Scattering of electromagnetic waves by infinitely long, perfectly electrically conducting (PEC) cylinders of arbitrary cross-section, either closed or open (i.e., with cavity-backed apertures) has been studied by many authors, When the structure is closed and of canonical shape (e.g., of circular or elliptical cross-section) many approaches (such as the method of separation of variables) are available; a wide selection of results is given in [1]. However, for non-canonical structures of arbitrary shape, including those in which an aperture has been opened, far fewer tools are available; the most usual approaches in the low and intermediate (resonance) wavenumber regime usually prefer integral equation methods over differential equation approaches (finite-difference or finite element methods). A single- or double-layer density on the surface of the scattering structure is employed to represent the scattered field in the E-pol or H-pol cases respectively; enforcement of the boundary condition (the vanishing of the tangential electric field on the surface) results in a surface integral equation (IE).