A UTD solution for surface and leaky wave diffraction at the edge of a metallic wedge with a material coating

The diffraction from a wedge is an important canonical problem for the high-frequency description of electromagnetic scattering from complex bodies. Considerable interest has been devoted to the scattering from metallic bodies with dielectric or magnetic coatings. To simulate the effect of coatings, uniform Leontovich impedance boundary conditions (BCs) have been traditionally employed. Within this approximation, the problem of scattering from a wedge with uniform impedance faces, illuminated by a plane wave at normal incidence, has been rigorously solved by Maliuzhinets (1958). An alternative approach to the same problem, which allows one to rigorously account for the effect of material coatings with arbitrary permittivity and permeability, can be devised by an extension of Maliuzhinets method. In particular, a rigorous integral representation for the total field is obtained by taking into account the actual dependence of the surface impedances on the incidence angle. This integral representation for the field is asymptotically evaluated to provide high-frequency expressions in the standard format of the uniform geometrical theory of diffraction (UTD). Rigorous representations are obtained for the reflected field, surface waves and leaky waves which can be supported by the metal-backed material slabs. Moreover, by accurately evaluating diffraction integrals, suitable uniform coefficients are derived for surface and leaky wave diffraction. They may provide a useful simulation tool in applications concerning, for instance, patch and surface wave antennas.