Scattering of electromagnetic waves by a half plane with varying resistivity

Abstract

The scattering of electromagnetic waves by a resistive half plane with varying resistivity is important in the geometrical theory of diffraction as a canonical problem of edge diffraction, and in various application fields such as scattering by tapered resistive strips, reduction of radar cross section. Fields scattered by a resistive half plane with linearly (or inversely) varying resistivity is obtained in the closed form integral for the E-polarized (or H-polarized) plane wave incidence. By using the Kontorovich-Lebedev transform with the corresponding boundary conditions for the scattered field in the transformed domain, the scattered field is obtained in the integral form. The integral expression, however, is valid only in the limited angular region. One may analytically continue the integral representation such that it is valid in the whole angular region. The integral for the scattered field may be asymptotically evaluated and we may obtain contributions of geometric optics and edge diffraction. The geometric optic contributions, i.e., reflected and transmitted rays for the non-uniform resistive half plane may be interpreted as the rays reflected and transmitted from the locally uniform resistive plane. The edge diffraction coefficient may be shown to approach that of a conducting half plane as the resistivity of the half plane vanishes. As the proportionality of resistivity increases, it approaches that of the conducting wire for the E-polarization. For the transition angles, the asymptotic edge diffraction coefficient blows up and a uniform asymptotic representation is used to calculate the scattered fields, where a logarithmic branch point or a simple pole approaches the first-order saddle point.