Scattering of electromagnetic plane wave by conducting convex plate

摘要

Scattering problems of electromagnetic plane wave by conducting plate of arbitrary shape are studied nsing physical theory of diffraction (PTD). PTD solution consists of physical optic (PO) solution and its correction due to nonuniform edge current. Usually PO solution is given by surface integral with integrand which includes the amplitude multiplied by linear phase term. When this amplitude is constant, the PO radiation integral can be transformed into contour integral using Stokes's theorem which has been developed by Gordon [1]. This contour integral may be performed analytically for special cases of triangular, rectangular, circular and elliptic conducting disks, but we have to rely on numerical integration for general disks. For convex plate, an asymptotic solution for the contour integral is derived using the stationary phase method of integration. There are two stationary points in this integrand which correspond to diffraction points and the solution has a simple physical interpretation that diffracted field comes from these two diffraction points [2]. The amplitudes of the diffracted rays are found to be proportional to the square root of the radius of curvature at the diffraction point. Using the similarity of the derived asymptotic solution with that of circular disk which is obtained by applying asymptotic expansion to the Airy pattern, we deduce the caustic corrected solution [3]. The validity of the expression is verified numerically for special shaped convex plate. Next, the expression for the non-unifourm edge correction is derived by applying the equivalent current method (ECM) to Ufimtsev's edge current [4],[5]. For convex plate, the asymptotic expression is derived usiug the stationary phase method of integration. For special case of circular disk the PTD solution agrees completely with that obtained by Ufimtsev [3].