An incremental theory of diffraction formulation for circular cylinders

Abstract

An incremental theory of diffraction (ITD) [Tiberio and Maci, 1994; and Tiberio et al., 1995) has been introduced, which may provide a self-consistent, high-frequency description of a wide class of scattering phenomena within a unified framework. In this paper an ITD treatment of circular cylinder-shaped structures is presented. A quite general formulation is developed which is based on a suitable interpretation of the exact solution for the scattering in the near zone from a canonical circular cylinder, when it is illuminated by a spherical source. It is shown that its spectral integral representation may also be represented as an integral convolution along the axis of the cylinder. This leads to directly defining the local incremental field contribution. Explicit expressions for incremental scattering coefficients are obtained that are applicable to moderately sized local cylinders. For the sake of simplicity, the scalar cases for both hard and soft boundary conditions (b.c.) are treated here. In this same scalar case, the formulation is easily extended to impedance b.c.. Its extension to the more general vector problem of electromagnetic wave scattering from perfectly conducting circular cylinders is a relatively simple matter. It is suggested that the same general formulation is applicable to treat the case of local circular cylinders that are large in terms of a wavelength; however, this requires a more involved asymptotic analysis.