Integral equation analysis of an arbitrary-profile and varying-resistivity cylindrical reflector illuminated by an E-polarized complex-source-point beam.

A two-dimensional reflector with resistive-type boundary conditions and varying resistivity is considered. The incident wave is a beam emitted by a complex-source-point feed simulating an aperture source. The problem is formulated as an electromagnetic time-harmonic boundary value problem and cast into the electric field integral equation form. This is a Fredholm second kind equation that can be solved numerically in several ways. We develop a Galerkin projection scheme with entire-domain expansion functions defined on an auxiliary circle and demonstrate its advantage over a conventional moment-method solution in terms of faster convergence. Hence, larger reflectors can be computed with a higher accuracy. The results presented relate to the elliptic, parabolic, and hyperbolic profile reflectors fed by in-focus feeds. They demonstrate that a partially or fully resistive parabolic reflector is able to form a sharp main beam of the far-field pattern in the forward half-space; however, partial transparency leads to a drop in the overall directivity of emission due to the leakage of the field to the shadow half-space. This can be avoided if only small parts of the reflector near the edges are made resistive, with resisitivity increasing to the edge.