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

Abstract

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.

Focusing of THz waves with a microsize parabolic reflector made of graphene in the free space

“…The numerical accuracy and convergence of the explained above in-house algorithms have already been verified in [9,12]. In the current work, we apply it to the analysis of both the plane-wave scattering and absorption and the effect of focusing by the graphene reflector.…”

“…Such a smooth contour C is necessary for obtaining the regularized (i.e. Fredholm second kind) matrix equation -see [9,12].…”

“…Therefore we apply the projection to the set of entire-domain angular exponents [12]. In either polarization case we adapt the matrix truncation number to provide the 4-digit or better accuracy of computations.…”

“…In the E-polarization case, the associated SIE has a logarithmically singular kernel [12] and hence is already a Fredholm second kind equation. This guarantees convergence of discretization schemes.…”

“…Still projecting it on the set of entire-domain expansion functions brings additional advantages and makes the resulting numerical algorithm more economic. The E-polarized beam scattering and collimation by parabolic resistive reflectors was analyzed in this manner in [12].…”