Analysis of an arbitrary-profile, cylindrical, impedance reflector surface illuminated by an E-polarized complex line source beam

Abstract

Electromagnetic scattering from a cylindrical reflector surface having an arbitrary conic section profile is studied. We assumed an electrically thin layer antenna illuminated by a complex line source in E-polarization mode. Our boundary value formulation, without loss of generality, involves an integral equation approach having impedance-type thin-layer boundary conditions. For simplicity, we also considered both faces of the reflector of the same uniform impedance value. Our computation employs the Method of Analytical Regularization (MAR) technique: the integral equations are converted into the discrete Fourier transform domain yielding two coupled dual series equations, which are then solved by the Fourier inversion and Riemann Hilbert Problem techniques. We demonstrate the accuracy and the convergence behaviors of our numerically solved MAR results that can serve as an accurate benchmark for comparison with widely used results obtained by approximate boundary conditions. © 2013 Taylor and Francis

Evaluation of the E‐polarization focusing ability in Thz range for microsize cylindrical parabolic reflector made of thin dielectric layer sandwiched between graphene

“…where I is the identity matrix and A ¼ fA mn g þ∞ m;n¼−∞ is a fully populated 2 � 2 block matrix with elements similar to those in, for example, equations (26) and (27) of [20].…”

“…The differential length on L is written as , where , is the angle between the normal to arc L and the x ‐direction, and is the angle between the normal and radial direction. All these quantities have explicit expressions [9, 16–20].…”

“…Therefore, to build a convergent numerical code, we need to either use a MAR procedure in combination with a suitable projection scheme or apply a Nystrom-type interpolation with the aid of quadratures. We follow [9,[16][17][18][19][20], where we studied perfect electric conductor (PEC), resistive, thin dielectric, and graphene reflectors, respectively, with the aid of the MAR-RHP scheme.…”

Analysis of thin dielectric cylindrical reflector having an arbitrary conic section profile illuminated by complex line source: H-polarization case

“…Furthermore to work with this formulation and make computations more economic, we add and subtract the similar functions from the originally givens. These functions are defined at the full circle of the closed contour C and they are introduced in [9].…”

Analysis of a thin, penetrable, and non‐uniformly loaded cylindrical reflector illuminated by a complex line source

“…A curved and thin impedance reflector having the non-circular profile is considered and the resultant two coupled systems of SIE are solved by a more accurate MAR technique [23]. The reflector is a smooth surface and locally planar.…”