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

Abstract

A thin, penetrable, and cylindrical reflector is illuminated by the incident field of a complex source point. The scattered field inside the reflector is not considered and its effect is modelled through a thin layer generalised boundary condition (GBC). The authors formulate the structure as an electromagnetic boundary value problem and two resultant coupled singular integral equation system of equations are solved by using regularisation techniques. The GBC provides us to simulate the thin layer better than the resistive model which is applicable only for very thin sheets. Hence, the more reliable data can be obtained for high-contrast and low-loss dielectric material. The scattering and absorption characteristics of the front-fed and offset reflectors are obtained depending on system parameters. Also, the effects of the edge loading are examined for both E-and Hpolarisations. The convergence and the accuracy of the formulation are verified in reasonable computational running time.

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

“…As explained in [9,[16][17][18][19][20], we have to cast the dual functional Equations ( 11) and (12) to two coupled dual-series equations and exploit their analytical regularization with the aid of the analytical solution of associated RHP. In this way, we introduce an auxiliary arc S complementing the parabolic arc L to the closed contour C.…”

“…This ensures that C is a continuous curve with a continuous first derivative, and the second derivative has finite jumps at the junction points. Further, C can be conveniently parametrized in terms of the polar angle ϕ associated with natural coordinates of arc S. The parametric equation of the parabola associated with L can be defined x ¼ xðϕÞ; y ¼ yðϕÞ and can be found in [9,[16][17][18][19][20]. The differential length on L is written as dl ¼ aβðϕÞdϕ, where βðϕÞ ¼ rðϕÞ=½a cos γðϕÞ�, rðϕÞ is the angle between the normal to arc L and the xdirection, and γðϕÞ is the angle between the normal and radial direction.…”

“…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].…”

“…Further, C can be conveniently parametrized in terms of the polar angle associated with natural coordinates of arc S . The parametric equation of the parabola associated with L can be defined and can be found in [9, 16–20]. 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.…”

“…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.…”