Analysis of the elliptic-profile cylindrical reflector with a non-uniform resistivity using the complex source and dual-series approach: H-polarization case

Abstract

An elliptic-profile reflector with varying resistivity is analyzed under the illumination by an H-polarized beam generated by a complex-source-point (CSP) feed. The emphasis is done on the focusing ability that is potentially important in the applications in the optical range related to the partially transparent mirrors. We formulate the corresponding electromagnetic boundary-value problem and derive a singular integral equation from the resistive-surface boundary conditions. This equation is treated with the aid of the regularization technique called Riemann Hilbert Problem approach, which inverts the stronger singular part analytically, and converted to an infinite-matrix equation of the Fredholm 2nd kind. The resulting numerical algorithm has guaranteed convergence. This type of solution provides more accurate and faster results compared to the known method of moments. In the computations, a CSP feed is placed into a more distant geometrical focus of the elliptic reflector, and the near-field values at the closer focus are plotted and discussed. Various far-field radiation patterns including those for the non-uniform resistive variation on the reflector are also presented. © 2013 Springer Science+Business Media New York

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

“…We introduce also a function β(φ) = r(φ)/[a cos γ(φ)], where γ(φ) is the angle between the normal on M and the radial direction. Then we extend the surface-current density J t with zero value to arc S and cast IE (2) to a dual equation on the arcs S and M [9].…”

“…Then the discretized version of the SIE and the zero current condition on the aperture S give us a dual series equation. Its semi-inversion, based on the MAR approach using the RHP technique [7,10], finally produces an algebraic equation set [9]. This infinite matrix equation is of the Fredholm second kind hence the Fredholm theorems guarantee the existence of the unique solution and also the convergence of the approximate numerical solutions when truncating the set with progressively larger orders.…”

“…With MAR, the kernel of the associated SIE for the current on the reflector is presented as a sum of two parts, a more singular part (usually static) and a remainder. Then the more singular part is analytically inverted by using some special technique like the Riemann-Hilbert Problem (RHP) method [7,9,10]. The remainder leads to the Fredholm second-kind matrix equation that provides a convergent numerical solution.…”

“…In either case the SIE-MAR technique enables accurate and economic full-wave analysis of electromagnetic scattering problems for both PEC and imperfect reflectors. For instance, in [9], the H-wave scattering and the focusing were studied for the resistive 2-D reflectors having elliptical contours.…”