Aplicação de óptica geométrica na síntese de antenas duplo-refletoras offset e de lentes dielétricas sem simetria circular

Abstract

This work investigates an alternative numerical procedure for the solution of an exact formulation based on Geometrical Optics (GO) principles to the synthesis of offset dual reflector antennas and dielectric lenses without circular symmetry. The solution to synthesis problem consists in to evaluate a second-order nonlinear partial differential equation of the Monge-Ampère type as a boundary value problem in complex coordinates. For such, iterative algorithms based on Newton method were developed, using axis-displaced confocal quadrics to locally represent the synthesized surfaces, so that partial derivatives involved in the formulation were analytically expressed. To illustrate the numerical method, offset dual reflector antennas were synthesized to provide an aperture Gaussian power density distribution with uniform and non-uniform phase distributions, within circular, elliptical and super-elliptical contours, to yield radiation patterns with shaped beams. The synthesized reflector surfaces were further interpolated by quintic pseudo-splines and analyzed by Physical Optics (PO) with equivalent edge currents, at 11,725 GHz and 30 GHz. The algorithm synthesized offset dual reflectors with illumination efficiency up to 86.46% for a uniform circular aperture. Verif ied the robustness of the numerical technique employed in the synthesis of dual offset reflectors, the procedure was further applied to design dielectric lenses without circular symmetry, aiming to control beam width as well as the power density in the coverage region of a lens. For this, an exact mathematical formulation, based on GO principles, was developed for the synthesis problem of dielectric lenses without circular symmetry in complex coordinates. The synthesized surfaces were further interpolated by cubic splines and analyzed by a classical hybrid method, combining GO and PO principles, to compute the far- field radiation patterns of the designed dielectric lenses, at 30 GHz, 60 GHz and 120 GHz.