Computation of reflector surfaces for bivariate beamshaping in the elliptic case

Abstract

A numerical method for designing reflector surfaces that produce a specified far-field over a given solid angle when illuminated by an isotropic source is presented. The technique, which uses the geometrical optics approximation, requires the solution of a particular non-linear, elliptic partial differential equation, previously derived by the authors. The equation is solved iteratively by applying a finite difference model to a linearised form. Examples of some generated reflector surfaces are given showing the existence of two distinct solutions for each case. The method is applicable to problems in microwave antenna design optics and acoustics.