Abstract This work investigates an alternative numerical scheme for the solution of an exact formulation based on Geometrical Optics (GO) principles to synthesize offset dual reflector antennas. The technique is suited to solve a second-order nonlinear partial differential equation of the Monge-Ampère type as a boundary value problem. An iterative algorithm based on Newton's method was developed, using axis-displaced confocal quadrics to locally represent the subreflector surface, thus enabling an analytical description of the partial derivatives within the formulation. Such approach reduces discretization errors, as exact expressions for the mapping function and its derivatives are analytically determined. To check the robustness of the methodology, an offset dual-reflector Gregorian antenna was shaped to provide a Gaussian aperture field distribution with uniform phase within a superelliptical contour. The shaped surfaces were further interpolated by quintic pseudo-splines and analyzed by Physical Optics (PO) with equivalent edge currents to validate the synthesis procedure at 11,725 GHz.

The work investigates the electromagnetic performance of omnidirectional dual-reflector antennas designed to operate with a frequency bandwidth larger than 45% (25-40 GHz). We consider two antenna configurations, distinguished from each other by two different optical ray mappings. A conventional coaxial horn is designed to ensure vertical polarization and stable primary radiation pattern along the operating bandwidth. By employing a geometrical optics synthesis technique, the omnidirectional reflectors are shaped to maximize the directivity of the broadside secondary radiation patterns. For the synthesis, we employ different aperture power distributions and investigate their effect on the antenna gain and return loss when operating over the 40% frequency bandwidth. To access the antenna performance, a full-wave electromagnetic analysis based on the combination of mode matching and method of moments is employed.