Journal
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
Volume 71, Issue 3, Pages 2640-2651Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAP.2022.3233643
Keywords
geodesic-lenses; lens antennas; non-euclidean transformation optics; parallel plate waveguides (PPWs); ray tracing
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A fast and efficient method for designing and analyzing geodesic lens antennas is presented in this article, based on geometrical optics and scalar diffraction theory. The method is validated by comparing the results with commercial full-wave simulators, showing a significant reduction in computational resources.
Geodesic lenses are a compelling alternative to traditional planar dielectric lens antennas, as they are low loss and can be manufactured with a simple mechanical design. However, a general approach for the design and analysis of more advanced geodesic-lens antennas has been elusive, limiting the available tools to rotationally symmetric surfaces. In this article, we present a fast and efficient implementation built on geometrical optics and scalar diffraction theory. A numerical calculation of the shortest ray path (geodesic) using an open-source library helps quantify the phase of the electric field in the lens aperture, while the amplitude is evaluated by applying ray-tube power conservation theory. The Kirchhoff-Fresnel diffraction formula is then employed to compute the far field of the lens antenna. This approach is validated by comparing the radiation patterns of a transversely compressed geodesic Luneburg lens (elliptical base instead of circular) with the ones computed using commercial full-wave simulators, demonstrating a substantial reduction in computational resources. The proposed method is then used in combination with an optimization procedure to study possible compact alternatives of the geodesic Luneburg lens with size reduction in both the transverse and vertical directions.
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