A Luneburg Lens Optimization Design Approach Based on Conformal Mapping

An analysis and optimization design approach suitable for non-uniform multilayer Luneburg lenses is proposed. Employed conformal transformation, combined with ray tracing model, the ray propagation trajectory equation for layered lenses is derived. Sequentially an optimization model is established with the goals of uniform phase distribution at the aperture, minimal lens reflection loss, and output ray perpendicular to the aperture. A heuristic optimization module is used to solve this model, and finally the structural parameters of a 7-layer Luneburg lens are provided. Full-wave simulation results show that, compared with schemes obtained by other approaches, this layered solution has higher aperture efficiency, lower sidelobe level and better engineering feasibility.