A Novel and Systematic Approach to Inhomogeneous Dielectric Lens Design Based on Curved Ray Geometrical Optics and Particle Swarm Optimization

A numerical synthesis algorithm is presented to design inhomogeneous 3-D-printed lenses for any aperture field and, hence, beam pattern. The algorithm is based on geometrical optics (GO), a numerical method for wave propagation in inhomogeneous media, particle swarm optimization, and a global stochastic optimization technique. The approach allows the synthesis of either optimal geometry with known constant permittivity (shape only), optimal nonconstant permittivity with known geometry (material only), or optimal geometry and nonconstant permittivity (shape and material). The presented approach is validated against the analytic test case of the Maxwell fish eye and is shown to provide excellent agreement. A spherical lens is optimized for nonconstant permittivity function and is shown to recover the permittivity of the Luneburg lens. Instructions on how to fabricate the resultant inhomogeneous lenses via 3-D-printing techniques is given. Examples of optimum inhomogeneous lenses synthesized with our approach are provided along with the full-wave simulation verification. A 30 cm inhomogeneous lens is fabricated via 3-D-printing and measured in the UCLA's plane bipolar near-field measurement range and compared with the results of the GO algorithm.