On the Frequency Limits of Gradient Refractive INdex (GRIN) Media

In this study, we investigate the high-frequency limits of artificial dielectrics in the context of gradient index (GRIN) lens antennas. We provide an overview of general GRIN media structures and introduce three factors which determine lens frequency limits: i) the permittivity profile discretization, ii) the unit cell (UC) lattice constantLc, and iii) the surface impedance matching layer thickness, Δzmatch. Multi-modal Eigenmode analysis is performed for two common GRIN media UCs, the cubic gyroid, and the hexagonal drilled substrate. Soft- and hard-cutoff frequency limits (fscandfhc) are defined, and corresponding lattice constant size limits are provided asLscg,eff, andLhcg,eff. These limits are validated with 3D-printed spherical Luneburg lenses having various lattice constants as well as a low-profile 3D-printed cylindrical GRIN lens employing multiple materials and having a large permittivity range. The results in this work enable designers to use the simplest possible UC for GRIN media realization while guaranteeing performance at a desired frequency. This not only improves performance, but also saves cost by obviating the need for overly conservative approximations.