Ray-tracing in Dielectric Inhomogeneous Metalenses

A flexible and efficient algorithm, based on Geometrical Optics (GO) ray-tracing, is presented. The algorithm allows the analysis of graded index (GRIN) lenses, namely dielectric inhomogeneous lenses with radially varying refractive index. The source incident field in absence of the lens is supposed to be known by simulation or by measurements. Phase and amplitude distributions at the output interface of the lens are obtained by solving the ray-equation and the energy transport equations, respectively. Once the field distribution at the lens-antenna aperture has been achieved, the radiation pattern is derived by aperture type radiation integrals. The ray-tracing algorithm is validated by full-wave analysis, after predetermining the feed source, the lens dimensions and the refractive index profile. Moreover, beam scanning capability of GRIN lenes can be investigated with the aid of the presented algorithm. Results achieved by the raytracing algorithm and the full-wave analysis have shown to be in good agreement, demonstrating that the proposed algorithm is a valuable alternative to time-consuming full-wave simulations in the GRIN lens analysis.