Analysis and design of inhomogeneous dielectric lens antennas by using geometrical optics

In this paper we present a novel approach for the analysis and design of inhomogeneous lenses. The standard method of Geometrical Optics for inhomogeneous media is augmented by introducing a novel wavefront-curvature transport equation, which allows the implementation of a full electromagnetic ray tracing (i.e., vector problem including polarization) in a real 1-D fashion, namely along the ray. This opens the possibility of easy parallelization and ultra-fast analysis of inhomogeneous lenses. The design of the lens is then accomplished by resorting to a novel direct synthesis method which, by inverting the analysis problem, directly provides the refractive index spatial distribution capable to drive the rays along prescribed paths which are defined to transform the impinging field on the input surface into the target aperture distribution on the output surface of the lens.