Collimating and resonant properties of two-shell radially symmetric lenses

The collimating and resonant properties of a two-shell radially symmetric dielectric lens are studied in 2-D formulation using exact series solution. It is demonstrated that such a lens built from standard low permittivity materials can compete with the classical uniformly-layered multi-shell Luneburg lens in terms of collimating capabilities provided the layer thickness is properly selected. The simulation results obtained for lenses with cores made of Teflon, Rexolite, Fused Silica and Quartz are tabulated and represented in the form of a chart that enables determination of the optimal lens parameters without solving the corresponding diffraction problem. Validity of the obtained results for design of cylindrical and spherical lenses is proven by comparison with numerical and measure data reported by other authors. In addition, the impacts of air gap and whispering gallery modes on the collimating capabilities of the two-shell lenses are illustrated.