Two-Shell Radially Symmetric Dielectric Lenses as Low-Cost Analogs of the Luneburg Lens

This communication provides guidelines for the design of two-shell radially symmetric dielectric lenses with collimating capabilities compatible with those of the classical Luneburg lens. Unlike earlier publications, it is demonstrated that such a lens can be designed using any standard low permittivity dielectric materials, provided the optimal shell thickness is selected. The lens characteristics are studied in 2-D formulation using exact series representation. A detailed description is given for lenses with radius of 10
$\lambda_{0}$
and core made of Rexolite. The design recommendations are then generalized for lenses with radii of 5 to 15
$\lambda_{0}$
and cores made of Teflon, Fused Silica and Quartz. Finally, a chart defining the optimal shell thickness for lenses made of two arbitrary dielectric materials is provided. Validity of the recommendations for design of 2-D and 3-D radially symmetric lenses is proven by comparison with optimal designs reported by other authors.