Mismatched Luneburg Lenses: Numerical Analysis and Design Rules

While Luneburg lenses are among the best multibeam antenna topologies if one seeks low scan losses and large bandwidths, they also require very specific refractive indices and therefore limit a designer’s degrees of freedom when realizing such a lens. The purpose of this article is to find a generalized expression for the optimal refractive index distribution, by loosening the hypothesis that the value at the lens edge is equal to that of the external medium. By addressing the problem with different methods offering different levels of complexity, we propose a simple empirical expression linking the refractive index at the lens center and the lens edge. The existence of WGMs, as the lens edge is no longer matched with the external medium, causes the generalized lenses to behave poorly at specific frequencies. We eventually show that this effect can be mitigated by following appropriate design rules.