The recently introduced Mismatched Luneburg Lenses are studied with an in-depth analysis regarding their frequency dependence. This article proposes an analytical expression of the ray paths inside such lenses, which is then used to derive a radiation integral. The effect of the mismatch appears to be frequency-dependent, and an expression for the optimal homogeneous lens is given as a function of frequency. The previously proposed law linking the refractive index at the lens center and the lens edge is now modified into a generalized rule, taking into account that frequency dependence.
Kaschten, V., Lederer, D., & Craeye, C. (2025). Ray Paths and Frequency Dependence of Mismatched Luneburg Lenses. IEEE Transactions on Antennas and Propagation, 1. https://doi.org/10.1109/TAP.2025.3572609 (Original work published 2025)