Reflecting Luneburg Lenses

This article presents the exact closed-form solution for a new planar lens, hereinafter referred to as reflecting Luneburg lens (RLL). The proposed structure consists of two stacked parallel-plate waveguides circular shape. rays generated by point source located at periphery bottom waveguide propagate along curvilinear paths, whose trajectories result from variable refractive index profile with azimuthal symmetry. Then, these encounter boundary and emerge all parallel in upper uniform waveguide. behavior this resembles that flat fundamental difference it works reflection. is found solving nonlinear integral equation ray congruence through truncated Abel transform method. concept numerically verified different implementations effective profile, including metasurface-based implementation. triggers possibilities normal does not offer, applicable large variety microwave, terahertz, optical devices.