Distortion of Focal Plane in Flattened 2D Luneburg Lens

A parametric study of focal plane distortion in 2D flattened Luneburg lenses is studied. Numerical simulations show that directivity is strongly dependent on feed position near the flattened side of the lens. This paper demonstrates that this suboptimal directivity is the consequence of a non-planar focal surface for the Luneburg lens after deformation through transformation optics (QCTO). Simulation results show that the focal point shifts as much as $\lambda/2$ away from the flattened side of the lens and this focal plane distortion varies with lateral movement of the feed point as it moves along the lens.