Analysis and Correction of Focal Plane Distortion in Flattened Luneburg Lenses

This paper presents a detailed study on 2D flattened Luneburg lenses using quasi-conformal transformation optics (QCTO) and their performance at 30 GHz. This analysis reveals that QCTO transformations distort the focal circle of the original 2-D circular Luneburg lens, resulting in degraded performance, particularly for severe flattening angles and large sizes. Two different transformations are compared in terms of their resulting focal plane aberration and far field performance. Furthermore, we introduce two methods to correct the focal plane aberration and improve the directivity of the flattened lenses by over 3 dB in select directions.