Flattened generalized luneburg lens via quasi-conformal mapping

Curved lenses and antennas have pivotal meaning in various applications. For example, gradient index lenses such as the Luneburg lens are used to realize perfect imaging. However, the procedure of fabricating the bended surface of these lenses and antennas is difficult and not cost effective. In order to solve this issue, in this paper, we propose to apply transformation optics techniques to re-design these curved lenses antennas. Based on the quasi-conformal mapping technique, the spherical surfaces of various Luneburg lens antennas with different focal lengths will be transformed to flattened shapes, which can be easily implemented with low cost substrates and fabrication techniques. Preliminary simulation results of the designed devices are also given in this paper.