Elliptical generalized Maxwell fish-eye lens using conformal mapping

Abstract

A circular graded index lens is conformally transformed to an elliptical shape using a closed-form transformation. The proposed transformation is then employed to compress a Maxwell fish-eye and its generalized version. Since the transformation is conformal, the electromagnetic properties of the device are perfectly preserved after the transformation with fully isotropic and dielectric-only materials. Ray-tracing and full-wave simulations are carried out for several cases to verify the functionality of the optically transformed lenses in geometrical optics and wave optics regimes.