Lenses on curved surfaces

This Letter presents a theory that allows graded index lenses to be mapped onto arbitrary rotationally symmetric curved surfaces. Examples of the Luneburg and Maxwell fish-eye lens are given, for numerous surfaces, always resulting in isotropic permittivity requirements. The performance of these lenses is initially illustrated with full-wave simulations utilizing a waveguide structure. A transformation of the refractive index profiles is then performed to design surface-wave lenses, where the dielectric layer is not only isotropic but also homogenous, demonstrating the applicability and ease of fabrication.