Bi-functional Fresnel zone plate from transformation optics

Instead of reshaping the standard parabolic reflector or the hyperbolic lens to propose their planar counterparts, here we choose to flatten the primary spherical wave front based on the quasi-conformal transformation optics. Ray traces, travelling from the source to the transformed planar surface, can thus be maintained of the equal electrical path length in terms of the transformation-optics Fresnel zone plate. Due to the symmetrical feature of our transformation setup, the proposed device would readily possess dual functionalities in the light focusing and collimation that can either be applied to a reflector when incorporated with a plane mirror or directly employed as a standalone lens according to the principle of the image theory.