The Constant-thickness Zone Plate as a Variational Solution

Abstract

The diffractive properties of constant-thickness zone plates composed of arbitrary materials are presently well known. Less well known, however, is the fact that the constant-thickness zone plate is the best possible profile that can be created for maximizing the throughput diffraction efficiency of a zone plate system which has a certain symmetry constraint imposed on its geometry. The formal statement of this claim is set forth in this Letter as a variational exercise and the derived optimum constant-thickness solutions are shown to hold for materials of arbitrary complex indices of refraction ṋ.