Low-data simulation of diffractive optical elements based on the zones geometry

Design and simulation of two-dimensional diffractive optical elements are often limited by the amount of data required to represent the element in the computer's memory. We present a technique based on a geometrical description of the element, which requires fewer data than the traditional pixel description. Moreover, the element is being described more accurately and consequently the pixel-related artefacts are suppressed. This technique can be used for both periodic and non-periodic structures of large dimensions under Fraunhofer or Fresnel approximations. We apply the method to analysis of far-field beam-shaping elements and discuss possible extensions and refinements of the technique.