An asymptotic method for solving problems of diffraction by diffractive optical elements with zone structure

I propose an asymptotic method for calculating the amplitude of a field resulting from diffraction by non-periodic zone structures. The novelty of the approach consists in the fact that the solution of the integral equation first expanded into a basis that describes the propagation of light through a diffractive optical element (DOE) within geometric optics is then changed to a basis of plane waves used for designing diffraction gratings. I report on the results of obtaining a tight focus by means of a DOE with zone structure. The efficiency of the proposed method is confirmed by the simulation results.