Asymptotic methods of solving problems of diffraction by non-periodic structures

An asymptotic method for calculating the complex amplitude of a light field in the case of diffraction by non-periodic band gap structures. The novelty of the approach consists in the expansion of the solution of the integral equation into a basis that describes the propagation of light through a DOE within the geometrical optics approximation and changes into a basis of plane waves used in the calculation of diffraction gratings. We present the results of focusing into a point by a gradient-index diffractive optical element with a band-gap structure. Simulation results confirm the efficiency of the proposed method.