Analytical approach to the problem of electromagnetic wave scattering by a cylindrical hole in a thin metal screen

A method of analytical study of a metal film perforated by cylindrical nanoholes as the basis of a metasurface has been proposed. The formulas deduced completely determine the electromagnetic field of a wave scattered by the hole at any distance from the surface. The calculation of the transmission and absorption spectra of the studied structure, as well as the dependence of the phase of the scattered wave on the radius of the hole, is carried out using analytical formulas. The calculation results are consistent with the literature data for calculating the efficiency of a quantum photodetector and the phase change interval of light scattered by meta-atoms required for lens design.