MATHEMATICAL MODELING OF SCATTERING OF ELECTROMAGNETIC WAVES ON PLANE TWO-PERIODIC STRUCTURES

Abstract

One of the scientific hypotheses for the creation of nonreciprocal optical metasurfaces is based on the use of a wave channel in which rays of the direct and reverse diffraction scenarios are realized on two-periodic flat structures with nonlinear elements.
 To test this hypothesis, it is necessary to carry out mathematical modeling of the process of scattering of electromagnetic waves by metasurfaces under conditions of excitation of several diffraction orders. It is known that among two-periodic flat lattices of different structures there are five types that fill the plane. These are the Bravais lattices. The problem of scattering of an incident monochromatic TE polarized wave on a metal screen with recesses in two-periodic structures filled with silicon was considered.
 In this paper, mathematical models are constructed for studying the spatial amplitude spectra of metasurfaces on Bravais lattices and some results of their numerical study are presented. Relationships are obtained for the diffraction orders of scattered electromagnetic waves by a diffraction grating. The existence of wavelengths of incident waves on a two-periodic grating for which there is no reflected wave is shown for different shapes (rectangular, square, hexagonal) of periodic elements in the center of which a recess filled with silicon was made. The distributions of the reflection coefficient are given for various geometric dimensions of periodic elements and recesses.