A Mathematical Model and Results of Analysis of Nonlinear Diffraction of Electromagnetic Waves by Magnetic Nanogratings

Abstract

A mathematical model of nonlinear diffraction of electromagnetic waves by 2D magnetic nanogratings has been developed; it is based on the solution of a nonlinear boundary value problem of diffraction for the system of Maxwell’s equations along with the Landau–Lifshitz equation (taking into account the exchange interaction field), supplemented with the electrodynamic boundary conditions and the condition of nonasymptotic radiation. Using a computational algorithm developed by the method of magnetic Floquet autonomous blocks, the electrodynamic calculation of scattering matrix element $\left| {{{S}_{{12}}}} \right|$ of periodic 2D gratings of magnetic micro- and nanoparticles (ferrite nanospheres) depending on the normalized frequency with a change in the grating period have been performed, taking into account the spectrum of magnetostatic and spin-wave oscillations in the microwave frequency range.