Homogenization of the dielectric and magnetic permeability tensors for anisotropic and bianisotropic layered media

Abstract

The paper deals with the problem of calculating the effective properties of a multilayer system consisting of layers of anisotropic or bianisotropic media. It is assumed that the electromagnetic field is described by the Maxwell equations, and the layers are coordinate surfaces in some orthogonal coordinate system. No assumptions are made in advance about the properties of the dielectric and magnetic permeability tensors. The thickness of the layers is considered to be small in comparison with the wavelengths of all waves that can propagate in the system (long-wave approximation) and in comparison with the curvature radii of the layers as well as with the characteristic size of inhomogeneity in the layers. To construct an approximate solution, it is proposed to use a generalization of the matrix homogenization method. For the applicability of the method, it is necessary to rewrite the system of initial equations for a layered medium in a special form. The main advantage of the proposed approach, to find the parameters of an effective medium, is the absence of the need to solve complex partial differential equations. It is enough only to operate with matrices. The matrix homogenization method also makes it possible to obtain effective characteristics of a periodic structure with each period consisting of a set of thin layers. The study is illustrated by examples of finding effective tensors of dielectric and magnetic permeabilities for a system of planar, cylindrical, and spherical layers. In addition, the dependence of the magnetoelectric coefficient on the layer thicknesses for the cases listed above are compared.