Inhomogeneous chiral metamaterials: optical wave reflection analysis with regard to the dispersion of material parameters

The paper considers a planar chiral metamaterial of the optical spectrum. The material parameters of metamaterial depend on the frequency and one spatial coordinate. The mathematical model of metastructure is based on the well-known dispersion models of the permittivity, permeability and chirality parameter. A novelty in the mathematical model of a metamaterial is the consideration of the heterogeneity of all material parameters. In this paper we consider a problem of the incidence of a plane linearly polarized optical wave on a planar layer of a chiral metamaterial. We develop a method for calculating reflection coefficients of an optical wave from the considered inhomogeneous chiral structure, which is based on using a differential sweep method. When constructing a mathematical model, the cross-polarization of the optical wave field was taken into account, which consists in the appearance of orthogonal components during the interaction of the field with a chiral metamaterial. The solution of the problem was reduced to a matrix differential equation for the unknown reflection coefficients of the main and cross-polarized components of the optical field. Chiral metamaterials with linear and parabolic inhomogeneity profiles were considered in the work. Based on the results of numerical calculation of reflection coefficients of the main and cross-polarized components, it is proved that the inhomogeneity of the material parameters leads to a significant decrease in the level of cross-polarized component of reflection. It is shown that the use of inhomogeneous chiral layers also makes it possible to lower the level of reflection of the optical field main component. It is also proved that a layer of a planar inhomogeneous chiral metamaterial in the optical spectrum reflects waves of s- and p- polarizations differently.