Development of a mathematical model of a chiral metamaterial based on a cylindrical helical elements accounting for the dispersion and concentration of elements

Background. Interest in the study of microwave metamaterials is associated with the possibility of using them to achieve the required frequency and polarization selective properties of interaction with electromagnetic radiation, which can’t be obtained for structures based on homogeneous media. Aim. The mathematical model of a chiral metamaterial based on a periodic matrix of arbitrarily oriented conducting thin-wire cylindrical helices located in a homogeneous isotropic container creation is considered. Unlike known models, it takes into account the explicit form of the dependence of the effective permittivity and the relative chirality parameter on the helices concentration. Methods. The heterogeneity of a chiral metamaterial based on the Maxwell Garnett formula, which makes it possible to determine the effective dielectric permittivity from the permeabilities of the container and the region occupied by conducting mirror asymmetric inclusions is taken into account when creating a mathematical model. The dispersion of permittivity using the quadratic Lorentz formula and the dispersion of the chirality parameter based on the Condon model are taken into account. Results. Analytical frequency-dependent expressions for the effective permittivity and the chirality parameter taking into account the concentration of helices and their geometric parameters, were obtained in the work. The expression for the relationship between the dimensionless volume concentration of inclusions and the distance between adjacent elements is obtained. The quasi-static approach is used to calculate the resonant frequency of conducting thin-wire cylindrical helices. Conclusion. The proposed method for constructing a mathematical model can be applied to chiral metamaterials based on periodic matrices of conductive elements of an arbitrary mirror asymmetric spatial configuration.