Mathematical models of chiral metamaterials based on multi-turned conductive elements

The paper considers mathematical models of metamaterials based on a combination of multi-turned conductive elements, such as helices and gammadions. Analytical expressions are obtained for the resonant frequencies of these elements and relations for material parameters are determined using by the Maxwell Garnett model taking into account the metamaterials dispersion. The propagation constants of circular polarizations waves in these metamaterials are determined. As an example of the constructed mathematical models using, the solution of the problem of reflection of a plane linearly polarized electromagnetic wave from a planar layer of metamaterial, which is a matrix of fine-wire perfectly conducting elements in the form of N mutually orthogonal spirals is considered. The problem was solved by the partial domains method and its solution was reduced to a system of linear algebraic equations for unknown reflection and transmission coefficients of the main and cross-polarized field components. As a result of mathematical modeling, the frequency and polarization-selective properties of investigated metamaterials were revealed.