Algorithm for calculation of wave numbers in a chiral metamaterial based on composite spiral elements

Materials with various exotic electromagnetic characteristics have been extensively studied in recent decades to satisfy the growing interest in various fields, including visualization, telecommunications, energy use, and so on. As a particularly promising candidate, electromagnetic metamaterials exhibit electromagnetic properties that are inaccessible to natural materials. Due to the fact that the chiral medium (metamaterial) is a set of uniformly distributed conductive mirror-asymmetric (chiral) elements in an isotropic dielectric medium. In addition to the material from which the chiral element is made, its shape also plays an important role. That is why it is so important to study new types of chiral elements, as well as to determine the electrodynamic properties of chiral metamaterials based on them. The paper considers the solution of the problem of determining the reflection and transmission coefficients when a plane electromagnetic wave falls on a planar layer of a chiral metamaterial based on multi-pass conducting elements of the spiral type, taking into account the structural parameters of the metamaterial, which is a matrix of thin-wire ideally conducting elements in the form of N mutually orthogonal spirals. To determine the parameters of a chiral metamaterial based on composite spiral elements, the construction of a particular mathematical model of a composite element based on an arbitrary number of spiral elements in a spatial configuration, as well as a metamaterial based on a matrix of such elements, is considered. An algorithm for calculating the propagation constants of waves with circular polarizations in the specified metamaterial is proposed. From the calculations presented, it can be noted that the metastructure under study at one frequency can act as a frequency-selective protective shield that is not transparent to radiation near the main resonant frequency.