The using of Maxwell Garnett and Bruggman models to describe heterogeneity of a chiral metamaterial based on gammadions

This paper assesses the various generalized mathematical models of microwave chiral metamaterials based on various forms of material equations. The article concludes that it is necessary to describe a chiral metamaterial as a heterogeneous media, taking into account the dependence of the effective dielectric permittivity on the container permittivity and permittivity of a volumes with chiral inclusions. In this work, mathematical models of a chiral metamaterial are constructed based on the Maxwell Garnett and Bruggeman formulas, taking into account the properties of heterogeneity. As the investigated chiral metamaterial we chose a metastructure based on fine-wire curved gammadions with different numbers of loops. For this structure, the resonance frequencies of chiral inclusions in the form of multi-loop fine-wire curvilinear gammadions were determined. As an example, we solved the problem of reflection (transmission) of a plane electromagnetic wave with linear polarization from a planar layer of a chiral metamaterial based on a uniform matrix of multi-loop fine-wire curvilinear gammadions. In this work, the influence of the number of gammadion loops on the reflecting and transmitting properties of the chiral metamaterial is determined. The article analyzes the issues of using the Maxwell Garnett and Bruggeman formulas to take into account the heterogeneity of the chiral metamaterial and their influence on the results of calculating the reflection and transmission coefficients of the wave. It is proved in this work that a planar layer of a chiral metamaterial based on multi-loop fine-wire curvilinear gammadions allows concentrating the incident electromagnetic field in the plane of the metastructure.