Effective parameter extraction of 3D metamaterial arrays via first-principles homogenization theory

In this paper, the effective parameters of diverse single-negative bulk structures are extracted in terms of first-principles homogenization techniques. Each metamaterial unit-cell is initially considered to be an electrically small scatterer, and under this assumption, its polarizabilities are derived via a dynamic approach. Also, the wavenumber of a normally incident propagating plane wave through the aforementioned single-negative structures is obtained by means of several algorithms. The retrieved polarizabilities of a single scatterer and the wavenumber of the periodic medium are, finally, incorporated in the homogenization formulas to compute the desired effective parameters. Numerical verification addressing the analysis of two different resonators and comparisons with the results of a popular homogenization method, reveals the merits of the proposed formulation and proves its overall efficiency.