Numerical study and parameter estimation for double-negative metamaterials with Hilbert-curve inclusions

The electromagnetic wave interaction with metallic Hilbert-curve inclusions of the 3^rd order embedded in a homogenous isotropic host medium is numerically studied. The electric and magnetic polarizability tensors for this inclusion are analyzed and the Maxwell-Garnett and periodic mixing formulations are applied to this class of inclusions in order to obtain approximate values for the effective permittivity and permeability of the bulk media. In addition, the effective parameters of the bulk medium are also extracted from the S-parameters of a finite element method (FEM) waveguide simulation and the agreement between these various approaches is examined.