Investigation of isotropicity for 3-D metamaterial bulk structure

In this paper, we investigate the isotropicity of a 3-D metamaterial bulk structure consisting of ring resonators (RR) and thin wires based on the modeling of them using the definition of magnetization and polarization. The presented 3-D metamaterial bulk structure is shown to be synthesized to have the effective permeability and permittivity of near -1 at 8 GHz. Its refractive index is also about -1. The computed Brillouin dispersion diagram also showed that the proposed structure is almost near isotropic. The electrical length of the unit cell, examined based on the Brillouin zone, showed the deviation of about 20%.