New assembly route for three-dimensional metamaterials through effect medium theory

In this study, we illustrate the effective medium theories in the designs of three-dimensional composite metametails of both negative permittivity and permeability. The proposed metamaterials consist of coated spheres embedded in a dielectric host. Simple design rules and formulas following the effective medium models are numerically and analytically presented. We demonstrate that the revised Maxwell-Garnett effective medium theory enables us to design three-dimensional composite metamaterials through assembly of coated small spheres. The proposed approach allows for precise control of the permittivity and permeability and guides a facile, flexible and versatile way for the fabrication of composite metamaterials.