In this study, we illustrate the effective medium theories in the designs of three-dimensional composite metama- terials of both negative permittivity and negative permeability. The proposed metamaterial consists of random coated spheres with sizes smaller compared to the wavelength 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 the assembly of coated spheres which are random and much smaller than the wavelength of the light. The proposed ap- proach allows for the precise control of the permittivity and the permeability and guides a facile, flexible, and versatile way for the fabrication of composite metamaterials.
