Design of 3-D Periodic Metamaterials for Electromagnetic Properties

This paper presents a new homogenization formula to compute the effective electromagnetic properties for periodic metamaterials. Numerical examples showed that the effective permittivity and permeability of the composites with cubic inclusions, formerly known to have the lowest permittivity, are closer to the Hashin-Strikman bounds than those obtained from other methods. To tailor the specific effective properties, an inverse homogenization procedure is proposed within the framework of vector wave equations. Some novel metamaterial microstructures with a range of specific effective permittivity and/or permeability are obtained. By maximizing the permittivity and permeability at the same time, a structure with minimal surface area (the mean curvature of the surface equals zero everywhere), namely, the well-known Schwarz primitive structure, is obtained. Similarly to the nano-spheres (dielectric spheres covered by plasmonic shells) with negative refraction, we generalize the Schwarz primitive structure and its analogy (e.g., those with a constant mean curvature surface) to one class of chiral composites by embedding one of these structures with smaller volume fraction (nonmagnetic inclusive cores) into another with large volume fraction (metal shell). Such composites have potential to provide better behaviors because they can best utilize different components. The anisotropic composites and multiple solutions to the inverse homogenization are also illustrated.