Rational design of double-negative metamaterials consisting of 3D arrays of two different non-metallic spheres arranged on a simple tetragonal lattice

Non-metallic, low-loss double-negative (DNG) metamaterials can be formed by three-dimensional (3D) arrays of two different non-metallic spheres arranged on a simple tetragonal lattice. Such DNG metamaterials have recently been found to provide DNG bandwidths of 10% through 3D arrays of two different dielectric spheres, and of 18% through 3D arrays of dielectric and magnetic spheres. However, a method of rational design of these DNG metamaterials has not yet been presented. This paper develops a design procedure based on the theoretical description of traveling waves supported by the 3D arrays. Analytical calculations of k-β (dispersion) diagram and effective constitutive parameters of several DNG metamaterials designed using this rule are presented.