Dispersion Diagram Characteristics of Periodic Array of Dielectric and Magnetic Materials Based Spheres

In this paper, the characteristics of electromagnetic (EM) waves supported by three dimensional (3D) periodic arrays of dielectric and magneto-dielectric spheres are theoretically investigated. The sphere particles have the potential to offer electric and magnetic dipole modes, where their novel arrangements engineer desired metamaterial performance. A full wave spherical modal analysis is applied to express the electromagnetic fields in terms of the electric and magnetic dipole modes and the higher order terms. Imposing the boundary conditions, determine the required equations for obtaining kd-betad dispersion characteristics. A metamaterial constructed from unit-cells of two different spheres is created, where one set of spheres develops electric modes, and the other set establishes magnetic modes. It is demonstrated that such a composite of high dielectric spheres provides double negative (DNG) metamaterial in a narrow frequency band spectrum where kd,betad<1. We also investigate the dispersion diagram for a 3D array of one-set of highly coupled dielectric spheres. Here, the couplings between the electric and magnetic dipoles of the spheres generate hybrid modes, resulting in a backward wave medium for kd > 1. The developments of DNG and backward wave metamaterials utilizing 3D array of magneto-dielectric spheres located inside space, and dielectric spheres embedded in a negative mu host, are also addressed. The use of magnetic materials allows accomplishing wider dispersion characteristic bandwidths and tunable feasibility.