All-dielectric metamaterials based on spherical and cubic inclusions

The 3D regular lattice of bi-spherical dielectric resonant inclusions arranged in a cubic lattice as two sets of spheres made from the same dielectric material having different radii and embedded in a host dielectric material with lower dielectric permittivity was carefully investigated. The magnetic resonance corresponding to the first Mie resonance in the spherical particles is achieved by forming a regular array of effective magnetic dipoles, and the structure of the identical spherical dielectric resonators can be designed as an isotropic μ-negative 3D-metamaterial. For the electric resonance it was found experimentally and by simulation that the resonant response of the electric dipole is weakly pronounced and the μ-negative behavior is remarkably suppressed. To enhance the electric dipole contribution we considered another kind of the symmetry of the bi-spherical arrangement of the particles corresponding to the face-centered cubic symmetry instead of the symmetry of NaCl analogue considered previously. Electromagnetic properties of a volumetric structure based on a regular lattice of identical cubic dielectric particles are also considered and analyzed as μ-negative metamaterial. The cubic particle based 3D-metamaterial is preferable for practical realization as compared with the spherical inclusions. For practical realization of all dielectric metamaterial the limitation of the dielectric permittivity of spherical inclusions should be taken into account. It is shown that to get double negative behavior of bi-spherical metamaterial, resonators with permittivity higher than 100 should be used. The same estimations could be made for rod, cylindrical resonators or any kind of dielectric resonators used as components for metamaterial design.