Artificial magnetism at terahertz frequencies in 3D arrays of TiO2 microspheres including spatial dispersion and magnetoelectric coupling

In this work, we study the electromagnetic properties of a metamaterial made by a cubic array of TiO₂ microspheres embedded in a host medium at terahertz frequencies. By employing the method reported in [1] by Silveirinha, we are able to consider in the computation the effect of magnetoelectric coupling between TiO₂ microspheres, as well as spatial dispersion. After calculation of the dominant mode inside the structure, we show that the effect of spatial dispersion on the effective parameters for this kind of systems is relatively weak. Accuracy of the results and effectiveness of homogenized parameters have been demonstrated by comparison against full-wave simulations for a 5-layer slab of such a metamaterial.