Homogenization of quasi-isotropic metamaterials composed by dense arrays of magnetodielectric spheres

In this work, we discuss the homogenization of a metamaterial geometry composed of periodic arrays of densely packed subwavelength magnetodielectric spheres, in order to study whether a local quasi-isotropic homogenization model may accurately describe its wave interaction in its negative-index or zero-index operation. We analyze and compare the electromagnetic response of these arrays with their retrieved metamaterial model, for frequency regimes in which positive or negative values of effective index of refraction are expected. We pay special attention to the effects of array truncation and complex forms of excitation, showing that it is possible to realize quasi-isotropic negative-index or zero-index metamaterials with negligible spatial dispersion effects in certain frequency bands. We then apply these concepts to specific configurations of interest for metamaterial devices, showing that, despite their finite size and complex operation, their response is consistent with the one associated with their homogenized local description.