Spatial dispersion in metamaterials based on three-dimensional arrays of spheres and disks

We consider the effect of spatial-dispersion-induced birefringence in metamaterial composed of isotropic spheres located in the sites of a cubic lattice. Strong anisotropy of such metamaterial due to nonlocality is demonstrated both numerically and analytically. For metamaterial composed of dielectric disks, we explore electromagnetic modes that are not captured by the local effective medium model, namely, the longitudinal magnetic mode.