All-dielectric metamaterials: irrelevance of negative refraction to overlapped Mie resonances

All-dielectric metamaterials comprised of identical resonators draw a lot of attention as low-loss media providing for negative refraction, which is commonly attributed to the double negativity of effective material parameters caused by overlapping of Mie resonances. We study dispersion diagrams of such metamaterials composed of dielectric rod arrays and show that bandwidths of positive and negative refraction and its type are irrelevant to the negativity of effective parameters; instead, they are unambiguously defined by the shape and the location of the second transmission branch in dispersion diagrams and thus can be controlled by the lattice constants