Negative index and mode coupling in all-dielectric metamaterials at terahertz frequencies

We elucidate the role of the mode coupling of the Mie resonances in all-dielectric metamaterials to ensure a negative effective index at terahertz frequencies. We perform a study as a function of the lattice period and of the frequency overlapping of the modes of resonance. We show that negative effective refractive index requires sufficiently strong mode coupling and that for even more strong mode coupling, the first two modes of Mie resonances are degenerate; the effective refractive index is then undetermined. We also show that it is possible to obtain near-zero, or even null, effective index with a judicious adjustment of the mode coupling. Further, we discuss the mode coupling effect with hybridization in metamaterials.