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

We report on the role of the coupling of the modes of Mie resonances in all-dielectric metamaterials to ensure negative effective index at terahertz frequencies. We study this role according to the lattice period and according to 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 degenerated; the effective refractive index is then undeterminded. We also show that adjusting the mode coupling leads to near-zero effective index, or even null effective index. Further, we compare the mode coupling effect with hybridization in metamaterials.