  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.
