Dirac-cone based negative/zero/positive refractive index metamaterials

Based on accidental degeneracy, a Dirac-cone can be formed at the center of the Brillouin zone of a photonic crystal, which can be treated as a homogeneous bulk metamaterial in the vicinity of Dirac-point. In the vicinity below (above) the Dirac-point, the backward-wave (forward-wave) implies negative (positive) n_eff; at Dirac-point, k=0 induces zero n_eff. This negative/zero/positive refractive index shows low-loss and good impedance matching to free-space. According to this principle, we designed a Dirac-cone based metamaterial consisting of 2D square array of silicon pillars operating around 1.55 μm and demonstrated its negative/zero/positive refractive index analytically, numerically, and experimentally.