Refractive index from negative to positive with frequencies at the Dirac-like cone in a photonic crystal

In this paper, we numerically study the threefold accidental degeneracy conical dispersion (Driac-like cone) at the Brillouin zone center of the two-dimensional photonic crystals, which are composed of silicon pillars arranging in a triangular lattice. The effective permittivity and permeability near the Dirac-like point evolve from negative to positive by using the method of eigen-field averaging. Also, the isotropic behaviour of the Dirac-like cone is revealed by analysing the isofrequency contours. Moreover, we carry out numerical simulations including the reverse Snell’s law effect, negative Goos–Hänchen shifts and superfocusing lens to verify the negative refractive index characteristics of the designed structure. The proposed structure might find significant applications in the on-chip photonic interconnect and the photonic integrated circuit techniques.