Double Dirac point in a photonic graphene

The band structure of the photonic graphene composed of an array of dielectric cylinders in air with honeycomb lattice is computed in this work. The results reveal that there is a double Dirac point at the Brillouin zone center with a frequency of 0.870 61c/a in our proposed photonic graphene structure. By using average eigen-field calculation, we demonstrate that such a photonic graphene structure possesses both zero effective permittivity and effective permeability, which implied that this structure can serve as zero-index medium. Furthermore, applications including focusing, multidirectional emission and super-coupling are numerically demonstrated with the proposed structure at the double Dirac point frequency, which further conformed the zero-index properties of the photonic graphene structure.