Dirac cone in two- and three-dimensional metamaterials

It is shown by analytical calculation based on the tight-binding approximation that the isotropic Dirac cone in the Brillouin zone center can be created in two- and three-dimensional periodic metamaterials by accidental degeneracy of two modes. In the case of two dimensions, the combination of a doubly degenerate E mode and a non-degenerate A(1) mode of the square lattice of the C-4v symmetry is examined. For three dimensions, the combination of a triply degenerate T-1u mode and a non-degenerate A(1g) mode of the cubic lattice of the O-h symmetry is examined. The secular equation of the electromagnetic field is derived and solved with detailed analysis of electromagnetic transfer integrals by group theory. This is the first theoretical prediction of the presence of the Dirac cone in the three-dimensional periodic structure. (C) 2012 Optical Society of America