TE Band Structure for High Contrast Honeycomb Media

We study the band structure of transverse electric (TE) waves in a 2D medium consisting of a homogeneous bulk and a honeycomb array of higher permittivity dielectric “inclusions” In the high contrast regime and under a non-degeneracy condition, the first two dispersion surfaces touch at conical singularities, Dirac points, over the vertices of the Brillouin zone. We use analytical ideas, together with numerical simulations, to deduce detailed local information at the conical crossings as well as global behavior over the full Brillouin zone. Essential differences between this E & M setting and the quantum model of graphene are discussed.