Optical properties of honeycomb photonic structures

Abstract

We study, theoretically and experimentally, optical properties of different\ntypes of honeycomb photonic structures, known also as `photonic graphene'.\nFirst, we employ the two-photon polymerization method to fabricate the\nhoneycomb structures. In experiment, we observe a strong diffraction from a\nfinite number of elements, thus providing a unique tool to define the exact\nnumber of scattering elements in the structure by a naked eye. Then, we study\ntheoretically the transmission spectra of both honeycomb single layer and 2D\nstructures of parallel dielectric circular rods. When the dielectric constant\nof the rod materials $\\varepsilon$ is increasing, we reveal that a\ntwo-dimensional photonic graphene structure transforms into a metamaterial when\nthe lowest TE${}_{01}$ Mie gap opens up below the lowest Bragg bandgap. We also\nobserve two Dirac points in the band structure of 2D photonic graphene at the\n$K$ point of the Brillouin zone and demonstrate a manifestation of the Dirac\nlensing for the TM polarization. The performance of the Dirac lens is that the\n2D photonic graphene layer converts a wave from point source into a beam with\nflat phase surfaces at the Dirac frequency for the TM polarization.\n