Light scattering by photonic crystals with a Dirac spectrum

Abstract

In this thesis we consider several effects of a Dirac spectrum in photonic crystals on the scattering and propagation of light. We calculate the effect of a Dirac point (a conical singularity in the band structure) on the transmission of radiation through a photonic crystal. We find that the transmission at the Dirac point is inversely proportional to the longitudinal dimension of the crystal. Further we propose a method to detect the pseudospin-1/2 Berry phase produced by the Dirac-type band structure of a triangular-lattice photonic crystal. In addition we show that the half-integer spin and the associated Berry phase remain observable in the presence of disorder in the crystal: the destructive interference caused by the Berry phase suppresses the reflected intensity at an angle which is related to the angle of incidence by time-reversal symmetry causing extinction of coherent backscattering. We test all our predictions numerically by solving the full Maxwell equations. We also demonstrate that the Goos-Hanchen effect, which has been observed for the first time in optics and has applications in particular in photonic crystals, is of high importance for graphene. We show that the Goos-Hanchen effect in an n-doped channel with p-doped boundaries doubles the degeneracy of the lowest propagating mode, introducing a two-fold degeneracy on top of the usual spin and valley degeneracies. This can be observed as a stepwise increase by 8e^2/h of the conductance with increasing channel width.