We study theoretically light propagations at the zigzag edge of a honeycomb photonic crystal consisting of dielectric rods in air, analogous to graphene. Within the photonic band gap of the honeycomb photonic crystal, a unimodal edge state may exist
with a sharp confinement of optical fields. Its dispersion can be tuned simply by adjusting the radius of the edge rods. For the edge rods with a graded variation in radius along the edge direction, we show numerically that light beams of different frequencies can be trapped sharply in different spatial locations, rendering wideband trapping of light.
A transfer matrix method is developed for optical calculations of non-interacting graphene layers. Within the framework of this method, optical properties such as reflection, transmission and absorption for single-, double- and multi-layer graphene a
re studied. We also apply the method to structures consisting of periodically arranged graphene layers, revealing well-defined photonic band structures and even photonic bandgaps. Finally, we discuss graphene plasmons and introduce a simple way to tune the plasmon dispersion.
The authors study theoretically reflection on the surface of a metamaterial with a hyperbolic dispersion. It is found that reflection is strongly dependent on how the surface is terminated with respect to the asymptote of the hyperbolic dispersion. F
or a surface terminated normally to the asymptote, zero reflection occurs for all incident angles. It is exemplified by a metamaterial made of a periodic metal-dielectric layered structure with its surface properly cut through numerical simulations.
