Extremal transmission at the Dirac point of a photonic band structure

Abstract

We calculate the effect of a Dirac point (a conical singularity in the band structure) on the transmission of monochromatic radiation through a photonic crystal. The transmission as a function of frequency has an extremum at the Dirac point, depending on the transparencies of the interfaces with free space. The extremal transmission $T_{0}=\Gamma_{0} W/L$ is inversely proportional to the longitudinal dimension $L$ of the crystal (for $L$ larger than the lattice constant and smaller than the transverse dimension $W$). The interface transparencies affect the proportionality constant $\Gamma_{0}$, and they determine whether the extremum is a minimum or a maximum, but they do not affect the ``pseudo-diffusive'' 1/L dependence of $T_{0}$.