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 near 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 “pseudodiffusive” $1∕L$ dependence of $T_0$.

• Received 19 March 2007

DOI:https://doi.org/10.1103/PhysRevA.75.063813