Extremal transmission at the Dirac point of a photonic band structure

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 W-0/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.