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It has recently been predicted that a conical singularity (= Dirac point) inthe band structure of a photonic crystal produces an unusual 1/L scaling of thephoton flux transmitted through a slab of thickness L. This inverse-linearscaling is unusual, because it is characteristic of radiative transport viadiffusion modes through a disordered medium -- while here it appears forpropagation of Bloch modes in an ideal crystal without any disorder. We presenta quantitative numerical test of the predicted scaling, by calculating thescattering of transverse-electric (TE) modes by a two-dimensional triangularlattice of dielectric rods in air. We verify the 1/L scaling and show that theslope differs by less than 10% from the value predicted for maximal coupling ofthe Bloch modes in the photonic crystal to the plane waves in free space.

Numerical test of the theory of pseudo-diffusive transmission at the Dirac point of a photonic band structure