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

TL;DR

This paper numerically verifies the predicted 1/L scaling of photon transmission at the Dirac point in a photonic crystal, demonstrating an unusual diffusion-like behavior in an ideal, disorder-free system.

Contribution

It provides a quantitative numerical test confirming the theoretical prediction of pseudo-diffusive transmission scaling at the Dirac point in photonic band structures.

Findings

Confirmed the 1/L scaling of photon flux transmission at the Dirac point.

Showed the slope of the scaling closely matches theoretical predictions.

Demonstrated the diffusion-like behavior occurs in an ideal crystal without disorder.

Abstract

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