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

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.

arXiv comment4 pages, 7 figures. Figure added

References in corpus (7)

• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Quantum-limited shot noise in graphene
• Negative Refraction and Left-handed electromagnetism in Microwave Photonic Crystals
• Negative refraction and left-handed behavior in two-dimensional photonic crystals
• Extremal transmission at the Dirac point of a photonic band structure
• All-angle left-handed negative refraction in Kagome and honeycomb lattice photonic crystals
• Demonstration of a New Transport Regime of Photon in Two-dimensional Photonic Crystal

Cited by in corpus (4)

• Do Linear Dispersions of Classical Waves Mean Dirac Cones?
• Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard
• Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum
• Pseudodiffusive transmission of nodal Dirac fermions through a clean d-wave superconductor