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

R. A. Sepkhanov; C. W. J. Beenakker

doi:10.1016/j.optcom.2008.07.017

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arXiv · 0712.1158

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

R. A. Sepkhanov·C. W. J. Beenakker

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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.

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R. A. Sepkhanov, C. W. J. Beenakker. 2008-07-11. Numerical test of the theory of pseudo-diffusive transmission at the Dirac point of a photonic band structure. https://doi.org/10.1016/j.optcom.2008.07.017

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