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Extremal transmission at the Dirac point of a photonic band structure

R. A. Sepkhanov·Ya. B. Bazaliy·C. W. J. Beenakker
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Abstract

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 at the Dirac point, depending on the transparencies of the interfaces with free space. The extremal transmission $T_{0}=Γ_{0} W/L$ 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 $Γ_{0}$, and they determine whether the extremum is a minimum or a maximum, but they do not affect the ``pseudo-diffusive'' 1/L dependence of $T_{0}$.

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R. A. Sepkhanov, Ya. B. Bazaliy, C. W. J. Beenakker. 2007-05-21. Extremal transmission at the Dirac point of a photonic band structure. https://doi.org/10.1103/physreva.75.063813

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