"Cartesian light": unconventional propagation of light in a 3D superlattice of coupled cavities within a 3D photonic band gap

Abstract

We explore the unconventional propagation of light in a three-dimensional (3D) superlattice of coupled resonant cavities in a 3D photonic band gap crystal. Such a 3D cavity superlattice is the photonic analogue of the Anderson model for spins and electrons in the limit of zero disorder. Using the plane-wave expansion method, we calculate the dispersion relations of the 3D cavity superlattice with the cubic inverse woodpile structure that reveal five coupled-cavity bands, typical of quadrupole-like resonances. For three out of five bands, we observe that the dispersion bandwidth is significantly larger in the $(k_x,k_z)$-diagonal directions than in other directions. To explain the directionality of the dispersion bandwidth, we employ the tight-binding method from which we derive coupling coefficients in 3D. For all converged coupled-cavity bands, we find that light hops predominantly in a few high-symmetry directions including the Cartesian $(x,y,z)$ directions, therefore we propose the name "Cartesian light". Such 3D Cartesian hopping of light in a band gap yields propagation as superlattice Bloch modes that differ fundamentally from the conventional 3D spatially-extended Bloch wave propagation in crystals, from light tunneling through a band gap, from coupled-resonator optical waveguiding, and also from light diffusing at the edge of a gap.

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• Dispersion of backward-propagating waves in a surface defect on a 3D photonic band gap crystal
• Unsupervised Machine Learning to Classify the Confinement of Waves in Periodic Superstructures
• Symmetries and Wavefunctions of Photons Confined in 3D Photonic Band Gap Superlattices