Cartesian light: Unconventional propagation of light in a three-dimensional superlattice of coupled cavities within a three-dimensional photonic band gap

Sjoerd A. Hack, Jaap J.W. van der Vegt, Willem L. Vos (Corresponding Author)

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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 analog 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 (kx,kz) -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 three dimensions. 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.
Original languageEnglish
Article number115308
JournalPhysical review B: Covering condensed matter and materials physics
Issue number11
Publication statusPublished - 12 Mar 2019

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