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

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

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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 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
Volume99
Issue number11
DOIs
Publication statusPublished - 12 Mar 2019

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Photonic band gap
Wave propagation
photonics
cavities
propagation
Energy gap
Optical resonators
bandwidth
Bandwidth
Crystals
optical resonators
Cavity resonators
cavity resonators
coupling coefficients
Photonics
crystals
wave propagation
plane waves
quadrupoles
disorders

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title = "Cartesian light: Unconventional propagation of light in a three-dimensional superlattice of coupled cavities within a three-dimensional 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 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.",
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