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.
Highlights
Ever since the emergence of the field of nanophotonics, it has been well known that fruitful analogies can be drawn between the behavior of photons at the nanoscale on the one hand, and the physics of electrons, spins, and phonons in condensed matter on the other hand [1,2,3,4,5,6]
Cartesian light propagation on a 3D superlattice of cavities differs fundamentally from other known modes of propagation in periodic nanophotonic systems, notably from the conventional 3D spatially extended Bloch wave propagation in crystals, from light tunneling through a band gap, from coupled-resonator optical waveguiding, and from light diffusing at the edge of a gap
(i) A characteristic feature of the 3D superlattice Bloch modes is that they are constructed from modes where the light field is hopping from lattice site to lattice site
Summary
Ever since the emergence of the field of nanophotonics, it has been well known that fruitful analogies can be drawn between the behavior of photons at the nanoscale on the one hand, and the physics of electrons, spins, and phonons in condensed matter on the other hand [1,2,3,4,5,6]. The seminal phenomenon considered in this respect was the threedimensional (3D) Anderson localization of light [7,8]—in analogy to Anderson localization of spins [9]—that continues to receive attention to this day [10,11]. We explore the propagation of light in a 3D superlattice of coupled resonant cavities inside a 3D photonic band gap. The propagation of light in such a 3D cavity superlattice is analogous to electronic transport in an impurity band
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