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

## TL;DR

This paper investigates the unique propagation of light in a 3D superlattice of coupled cavities within a photonic band gap, revealing a directional hopping behavior termed 'Cartesian light' that differs from traditional wave propagation.

## Contribution

It introduces the concept of 'Cartesian light' and demonstrates its directional hopping behavior in a 3D cavity superlattice, expanding understanding of light dynamics in photonic band gap structures.

## Key findings

- Light hops predominantly along high-symmetry Cartesian directions.
- Dispersion relations show significant bandwidth anisotropy in certain directions.
- Propagation occurs via superlattice Bloch modes, distinct from conventional mechanisms.

## 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.