Cartesian light': How does light propagate in a 3D superlattice of photonic bandgap cavities?

We explore the unconventional propagation of light in a three-dimensional (3D) superlattice of coupled resonant cavities in a 3D photonic band gap crystal (Fig. 1). Such a 3D cavity superlattice is the photonic analogue of the Anderson model for spins and electrons in the limit of zero disorder [1]. Using the plane-wave expansion method [2], we calculate the dispersion relations of the 3D cavity superlattice with the cubic inverse woodpile structure [3,4] that reveal five coupled-cavity bands. These bands have quadrupolar symmetry and are the optical analogues of d-orbitals in solid-state physics [4,5]. Therefore, one might naively expect neighboring cavities to couple mostly in diagonal directions.