Symmetries and wave functions of photons confined in three-dimensional photonic band gap superlattices

We perform a computational study of confined photonic states that appear in a three-dimensional (3D) superlattice of coupled cavities, resulting from a superstructure of intentional defects. The states are isolated from the vacuum by a 3D photonic band gap, using a diamondlike inverse woodpile crystal structure, and they exhibit "Cartesian" hopping of photons in high-symmetry directions. We investigate the confinement dimensionality to verify which states are fully 3D-confined, using a recently developed scaling theory to analyze the influence of the structural parameters of the 3D crystal. We create confinement maps that trace the frequencies of 3D-confined bands for select combinations of key structural parameters, namely the pore radii of the underlying regular crystal and of the defect pores. We find that a certain minimum difference between the regular and defect pore radii is necessary for 3D-confined bands to appear, and that an increasing difference between the defect pore radii from the regular radii supports more 3D-confined bands. In our analysis, we find that their symmetries and spatial distributions are more varied than electronic orbitals known from solid-state physics. We surmise that this difference occurs since the confined photonic orbitals derive from global Bloch states governed by the underlying superlattice structure, whereas single-atom orbitals are localized. Based on this realization, we suggest that the extent symmetries of "photonic orbitals" could possibly translate to novel macroscopic behaviors of "photonic solid-state matter," never before seen in the standard electronic solid-state systems. We also discover pairs of degenerate 3D-confined bands with p-like orbital shapes and mirror symmetries matching the symmetry of the superlattice. Finally, we investigate the enhancement of the local density of optical states for cavity quantum electrodynamics applications. We find that donorlike superlattices, i.e., where the defect pores are smaller than the regular pores, provide greater enhancement in the air region than acceptorlike structures with larger defect pores, and thus offer better prospects for doping with quantum dots and ultimately for 3D networks of single photons steered across strongly coupled cavities.