Abstract
We demonstrate the method of three-dimensional (3D) optical Wannier functions (WFs) for quantitative description of electromagnetic wave localization and propagation in 3D photonic band gap (PBG) micro-circuits. Using these localized "light orbitals" we accurately reconstruct electromagnetic flow in bulk 3D PBG materials, 2D-3D PBG heterostructures and 2D membrane photonic crystals. The localized orbitals provide a more efficient basis than those used in plane-wave expansions and finite-difference time-domain methods. In 3D photonic crystal circuits, using twenty or fewer WFs, we accurately recapture electromagnetic phenomena over a significant spectral bandwidth surrounding the PBG.