Photonic band gap formation in certain self-organizing systems

We present a detailed study of photonic band structure in certain self-organizing systems that self-assemble into large-scale photonic crystals with photonic band gaps (PBGs) or pseudogaps in the near-visible frequency regime. These include colloidal suspensions, inverted opals, and macroporous silicon. We show that complete three-dimensional PBGs spanning roughly 10% and 15% of the gap center frequency are attainable by incomplete infiltration of an opal with silicon and germanium, respectively. The photonic band structure of both face center cubic and hexagonal close packed photonic crystals are evaluated. We delineate how the PBG is modified by sintering the opal prior to infiltration and by applying strain along various crystallographic directions. We evaluate the total photon density of states as well as the local density of states (LDOS) projected onto various points within the photonic crystal. It is shown that the LDOS may exhibit considerable pseudogap structure even for systems that do not exhibit a complete PBG. These results are directly relevant to quantum optical experiments in which atoms, dye molecules, or other active materials are inserted into specific locations within the photonic crystal. When the resonant optical transition of these dopants is tuned close to a pseudogap or other abrupt structure in the LDOS, novel effects in radiative dynamics associated with a ``colored vacuum'' may be realized.