We describe the microfabrication and bandstructure of large scale three-dimensional (3-D) photonic bandgap (PBG) materials based on self-organizing templates. The simplest of these templates is an fcc lattice of close-packed, weakly sintered spheres. Other templates include hcp and hexagonal AB2 self-organizing photonic crystals. These photonic crystals may be converted into PBG materials by partially infiltrating the template with high refractive index semiconductors such as Si, Ge, or GaP and subsequently removing the template. The resulting "inverse opal" structure exhibits both a photonic pseudogap and a complete (3-D) PBG in the near visible spectrum, spanning up to 15% of the gap center frequency. The local density of states (LDOS) for photons exhibits considerable variation from point to point in coordinate space and reveals large spectral gaps even in the absence of a PBG in the total density of states. These gaps in the LDOS may lead to novel effects in quantum and nonlinear optics when active atoms or molecules are placed within the PBG material. These effects include anomalous, low threshold nonlinear response, collective atomic switching, and low-threshold all-optical transistor action. When an optically birefringent nematic liquid crystal is infiltrated into the void regions of the "inverse" opal PBG material, the resulting composite material exhibits a completely tunable PBG. In particular, the 3-D PBG can be completely opened or closed by applying an electric field which rotates the axis of the nematic molecules relative to the inverse opal backbone.
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