Tetrahedral framework of inverse opal photonic crystals defines the optical response and photonic band gap

By forming anatase TiO₂ inverse opals by infiltration of an opal photonic crystal, we demonstrate that the optical response and angle-resolved blue-shift of the band-gap of the inverse opal structure are defined by a particular three-dimensional structure of the infilled voids. The optical structure of TiO₂ inverse opals usually displays significant deviation from its physical structure and from the theoretically predicted position of the photonic band-gap. Following rigorous structural characterization of the parent opal template and TiO₂ inverse opals, alternative explanations for the signature of optical transmission through inverse opals are proposed. These approaches posit that, for light-matter interaction, an inverse opal is not precisely the inverse of an opal. Accurate parameters for the structure and material properties can be obtained by invoking a Bragg FCC selection rule-forbidden (-211) plane, which is not a realistic model for diffraction in the IO. Alternatively, by assuming optical interactions with just the periodic arrangement of tetrahedral filled interstitial sites in the structure of the inverse opal, a complete reconciliation with the spectral blue-shift with the angle, photonic band gap, and material parameters is obtained when a reduced unit cell is defined based on interstitial void filling. The analysis suggests a reduced interplanar spacing (d = $1/√3$ D, for pore diameter D), based on the actual structure of an inverse opal in general, rather than a definition based on the inverse of an FCC packed opal. This approach provides an accurate and general description for predicting the spectral response and material parameters of ordered inverse opal photonic crystal materials.