A simple a priori determination of optical transmission gaps in photonic crystals of weak symmetry

Pair correlation and radial distribution functions of a disordered SiO2 colloidal photonic crystal (PC) were generated directly from binary color scale rendering of a focussed ion beam milled cross-section that was imaged by common electron microscopy techniques. The bandwidth and mid-gap frequency of the optical band gap are calculated to within 6% and 30%, respectively, of their measured values by considering a simple variation of the Ioffe–Regel conditions and symmetries derived from the experimentally determined correlation functions. This work provides a simple a priori approach to a first-order prediction of the structure/optical property relationships in PCs directly from standard microstructural imaging techniques. 2002 Elsevier Science B.V. All rights reserved.