Quantitative analysis of lattice ordering in thin film opal-based photonic crystals

This work is devoted to the quantitative evaluation of the lattice ordering of opal films. Assembling colloidal crystals in a moving meniscus under random noise agitation produced opal films with generically the same lattice but different disorders. The lattice ordering is quantified by the magnitudes of harmonics in the Fourier transforms of (i) the scanning electron microscopy images to address the in-plane lattice ordering and (ii) rotation diagrams of the optical transmission to address the regularity of crystal planes. In prepared opals, the strong deviation of the lattice from tile face-centered cubic symmetry is demonstrated. We find uneven lattice responses to changing the growth conditions, e.g., the 30% improvement of the hexagonal lattice ordering in the (111) growth plane accompanied by a ten-time better ordering of (220) planes as a result of noise agitation. The suggested approach to characterize crystalline quality of tile lattice is a general methodology that can be applied to the analysis of other three-dimensional photonic crystals.