Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory

Abstract

We report on a comprehensive experimental and theoretical study of light diffraction from synthetic opals. A general theory of coherent elastic scattering (Bragg diffraction) is proposed, taking into account growth-induced effects of interlayer disorder and the refraction of light waves due to a background dielectric permittivity. The diffraction patterns were investigated using monochromatic or white light illumination in various scattering geometries. It is shown that the scattering of a monochromatic beam produces a set of diffraction spots (reflexes), which obey the conditions for Bragg light reflection by the ${hkl}$ crystal planes in a twinned face-centered cubic (fcc) structure made up of closely packed amorphous silica spherical particles. The white light diffraction patterns registered in different geometries are analyzed for a one dimensional (1D) disorder in hexagonal closely packed layers normal to the growth axis. The data analysis is performed in terms of the suggested diffraction theory of photonic crystals, taking into account the effects of random 1D packing of growing layers. A good quantitative agreement between the experimental data and calculations has been obtained for all diffraction patterns, including the angular and spectral dependencies of the radiation intensity. We have also estimated the statistical parameters of the opal structure composed of fcc lattice twins of random lengths along the sample growth axis. The long-wavelength diffraction edge is found for the principal scattering geometries.