Reflectance of topologically disordered photonic-crystal films

Periodicity implies the creation of discretely diffracted beams while various departures from periodicity lead to broadened scattering angles. This effect is investigated for disturbed lattices exhibiting randomly varying periods. In the Born approximation, the diffused reflection is shown to be related to a pair correlation function constructed from the distribution of the film scattering power. The technique is first applied to a natural photonic crystal found on the ventral side of the wings of the butterfly Cyanophrys remus, where scanning electron microscopy reveals the formation of polycrystalline photonic structures. Second, the disorder in the distribution of the cross-ribs on the scales another butterfly, Lycaena virgaureae, is investigated. The irregular arrangement of scatterers found in chitin structure of this insect produces light reflection in the long-wavelength part of the visible range, with a quite unusual broad directionality. The use of the pair correlation function allows to propose estimates of the diffusive spreading in these very different systems.