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||Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales
||In order to study local and global order in butterfly wing scales possessing structural colors, we have
developed a direct space algorithm, based on averaging the local environment of the repetitive units building
up the structure. The method provides the statistical distribution of the local environments, including the
histogram of the nearest-neighbor distance and the number of nearest neighbors. We have analyzed how the
different kinds of randomness present in the direct space structure influence the reciprocal space structure. It
was found that the Fourier method is useful in the case of a structure randomly deviating from an ordered
lattice. The direct space averaging method remains applicable even for structures lacking long-range order.
Based on the first Born approximation, a link is established between the reciprocal space image and the optical
reflectance spectrum. Results calculated within this framework agree well with measured reflectance spectra
because of the small width and moderate refractive index contrast of butterfly scales. By the analysis of the
wing scales of Cyanophrys remus and Albulina metallica butterflies, we tested the methods for structures
having long-range order, medium-range order, and short-range order.
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