Influence of disorders on the optical properties of butterfly wing: Analysis with a finite-difference time-domain method

Many butterfly wing scales (BWSs) possess novel periodic fine structures and can influence and manipulate the propagation of light in a certain wavelength range though an interaction similar to that occurring in photonic crystals. Such optical properties and their physical origin can be theoretically analysed by solving Maxwell's equations. Many previous works have successfully applied a model of strict periodic pine-tree structure to the analysis of the scattering property of BWSs. However, fluctuation of the periodicity is common in the structure of BWSs. Thus clarification of the influence of size or periodicity variations on the optical properties of BWSs is then needed. In the present article, size variations have been considered and their influence on the scattering properties of BWSs is simulated in detail using a Finite-Difference-Time-Domain method (FDTD). The calculated reflectance spectrum will be more representative to the experimental result in the case where disorders, caused by size or periodicity variations, are considered. A detailed analysis shows that the main reflectance peak will be broadened and red-shifted especially when the angle of incidence is confined to a narrow range within 0 degrees +/- 10 degrees (-10 degrees <= theta <= 10 degrees). The results will be stable if the maximal deviation - the pine-tree unit away from its original equilibrium position - is smaller than 50 nm. Finally, we test the visible spectrum of the butterfly Morpho Didius and compare the results to those of our simulation. It is shown that the present results are in good agreement with experimentally observed trends, and this work will be helpful for a better understanding of the colorisation mechanism of materials with the structure of BWSs.