# Investigation of structural colors in Morpho butterflies using the nonstandard-finite-difference time-domain method: Effects of alternately stacked shelves and ridge density

Journal | Phys Rev E 80, 051924 (2009) |
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Authors | Dong Zhu, Shuichi Kinoshita, Dongsheng Cai and James B. Cole |

Title | Investigation of structural colors in Morpho butterflies using the nonstandard-finite-difference time-domain method: Effects of alternately stacked shelves and ridge density |

PubMed | 20365023 |

Abstract | We use the nonstandard-finite-difference time-domain (NS-FDTD) method to investigate the interaction of light with the complicated microstructures in the Morpho butterfly scales, which produce the well-known brilliant blue coloring. The NS-FDTD algorithm is particularly suitable to analyze such complex structures because the calculation can be performed in a short time with high accuracy on a relatively coarse numerical grid. We analyze (1) the microstructure obtained directly by binarizing an electron microgram of the cross section of a scale, (2) the reflection and diffraction properties of three model structures--flat, alternating, and tree-shaped alternating multilayers, and (3) an array of alternating multilayers with random noise superposed on the height of the structures. We found that the actual microstructure well reproduced the reflection spectrum in a blue region by integrating the reflection intensities over all the reflection angles. Under normal incidence, the flat multilayer mainly stresses on multilayer interference except for shorter wavelengths, while alternating multilayer rather enhances the effect of diffraction grating due to longitudinally repeating structure by strongly suppressing the reflection toward the normal direction. In the array of alternating multilayers, the reflection into larger angles is considerably suppressed and the spectral shape becomes different from that expected for a single alternating multilayer. This suppression mainly comes from the scattering of reflected light by adjacent structures, which is particularly prominent for the TM mode. Thus a clear difference between the TE and TM modes is observed with respect to the origin of spectral shape, though the obtained spectra are similar to each other. Finally, the polarization dependence of the reflection and the importance of the alternating multilayer are discussed. |

*Morpho*butterflies living in Central and South America show intense blue color, which is resulted from nano-sized structures instead of pigments. The ridges with ten layers of alternating shelves are densely arranged on the scales, which cover the whole wing of the

*Morpho*butterfly. So far, various models have been proposed by simplifying the complicated structures and give us understanding that regularly arranged shelves are the key point for the blue coloring. However, these models cannot explain broad angular range of the reflection, which is essential for the

*Morpho*blue. In order to improve this, we have simulated the light intensity reflected directly from the very structure obtained by electron microscopy using high-accuracy non-standard finite-difference time-domain (NS-FDTD) method. From the simulation, we have found that the following structural features are particularly important for the

*Morpho*blue. Firstly, alternating shelves strongly suppress light reflected toward the normal direction and broaden the angular range of the reflection. Secondly, densely arranged ridges block the reflection toward large angles, which restricts the wavelength range of the reflection within a blue region. These findings offer us a new insight in the mechanism of the blue coloring of the

*Morpho*butterfly.

Figure.

*Morpho*butterfly, its scales,

and electron microscopy image of the cross-section
of the scales.

Figure.

Reflected light from the structure of electron microscopy image

calculated
using NS-FDTD method