An Optimal Design Approach For Bio-mimicking The Micro-Nano Structures On Butterfly Wing Scales

Brilliant and iridescent blue color of Morpho butterfly wing is closely related tomicro-nano structures on the wing scales. Based on the structural color, an optimal designapproach is proposed to do a series of related studies, which combines the optical propertiesof biological structures with biomimetic design.First, the morphology of micro-nano structures on Morpho didius butterfly wing scale isanalyzed. The size parameters of the biological structures are measured for constructing aaccurate biological model. The biological model is simplified to two kinds of biomimeticstructures which are asymmetric and symmetric, in order to facilitating the simulation andmanufacturing.Then a theory and a methods is established for optimal design. We use rigorouscoupled-wave analysis to solve the reflectivity of micro-nano structure, and use geneticalgorithm as optimization algorithm. By studying and testing the algorithm, a set of operationsteps and algorithm parameters are selected, which include real number encoding, Rank forfitness scaling, Stochastic Uniform for selection, Scattered for crossover, Adaptive Feasiblefor mutation,30~50for population size,0.2for crossover fraction,200for stall generations.The high efficiency of the optimization algorithm is verified by a lot of tests.The symmetric biomimetic structures with different number of layers are optimized attwo polarization modes with the target of maximizing the reflectivity at blue band. All theresulting optimal structures have selective reflection characteristics, and have maximalreflection at about470nm. The reflection peaks are higher than that of the biomimeticstructures.Furthermore, several groups of structures with different optimization objectives,constraints and structure parameters from that of original optimization tests are optimized.Compared the results, we get a series of conclusion. The high reflectivity of optimal structureat specific wavelength originate from multilayer interference effects. The thickness and widthof layers play a leading role in multilayer interference and make a major contribution toreflection. The reflectance spectrum is influenced by spine width w, minimum gap width b,tree periodic p and refractive index n2, in which the spine affected it obviously. Higherreflectivity of optimal structures can be obtained with more numbers of layers, lower value ofw/b/n2, higher value of p. The conclusions above help us understand the internal links between the phenomenon ofstructural color in butterfly wings and the dimensions and physical parameters of micro-nanostructures. The optimal design work improves or changes the optical properties of biologicalstructure, improves its workability and reduces its difficulty of processing, so that it can bettermeet the requirement of manufacturing technology and practical applications.