Reproducing the hierarchy of disorder for Morpho-inspired, broad-angle color reflection

The scales of Morpho butterflies are covered with intricate, hierarchical ridge structures that produce a bright, blue reflection that remains stable across wide viewing angles. This effect has been researched extensively, and much understanding has been achieved using modeling that has focused on the positional disorder among the identical, multilayered ridges as the critical factor for producing angular independent color. Realizing such positional disorder of identical nanostructures is difficult, which in turn has limited experimental verification of different physical mechanisms that have been proposed. In this paper, we suggest an alternative model of inter-structural disorder that can achieve the same broad-angle color reflection, and is applicable to wafer-scale fabrication using conventional thin film technologies. Fabrication of a thin film that produces pure, stable blue across a viewing angle of more than 120 ° is demonstrated, together with a robust, conformal color coating.

. Effect of the ridge shape on the unit response.
The effect of the ridge shape was investigated using two dimensional finite element method (COMSOL™) with perfectly matched layer (PML) boundary conditions. Far-field reflected intensities were obtained by near-to-far-field transformation. Each ridge is composed of 8 pairs of SiO2/TiO2 layers with experimentally obtained refractive index values. Two variables (the bottom width of the ridge for a fixed height and the height for a fixed width) were varied, and their effect on the reflection spectrum upon normal incidence investigated.
We find that while all show suppression of reflection in the red, the details of the reflection spectra depend on the detailed shape of the ridge even though the multilayer period and the multilayer materials were held constant throughout the simulation. This demonstrates that the shape of the reflecting multilayer ridge contributes significantly to the final color of the Morpho butterflies. Indeed, the tapered shape is quite effective in generating pure blue. Corresponding data for a 45 incident angle. Note that all graphs are plotted in log scale. All simulations were performed by the in-house FEM solver which was also used for the simulation of Fig.   4. indicating that the directionality of deposition is perfect. (b) Corresponding data for a ridged structure with irregular layers, whose vertical disorder linearly decreases from bottom to top layer, 46 nm to 20 nm, indicating that the directionality of deposition is not as perfect as the fabricated ridge structure. (c) Corresponding data for a ridged structure with irregular layers, whose vertical disorder is 46 nm for all layers, indicating that the directionality of deposition is perfect.
We find that increasing the directionality deposition is necessary for generating enough disorder. And  (Fig. S6b), and a ridge structure with irregular layers (Fig. S6c). The viewing angles are, from the top, approximately 10, 35, 45, and 55 degrees. The red-colored structure also shows a blueshift of its hue just as seen for the blue structure. The ridged structures show a yellowish color, while the continuous structure shows red color. (e) Calculated far-field reflected intensities of a ridged structure with regular layers. The simulation was performed by finite element method (COMSOL™) using the actual shape of the ridges obtained from SEM images (Fig. S6b)

. (f)
Corresponding data for a ridged structure with irregular layers, whose structural parameters are obtained by SEM images (Fig. S6c). (g) Corresponding data for a ridged structure with irregular layers, assuming that 1.5 times the size of microspheres is used for the disordered substrate.
We find that the red-shifted color can be defined simply by upscaling the multilayer thickness.
However, for broad-angle reflection of the red-shifted color, it is obvious that the scale of disorder has to increase as multilayer thickness increases.  By numerical simulation, we confirm that inter-structural disorder is quite effective for broad-angle reflection. On the other hand, both the strong specular reflection and the sharp diffraction peaks remain almost the same after etch damage, even though the standard deviation of damage is the same as that of the inter-structural disorder. We conclude that etch damage has little effect on the overall optical response of the system compared to disorder. The effect of parylene coating was investigated by the finite element method (COMSOL™) which was used for the simulation of Fig. 2. (a) Calculated far-field reflected intensities of a ridged structure with regular layers. (b) Corresponding data for a ridged structure with regular layers coated by parylene.

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Refractive index of parylene is 1.639. Total thickness of film is 4 μm obtained from the SEM image of Fig. 5a. (c) Corresponding data for a ridged structure with irregular layers, whose vertical disorder is 46 nm to 20 nm from bottom to top layer. (d) Corresponding data for a ridged structure with irregular layers coated by parylene. A schematic of the corresponding structure together with reflection property is given on top.
By parylene coating, some enhancement of normal reflection is observed due to specular reflection on the boundary of air and parylene as indicated in the schematic of (b). But, two positive effects for broad-angle blue reflection are also confirmed. First, diffraction peaks of longer wavelength region are suppressed by internal reflection as indicated in a schematic of (b). Second, the reflection angle is slightly broadened due to refraction as indicated in a schematic of (d).  The two responses are similar with only minor differences. We conclude from this, that when averaging the incoherent response of 200 such structures, we get a good approximation of the result which could be obtained by full simulations of the same number of large simulation domains.

Supplementary Video
This video shows the parylene-deposited Morpho-inspired structure shown in Figure 5, being shaken in liquid nitrogen. The film is robust enough to be repeatedly folded in liquid nitrogen without suffering visible damage.