The gyroid is a continuous and triply periodic cubic morphology which possesses a constant mean curvature surface across a range of volumetric fi ll fractions. Found in a variety of natural and synthetic systems which form through self-assembly, from butterfl y wing scales to block copolymers, the gyroid also exhibits an inherent chirality not observed in any other similar morphologies. These unique geometrical properties impart to gyroid structured materials a host of interesting optical properties. Depending on the length scale on which the constituent materials are organised, these properties arise from starkly different physical mechanisms (such as a complete photonic bandgap for photonic crystals and a greatly depressed plasma frequency for optical metamaterials). This article reviews the theoretical predictions and experimental observations of the optical properties of two fundamental classes of gyroid structured materials: photonic crystals (wavelength scale) and metamaterials (sub-wavelength scale).

Using Jamin-Lebedeff interference microscopy, we measured the wavelength dependence of the refractive index of butterfly wing scales and bird feathers. The refractive index values of the glass scales of the butterfly Graphium sarpedon are, at wavelengths 400, 500 and 600 nm, 1.572, 1.552 and 1.541, and those of the feather barbules of the white goose Anas anas domestica are 1.569, 1.556 and 1.548, respectively. The dispersion spectra of the chitin in the butterfly scales and the keratin in the bird barbules are well described by the Cauchy equation n(λ) = A + B/λ(2), with A = 1.517 and B = 8.80·10(3) nm(2) for the butterfly chitin and A = 1.532 and B = 5.89·10(3) nm(2) for the bird keratin.

The elytra of the Japanese jewel beetle Chrysochroa fulgidissima are metallic green with purple stripes. Scanning electron microscopy and atomic force microscopy demonstrated that the elytral surface is approximately flat. The accordingly specular green and purple areas have, with normal illumination, 100 -150 nm broad reflectance bands, peaking at about 530 and 700 nm. The bands shift progressively towards shorter wavelengths with increasing oblique illumination, and the reflection then becomes highly polarized. Transmission electron microscopy revealed that the epicuticle of the green and purple areas consists of stacks of 16 and 12 layers, respectively. Assuming gradient refractive index values of the layers between 1.6 and 1.7 and applying the classical multilayer theory allowed modelling of the measured polarization-and angle-dependent reflectance spectra. The extreme polarized iridescence exhibited by the elytra of the jewel beetle may have a function in intraspecific recognition.

Whiteness arises from the random scattering of incident light from disordered structures. [1] Opaque white materials have to contain a sufficiently large number of scatterers and therefore usually require thicker, material-rich nanostructures than structural color arising from the coherent interference of light. [2,3] In nature, bright white appearance arises from the dense arrays of pterin pigments in pierid butterflies, [4] guanine crystals in spiders, [5] or leucophore cells in the flexible skin of cuttlefish. [6] A striking example of such whiteness is found in the chitinous networks of white beetles, e.g., Lepidiota stigma and Cyphochilus sp. [7][8][9] Previous research investigating these beetle structures has shown that the chitinous network is one of the most strongly scattering materials in nature, and therefore the question arises whether this structure is evolutionary optimized for strong scattering while minimizing the Most studies of structural color in nature concern periodic arrays, which through the interference of light create color. The "color" white however relies on the multiple scattering of light within a randomly structured medium, which randomizes the direction and phase of incident light. Opaque white materials therefore must be much thicker than periodic structures. It is known that flying insects create "white" in extremely thin layers. This raises the question, whether evolution has optimized the wing scale morphology for white reflection at a minimum material use. This hypothesis is difficult to prove, since this requires the detailed knowledge of the scattering morphology combined with a suitable theoretical model. Here, a cryoptychographic X-ray tomography method is employed to obtain a full 3D structural dataset of the network morphology within a white beetle wing scale. By digitally manipulating this 3D representation, this study demonstrates that this morphology indeed provides the highest white retroreflection at the minimum use of material, and hence weight for the organism. Changing any of the network parameters (within the parameter space accessible by biological materials) either increases the weight, increases the thickness, or reduces reflectivity, providing clear evidence for the evolutionary optimization of this morphology. amount of employed material, thus reducing the weight of the organism. The brilliant white reflection from Cyphochilus beetles is assumed to be important for camouflage among white fungi and in a shady environment.In contrast to periodic photonic materials, for which the optical response is straightforward to calculate, the reflection of light from such disordered network morphologies requires a detailed knowledge of local geometry. [2,3,9,10] For these complex cases, the validity of the diffusion approximation is limited, since single scattering elements are difficult to be identified. [7] To fully understand the correlation between the structure and (optical) properties of complex materials, the detailed real-space structure in combination with a s...

The coloration of the common butterflies Aglais urticae (small tortoiseshell), Aglais io (peacock) and Vanessa atalanta (red admiral), belonging to the butterfly subfamily Nymphalinae, is due to the species-specific patterning of differently coloured scales on their wings. We investigated the scales' structural and pigmentary properties by applying scanning electron microscopy, (micro)spectrophotometry and imaging scatterometry. The anatomy of the wing scales appears to be basically identical, with an approximately flat lower lamina connected by trabeculae to a highly structured upper lamina, which consists of an array of longitudinal, parallel ridges and transversal crossribs. Isolated scales observed at the abwing (upper) side are blue, yellow, orange, red, brown or black, depending on their pigmentation. The yellow, orange and red scales contain various amounts of 3-OH-kynurenine and ommochrome pigment, black scales contain a high density of melanin, and blue scales have a minor amount of melanin pigment. Observing the scales from their adwing (lower) side always revealed a structural colour, which is blue in the case of blue, red and black scales, but orange for orange scales. The structural colours are created by the lower lamina, which acts as an optical thin film. Its reflectance spectrum, crucially determined by the lamina thickness, appears to be well tuned to the scales' pigmentary spectrum. The colours observed locally on the wing are also due to the degree of scale stacking. Thin films, tuned pigments and combinations of stacked scales together determine the wing coloration of nymphaline butterflies.

High-resolution microscopy of hierarchically organized solid gyroid nanostructures sheds light on the underlying dynamic formation process.

include solar cells that make use of mesoporous TiO 2 electrodes to collect and transport the electronic charges generated in metal-organic dyes, fi rst demonstrated by O'Regan and Grätzel. [ 3 ] Since this fi rst pioneering work, the performance of dye-sensitized TiO 2 solar cells (DSSCs) improved mainly by the development of new pigments that more effectively absorb the solar light spectrum. [ 4,5 ] A recent breakthrough was the introduction of organicinorganic perovskites, which combine high light absorption with good charge transport. [6][7][8][9][10][11][12] The high perovskite conductivity enabled the exploration of new device architectures spanning from a perovskite-sensitized mesoporous TiO 2 to TiO 2 -free planar heterojunction solar cells. [ 13 ] Currently, the best performing perovskite-based solar cells (PSCs), with a certifi ed power conversion effi ciency of more than 20%, employ a thin mesoporous TiO 2 layer as electron selective contact in combination with a thick solid perovskite absorber over-layer. [ 2 ] Due to the favorable position of its conduction band (CB), a large band gap, long electron lifetimes and low fabrication costs, TiO 2 is frequently used to prepare mesoporous electrodes in several optoelectronic applications. [14][15][16][17] Nevertheless, the relatively high density of electronic trap states below the CB are a signifi cant drawback for the application of TiO 2 electrodes in solar cells. [ 18 ] Indeed, trap states may have a large infl uence on charge recombination and charge transport, which in turn infl uence the solar cell voltage and current. [19][20][21] One method to reduce the trap states in TiO 2 is doping. A wide range of doping elements have been investigated for mesoporous TiO 2 electrodes in DSSCs [ 17,[22][23][24][25][26][27] and more recently in PSCs. [28][29][30][31] Some dopants reduce the charge recombination [ 24 ] or increase electron transport in DSSCs [ 25 ] by reducing trap states below the CB. In addition to changes in the density of trap states, doping may induce a complex interplay of other effects that impact the device performance; for example, it can affect dye absorption or change the nanoparticle size and distribution and thereby the morphology of the mesostructured fi lm, leading to a changed TiO 2 -absorber interface area in DSSCs. [ 22 ] Furthermore, modifying the CB position by TiO 2 doping can either through a downward shift increase electron injection from the dye into the TiO 2 [ 26 ] or through an upward shift increase the open-circuit voltage ( V oc ). [ 27 ] These two effects however adversely affect each other. In PSCs, reduced recombination [ 28 ] and increased Block-copolymer templated chemical solution deposition is used to prepare mesoporous Nd-doped TiO 2 electrodes for perovskite-based solar cells. X-ray diffraction and photothermal defl ection spectroscopy show substitutional incorporation into the TiO 2 crystal lattice for low Nd concentration, and increasing interstitial doping for higher concentrations. Substitutional Nd-doping...

Male Lawes's Parotia, a bird of paradise, use the highly directional reflection of the structurally colored, brilliant-silvery occipital feathers in their courtship display. As in other birds, the structural coloration is produced by ordered melanin pigmentation. The barbules of the Parotia's occipital feathers, with thickness ,3 mm, contain 6-7 layers of densely packed melanin rodlets (diameter ,0.25 mm, length ,2 mm). The effectively ,0.2 mm thick melanin layers separated by ,0.2 mm thick keratin layers create a multilayer interference reflector. Reflectance measurements yielded peak wavelengths in the near-infrared at ,1.3 mm, i.e., far outside the visible wavelength range. With the Jamin-Lebedeff interference microscopy method recently developed for pigmented media, we here determined the refractive index of the intact barbules. We thus derived the wavelength dependence of the refractive index of the barbules' melanin to be 1.7-1.8 in the visible wavelength range. Implementing the anatomical and refractive index data in an optical multilayer model, we calculated the barbules' reflectance, transmittance and absorptance spectra, thereby confirming measured spectra. Keywords: bird of paradise; interference reflector; iridescence; Jamin-Lebedeff microscopy; multilayer INTRODUCTIONIn animal integuments melanins commonly produce dull red, brown and black colors. With nanoscale order, melanin in a matrix of vertebrate keratin or arthropod chitin can produce striking structural colors. [1][2][3][4] The magnificent displays of birds of paradise exemplify how the fine branches of the bird feathers, the barbules, are modified to achieve a diverse range of visual effects through structural coloration. In Lawes's Parotia (Parotia lawesii), the barbules of the males' breast feathers have a boomerang-shaped cross-section, which produces three directional-colored reflectors. 5 Here we investigate the male Parotia's occipital (or nape) feathers, which produce a shiny, silvery patch (Figure 1a and 1b). Compared to the breast feathers they are less colorful, but the barbules of the occipital feathers exhibit a mirror-like, directional reflection due to nanostructured melanin. 6 The uniquely colorful breast feathers allows the breast color to switch sharply between yellow, blue and black as the bird moves, during the ballerina dance, which is performed as part of the courtship display. [7][8][9] The shiny occipital feathers have a similar function. Recent behavioral observations on the closely related Wahnes's Parotia demonstrate that the occipital feather reflections are sharply directed to the observing females during part of the courtship performance, presumably to impress a potential mate, viewing from an elevated position on a tree branch. [6][7][8][9][10] To unravel the optical basis of the shiny occipital reflectors, we investigated the barbule anatomy. This revealed very regularly arranged melanosomes, i.e., small melanin rodlets, arranged in layers. To achieve an in-depth, quantitative understanding of the feathers'