Contribution of double scattering to structural coloration in quasiordered nanostructures of bird feathers

Enhancing color saturation in photonic glasses through optimized absorption

Photonic glasses, isotropically assembled nanoparticles with short-range correlation, can produce angle independent structural colors. They show broader reflectance spectra and lower saturated colors, compared to photonic crystals. Low color saturation creates barriers for photonic glasses to be used for coatings, cosmetics, and colors. Broadband absorbing materials are commonly used to absorb incoherently scattered light to enhance the saturation. However, there is limited understanding on how the absorption quantitatively affects the colors of photonic glasses. To this end, we here use a validated Monte Carlo-based multiple scattering model to investigate how absorption impacts the reflectance spectra in photonic glasses. We show that the color saturation can be maximized with an optimal level of absorption regardless of sample thickness or refractive index contrast between particles and matrix. We quantitatively demonstrate that the multiple scattering is largely reduced with the optimal absorption level and the reflectance is dominantly contributed by the single scattering. The optimal absorption occurs when the sample absorption mean free path is comparable to the transport mean free path, which offers a guidance on how much absorbing material is needed for creating highly saturated photonic glasses. This work will not only pave ways for pushing applications of angle-independent structural colors, but also improve our understanding of light scattering and absorption in short-range correlated disordered systems.

A bioinspired, electroactive colorable and additive manufactured photonic artificial muscle

Structural coloration in biomimetic nanostructures has remarkable application potential in vivid display devices, but their color change effect is still insufficiently competitive towards biology. Inspired by the feather color change of a hummingbird, a new methodology for coloration is proposed. A structure-colorable flexural artificial muscle (FlexAM) is developed by integrating a view-angle dependent photonic diffraction grating pattern and voltage-actuated dielectric elastomers as an electroactive entity via laminated object additive manufacturing. A multi-physics model is developed which guides the FlexAM to harness the view-angle dependence for the new coloration strategy. The electro-mechanochromic performances are experimentally characterized to verify the prediction of the multi-physics model. An ultrafast coloration in the FlexAM with an advancing figure-of-merit at a color-shift rate of 2.814 nm ms^-1 is realized, in addition to an excellent fatigue resistance up to 10 000 cycles. A photonic display with arrayed FlexAM elements is designed, which can be used to display numbers and letters. The current research offers an advanced artificial muscle towards active photonic and visible strain sensing.

A synergistic combination of structural and pigmentary colour produces non-spectral colour in the purple-breasted cotinga, Cotinga cotinga (Passeriformes: Cotingidae)

Most studies of animal coloration focus on spectral colours, which are colours evoked by single peaks within the wavelengths of visible light. It is poorly understood how non-spectral colours (those produced by a combination of reflectance peaks) are produced, despite their potential significance to both animal communication and biomimicry. Moreover, although both pigmentary and structural colour production mechanisms have been well characterized in feathers independently, their interactions have received considerably less attention, despite their potential to broaden the available colour spectrum. Here, we investigate the colour production mechanisms of the purple feathers of the purple-breasted cotinga (Cotinga cotinga). The purple feather colour results from both the coherent scattering of light by a sphere-type nanomatrix of β-keratin and air (spongy layer) in the barbs, which produces a blue–green colour, and the selective absorption of light in the centre of the bird-visible spectrum by the methoxy-carotenoid, cotingin. This unusual combination of carotenoid and nanostructure with a central air vacuole, in the absence of melanin, is a blueprint of a synergistic way to produce a non-spectral colour that would be difficult to achieve with only a single colour production mechanism.

Theoretical approaches to study the optical response of the red-legged honeycreeper's plumage (Cyanerpes cyaneus)

In this paper, we investigate the unusual color effect exhibited by the plumage of the heads of Cyanerpes cyaneus males, whose color turns from green to turquoise as the angle between the illumination and observation directions is increased. This singular color effect is characteristic of species that have quasi-ordered nanostructures of short-range order within the feather barbs. However, among species of the same family and even within feather patches of the same individual, one can find barbs with different characteristics, both macroscopic (curvature, shape, cross-sectional area) and in their internal microstructure. We apply the Korringa-Kohn-Rostoker method with the averaging technique to model the reflectance spectra for different angles of incidence and explain the dependence of the observed color with the incidence-collection angle. To investigate the influence of the disorder in the optical response of the spongy matrix, we apply the integral method for a two-dimensional cylinder system that simulates the distribution of air cavities within the $ \beta $β-keratin medium. The experimental reflectance was interpreted as the result of multiple reflections in the internal interfaces generated by large air voids present within the spongy matrix. The application of rigorous methods to the study of natural photonic structures is of fundamental relevance for the design of efficient bioinspired artificial materials.

Effects of multiple scattering on angle-independent structural color in disordered colloidal materials

Disordered packings of colloidal spheres show angle-independent structural color when the particles are on the scale of the wavelength of visible light. Previous work has shown that the positions of the peaks in the reflectance spectra can be predicted accurately from a single-scattering model that accounts for the effective refractive index of the material. This agreement shows that the main color peak arises from short-range correlations between particles. However, the single-scattering model does not quantitatively reproduce the observed color: the main peak in the reflectance spectrum is much broader and the reflectance at low wavelengths is much larger than predicted by the model. We use a combination of experiment and theory to understand these features. We find that one significant contribution to the breadth of the main peak is light that is scattered, totally internally reflected from the boundary of the sample, and then scattered again. The high reflectance at low wavelengths also results from multiple scattering but can be traced to the increase in the scattering cross section of individual particles with decreasing wavelength. Both of these effects tend to reduce the saturation of the structural color, which limits the use of these materials in applications. We show that while the single-scattering model cannot reproduce the observed saturations, it can be used as a design tool to reduce the amount of multiple scattering and increase the color saturation of materials, even in the absence of absorbing components.

Quantitative characterization of iridescent colours in biological studies: a novel method using optical theory

Iridescent colours are colours that change with viewing or illumination geometry. While they are widespread in many living organisms, most evolutionary studies on iridescence do not take into account their full complexity. Few studies try to precisely characterize what makes iridescent colours special: their angular dependency. Yet, it is likely that this angular dependency has biological functions and is therefore submitted to evolutionary pressures. For this reason, evolutionary biologists need a repeatable method to measure iridescent colours as well as variables to precisely quantify the angular dependency. In this study, we use a theoretical approach to propose five variables that allow one to fully describe iridescent colours at every angle combination. Based on the results, we propose a new measurement protocol and statistical method to reliably characterize iridescence while minimizing the required number of time-consuming measurements. We use hummingbird iridescent feathers and butterfly iridescent wings as test cases to demonstrate the strengths of this new method. We show that our method is precise enough to be potentially used at intraspecific level while being also time-efficient enough to encompass large taxonomic scales.

Spatially modulated structural colour in bird feathers

Eurasian Jay (Garrulus glandarius) feathers display periodic variations in the reflected colour from white through light blue, dark blue and black. We find the structures responsible for the colour are continuous in their size and spatially controlled by the degree of spinodal phase separation in the corresponding region of the feather barb. Blue structures have a well-defined broadband ultra-violet (UV) to blue wavelength distribution; the corresponding nanostructure has characteristic spinodal morphology with a lengthscale of order 150 nm. White regions have a larger 200 nm nanostructure, consistent with a spinodal process that has coarsened further, yielding broader wavelength white reflectance. Our analysis shows that nanostructure in single bird feather barbs can be varied continuously by controlling the time the keratin network is allowed to phase separate before mobility in the system is arrested. Dynamic scaling analysis of the single barb scattering data implies that the phase separation arrest mechanism is rapid and also distinct from the spinodal phase separation mechanism i.e. it is not gelation or intermolecular re-association. Any growing lengthscale using this spinodal phase separation approach must first traverse the UV and blue wavelength regions, growing the structure by coarsening, resulting in a broad distribution of domain sizes.

Cryptic iridescence in a fossil weevil generated by single diamond photonic crystals

Nature's most spectacular colours originate in integumentary tissue architectures that scatter light via nanoscale modulations of the refractive index. The most intricate biophotonic nanostructures are three-dimensional crystals with opal, single diamond or single gyroid lattices. Despite intense interest in their optical and structural properties, the evolution of such nanostructures is poorly understood, due in part to a lack of data from the fossil record. Here, we report preservation of single diamond (Fd-3m) three-dimensional photonic crystals in scales of a 735,000 year old specimen of the brown Nearctic weevil Hypera diversipunctata from Gold Run, Canada, and in extant conspecifics. The preserved red to green structural colours exhibit near-field brilliancy yet are inconspicuous from afar; they most likely had cryptic functions in substrate matching. The discovery of pristine fossil examples indicates that the fossil record is likely to yield further data on the evolution of three-dimensional photonic nanostructures and their biological functions.

Absence of red structural color in photonic glasses, bird feathers, and certain beetles

Colloidal glasses, bird feathers, and beetle scales can all show structural colors arising from short-ranged spatial correlations between scattering centers. Unlike the structural colors arising from Bragg diffraction in ordered materials like opals, the colors of these photonic glasses are independent of orientation, owing to their disordered, isotropic microstructures. However, there are few examples of photonic glasses with angle-independent red colors in nature, and colloidal glasses with particle sizes chosen to yield structural colors in the red show weak color saturation. Using scattering theory, we show that the absence of angle-independent red color can be explained by the tendency of individual particles to backscatter light more strongly in the blue. We discuss how the backscattering resonances of individual particles arise from cavity-like modes and how they interact with the structural resonances to prevent red. Finally, we use the model to develop design rules for colloidal glasses with red, angle-independent structural colors.

Structurally coloured secondary particles composed of black and white colloidal particles

This study investigated the colourful secondary particles formed by controlling the aggregation states of colloidal silica particles and the enhancement of the structural colouration of the secondary particles caused by adding black particles. We obtained glossy, partially structurally coloured secondary particles in the absence of NaCl, but matte, whitish secondary particles were obtained in the presence of NaCl. When a small amount of carbon black was incorporated into both types of secondary particles, the incoherent multiple scattering of light from the amorphous region was considerably reduced. However, the peak intensities in the reflection spectra, caused by Bragg reflection and by coherent single wavelength scattering, were only slightly decreased. Consequently, a brighter structural colour of these secondary particles was observed with the naked eye. Furthermore, when magnetite was added as a black particle, the coloured secondary particles could be moved and collected by applying an external magnetic field.

Structure and optical function of amorphous photonic nanostructures from avian feather barbs: a comparative small angle X-ray scattering (SAXS) analysis of 230 bird species

Non-iridescent structural colours of feathers are a diverse and an important part of the phenotype of many birds. These colours are generally produced by three-dimensional, amorphous (or quasi-ordered) spongy β-keratin and air nanostructures found in the medullary cells of feather barbs. Two main classes of three-dimensional barb nanostructures are known, characterized by a tortuous network of air channels or a close packing of spheroidal air cavities. Using synchrotron small angle X-ray scattering (SAXS) and optical spectrophotometry, we characterized the nanostructure and optical function of 297 distinctly coloured feathers from 230 species belonging to 163 genera in 51 avian families. The SAXS data provided quantitative diagnoses of the channel- and sphere-type nanostructures, and confirmed the presence of a predominant, isotropic length scale of variation in refractive index that produces strong reinforcement of a narrow band of scattered wavelengths. The SAXS structural data identified a new class of rudimentary or weakly nanostructured feathers responsible for slate-grey, and blue-grey structural colours. SAXS structural data provided good predictions of the single-scattering peak of the optical reflectance of the feathers. The SAXS structural measurements of channel- and sphere-type nanostructures are also similar to experimental scattering data from synthetic soft matter systems that self-assemble by phase separation. These results further support the hypothesis that colour-producing protein and air nanostructures in feather barbs are probably self-assembled by arrested phase separation of polymerizing β-keratin from the cytoplasm of medullary cells. Such avian amorphous photonic nanostructures with isotropic optical properties may provide biomimetic inspiration for photonic technology.

Direct determination of the refractive index of natural multilayer systems

It is well known that the metal-like strong reflection observed in the elytra of some kinds of beetles is produced by multilayer thin-film interference. For the quantitative analyses of the structural colors in these elytra, it is necessary to know accurate values of the refractive indices of the materials that comprise the multilayer structure. However, index determination is not an easy task: The elytron surface is not flat but curved and usually contains many irregular bumps, which cause scattering loss. These structural characteristics prevent us from directly applying conventional optical techniques for index determination, such as ellipsometry, since these techniques require a perfectly specular surface. In this paper, we report a new experimental procedure that can directly determine the refractive indices of individual layers in natural multilayer systems. This procedure involves semi-frontal thin-sectioning of the sample and subsequent optical examinations using a microspectrophotometer. We demonstrate that the complex refractive index and its wavelength dependence can be successfully determined for one kind of beetle.

Short-range order and near-field effects on optical scattering and structural coloration

We have investigated wavelength-dependent light scattering in biomimetic structures with short-range order. Coherent backscattering experiments are performed to measure the transport mean free path over a wide wavelength range. Overall scattering strength is reduced significantly due to short-range order and near-field effects. Our analysis explains why single scattering of light is dominant over multiple scattering in similar biological structures and is responsible for color generation.