Analysis of the optical response of reptile tissues in the visible and UV applying the KKR method.

Structural colors in nature are frequently produced by the ordered arrangement of nanoparticles. Interesting examples include reptiles and birds utilizing lattice-like formation of nanoparticles to produce a variety of colors. A famous example is the panther chameleon which is even able to change its color by actively varying the distance between guanine nanocrystals in its skin. Here, we demonstrate that the application of rigorous electromagnetic methods is important to determine the actual optical response of such biological systems. By applying the Korringa-Kohn-Rostoker (KKR) method we calculate the efficiencies of the reflected diffraction orders that can be viewed from directions other than the specular. Our results reveal that important characteristics of the reflectance spectra, especially within the ultraviolet (UV) and short visible wavelengths region, cannot be predicted by approximate models like the often-applied Maxwell-Garnett approach. Additionally, we show that the KKR method can be employed for the design of multi-layer structures with a desired optical response in the UV regime.

Electromagnetic response of corrugated multilayer systems inspired by the Dione vanillae butterfly scales.

Inspired by the microstructures in the wing scales of the butterfly Dione vanillae, we investigate the optical response of two multilayer structures, which include one or two corrugated interfaces. The reflectance is calculated using the C-method and is compared with that of a planar multilayer. We perform a detailed analysis of the influence of each geometric parameter and study the angular response, which is important for structures exhibiting iridescence. The results of this study aim to contribute to the design of multilayer structures with predetermined optical responses.

Analysis of the optical properties of the silvery spots on the wings of the Gulf Fritillary, Dione vanillae.

The ventral face of the wings of the butterfly Dione vanillae is covered with bright and shiny silvery spots. These areas contain densely packed ground- and coverscales with a bright metallic appearance reflecting more than 50% of light uniformly over the visible range. Our analysis shows that this optically attractive feature is caused by the inner microstructure of the scales located in these areas. Electron microscopy of cross sections through the scales shows that upper and lower lamina, supporting trabeculae, and topping ridges can be approximated by a 'circus tent'-like geometry. By simulating its optical properties, we show that a moderate disorder of this geometry is important for the uniform reflection of light resulting in the silvery appearance.

Mechanisms involved in the production of differently colored feathers in the structurally colored swallow tanager (Tersina viridis; Aves: Thraupidae).

Non-iridescent, structural coloration in birds originates from the feather's internal nanostructure (the spongy matrix) but melanin pigments and the barb's cortex can affect the resulting color. Here, we explore how this nanostructure is combined with other elements in differently colored plumage patches within a bird. We investigated the association between light reflectance and the morphology of feathers from the back and belly plumage patches of male swallow tanagers (Tersina viridis), which look greenish-blue and white, respectively. Both plumage patches have a reflectance peak around 550 nm but the reflectance spectrum is much less saturated in the belly. The barbs of both types of feathers have similar spongy matrices at their tips, rendering their reflectance spectra alike. However, the color of the belly feather barbs changes from light green at their tips to white closer to the rachis. These barbs lack pigments and their morphology changes considerably throughout. Toward the rachis, the barb is almost hollow, with a reduced area occupied by spongy matrix, and has a flattened shape. By contrast, the blue back feathers' barbs have melanin underneath the spongy matrix resulting in a much more saturated coloration. The color of these barbs is also even along the barbs' length. Our results suggest that the color differences between the white and greenish-blue plumage are mostly due to the differential deposition of melanin and a reduction of the spongy matrix near the rachis of the belly feather barbs and not a result of changes in the characteristics of the spongy matrix.

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 $ß-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.

Optical function of the finite-thickness corrugated pellicle of euglenoids.

We explore the electromagnetic response of the pellicle of selected species of euglenoids. These microorganisms are bounded by a typical surface pellicle formed by S-shaped overlapping bands that resemble a corrugated film. We investigate the role played by this structure in the protection of the cell against UV radiation. By considering the pellicle as a periodically corrugated film of finite thickness, we applied the C-method to compute the reflectance spectra. The far-field results revealed reflectance peaks with a Q-factor larger than 103 in the UV region for all the illumination conditions investigated. The resonant behavior responsible for this enhancement has also been illustrated by near-field computations performed by a photonic simulation method. These results confirm that the corrugated pellicle of euglenoids shields the cell from harmful UV radiation and open up new possibilities for the design of highly UV-reflective surfaces.

Determination of the spectral-dependent refractive index of a single layer in a natural multilayer system: comparison of different approaches.

By means of heuristic optimization techniques, we estimate the unknown refractive index of one layer of a periodic natural multilayer system from far-field reflectance data. To take into account the dispersive characteristics of the material, we employ two different strategies. The first is based on the retrieval of Lorentz model-related parameters, to describe the unknown dielectric permittivity within a specific spectral range. The second strategy, based on a wavelength-by-wavelength approach, takes into account the reflectance values for each wavelength at a time. Through some examples, we compare the performance of both strategies when they look for the best estimates and analyze the error involved in each case. The applicability of both approaches to the case of noisy reflectance spectra is also explored.

Characterization of the iridescence-causing multilayer structure of the Ceroglossus suturalis beetle using bio-inspired optimization strategies.

We investigate the iridescence exhibited by Ceroglossus suturalis beetles, which mostly live endemically in the southern end of South America. Two differently colored specimens have been studied. We observed and characterized the samples by different microscopy techniques, which revealed a multilayer structure within their cuticle. Using measured reflectance spectra as input data, we applied heuristic optimization techniques to estimate the refractive index values of the constituent materials, to be introduced within the theoretical model. The color of the samples was calculated for different incidence angles, showing that multilayer interference is the mechanism responsible for the observed iridescence.

Autofluorescence and ultrastructure in the Myxomycete Diachea leucopodia (Physarales).

Autofluorescence is reported for the first time in Myxomycete fruiting bodies. Ultrastructure of stalked sporangia of Diachea leucopodia (Didymiaceae, Physarales) was studied using scanning and transmission electron microscopy, energy-dispersive X-ray microanalysis, and fluorescence microscopy. External and internal properties of the peridium that surround the spores and capillitium exhibit autofluorescence. The stalk is composed of calcareous granules and energy-dispersive X-ray microanalysis demonstrates that the elemental composition of the peridium, capillitium, and stalk has varying concentrations of calcium.

Retrieval of relevant parameters of natural multilayer systems by means of bio-inspired optimization strategies.

Natural photonic structures exhibit remarkable color effects such as metallic appearance and iridescence. A rigorous study of the electromagnetic response of such complex structures requires to accurately determine some of their relevant optical parameters, such as the refractive indices of the materials involved. In this paper, we apply different heuristic optimization strategies to retrieve the real and imaginary parts of the refractive index of the materials comprising natural multilayer systems. Through some examples, we compare the performances of the inversion methods proposed and show that these kinds of algorithms have a great potential as a tool to investigate natural photonic structures.

Photonic simulation method applied to the study of structural color in Myxomycetes.

We present a novel simulation method to investigate the multicolored effect of the Diachea leucopoda (Physarales order, Myxomycetes class), which is a microorganism that has a characteristic pointillistic iridescent appearance. It was shown that this appearance is of structural origin, and is produced within the peridium -protective layer that encloses the mass of spores-, which is basically a corrugated sheet of a transparent material. The main characteristics of the observed color were explained in terms of interference effects using a simple model of homogeneous planar slab. In this paper we apply a novel simulation method to investigate the electromagnetic response of such structure in more detail, i.e., taking into account the inhomogeneities of the biological material within the peridium and its curvature. We show that both features, which could not be considered within the simplified model, affect the observed color. The proposed method is of great potential for the study of biological structures, which present a high degree of complexity in the geometrical shapes as well as in the materials involved.

Structural color in Myxomycetes.

In this paper we report evidence of structural color in Myxomycetes, a group of eukaryotic microorganisms with an uncertain taxonomic position. We investigated the Diachea leucopoda, which belongs to the Physarales order, Myxomycetes class, and found that its peridium -protective layer that encloses the mass of spores- is basically a corrugated layer of a transparent material, which produces a multicolored pointillistic effect, characteristic of this species. Scanning (SEM) and transmission (TEM) electron microscopy techniques have been employed to characterize the samples. A simple optical model of a planar slab is proposed to calculate the reflectance. The chromaticity coordinates are obtained, and the results confirm that the color observed is a result of an interference effect.

Classification of dispersion equations for homogeneous, dielectric-magnetic, uniaxial materials.

The geometric representation at a fixed frequency of the wave vector (or dispersion) surface omega(k) for lossless, homogeneous, dielectric-magnetic uniaxial materials is explored for the case when the elements of the relative permittivity and permeability tensors of the material can have any sign. Electromagnetic plane waves propagating inside the material can exhibit dispersion surfaces in the form of ellipsoids of revolution, hyperboloids of one sheet, or hyperboloids of two sheets. Furthermore, depending on the relative orientation of the optic axis, the intersections of these surfaces with fixed planes of propagation can be circles, ellipses, hyperbolas, or straight lines. The understanding obtained is used to study the reflection and refraction of electromagnetic plane waves due to a planar interface with an isotropic medium.

Polarization conversion from highly conducting, asymmetric trapezoidal gratings.

The differences in the curves of the zeroth-order cross-polarization reflection coeffients (p --> s and s --> p) versus angle of incidence have remarkable potential for application in scatterometry because, if the differences are larger than the measurement error, they could contribute to a reliable nondestructive technique for detecting asymmetries in grating profiles. The cross-polarization efficiencies of highly conducting metallic gratings with asymmetric trapezoidal profiles are investigated theoretically by means of a rigorous electromagnetic code. The results show that the differences between p --> s and s --> p conversion tend to be undetectable for highly conducting materials, a fact that limits, in principle, the application of this potential detection technique.