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.

Rayleigh method adapted for the study of the optical response of natural photonic structures.

To study the electromagnetic response of natural structures that exhibit interesting optical properties, we developed a computational tool to solve the problem of electromagnetic scattering by a rough interface between two isotropic media, based on the Rayleigh method. The key aspect of the developed formalism is its capability of introducing the interface profile within the code by means of a digitalized image of the structure, which can be either obtained from an electron microscopy image or simply by design according to the complexity of the scattering surface. As application examples, we show the results obtained for surfaces taken directly from microscopy images of two different biological species. This approach constitutes a fundamental step in order to model the electromagnetic response of natural photonic structures.

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.

Influence of finite conductivity on the excitation of phase resonances in metallic surfaces with cavities of circular cross sections.

Phase resonances have been investigated in the last few years, not only because of their striking features, such as extremely high quality factor and huge enhancement of the electromagnetic field inside cavities/grooves, but also for their promising applications. However, taking into account that these resonances are more efficiently excited in highly conducting structures, most of the studies have been devoted to explore this phenomenon at wavelengths in the infrared or larger, using different approaches for the boundary conditions. In this paper, we investigate the validity of the perfect conductor approximation and the surface impedance boundary condition to appropriately represent the electromagnetic response of a metallic surface comprising a finite number of subwavelength cavities of circular cross sections. Far- and near-field plots are shown and analyzed in order to investigate the validity ranges and discuss to what extent phase resonances can be excited at shorter wavelengths in these structures.

Refraction index sensor based on phase resonances in a subwavelength structure with double period.

In this paper, we numerically demonstrate a refraction index sensor based on phase resonance excitation in a subwavelength-slit structure with a double period. The sensor consists of a metal layer with subwavelength slots arranged in a bi-periodic form, separated from a high refraction index medium. Between the metallic structure and the incident medium, a dielectric waveguide is formed whose refraction index is going to be determined. Variations in the refraction index of the waveguide are detected as shifts in the peaks of transmitted intensity originated by resonant modes supported by the compound metallic structure. At normal incidence, the spectral position of these resonant peaks exhibits a linear or a quadratic dependence with the refraction index, which permits us to obtain the unknown refraction index value with a high precision for a wide range of wavelengths. Since the operating principle of the sensor is due to the morphological resonances of the slits' structure, this device can be scaled to operate in different wavelength ranges while keeping similar characteristics.

Phase resonances induced by a subwavelength particle near a surface with two cavities.

It is well known that finite groove gratings with subwavelength features exhibit phase resonances, which are associated with a particular distribution of the magnetic field phase within the cavities and are characterized by a significant enhancement of the internal field. For a flat surface with identical grooves under symmetrical conditions of incidence, it was shown that a minimum of three cavities is required to excite a phase resonance. In this paper we show that by approaching a particle to the surface, this requirement is removed and the particle enables the excitation of phase resonances even in a system of two identical cavities under normal incidence. The influence of the position and the radius of the particle in the reflected far field response, as well as in the near and internal field, is analyzed. The possibility of exciting phase resonances in this system opens up new means for the design of sensing devices.

Enhanced method for determining the optical response of highly complex biological photonic structures.

We present a set of techniques that enhances a previously developed time domain simulation of wave propagation and allows the study of the optical response of a broad range of dielectric photonic structures. This method is particularly suitable for dealing with complex biological structures, especially due to the simple and intuitive way of defining the setup and the photonic structure to be simulated, which can be done via a digital image of the structure. The presented techniques include a direction filter that permits the decoupling of waves traveling simultaneously in different directions, a dynamic differential absorber to cancel the waves reflected at the edges of the simulation space, and a multifrequency excitation scheme. We also show how the simulation can be adapted to apply a near to far field method in order to evaluate the resulting wavefield outside the simulation domain. We validate these techniques, and, as an example, we apply the method to the complex structure of a microorganism called Diachea leucopoda, which exhibits a multicolor iridescent appearance.

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.

Millimeter-wave phase resonances in compound reflection gratings with subwavelength grooves.

Experimental evidence of phase resonances in a dual-period reflection structure comprising three subwavelength grooves in each period is provided in the millimeter-wave regime. We have analyzed and measured the response of these structures and show that phase resonances are characterized by a minimum in the reflected response, as predicted by numerical calculations. It is also shown that under oblique incidence these structures exhibit additional phase resonances not present for normal illumination because of the potentially permitted odd field distribution. A satisfactory agreement between the experimental and numerical reflectance curves is obtained. These results confirm the recent theoretical predictions of phase resonances in reflection gratings in the millimeter-wave regime, and encourage research in this subject due to the multiple potential applications, such as frequency selective surfaces, backscattering reduction and complex-surface-wave-based sensing. In addition, it is underlined here that the response becomes much more complex than the mere infinite analysis when one considers finite periodic structures as in the real experiment.

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.

Anomalous reflection in a metallic plate with subwavelength grooves of circular cross section.

Resonant features in the response of finite arrays of rectangular grooves ruled on a metallic plate have been reported in connection with the excitation of phase resonances. These anomalies are generated by a particular arrangement of the magnetic field phases inside the subwavelength grooves when the structure is illuminated by a p-polarized electromagnetic wave. We show that this kind of resonance is also present for grooves of circular cross section and appear as sharp peaks in the specular response, the number of which increases with the number of grooves in the structure. A significant intensification of the field within the grooves is also found for these particular phase configurations. The dependence of the response on the geometrical parameters of the structure is analyzed in detail, in order to consider these structures for potential applications such as frequency selectors and polarizers.