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.

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.

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.

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.

Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane: comment.

We show that the problem of scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane, which was recently studied by Basha et al. [J. Opt. Soc. Am. A24, 1647 (2007)], was solved 11 years ago using the same formulation. This method was further extended to deal with a finite number of grooves and also with complex apertures including several nonlossy and lossy dielectrics, as well as real metals.

Control of the diffracted response of wire arrays with double periods.

The possibility of controlling the diffracted response of a periodic structure is investigated by using dual-period arrays, i.e., periodic arrays with a compound unit cell. We consider wire gratings in which each period comprises several cylinders with circular cross sections and all the cylinder axes are contained in the same plane. It is shown that this kind of structure permits one to control the diffracted response, regardless of the cylinder material and the incident polarization. Our numerical results suggest that the effect produced by wire gratings with dual-period characteristics is basically a geometric effect, and it can be present for other shapes of individual scatterers within each subarray.

Bandwidth control of forbidden transmission gaps in compound structures with subwavelength slits.

Phase resonances in transmission compound structures with subwavelength slits produce sharp dips in the transmission response. For all equal slits, the wavelengths of these sharp transmission minima can be varied by changing the width or the length of all the slits. In this paper we show that the width of the dip, i.e., the frequency range of minimum transmittance, can be controlled by making at least one slit different from the rest within a compound unit cell. In particular, we investigate the effect that a change in the dielectric filling, or in the length of a single slit, produces in the transmission response. We also analyze the scan angle behavior of these structures by means of band diagrams and compare them with previous results for all-equal slit structures.

Diffraction by dual-period gratings.

The dynamical characteristics of dual-period perfectly conducting gratings are explored. Gratings with several grooves (reflection) or slits (transmission) within each period are considered. A scalar approach is proposed to derive the general characteristics of the diffracted response. It was found that compound gratings can be designed to cancel as well as to intensify a given diffraction order. These preliminary estimations for finite gratings are validated by numerical examples for infinitely periodic reflection and transmission gratings with finite thickness, performed using an extension of the rigorous modal method to compound gratings, for both polarization cases.

Diffraction by fractal metallic supergratings.

The reflectance of corrugated surfaces with a fractal distribution of grooves is investigated. Triadic and polyadic Cantor fractal distributions are considered, and the reflected intensity is compared with that of the corresponding periodic structure. The self-similarity property of the response is analyzed when varying the depth of the grooves and the lacunarity parameter. The results confirm that the response is self-similar for the whole range of depths considered, and this property is also maintained for all values of the lacunarity parameter.

Narrow gaps for transmission through metallic structured gratings with subwavelength slits.

Transmission dips in the response of metallic compound gratings formed by several wires and slits in each period have been recently reported for normal illumination. These anomalies are generated by a particular arrangement of the magnetic field phases inside the subwavelength slits, and they are characterized by a significant enhancement of the interior field. We investigate the microwave response of such systems under non-normal illumination and show that new phase modes appear in this configuration. Contrary to the effect produced by a defect in a photonic crystal, these systems exhibit forbidden channels within a permitted band. We also found that the appearance of these resonances is not highly dependent on the slits' width and thickness, even though these parameters modify the overall transmittance.

Transmission resonances of metallic compound gratings with subwavelength slits.

Transmission metallic gratings with subwavelength slits are known to produce enhanced transmitted intensity for certain resonant wavelengths. One of the mechanisms that produce these resonances is the excitation of waveguide modes inside the slits. We show that by adding slits to the period, the transmission maxima are widened and, simultaneously, this generates phase resonances that appear as sharp dips in the transmission response. These resonances are characterized by a significant enhancement of the interior field.

Resonant effects in compound diffraction gratings: Influence of the geometrical parameters of the surface.

We explore and discuss the influence of the geometrical parameters of a compound diffraction grating on the generation of pi resonances, which appear when the surface is illuminated by a p-polarized plane wave. We consider a grating with rectangular grooves, and analyze the evolution of pi resonances when depth, width, distance between grooves, and period of the grating are varied. In particular, we performed a detailed study for a grating with five grooves per period, and found that there are certain values of the geometrical parameters that optimize the enhancement of the electromagnetic field inside the corrugations. For an increasing depth of the grating, the resonant frequency verges on the value that corresponds to a finite grating. We also show numerical examples of the amplitude and phase of the electromagnetic field, where the differences in the near field for resonant and nonresonant configurations become apparent.