Marina E. Inchaussandague

CORRUGATED DIFFRACTION GRATINGS IN UNIAXIAL CRYSTALS

We present a rigorous electromagnetic approach to wave diffraction by corrugated gratings made of uniaxial crystals. The optic axis of the anisotropic medium is assumed to lie on the mean surface of the grating, inclined at an arbitrary angle with respect to the grooves. The diffraction problem is exactly analyzed as a two-medium boundary-value problem. We simplify the fully vectorial treatment by first writing the fields everywhere in terms of the components of the electric and magnetic fields along the groove direction. Then a coordinate transformation mapping the corrugated interface into a plane is used, and the transformed propagation equations are solved by means of a differential method. The theory is exemplified numerically for the case of gratings made of sodium nitrate, and the results are compared against those obtained with a simplified formalism invoking the Rayleigh hypothesis.

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.

Rigorous vector theory for diffraction from gratings made of biaxial crystals

We present a rigorous formalism to solve the problem of diffraction of light at a periodically corrugated boundary between an isotropic medium (dielectric or metal with losses) and a biaxial crystal. The method applies to gratings illuminated either from the isotropic or from the biaxial side by waves with wave vectors inclined at an arbitrary angle with respect to the grooves and for arbitrary orientations of the crystal optic axes. Using a nonorthogonal curvilinear coordinate transformation that simplifies the boundary conditions at the grating interface and writing Maxwells equations for the covariant components of the fields in the transformed frame, the problem can be reduced to the numerical solution of a system of first order differential equations with constant coefficients. The application of the method is illustrated in two cases: (i) diffraction of s- and p-polarized waves at a sinusoidal boundary between a transparent dielectric and a biaxial crystal and (ii) excitation of surface plasmons along the corrugated interface between a metal and a biaxial crystal.

Diffraction gratings in uniaxial crystals with arbitrary orientation of the optic axis

We present a fully vectorial, rigorous electromagnetic approach to wave diffraction from one-dimensional periodic interfaces between isotropic and uniaxial media. The isotropic medium can be either a dielectric or a metal with losses, whereas the uniaxial medium is nonlossy, with its optic axis arbitrarily oriented with respect to the interface. Both media are magnetic. The incident wave vector can be associated with waves incident either from the isotropic or from the anisotropic side. Particular attention is devoted to the case of interfaces between a uniaxial dielectric and a metal illuminated from the anisotropic side. The examples include comparisons with a method invoking the Rayleigh hypothesis and the study of resonant excitation of surface plasmons at anisotropic interfaces.

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.

Scattering by a periodically corrugated interface between free space and a gyroelectromagnetic uniaxial medium

Diffraction of plane waves by a corrugated grating made of a gyroelectromagnetic uniaxial material is set up by using the T-matrix formalism. The fully vectorial treatment presented here is limited in its range of applicability by the use of the Rayleigh hypothesis. The preferred axis of the anisotropic medium is considered parallel to the mean surface of the periodic interface between the medium and the free space. The analysis is exemplified numerically by calculations performed for sinusoidal gratings.

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 beetles of South America

Photonic microstructures in nature, specifically in endemic species of Coleoptera from Argentina and the south of Chile have been identified, analyzed and modeled. These natural systems produce partial photonic bandgaps (PBGs) as a result of the high periodicity of the microstructures found in some parts of their bodies. With the aid of scanning (SEM) and transmission (TEM) electron microscopy we have identified that the elytron (modified forewing of a beetle that encases the thin hind wings used in flight) of these insects shows a periodic structure which originates diffractive phenomena resulting in extraordinary physical effects such as iridescent or metallic colors. We measured the reflectance spectrum and obtained the chromaticity diagrams of the samples with an Ocean Optics 4000 spectrophotometer. The geometrical parameters of the structure were obtained by processing the SEM images with the ImageJ software, to introduce them in our electromagnetic model. In all cases, a satisfactory agreement between the measurements and the numerical results was obtained. This permits us to explain the mechanism of color production in those specimens. The study of structural colors in the natural world can inspire the development of artificial devices with particular applications in technology, such as intelligent sensors and new kinds of filters.

Magnetic effects on the reflection of electromagnetic waves at isotropic–uniaxial interfaces

The ellipsometric properties of flat boundaries between isotropic and uniaxial materials with different magnetic permeabilities are studied for three particular orientations of the optic axis. The analysis can be applied either to synthetic anisotropic materials with magnetic properties or to nonmagnetic crystals in contact with magnetic isotropic media. By analysis of noticeable features in the curves of reflectivity versus angle of incidence, the space of constitutive parameters is divided into regions where the reflectivity exhibits very different qualitative behaviors. Some unusual reflection effects, such as the simultaneous existence of Brewster angles for p and s polarizations and the existence of angles for which the reflection matrix is null, are shown to be theoretically possible. Conditions for total reflection and total transmission are investigated and exemplified numerically by means of a parametric study.