Miriam L. Gigli

Diffraction from Corrugated Gratings Made with Uniaxial Crystals: Rayleigh Methods

Abstract A point-matching and a Fourier-series method based on the Rayleigh hypothesis are developed for calculating the electromagnetic fields diffracted by weakly corrugated interfaces between a non-lossy, uniaxial crystal and an isotropic dielectric or metal. The methods apply for gratings with shallow grooves of any shape, arbitrary orientations of the optic axis and for waves incident from either side of the interface. The results obtained using these methods are compared with rigorous results. Good agreements are obtained for gratings with groove heights almost 0·2 times their period. As applications, the following cases are studied: (a) TE-TM polarization conversion when the incidence is from an isotropic medium and (b) resonant excitation of surface plasmons at uniaxial-metallic interfaces.

Excitation of surface plasmons and total absorption of light at the flat boundary between a metal and a uniaxial crystal.

The excitation of surface plasmons at a flat interface between a uniaxial crystal and a metal is investigated theoretically. We show that strong couplings between surface plasmons and light incident from the crystal can be obtained without corrugation of the surface. These couplings are associated with significant reductions in the reflectivity of the structure and with strong enhancements of the electromagnetic field on the surface of the crystal. Numerical examples obtained for a flat interface between sodium nitrate and gold show the existence of critical orientations of the optic axis for which all the incident power is absorbed by the metal.

Resonant excitation of surface modes at a single flat uniaxial–metal interface

A theoretical study about the propagation and resonant excitation of surface modes at the flat interface between a uniaxial crystal and a metal is performed. We show the existence of a class of surface modes that, under adequate conditions, and contrary to what happens for isotropic interfaces, can be coupled directly to incident radiation. We also show that the resonant excitation of these surface modes is correlated with a strong enhancement of the field on the surface and with a strong absorption of power by the metal. We study the influence of the orientation of the optic axis on these phenomena and show the existence of critical orientations for which all the incident power is absorbed by the metal.

Conical diffraction from uniaxial gratings

We develop a method for solving the problem of conical diffraction at a corrugated interface between an isotropic medium and a uniaxial crystal. The method, based on the Rayleigh hypothesis, is valid for gratings with shallow grooves, arbitrary orientations of the optic axis, and arbitrary orientation of the plane of incidence with respect to the main section of the cylindrical corrugation. The theoretical formalism is applied to model the conversion between polarization states of electromagnetic waves reflected at the sinusoidally corrugated interface between a uniaxial crystal and an isotropic dielectric or metal, for incidences from the isotropic side or the uniaxial one. The combined effect of conical diffraction and material anisotropy on polarization conversion is exemplified in both cases.

Lateral displacement of a beam incident from a uniaxial medium onto a metal

Abstract The reflection of spatially limited beams at the flat boundary between a uniaxial crystal and a metal is studied theoretically. Incident limited beams are expanded in terms of the ordinary and extraordinary plane waves that can be propagated in uniaxial media. The spatial modifications in ordinary and extraordinary reflected field distributions are numerically calculated. Several effects, including polarization conversion between ordinary and extraordinary waves and field enhancement on the interface due to the excitation of surface waves, are discussed. The numerical calculations of the Goos–Hanchen lateral shift in the reflected fields are compared with the results predicted by the extension to uniaxial media of the stationary phase approximation used for limited beams in isotropic media.

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.

Nonlinear electromagnetic response of corrugated metallic gratings

We describe a theoretical formalism to study the second-harmonic generation in periodically corrugated surfaces illuminated by a plane wave. The incident wave vector is contained in the plane perpendicular to the grating grooves. Our analysis is based on the most general expression for the nonlinear polarization of a homogeneous and isotropic medium. The diffraction problem is solved using a Rayleigh method, and the numerical technique is illustrated by examples for which the nonlinear susceptibilities are calculated with a free-electron model.

Reciprocity relations for uniaxial gratings

Summary Starting from a formulation of the reciprocity theorem valid for uniaxial media, we derive symmetry properties for the co-polarized and cross-polarized efficiencies diffracted by a periodically corrugated surface that separates a uniaxial medium from a perfect conductor. These reciprocity relations are proved to be valid for arbitrary orientations of the optic axis of the crystal and for an arbitrary shape of the grating.

Reflection of light by a slab containing electrically small dielectric spheres

Theoriginal and theenhanced Maxwell-Garnett estimates for the permittivity of a particulate medium are applied to the reflection of light by a composite dielectric slab. The reflection coefficients for incident s and p polarizations are calculated and some curves are plotted and discussed.

Excitation of eigenmodes at uniaxial crystal-metal-isotropic films

Abstract We perform a theoretical study about the interaction between light and the eigenmodes of a metallic film that separates a uniaxial crystal from an isotropic medium. These structures support two different eigenmodes: a surface mode at the isotropic medium-metal interface and another mode at the crystal-metal interface. We show that, contrary to what happens in isotropic configurations, these two modes can couple to incident radiation without corrugating the surface or adding another interface. We give conditions to obtain zero reflected power and a strong enhancement of the fields at both interfaces. We also show that, owing to the different characteristics of the modes supported by each interface, the relative position of their propagation constants in the complex plane can be selected rather arbitrarily by tuning the film parameters. We give examples in which both couplings occur for angles of incidence either very different (separate resonances) or very close (almost double resonances). In the ...