Ricardo A. Depine

Highly conducting wire gratings in the resonance region.

We present a theoretical approach for calculating the fields diffracted by gratings made of highlyconducting wires that have a rectangular shape. The fields between the wires are represented in terms of modal expansions that satisfy the approximated impedance boundary condition. Our results show thatthis procedure is particularly suited to dealing with gold gratings used in the infrared range, a spectral region where the assumption of a perfect conductor does not hold, and where the rigorous modal method assuming penetrable wires exhibits numerical instabilities linked with the high conductivity of gold. Numerical results are presented, and the theory is used to determine wire parameters by fitting theoretical and experimental data.

Scattering from metallic surfaces having a finite number of rectangular grooves

A modal theory is presented for solving the problem of electromagnetic scattering from a surface consisting of a finite number of one-dimensional rectangular grooves in a metallic plane. The incident plane wave can be polarized with either its electric or its magnetic field along the grooves. The formalism is applicable to perfectly conducting materials and to real metals with high (but finite) conductivity. Particular attention is paid to the changes appearing in the scattering pattern when the conductivity of the structure is changed from an infinite value (perfect conductor) to a finite value (highly conducting metal). The excitation of surface waves when the incident wave is p polarized is illustrated in some numerical examples that demonstrate the differences between the spectral amplitudes corresponding to s and p polarizations.

Diffraction from Highly Conducting Wire Gratings of Arbitrary Cross-section

Abstract A theory describing the diffraction properties of highly conducting wire gratings with arbitrary cross-sections is presented. The method incorporates the surface impedance boundary condition on the field along metallic interfaces and relies on the solution of a coupled system of ordinary differential equations for finding the field between wires. The theory is exemplified numerically for different wire profiles. The numerical results for gold gratings in the resonance region are compared with those obtained from a theory valid for perfectly conducting wires. Comparisons to measurements validate the effectiveness of the developed algorithm and show that it is particularly suited for dealing with metallic gratings in the infrared region.

Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals

Abstract We consider layered heterostructures combining ordinary positive index materials and dispersive metamaterials. We show that these structures can exhibit a new type of photonic gap around frequencies where either the magnetic permeability μ or the electric permittivity ϵ of the metamaterial is zero. Although the interface of a semi-infinite medium with zero refractive index (a condition attained either when μ = 0 or when ϵ = 0 ) is known to give full reflectivity for all incident polarizations, here we show that a gap corresponding to μ = 0 occurs only for TE polarized waves, whereas a gap corresponding to ϵ = 0 occurs only for TM polarized waves. These band gaps are scale-length invariant and very robust against disorder, although they may disappear for the particular case of propagation along the stratification direction.

Interaction between non-Bragg band gaps in 1D metamaterial photonic crystals.

We consider periodic multilayers combining ordinary positive index materials and dispersive metamaterials with negative index in some frequency range. These structures can exhibit photonic band gaps which, in contrast with the usual Bragg gaps, are not based on interference mechanisms. We focus on effects produced by the interaction between non-Bragg gaps of different nature: a) the zero averaged refractive index, b) the zero permeability and c) the zero permittivity gaps. Our analysis highlights the role played by the unavoidable dispersive character of metamaterials. We show that the degree of overlap between these bands can be varied by a proper selection of the constructive parameters, a feature that introduces novel degrees of freedom for the design of photonic band gap structures. The numerical examples illustrate the evolution of the dispersion diagrams of a periodic multilayer with the filling fraction of the ordinary material constituent and show a range of filling fractions where propagation in the multilayer is forbidden for any propagation angle and polarization.

Perfectly conducting diffraction grating formalisms extended to good conductors via the surface impedance boundary condition

The surface impedance boundary condition is used to include the effect of high conductivity of meals in the integral theory of perfectly conducting gratings. As an intuitive approach, the diffraction formalism proposed by Petit for the treatment of infinitely conducting gratings in P polarization is extended to highly conducting materials by introducing the concept of equivalent surface current density. Then, integral equations for both polarizations are deduced in a mathematically rigorous way. The new method is used to calculate the efficiencies of sinusoidal gratings at infrared and visible light, and the numerical results are compared with those obtained using Maxwell boundary conditions and also with the perfect conductivity model.

Characterization of highly conducting wire gratings using an electromagnetic theory of diffraction

Abstract An electromagnetic method is used to reconstruct the cross section of galvanically manufactured wire gratings from efficiency measurements. The approach, based on a surface impedance approximation, allows us to deal with highly conducting wires of arbitrary cross sections. By varying the wire profile parameters, a total coincidence between theory and transmittance measurements in the resonance region can be found for different gold gratings.

Scattering of a wave at a periodic boundary: analytical expression for the surface impedance

A surface-impedance boundary condition is obtained from first principles for problems involving the scattering of two-dimensional waves by cylindrical periodical surfaces of arbitrary shape. The analysis is performed in the context of the electromagnetic theory of gratings, but it is also applicable to other physical situations, leading to the solution of a two-dimensional Helmholtz equation with high values for index of refraction. The boundary condition deduced here is shown to be analogous to the one suggested by Leontovich for quasi-planar boundaries if Z0 the quantity relating the field and its normal derivative at the boundary and depending only on the constitutive properties of the medium, is replaced by another quantity Z, which also depends on the local curvature of the surface. and on the polarization of the external fields; Z0 is the zero-order term in the expansion of Z in terms of the curvature.

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.

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.