Total absorption of unpolarized light by crossed gratings.

We present both experimental and numerical data showing the absorption of unpolarized, normally incident light by a gold crossed grating having a shallow sinusoidal profile. We show furthermore that the total absorption of unpolarized light can be achieved for an angle of incidence of 30 degrees with a crossed grating having its period adjusted appropriately from the normal incidence case to preserve the plasmonic resonance responsible for the enhanced absorptance. We contrast the process for achieving high absorptance in the principal plane of incidence aligned with the grooves of one of the gratings, with that for the principal plane at 45 degrees to each grating.

Nonlinear surface waves at the interfaces of left-handed electromagnetic media.

We report the existence of families of nonlinear TE-polarized surface waves propagating along the interface between different conventional and left-handed electromagnetic media as well as between two left-handed media. Both nonlinear/nonlinear and linear/nonlinear interfaces are considered. The constraints for the mode existence are identified and the energy flow associated with the surface modes is calculated.

Dichromatic nonlinear eigenmodes in slab waveguide with chi(2) nonlinearity.

The existence of purely nonlinear eigenmodes in a waveguiding structure composed of a slab with quadratic nonlinearity surrounded by (non)linear claddings is reported. Modes having bright and dark solitonlike shapes and consisting of two mutually locked harmonics are identified. Asymmetrical modes are shown to exist in symmetrical environments. Constraints for the existence of the modes are derived in terms of parameters of guiding structure materials.

Electromagnetic study of transmission gratings.

The performances of triangular groove photoresist gratings used in transmission are studied in the visible and near-infrared regions with the electromagnetic theory. The mounting considered here associates triangular groove gratings on the hypotenuse face of a right-angle prism in a configuration, usually called a grism, in such a way that for a chosen wavelength the deviations of the prism and the grating compensate. To assist designers of spectrometric systems, we have covered a complete range of blaze wavelengths and, consequently, of blaze angles. We studied the influence on grating efficiencies when the line density is increased, and the optimal choice angle of incidence is discussed.

Diffraction efficiencies for the higher orders of a reflection grating in the soft x-ray region: comparison between theory and experiment.

Diffraction efficiencies of a blazed grating measured in the soft x-ray region with photon energies between 60 and 925 eV are compared with calculations using the differential formalism of the exact electromagnetic theory. The parameters of the grating (gold coated with 1200 lines/mm and blaze angle 1.5 degrees ) are frequently used in soft x-ray monochromators. A quality check of this grating is made by investigating the total efficiency. Data for the -1, 0, +1, +2, and +3 orders are presented, so that the suppression capability for higher harmonics can be derived. Use of a blazed grating diffracting in 0. order is given.

Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media.

We establish the most general differential equations that are satisfied by the Fourier components of the electromagnetic field diffracted by an arbitrary periodic anisotropic medium. The equations are derived by use of the recently published fast-Fourier-factorization (FFF) method, which ensures fast convergence of the Fourier series of the field. The diffraction by classic isotropic gratings arises as a particular case of the derived equations; the case of anisotropic classic gratings was published elsewhere. The equations can be resolved either through classic differential theory or through the modal method for particular groove profiles. The new equations improve both methods in the same way. Crossed gratings, among which are grids and two-dimensional arbitrarily shaped periodic surfaces, appear as particular cases of the theory, as do three-dimensional photonic crystals. The method can be extended to nonperiodic media through the use of a Fourier transform.

Grating theory: new equations in Fourier space leading to fast converging results for TM polarization.

Using theorems of Fourier factorization, a recent paper [J. Opt. Soc. Am. A 13, 1870 (1996)] has shown that the truncated Fourier series of products of discontinuous functions that were used in the differential theory of gratings during the past 30 years are not converging everywhere in TM polarization. They turn out to be converging everywhere only at the limit of infinitely low modulated gratings. We derive new truncated equations and implement them numerically. The computed efficiencies turn out to converge about as fast as in the TE-polarization case with respect to the number of Fourier harmonics used to represent the field. The fast convergence is observed on both metallic and dielectric gratings with sinusoidal, triangular, and lamellar profiles as well as with cylindrical and rectangular rods, and examples are shown on gratings with 100% modulation. The new formulation opens a new wide range of applications of the method, concerning not only gratings used in TM polarization but also conical diffraction, crossed gratings, three-dimensional problems, nonperiodic objects, rough surfaces, photonic band gaps, nonlinear optics, etc. The formulation also concerns the TE polarization case for a grating ruled on a magnetic material as well as gratings ruled on anisotropic materials. The method developed is applicable to any theory that requires the Fourier analysis of continuous products of discontinuous periodic functions; we propose to call it the fast Fourier factorization method.

Differential theory for diffraction gratings: a new formulation for TM polarization with rapid convergence.

A new formulation of the differential method in TM polarization, based on correct representation of truncated Fourier series of products of discontinuous functions, is proposed. Although the derived equations are more complicated than in the classical formulation, the convergence rate with respect to the truncation parameter (with the number of diffraction orders taken into account) is much faster for arbitrary grating profiles, approaching the convergence rate in TE polarization. Numerical examples are presented for dielectric and metallic sinusoidal gratings with a 100% modulation ratio.

Almost perfect blazing by photonic crystal rod gratings.

A periodic array of dielectric rods or holes, known as two-dimensional photonic crystal, is shown to have blazing properties similar to those of classical diffraction gratings. Several different optogeometric configurations are shown numerically to exhibit an almost perfect blazing in the -1st reflected order with a plateaulike spectral dependence in nonpolarized light.

Dielectric coated gratings: a curious property.

Theoretical calculations predict that under certain special conditions a shallow fine pitch diffraction grating, given a precise dielectric overcoating, acts as a complete absorber of incident light of a specific wavelength and polarized in the P plane. Despite lack of a physical explanation, the phenomenon was confirmed by experiment.

Analysis of the changes in efficiency across the ruled area of a concave diffraction grating.

Measurements and calculations have been made to investigate the effects due to the change in groove orientation on efficiencies of gratings ruled on a spherical surface. Typical efficiency maps across the surface are given for various angles of incidence and wavelengths in the VUV and UV regions. Computations based on electromagnetic theory show a good agreement with the experimental data over the 150-2500-A wavelength range. A simple explanation is given to interpret and predict the shape of efficiency maps obtained from both theory and experiments.

X-ray gratings: the GMS mount.

Using rigorous electromagnetic theory, the interest of the specific off-plane mounting for x-ray gratings is discussed in detail. The optimization of the blaze angle for ruled gratings is considered, as well as the extension of the mounting to sinusoidal and lamellar profiles.

Second-harmonic-generation-induced optical bistability in prism or grating couplers.

We deal with second-harmonic generation in chi((2)) nonlinear-optical resonators such as prism or grating couplers. The theoretical study is performed within the framework of a recently developed coupled-mode analysis leading to a set of equations governing the amplitudes of pump and second-harmonic frequency fields. We predict analytically that second-harmonic generation in prism or grating couplers may lead to optical bistability. We believe this to be the first demonstration of such an effect in chi((2)) optical resonators.

Simple selection rules for VUV and XUV diffraction gratings.

The bulk of diffraction gratings used in the VUV and XUV regions are used at small angles of incidence and have shallow groove depths. Using rigorous electromagnetic theory, it is shown that such gratings behave in a scalar manner. It is then possible to derive universal efficiency curves from which one can obtain with simple rules the efficiencies of gratings with any metallic surface. The role of standard dielectric overcoatings is investigated and is found to be small. Some comparisons with experiments are given.

Grating efficiency theory as it applies to blazed and holographic gratings.

Recently developed rigorous theories have been used to investigate the diffraction efficiency behavior of both blazed and holographic gratings. In order to assist designers of spectrometric systems we have covered a complete range of blaze angles for triangular grooves and modulations for sinusoidal groove shape in first and second orders. Several types of mountings are included together with the role played by finite conductivity of aluminum. Useful classifications of both types of gratings are given, as they apply from the near uv to ir regions. Comparisons showing the close agreement between theory and experiment are presented.

Efficiency optimization of rectangular groove gratings for use in the visible and IR regions.

Rigorous electromagnetic theory is used to investigate the low order diffraction efficiency behavior of perfectly conducting rectangular groove plane diffraction gratings in the lambda/d domain of 0.25-1.8 of interest to spectrometry. We show how to optimize performance and make comparisons with blazed and holographic gratings. The role of finite conductivity and departure from Littrow conditions is also investigated. Comparison with experiment confirms the accuracy of the theory.

Transmission gratings for beam sampling and beam splitting.

Transmission gratings have rarely been used for beam sampling because they require special properties from dielectric overcoatings, which, to the best of our knowledge, are described here for the first time. Although such gratings are often used as beam splitters, their nature can be modified along the same principles with thin metal coatings, which are described.

Grating-enhanced second-harmonic generation in polymer waveguides: role of losses.

A numerical study of second-harmonic (SH) generation in a corrugated polymer waveguide is performed with a rigorous electromagnetic theory. Comparison with experiment reveals the role of losses inside the waveguide-small losses do not significantly affect the nonresonant response and reduce the resonant enhancement of SH generation. High losses can lead to the opposite effect-instead of enhancement, dips in the SH efficiency are observed in the vicinity of guided-wave excitation. The peculiarities of the angular dependencies of SH generation are explained from the phenomenological point of view, and the role of phase matching is discussed.