We consider rigorous theories of diffraction gratings in which the electromagnetic field can be considered as infinite series. Numerical implementation of these theories needs truncation of the series. We show that in many circumstances, some properties of the exact solution (conservation of energy, reciprocity relations) are also verified by the truncated solution. Consequently these properties can not be systematically used as a check of validity of the truncated solution.

As far as we know, only a few studies have been, up to now, devoted to anisotropic gratings. We only have heard of the paper by our Japanese colleagues of Osaka Prefecture University.1 We are also working in this field, in view of potential applications. Although some partial and unpublished results have been obtained some years ago in the framework of a contract with a private company (P.A. Technology, Cambridge), we think that we have to face a difficult problem which is far from being wholly resolved. We would like to report briefly on our theoretical work in order to inform "practical people" and, should the occasion arise, to initiate new collaborations. Throughout the paper we use a rectangular coordinate system Oxyz and we denote by ex, ey, ez the unit vectors (4, axes Ox, 0y, Oz. We deal with time-harmonic fields represented by complex vectors t and H, using a time dependence in exp(-iwt). The permeability is equal to μ0 everywhere and the relative permittivity is described by a 3 x 3 matrix [6] : xx xy xz [6]yxyy yz zx zy zz We denote by co the vacuum permittiviV, an4 we put ko = wicopo = 27/X0. We say that the fields are TE (or TM) polarized when E (or H) is parallel to Oz.

A comparison is made between the efficiencies in the XUV of diffraction gratings with laminar groove profile used in classic grazing incidence, constant blaze conical diffraction and a modified Littrow Conical Diffraction (LCD) configurations all operating in grazing incidence. It is seen that for a spectrograph configuration in classic diffraction, efficiency remains high over a wider spectral range than a monochromator. However, the efficiency of a LCD monochromator mount is greater than that obtained in classic grazing incidence and is maintained over a wider spectral range. The LCD has the benefit of simple rotation of the grating to change wavelength and is, therefore, mechanically easier to construct.

If the truth must be told, this paper does not contain novel and unpublished results. Two years ago, we published a long paper' on the same subject in Electromagnetics. But on the one hand, this paper requires a very good background in functional analysis and, on the other hand, Electromagnetics is probably not the favorite review for most engineers. Here our purpose is only to inform practical physicists of theoretical conclusions which, in our opinion, are worth knowing. The reader interested by the theoretical aspects of homogenization theory can refer to ¹.

This communication is concerned with surface enhanced second harmonic generation through delocalized electromagnetic resonances such as surface plasmons or guided waves at bare or coated metallic gratings. The formalisms presented here are rigorous in the sense that the groove depth of the grating is not considered as a perturbative parameter.This allows us to show that there exists an optimum groove depth of the grating for which the enhancement of the second harmonic efficiency as5compared to the flat case is the greatest : shallow modulated gratings (10%) lead to optimum enhancement as high as 10⁵.

A rigorous analysis for the wave diffraction and guidance in a planar anisotropic medium with tensor permittivity which is modulated periodically with respect to space and time is presented. The method applies to any anisotropic medium, any polarization of the incident plane wave and any orientation of the grating vector. The analysis is formulated in a unified matrix form so that calculations can be performed systematically. Numerical examples of both scattering and guiding properties peculiar to anisotropic waveguides are shown.

This paper describes a comparison of image quality between a toroidal grating monochromator and a specific modified conical diffraction monochromator. it was found that for an equivalent dispersion in the XUV and grazing incidence, the image quality of both configurations is equivalent. Throughput advantages or disadvantages are dependent on the spectral range demanded by the user when compared to alternative monochromator configurations.

Using a numerical optimization procedure, we investigate the Seya-Namioka 35° minimum for constant-deviation monochromators. We obtain the expected geometry for monochromators which use straight-grooved gratings, but find that the addition of holography changes the optimal geometry.

Coarse phase transmission gratings with symmetrical groove shape have found widespread use as 3-way beam splitters. Usually the light source is a laser and incidence is normal to the back surface of the grating. Theoretical energy distribution, especially in zero and first orders, is described for several of the most likely groove shapes.

A rigorous theory describing the diffraction of a plane wave by a doubly-periodic array of annular apertures in a thick, perfectly conducting screen is developed. It is found that such a structure exhibits excellent bandpass characteristics which can be adjusted by changing the size of the apertures and the thickness of the screen.

A diffraction grating sampler to detect wavefront and phase emitted by a high energy laser at 10.6 µm was calculated and manufactured. The grating extracted a small fraction of the incident energy and reflected the rest like a mirror. The portion of the beam sampled was diffracted into the 1st order to a detector that operated a servo control of the wavefront phase and power.

Modifications to the MIT-B grating ruling engine have recently been installed. In addition to a new ultra-quiet mechanical drive system for the diamond carriage an entirely new digital servo control system has been installed. It operates with a bit size of 0.09 nm, with virtually infinite control levels. Rowland ghost levels are no longer detectable, which implies that periodic error amplitudes are below 0.5 nm.

Basic equations of the holographic grating are expanded to those of a new holographic grating produced by recording the interference fringes of two aspherical beams. Aberration terms peculiar to this recording configuration show the possibility of the additional compensation of aberrations over the conventional holographic gratings recorded with plane or spherical beams. To confirm this advantage, we designed and fabricated some aberration-corrected blazed holographic gratings for use with a Seya-Namioka and a Czerny-Turner monochromators, and a polychromator suitable for an array detector. The experimental results indicated that the usefulness of our method to enhanse resolution and throughput of spectrometers.

Blazed zone plates have been manufactured by recording in photoresist the circular fringes transmitted by a Fabry Perot Interferometer. The fringe pattern is scanned through one order by an axial translation of one of the mirrors and a series of exposures is recorded in such a way that a triangular groove profile is generated. Their numerical aperture is limited by the properties of the camera used to photograph the fringes and this limits the range of application of the technique.

The feasibility of fabricating periodic structures using silicon micromachining for millimeter-and submillimeter-wave applications is investigated. Diffraction gratings and dichroic filters are fabricated and tested.

Accurate submicron holographic diffraction gratings are fabricated by utilizing the total internal reflection inside a right angle prism. The AlGaAs wafers are coated with photoresist and optically contacted to one face of the prism. Collimated laser radiation entering the hypotenuse of the prism is folded onto itself and interferes in the photoresist. The period of the resulting grating can be tuned by rotating the prism about the axis defined by the apex. This roof configuration not only allows for easy alignment but dictates that both beams interfere at equal and opposing angles with identical intensities. The effects of vibration are limited to rotations about the apex of the prism.

A method for measuring diffraction preting groove profiles using a scanning electron microscope is developed. The method is to observe a photoresist well that is straight and normal to the grating grooves. It is formed by using photolithography technology for seticonductor device fabrication. Several types of diffraction gratings are ruled by applying this measurement technology to help control the groove profiles, especially of those with extremely fine and shallow grooves.

The surfaces of several optical gratings have been observed by a scanning tunneling microscope (STM) in the atomosphere without contacting surface. Blaze angles of optical gratings with 3600 lines/mm and 1200 lines/mm have been measured. It is proved that the scanning tunneling microscopy is one of the useful techniques for topographic mapping of gratings with very fine pitches.

The efficiency of blazed holographic gratings, fabricated by Fourier synthesis are studied. Such Fourier gratings combine many of the attractive properties of holographic gratings, with the high efficiency of ruled gratings. We show that it is possible to superimpose two sinusoidal exposures with the required high precision, to obtain gratings with high, and even efficiency over the grating surface. The measured efficiencies agree within a few percent to calculated efficiency curves in the region studied, 250 - 700 nm.

The aberrations present in a Czerny Turner monochromator employing spherical mirrors may be corrected by using a plane diffraction grating produced holographically and incorporating aberrations that exactly cancel those produced by the system concave mirrors. It has been demonstrated that over the wavelength range typically used in Raman spectroscopy significant improvements in performance may be achieved.

We study the enhancement of second harmonic generation by nonlinear dielectrics deposited onto a rough metallic surface represented by a grating. If the dielectric is thick enough to support a guided mode, an increase of the local field occurs when that guided mode is resonantly excited. The result is an enhancement of the nonlinear polarisation and thus of the second harmonic signal. We try to optimize the enhancement by determining the optimum grating parameters. To this end, a new theory of gratings in nonlinear optics is developped and implemented numerically. Enhancements higher than 10⁵ are found for a convenient sinu-soidal grating. The influence of the groove shape is considered.

An exact numerical method of analyzing deep dielectric gratings with multistep lamellar profiles is presented. This method is able to predict the diffraction efficiencies of dielectric gratings for both TE and TM polarizations. In this paper we use a modal expansion method in terms of modal functions which are rigorous solutions of the Maxwell's equations and fulfill the boundary conditions on the upright enclosing sides of the rectangular profiles. The coefficients of the modal expansion are determined such that the mean-square boundary residual becomes minimum, and the sequence of approximate solutions converges rapidly and monotonically with respect to the truncation size of the expansion order with help of the smoothing procedure of the modal fields. To show the validity of this algorithm in the sinusoidal surface-relief gratings, the results are compared with those obtained by other methods.

Resonances in the scattering of light from layered structures occur due to the coupling of light into guided modes in the layers. In the case of layered gratings these resonances appear as large enhancements in the grating efficiency at certain angles. The angular width of these resonances is governed by the grating and by the absorption of the layers. The position of the resonance is controlled by the indices and thickness of the layers and by the wavelength of the light and the period of the grating. All these properties, including the mode coupling constants can be derived from the scattering matrix for the layered structure. Possible applications are briefly discussed.

Plasmon resonance absorption in periodically corrugated layered structures of silver was studied by the photoacoustic method. The layered structures were self-supporting and corrugated with a period of 1888 nm and amplitude varying from 6 to 12 nm, depending on the tnickness. Experimental results of resonance absorption of 633-nm photons were analyzed in terms of the propagation and damping constants of coupled modes of surface plasmons. The coupling efficiency of incident photons to these modes was found to be strongly dependent on corrugation amplitude and layer thickness.

Articulation is the special moving pair in the body of animal. In this article, the different forms and the comparative targets of the moire contour fringes on two condyles of knee of Pongidae, and comparative study of the articulation of knee between the Gorilla, Orangutan and Chimpanzee are given.

This paper concerns the work of the Opto-Electronic Precision Machinery Laboratory on the moire principle, manufacture, calibration, and application of radial and linear metrological gratings.