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Showing papers on "Diffraction published in 1985"


Journal ArticleDOI
01 May 1985
TL;DR: In this article, an exact formulation of the grating diffraction problem without approximations is presented, using a series of fundamental assumptions, which reduces to the various existing approximate theories in the appropriate limits.
Abstract: Diffraction characteristics of general dielectric planar (slab) gratings and surface-relief (corrugated) gratings are reviewed. Applications to laser-beam deflection, guidance, modulation, coupling, filtering, wavefront reconstruction, and distributed feedback in the fields of acoustooptics, integrated optics, holography, and spectral analysis are discussed. An exact formulation of the grating diffraction problem without approximations (rigorous coupled-wave theory developed by the authors) is presented. The method of solution is in terms of state variables and this is presented in detail. Then, using a series of fundamental assumptions, this rigorous theory is shown to reduce to the various existing approximate theories in the appropriate limits. The effects of these fundamental assumptions in the approximate theories are quantified and discussed.

989 citations


Journal ArticleDOI
Veit Elser1
TL;DR: Various features of quasicrystal diffraction patterns are discussed and the projection scheme is used throughout and applied in some detail to the pattern formed by icosahedral Al-Mn.
Abstract: Various features of quasicrystal diffraction patterns are discussed. The projection scheme is used throughout and applied in some detail to the pattern formed by icosahedral Al-Mn. Comparison with the diffraction pattern formed by the vertices of a three-dimensional Penrose tiling leads to the value 4.60 A\r{} for the rhombohedron edge length.

575 citations


Journal ArticleDOI
TL;DR: In this paper, a new concept is proposed for an optical probe with spatial resolution unlimited by diffraction effects, based on optical-field confinement by surface plasmons of a submicrometer-sized metal particle.
Abstract: A new concept is proposed for an optical probe with spatial resolution unlimited by diffraction effects. It is based on optical-field confinement by surface plasmons of a submicrometer-sized metal particle. The particle serves as an antenna that receives an incoming electromagnetic field. The field extends to a nearby sample surface and interacts with a small area on that surface through the nonlinear susceptibility tensors. The induced sample polarization is reradiated by the particle, thereby generating a Raman, a two-photon, or a second-harmonic spectrum. Microscopy is performed by rastering the position of the metal particle over the sample surface. Spatial resolution approaching 1 nm is projected. The concept is also applicable to submicrometer optical lithography and ultrahigh-density optical recording.

408 citations


Patent
12 Jul 1985
TL;DR: In this paper, a compact head-up display comprising a combiner which combines light energy from an outside view with light energy transmitted within the combiner and diffracted out by means of an upper diffraction grating is described.
Abstract: A compact head-up display comprising a combiner which combines light energy from an outside view with light energy transmitted within the combiner and diffracted out by means of an upper diffraction grating. The head-up display disclosed further comprises an image source, a collimating lens, and a lower diffraction grating for diffracting the collimated light energy into the combiner.

315 citations


Journal ArticleDOI
TL;DR: In this article, the stable monomode self-trapping of laser beams with adequate shape and power when they are propagating through homogeneous transparent dielectrics whose refractive index exhibits fluctuations proportional to the local intensity is demonstrated.

290 citations


Journal ArticleDOI
TL;DR: In this article, the microstructure of rapidly solidified Al−Mn alloys containing 18 to 25.3 wt pct Mn was studied by transmission electron microscopy.
Abstract: The microstructure of rapidly solidified Al−Mn alloys containing 18 to 25.3 wt pct Mn was studied by transmission electron microscopy. One of the phases found in the microstructure exhibits icosahedral symmetry manifested in electron diffraction patterns having five-fold symmetry. A new structural concept is proposed to account for the observed electron diffraction patterns. The structure is assumed to be composed of many connected polyhedra. Although not forming a regular lattice, such structures are able to produce sharp diffraction peaks. The terminal stability and transformation of the icosahedral phase was also studied and reported.

284 citations



Journal ArticleDOI
TL;DR: In this article, path integral Monte Carlo methods are applied to the ST2 model of water to examine both the importance of quantum effects on the structure of liquid water and the differences in the structures of light and heavy water.
Abstract: Path integral Monte Carlo methods are applied to the ST2 model of water to examine both the importance of quantum effects on the structure of liquid water and the differences in the structures of light and heavy water. Significant differences are apparent among the results for classical water, quantum H2O, and quantum D2O. For all quantities considered, the classical liquid is the most structured while quantum H2O is the least structured. The implications of these results for neutron and x‐ray diffraction experiments are examined; of the three atom–atom partial structure factors, the oxygen–oxygen function is found to be the most sensitive to quantum effects and the structural differences between light and heavy water appear to be large enough to be measured by x‐ray diffraction experiments.

270 citations


Journal ArticleDOI
TL;DR: In this paper, electron and crystallographic data for sapphire (α-Al2O3) were presented to enable ready and unique identification of TEM diffraction patterns and facilitate image analysis.
Abstract: Crystallographic and electron diffraction data for sapphire (α-Al2O3) are presented which enable ready and unique identification of TEM diffraction patterns and facilitate image analysis. Crystallographic data is presented in the form of stereographic projections and in figures listing angles between planes and angles between zones. Electron diffraction data consist of computer-simulated diffraction patterns and tables of extinction distances calculated using atomic and ionic electron scattering factors.

201 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that reflection of a plane monochromatic wave by the surface of a corrugated waveguide structure may excite a guided mode in one of the diffraction orders and thus alter greatly the reflection and transmission coefficients of the incident wave until total reflection or total transmission are achieved.
Abstract: It is shown that reflection of a plane monochromatic wave by the surface of a corrugated waveguide structure may excite a guided mode in one of the diffraction orders and thus alter greatly the reflection and transmission coefficients of the incident wave until total reflection or total transmission are achieved.

184 citations


Journal ArticleDOI
TL;DR: In this article, the authors extend the analysis to cover any one-dimensional distribution of steps which does not depend upon choice of origin and for which the surface consists of either (1) an infinite number of levels, each with identical terrace length distributions or (2) a finite number of steps, but with different distributions allowed.

Journal ArticleDOI
TL;DR: A simple result of scalar diffraction theory is used to derive the round trip phase accrual of a plane wave in dye laser oscillators containing gratings and it is found that at least one exactly synchronous configuration always exists regardless of oscillator type.
Abstract: A simple result of scalar diffraction theory is used to derive the round trip phase accrual of a plane wave in dye laser oscillators containing gratings. This is used to determine configurations where the standing wave condition is satisfied at the feedback wavelength throughout an angle scan. We find that at least one such exactly synchronous configuration always exists regardless of oscillator type.

Journal ArticleDOI
TL;DR: In this article, a uniform high-frequency solution is presented for the diffraction by a wedge with impedance faces illuminated by a plane wave perpendicularly incident on its edge, and both the transverse electric (TE) and transverse magnetic (TM) cases are considered.
Abstract: A uniform high-frequency solution is presented for the diffraction by a wedge with impedance faces illuminated by a plane wave perpendicularly incident on its edge. Arbitrary uniform isotropic impedance boundary conditions may be imposed on the faces of the wedge, and both the transverse electric (TE) and transverse magnetic (TM) cases are considered. This solution is formulated in terms of a diffraction coefficient which has the same structure as that of the uniform geometrical theory of diffraction (UTD) for a perfectly conducting wedge. Its extension to the present case is achieved by introducing suitable multiplying factors, which have been derived from an asymptotic evaluation of the exact solution given by Maliuzhinets. When the field point is located on the surface near the edge, a more accurate asymptotic evaluation is employed to obtain a high-frequency expression for the diffracted field, which is suitable for several specific applications. The formulation described in this paper may provide a useful, rigorous basis to search for a more numerically efficient but yet accurate approximation.

Journal ArticleDOI
TL;DR: In this article, the thermal variation of atomic beam diffraction intensities on (1, 1, 2n + 1) faces of Cu is discussed for large n. The main parameter of the theory is the energy W0 of a kink on a step.
Abstract: The thermal variation of atomic beam diffraction intensities on (1, 1, 2n + 1) faces of Cu is discussed for large n. the dramatic decrease of intensity at about 600K is attributed to a roughening transition, above which the steps are fuzzy. The steps are assumed to repel themselves with a repulsion energy proportional to (2n+1)-2, of elastic or electrostatic nature or both. The main parameter of the theory is the energy W0 of a kink on a step. Experimental data are consistent with a value of W0 between 0.2 and 0.3 eV, in agreement with very rough theoretical evaluations. Predictions are presented concerning the lineshape of diffraction spectra in the high-temperature rough phase, where intensities cannot be written as delta functions. The Bragg peak intensity vanishes just below the roughening transition temperature, TR, as exp(-constant*(TR-T)-12/), where the constant depends on the particular Bragg peak.

Journal ArticleDOI
TL;DR: In this article, it was shown that the coherent interaction between the light and the electron beam in a free-electron laser (FEL) can optically guide the light.
Abstract: By use of two-dimensional approximations for the equations that describe a high-gain free-electron laser (FEL) amplifier, and the properties of optical fibers, it is shown that the coherent interaction between the light and the electron beam in a FEL can optically guide the light. In the exponential-gain regime, the FEL performance in the presence of strong diffraction can be simply described by a cubic equation for the complex gain and the dispersion relation for an optical fiber. The phenomenon of optical guiding is illustrated with two-dimensional numerical simulations. The phenomenon has applications to short-wavelength FEL's, to directing of intense light, and to bending of x-rays.

Journal ArticleDOI
TL;DR: In this paper, a parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves, and two methods of approach are used.
Abstract: The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves. Two methods of approach are used. In the first method Boussinesq equations are used to derive evolution equations for spectral-wave components in a slowly varying two-dimensional domain. The second method modifies the K–P equation (Kadomtsev & Petviashvili 1970) to include varying depth in two dimensions. Comparisons are made between present numerical results, experimental data (Whalin 1971) and previous numerical calculations (Madsen & Warren 1984).

Patent
30 Dec 1985
TL;DR: In this article, the diffraction grating comprises a large number of substantially closed loop grating lines consecutively enclosing each other from inner to outer, with all of the lines extending substantially parallel to the phase fronts of the guided waves.
Abstract: Devices for controlling and guiding waves, such as electromagnetic waves, acoustic waves, and the like are disclosed which include at least one wave-transmitting medium and a diffraction grating, associated with the transmitting medium, for scattering wave energy into or out of the guided waves. The device may take the form of a "sandwich"-type or thin film waveguide, in which case the transmitting medium has at least one curvi-planar boundary, or it may take the form of a "rod"-shaped or cylindrical waveguide, in which case the transmitting medium has a substantially cylindrical boundary. According to the invention, the diffraction grating comprises a large number of substantially closed loop grating lines consecutively enclosing each other from inner to outer, with all of the grating lines extending substantially parallel to the phase fronts of the guided waves.

Journal ArticleDOI
TL;DR: In this article, a method for continuous reconstruction of volume holograms in cubic photorefractive crystals of the sillenite family using the effect of anisotropic diffraction is presented.

Journal ArticleDOI
TL;DR: In this article, the diffraction of SH waves by a wedge-shaped elastic medium is studied, and it is found that the motion at the vertex relative to the free space amplitude is given by 2/v, where vπ = internal angle of the wedge.
Abstract: The diffraction of SH waves by a wedge-shaped elastic medium is studied. Macdonald's (1902) solution is derived and applied to calculate the field in the wedge's surface on and near the vertex. It is found that the motion at the vertex, relative to the free space amplitude, is given by 2/ v , where vπ = internal angle of the wedge. In some cases, values much larger than 2/ v were found on the sides. Both frequency and time domain results are given.

Journal ArticleDOI
TL;DR: In this article, a numerical model is presented that predicts the transformation of monochromatic waves over complex bathymetry and includes both refractive and diffractive effects, and the solution is obtained for a finite number of rectilinear grid cells that comprise the domain of interest.
Abstract: A numerical model is presented that predicts the transformation of monochromatic waves over complex bathymetry and includes both refractive and diffractive effects. Finite difference approximations are used to solve the governing equations, and the solution is obtained for a finite number of rectilinear grid cells that comprise the domain of interest. Model results are compared with data from two experimental tests, and the capability and utility of the model for real coastal applications are illustrated by application to an ocean inlet system.

Journal ArticleDOI
TL;DR: The scattering phase matrices for finite hexagonal cylinders oriented randomly in space were computed by superposing the scattered intensities of Fraunhofer diffracted rays and geometrical optics rays, and the results appear to agree well with most field and laboratory observations.
Abstract: The scattering phase matrices for finite hexagonal cylinders oriented randomly in space were computed by superposing the scattered intensities of Fraunhofer diffracted rays and geometrical optics rays. However, the effect of interference is considered when the optical path lengths for two rays, split by some obstacle and scattered in the same direction, are equal to each other. Single models (c/a = 2.5 and 0.4) for a hexagonal column and a plate, resembling the corresponding crystals in atmospheric clouds, are used in the computations. Our results showed different values for the phase matrix elements, P33 and P44, from those obtained previously by Cai and Liou. The backscattering linear depolarization ratios and the asymmetry factor for hexagonal plates oriented horizontally were then computed. The backscattering linear depolarization ratios exceeded 1.0 at certain orientations. Within the limitation of the use of single-crystal models for a hexagonal column and a plate, the results appear to agree well with most field and laboratory observations.

Journal ArticleDOI
TL;DR: Gaussian modes with large sections have been experimentally produced in Cassegrain resonators using Gaussian reflectivity convex couplers and the far field of the beam, which was coupled through a Gaussian coupler, was found to be free from secondary rings.
Abstract: Gaussian modes with large sections have been experimentally produced in Cassegrain resonators using Gaussian reflectivity convex couplers. The far field of the beam, which was coupled through a Gaussian coupler, was found to be free from secondary rings.

Journal ArticleDOI
TL;DR: In this paper, the Pearson VII and pseudo-Voigt peak shape functions were used to analyze high-resolution neutron powder diffraction data, which revealed a range of peak shapes from essentially Gaussian to Lorentzian and beyond.
Abstract: Analyses of high-resolution neutron powder diffraction data, using both the Pearson VII and pseudo-Voigt peak shape functions, have revealed a range of peak shapes from essentially Gaussian to Lorentzian and beyond. Moreover, the refinements show that the Lorentzian character of the peaks in each pattern increases with increasing diffraction angle. Both kinds of shape change are associated with varying relative contributions to the peak profiles of the instrumental resolution, isotropic crystallite strain and crystallite size effects. Rietveld analysis of powder data with the standard Gaussian form when the peaks have significant Lorentzian character has little effect on atomic positional parameters, but it leads to an overestimation of the thermal vibration coefficients and higher least-squares residuals.

Patent
12 Jan 1985
TL;DR: In this article, the authors proposed to eliminate the use of an optical system which converts the form of luminous flux to reduce the weight of a reader and at the same time to facilitate positioning of a photodetector.
Abstract: PURPOSE:To eliminate the use of an optical system which converts the form of luminous flux to reduce the weight of a reader and at the same time to facilitate positioning of a photodetector, by obtaining a focusing error signal from the variation of reflection factor at a level close to a critical angle after combining a diffraction grating with a parallel plate. CONSTITUTION:When parallel beams 17 are made incident vertically on the 1st boundary surface 13 of a parallel plate 13, the beams 17 transmit through the 2nd boundary surface 13b of the plate 13 and are made incident on a diffraction grating 15 to be diffracted there. The diffracted beam 18 is made incident again on the surface 13b and travels straight to reach a point P. The constant of the grating 15 is decided so that the incident angle at the point P is equal to the critical angle of total reflection. Therefore the beam 18 is totally reflected at the point P and made incident on a photodetector 11. The beam 18 is totally reflected if the angle theta is larger than the critical angle thetaS; while the beam 18 transmits partially through the surface 13a if the angle theta is smaller. When a disk 7 gets close to an objective lens 6, the light made incident on the grating 15 is turned into the dispersed luminous fluxes. Then the luminous flux has a semicircular form and is made incident only on a photodetector 11b. While the incident light of the grating 15 is focused when the disk 7 goes further away from the lens 6. Then the luminous flux has a semicircular form and is made incident only on a photodetector 11a.

Journal ArticleDOI
TL;DR: In this paper, the authors derived bounds on the sensitivity and resolution of moire deflectometry caused by diffraction effects from the wave equation and showed that Fresnel diffraction is a necessary and sufficient framework for treating these effects.
Abstract: The bounds on the sensitivity and resolution of moire deflectometry caused by diffraction effects are derived from the wave equation. It is shown that Fresnel diffraction is a necessary and sufficient framework for treating these effects. Expressions are given for angular resolution, spatial resolution, and dynamic range. The proper selection of experimental parameters involves a trade-off between the angular resolution on the one hand and spatial resolution and dynamic range on the other.

Book ChapterDOI
01 Jan 1985
TL;DR: In this paper, the first sharp diffraction peak (FSDP) at low Q values in the vicinity of Q ≅ 1.5 A-1.0 A is explained and the connectivity of amorphous solids over intermediate ranges through the packing of basic structural or molecular units.
Abstract: Diffraction studies of glasses often yield a structure factor S(Q) with a pronounced first sharp diffraction peak (FSDP) at low Q values in the vicinity of Q ≅ 1.0-1.5 A-1. This feature, while often quite prominent, has none-the-less eluded detailed explanation because it arises from correlations at distances of 4.5 – 6.0 A rather than from simple nearest- or next-nearest-neighbors. In fact, much of the local structure of the glass can be inferred without reference to this FSDP. We discuss here this diffraction feature and how it gives a direct clue to the connectivity of glasses and amorphous solids over intermediate ranges through the packing of basic structural or molecular units. These considerations are common to a large number of amorphous solids and lead to a better understanding of the atomic structure of glasses as nominally diverse, for example, as SiO2, GeSe2 A2S3 P2Se3 MoS3, and the elemental glasses for which dense random packing is a more familiar concept.

Journal ArticleDOI
TL;DR: In this paper, a quasi-crystalline solid is an aperiodic array of atoms which gives rise to Bragg-like diffraction peaks, and a simple derivation of this paradoxical behaviour is provided.
Abstract: A quasi-crystalline solid is an aperiodic array of atoms which gives rise to Bragg-like diffraction peaks. Using the projection method for generating such structures, the authors provide a simple derivation of this paradoxical behaviour.

Journal ArticleDOI
TL;DR: In this article, the authors studied the mechanism and the dynamics of degenerate four-wave mixing in a nematic liquid crystal film, where nanosecond laser pulses are used to generate an index grating associated with the changes in the density and in the order parameter.
Abstract: We have studied the mechanism and the dynamics of degenerate four-wave mixing in a nematic liquid crystal film. Nanosecond laser pulses are used to generate an index grating associated with the changes in the density and in the order parameter. We have measured and analyzed the contributions from these two mechanisms, their interference effects rise and decay time constants, and have also performed a detailed analysis of the diffraction efficiency. This study quantitatively characterizes the potential usefulness of nematie films for four-wave mixing based applications.

Journal ArticleDOI
TL;DR: In this article, the authors present a method to calculate the diffraction of elastic SH waves by irregular surfaces, which is applicable to boundaries of arbitrary shape and steepness as well as to periodically corrugated surfaces; it is valid at all frequencies.
Abstract: We present a new method to calculate the diffraction of elastic SH waves by irregular surfaces. The technique developed is applicable to boundaries of arbitrary shape and steepness as well as to periodically corrugated surfaces; it is valid at all frequencies. The approach consists of determining the surface forces which cancel the incident stress along the surface. The method relies on the introduction of a periodicity in the surface shape and on a discretization of the boundary at regular spacing. The surface sources which radiate the scattered wave field are obtained by iteration. Examples of calculations and comparisons with other methods are presented.

Journal ArticleDOI
TL;DR: Femtosecond transform limited light pulse propagation in vacuum is described in scalar approximation of diffraction theory in this article, where evolution of the spatial and temporal characteristics of the pulse are presented.