Showing papers on "Diffraction published in 1986"

Laser-Induced Dynamic Gratings

Abstract: The invention ofthe laser 25years ago resulted in powerfullight sources which led to the observation of unexpected and striking phenomena. New fields of science such as holography and nonlinear optics developed constituting the basis of this volume. The classical principle of linear superposition of light wavesdoes not hold anymore. Two laser beams crossing in a suitable material may produce a set of new beams with different directions and frequencies. The interaction of light waves can be understood by considering the optical grating structures which develop in the overlap region. The optical properties of matter become spatially modulated in the interference region of two light waves. Permanent holographic gratings have been produced in this way by photographic processes for many years. In contrast, dynamic or transient gratings disappear after the inducing light source, usually a laser, has been switched off. The grating amplitude is controlled by the light intensity. Dynamic gratings have been induced in a large number ofsolids, liquids, and gases, and are detected by diffraction, 'forced light scattering' of a third probing beam, or by self-diffraction of the light waves inducing the grating. The combined interference and diffraction effect corresponds to four-wave mixing (FWM) in the language of nonlinear optics. The process is called degenerate ifthe frequenciesofthe three incident wavesand the scattered wave are equal. Degenerate four-wave mixing (DFWM) is a simple method to achieve phase conjugation, i.e. to generate a wave which propagates time reversed with respect to an incident wave.

Rigorous coupled-wave analysis of metallic surface-relief gratings

Abstract: A rigorous coupled-wave analysis for metallic surface-relief gratings is presented. This approach allows an arbitrary complex permittivity to be used for the material and thus avoids the infinite conductivity (perfect-conductor) approximation. Both TE and TM polarizations and arbitrary angles of incidence are treated. Diffraction characteristics for rectangular-groove gold gratings with equal groove and ridge widths are presented for free-space wavelengths of 0.5, 1.0 and 10.0 μm for all diffracted orders as a function of period, groove depth, polarization, and angle of incidence. Results include the following: (1) TM-polarization diffraction characteristics vary more rapidly than do those for TE polarization, (2) 95% first-order diffraction efficiency occurs for TM polarization at 10.0 μm, (3) 50% absorption of incident power occurs at 0.5 μm, and (5) the perfect-conductor approximation is not valid for TM polarization at any of the wavelengths and is not valid for TE polarization at 0.5 μm.

Indexing of icosahedral quasiperiodic crystals

Abstract: Since the definition of quasiperiodicity is intimately connected to the indexing of a Fourier transform, for the case of an icosahedral solid, the step necessary to prove, using diffraction, that an object is quasiperiodic, is described. Various coordinate systems are discussed and reasons are given for choosing one aligned with a set of three orthogonal two-fold axes. Based on this coordinate system, the main crystallographic projections are presented and several analyzed single-crystal electron diffraction patterns are demonstrated. The extinction rules for three of the five icosahedral Bravais quasilattices are compared, and some simple relationships with the six-dimensional cut and projection crystallography are derived. This analysis leads to a simple application for indexing powder diffraction patterns.

Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method

Abstract: This paper deals with three-dimensional water-wave diffraction and radiation by a structure consisting of a number of separate (vertically) non-overlapping members in the context of linearised potential flow. An interaction theory is developed which solves the complete problem, predicting wave exciting forces, hydrodynamic coefficients and second-order drift forces, but is based algebraically on the diffraction characteristics of single members only. This method, which includes also the diffraction interaction of evanescent waves, is in principle exact (within the context of linearised theory) for otherwise arbitrary configurations and spacings. This is confirmed by a number of numerical examples and comparisons involving two or four axisymmetric legs, where full three-dimensional diffraction calculations for the entire structures are also performed using a hybrid element method. To demonstrate the efficacy of the interaction theory, it is applied to an array of 33 (3 by 11) composite cylindrical legs, where experimental data are available. The comparison with measurements shows reasonable agreement. The present method is valid for a large class of arrays of arbitrary individual geometries, number and configuration of bodies with non-intersecting vertical projections. Its application should make it unnecessary to perform full diffraction computations for many multiple-member structures and arrays.

The diffraction pattern of projected structures

Abstract: A method for calculating the properties of structures obtained by projection is developed and applied to a three-dimensional generalization of the Penrose tiling. The diffraction pattern is shown in general to consist of a dense set of delta-function peaks. For the Penrose model the pattern in addition has the symmetry of the icosahedron.

X-ray diffraction of multilayers and superlattices

Abstract: Recursion formulae for calculating the reflected amplitude ratio of multilayers and superlattices have been derived from the Takagi-Taupin differential equations, which describe the dynamical diffraction of X-rays in deformed crystals. Calculated rocking curves of complicated layered structures, such as non-ideal superlattices on perfect crystals, are shown to be in good agreement with observed diffraction profiles. The kinematical theory can save computing time only in the case of an ideal superlattice, for which a geometric series can be used, but the reflectivity must be below 10% so that multiple reflections can be neglected. For a perfect crystal of arbitrary thickness the absorption at the center of the dynamical reflection is found to be proportional to the square root of the reflectivity. Sputter-deposited periodic multilayers of tungsten and carbon can be considered as an artificial crystal, for which dynamical X-ray diffraction calculations give results very similar to those of a macroscopic optical description in terms of the complex index of refraction and Fresnel reflection coefficients.

A geometrical theory for spiral waves in excitable media

Abstract: In this paper, we develop a geometrical theory for waves in excitable reacting media. Using singular perturbation arguments and dispersion of traveling plane wave trains, we derive an approximate theory of wave front propagation which has strong resemblance to the geometrical diffraction theory of high frequency waves in hyperbolic systems, governed by the eikonal equation. Using this theory, we study the effect of curvature on waves in excitable media, specifically, rotating spiral patterns in planar regions. From this theory we are able to determine the frequency and wavelength for spiral patterns in excitable, nonoscillatory media.

Stimulated Wood's anomalies on laser-illuminated surfaces

Abstract: Spontaneous, highly periodic, often permanent surface gratings or "ripples" can develop on the surface of almost any solid or liquid material illuminated by a single laser beam of sufficient intensity, under either pulsed or CW conditions. The grating periods are such that the incident laser beam is diffracted into a tangential wave which skims just along or under the illuminated surface. These spontaneously appearing surface ripples are generated by a runaway growth process analogous to stimulated Brillouin or Raman scattering or small-scale self focusing, but having many of the same properties as Wood's anomalies in diffraction gratings. Hence, it seems appropriate to refer to these spontaneous surface structures as "stimulated Wood's anomalies."

Dynamical x‐ray diffraction from nonuniform crystalline films: Application to x‐ray rocking curve analysis

Abstract: A dynamical model for the general case of Bragg x-ray diffraction from arbitrarily thick nonuniform crystalline films is presented. The model incorporates depth-dependent strain and a spherically symmetric Gaussian distribution of randomly displaced atoms and can be applied to the rocking curve analysis of ion-damaged single crystals and strained layer superlattices. The analysis of x-ray rocking curves using this model provides detailed strain and damage depth distributions for ion-implanted or MeV-ion-bombarded crystals and layer thickness, and lattice strain distributions for epitaxial layers and superlattices. The computation time using the dynamical model is comparable to that using a kinematical model. We also present detailed strain and damage depth distributions in MeV-ion-bombarded GaAs(100) crystals. The perpendicular strain at the sample surface, measured as a function of ion-beam dose (D), nuclear stopping power (Sn), and electronic stopping power (Se) is shown to vary according to (1–kSe)DSn and saturate at high doses.

Distortion and peak broadening in quasicrystal diffraction patterns.

Abstract: In this paper, we discuss how quenched strains in phonon and phason variables and/or quenched dislocations can lead to peak broadening and distortion in quasicrystal diffraction patterns. We argue that high-resolution electron micrographs and observations of distortions in electron diffraction patterns indicate the presence of anisotropic strains in the phason variable in the icosahedral phase of Al-Mn and related alloys. Such strains also contribute to the x-ray peak widths and line shapes.

Sharp diffraction maxima from an icosahedral glass.

Abstract: We consider densely packed assemblies of icosahedra, such that icosahedral bond-orientational order is enforced throughout the sample. The peaks in the calculated diffraction patterns may be put in a one-to-one correspondence with the electron and x-ray diffraction patterns from icosahedral Al-Mn alloys, allowing the determination of the packing-unit size. We show that these maxima are not Bragg diffraction peaks, but have an intrinsic width, and may be understood as resulting from the interference between two or more characteristic lengths, as originally discussed by Hendricks and Teller.

Polarization properties of photorefractive diffraction in electrooptic and optically active sillenite crystals (Bragg regime)

Abstract: The polarization properties of diffraction from volume phase gratings in photorefractive sillenite crystals such as bismuth silicon oxide (Bi12SiO20), bismuth germanium oxide (Bi12GeO20), and bismuth titanium oxide (Bi12TiO20) are strongly modified by the presence of concomitant natural optical activity and electric-field-induced linear birefringence. A set of coupled-wave equations that characterize the Bragg regime has been derived for the 〈110〉 and the 〈001〉 crystallographic orientations typically employed in volume holographic storage and multiwave-mixing applications. The predicted anisotropic behavior of the grating diffraction is experimentally confirmed, and a significant efficiency improvement is shown to occur for proper choice of the operating mode and the probe beam polarization in a given configuration.

Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings.

Abstract: Using rigorous coupled-wave analysis, high spatial-frequency rectangular-groove surface-relief phase gratings are shown to be capable of exhibiting zero reflectivity. Thus these corrugated surfaces may act as antireflection coatings in a variety of applications. The diffraction characteristics of rectangular-groove surface-relief gratings are presented for several ratios of incident wavelength to grating period as a function of filling factor, groove depth, angle of incidence, and polarization. The conditions for zero reflectivity are identified. Results are compared with single-homogeneous-layer approximate theory results. In the limit of long wavelengths for an electromagnetic wave in a dielectric of refractive index n1 normally incident on a dielectric of index n2, it is determined that for antireflection behavior, the grating groove depth should be λ/4(n1n2)1/2 and the filling factor should be n1/(n1 + n2) or n2/(n1 + n2) for the electric field perpendicular or parallel to the grating vector, respectively. The spectral and angular responses of these gratings are like those of single-homogeneous-layer antireflection coatings. These gratings also exhibit birefringent retardation.

Structure of poorly crystalline MoS2 - A modeling study

Abstract: Current interest in amorphous and poorly crystallized phases of the layered transition metal dichalcogenides arises primarily from their unique catalytic and electrochemical properties not present in the corresponding crystalline phases. Computer calcultions of the scattered X-ray intensity from model structures of poorly crystalline (px-) MoS2 are compared here with experimental patterns from materials prepared at different temperatures. The results are used to identify the salient features of the observed diffraction patterns of px-MoS2 in which the measured diffuse scattered intensity may be clearly attributed to the stacking and rotational disorder of the layers as well as the limited number of these layers. A procedure for the interpretation of the X-ray diffraction pattern of px-MoS2 has thereby been developed in which the entire scattering pattern may be calculated without separation into Bragg peaks (of varying breadth and shape) and diffuse background.

Brightness, coherence and propagation characteristics of synchrotron radiation

Abstract: A formalism is presented by means of which the propagation and imaging characteristics of synchrotron radiation can be studied, taking into account the effects of diffraction, electron beam emittance, and the transverse and longitudinal extent of the source. An important quantity in this approach is the Wigner distribution of the electric fields, which can be interpreted as a phase-space distribution of photon flux, and thus can be identified with the brightness. When integrated over the angular variables, the brightness becomes the intensity distribution in the spatial variables and when integrated over the spatial variables, it becomes the intensity distribution in angular variables. The brightness so defined transforms through a general optical medium in exactly the same way as in the case of a collection of geometric rays. Finally, the brightness of different electrons adds in a simple way. Optical characteristics of various synchrotron radiation sources — bending magnets, wigglers and undulators — are analyzed using this formalism.

Near-field diffraction by a slit: implications for superresolution microscopy.

Abstract: The transmission of light through an infinite slit in a thick perfectly conducting screen is investigated. The spatial distribution of the near-field energy flux is determined through the formulation of four coupled integral equations, which are solved numerically. Transmission coefficients calculated by this method are in agreement with those determined by an alternative formulation. The results theoretically demonstrate the feasibility of near-field superresolution microscopy, in which the collimated radiation passed by an aperture is used to circumvent the diffraction limit of conventional optics, and further suggest the feasibility of near-field superresolution acoustic imaging.

Distribution of light at and near the focus of high-numerical-aperture objectives

Abstract: Classical diffraction theory is used to investigate the effects of high numerical aperture on the focusing of coherent light. By expanding the diffracted beam in plane waves, we show that the lens action can be expressed as a succession of three Fourier transforms. Furthermore, polarization effects are included in the model in a natural way. Some numerical results of the theory are also presented.

JCPDS — International Centre for Diffraction Data Sample Preparation Methods in X-Ray Powder Diffraction

Abstract: The aim of any diffraction experiment is to obtain reproducible data of high accuracy and precision so that the data can be correctly interpreted and analyzed. Various methods of sample preparation have been devised so that reproducibility, precision and accuracy can be obtained. The success of a diffraction experiment will often depend on the correct choice of preparation method for the sample being analyzed and for the instrument being used in the analysis.A diffraction pattern contains three types of useful information: the positions of the diffraction maxima, the peak intensities, and the intensity distribution as a function of diffraction angle. This information can be used to identify and quantify the contents of the sample, as well as to calculate the material's crystallite size and distribution, crystallinity, and stress and strain. The ideal preparation for a given experiment depends largely on information desired.

The Lorentz-polarization factor and preferred orientation in oriented clay aggregates

Abstract: Abstraet--A closed-form equation was derived that describes the powder-ring distribution factor as a function of 20, soller slit collimation, and or*, which is defined as the standard deviation of an axiaUy symmetrical Gaussian orientation function. Methods were developed for measuring a* in the reflection mode by means of a 0/20 diffractometer. Six experimental arrangements for a sedimentary chlorite showed widely different intensity ratios of the 001/005 reflections and gave a standard deviation of  5.8% when corrected by the theory. The absolute integrated intensities of the 003 reflection from eleven illite samples provided an eight-fold maximum range which, when corrected, yielded a standard deviation of  The intensity distributions within each of two X-ray powder diffraction patterns obtained from instruments with different soller-slit configurations could not be directly compared at low diffraction angles unless corrections, based on a*, were introduced to allow for the differences in axial divergence.

Refractive and diffractive scattering in the interstellar medium

Abstract: Radio wave propagation through electron-density fluctuations in the ISM is studied. Observable propagation effects are explored using a one-dimensional thin-screen model for the turbulent medium. Diffraction caused by stochastic small-scale irregularities is combined with refraction from deterministic large-scale irregularities. Some of the effects are illustrated with numerical simulations of the wave propagation. Multiple imaging is considered, delineating the possible effects and discussing their extensions to two-dimensional screens and extended three-dimensional media. The case where refraction as well as diffraction is caused by a stochastic medium with a spectrum of a given form is considered. The magnitudes of observable effects is estimated for representative spectra that may be relevant to the ISM. The importance of the various effects for timing and scintillation observations of pulsars, VLBI observations of galactic and extragalactic radio sources, and for variability measurements of extragalactic sources is assessed. 47 references.

Dynamical diffraction calculations for RHEED and REM

Abstract: The multislice formulation of the many-beam dynamical diffraction theory has been applied to the Bragg case of electron diffraction for the extended surface of a perfect crystal and also for a crystal surface with a surface step. The wavefunctions within and outside the crystal have been calculated and used to derive the standing-wave pattern in the top atomic layers of the crystal, the intensities of the reflection high-energy electron diffraction (RHEED) pattern and the contrast of the reflection electron microscopy (REM) image. Calculations made for the diffraction of 19, 40 and 80 keV electrons from (111) surfaces of Pt and Au demonstrate the channeling of electrons under the conditions of surface resonance, the perturbation of the standing-wave field in the crystal by a one-atom-high surface step and the REM contrast for a through-focus series of images of a surface step. The method is applicable to models including surface relaxations and reconstructions and any kind of local defect of the surface or of the bulk crystal.

Uniform versus Gaussian beams: a comparison of the effects of diffraction, obscuration, and aberrations

Abstract: Much is said in the literature about Gaussian beams. However, there is little in terms of a quantitative comparison between the propagation of uniform and Gaussian beams. Even when results for both types of beam are given, they appear in a normalized form in such a way that some of the quantitative difference between them is lost. In this paper we first consider an aberration-free beam and investigate the effect of Gaussian amplitude across the aperture on the focal-plane irradiance and encircled-power distributions. The axial irradiance of focused uniform and Gaussian beams is calculated, and the problem of optimum focusing is discussed. The results for a collimated beam are obtained as a limiting case of a focused beam. Next, we consider the problem of aberration balancing and compare the effects of primary aberrations on the two types of beam. Finally, the limiting case of weakly truncated Gaussian beams is discussed, and simple results are obtained for the irradiance distribution and the balanced aberrations.

Essentials of Crystallography

Abstract: This text provides an introduction to the fundamental concepts of crystallography, crystalline solids, and the diffraction of X-rays, electrons, and neutrons. The objective of this text is to provide a physical understanding of the subject rather than a rigorous development of crystallography and diffraction theory. At the outset, the concepts of crystallography - periodicity and symmetry - are explored. The theory of diffraction by crystals and application to X-ray diffractions by single crystals and power are developed at length. This is the first such text to use a vector treatment of lattice and diffraction geometry; matrix methods have been adopted for the reason that they are suitable for computer programs. The chapter on crystal structure is concerned with principles of contemporary techniques, it introduces direct methods, the Rietveld method, and other modern methods of structure determination and refinement. The chapter on electron diffraction and microscopy concentrates on principles and keeps technological detail to the minimum; the treatment is in terms of the kinematical theory of diffraction, but nevertheless takes the reader as far as high-resolution images of unit-cells. This, the first of two volumes, is closely related to the authors' earlier book, Crystalline Solids. Problems are provided at the endmore » of each chapter, and answers are provided at the end of the volume.« less

Diffraction grating structures

Abstract: A diffraction grating responds to incoming radiation incident thereon within a given range of incidence angles and re-directs such incident radiation from the structure in a selected direction within relatively limited confines. A liquid crystal material is positioned in contact with the diffracting surface of said at least one diffraction structure, the liquid crystal material, when inactivated, having a refractive index substantially the same as that of the diffraction structure. Activation means place the liquid crystal material in an activated state so that the refractive index thereof is substantially different from that of the diffraction structure whereby incoming radiation within a given range of incidence angles is transmitted through the structure and exits in the selected direction.