Showing papers on "Diffraction published in 1996"

Transmission Electron Microscopy: A Textbook for Materials Science

Abstract: Basics.- The Transmission Electron Microscope.- Scattering and Diffraction.- Elastic Scattering.- Inelastic Scattering and Beam Damage.- Electron Sources.- Lenses, Apertures, and Resolution.- How to 'See' Electrons.- Pumps and Holders.- The Instrument.- Specimen Preparation.- Diffraction.- Diffraction in TEM.- Thinking in Reciprocal Space.- Diffracted Beams.- Bloch Waves.- Dispersion Surfaces.- Diffraction from Crystals.- Diffraction from Small Volumes.- Obtaining and Indexing Parallel-Beam Diffraction Patterns.- Kikuchi Diffraction.- Obtaining CBED Patterns.- Using Convergent-Beam Techniques.- Imaging.- Amplitude Contrast.- Phase-Contrast Images.- Thickness and Bending Effects.- Planar Defects.- Imaging Strain Fields.- Weak-Beam Dark-Field Microscopy.- High-Resolution TEM.- Other Imaging Techniques.- Image Simulation.- Processing and Quantifying Images.- Spectrometry.- X-ray Spectrometry.- X-ray Spectra and Images.- Qualitative X-ray Analysis and Imaging.- Quantitative X-ray Analysis.- Spatial Resolution and Minimum Detection.- Electron Energy-Loss Spectrometers and Filters.- Low-Loss and No-Loss Spectra and Images.- High Energy-Loss Spectra and Images.- Fine Structure and Finer Details.

Phase objects in synchrotron radiation hard x-ray imaging

Abstract: Phase objects are readily imaged through Fresnel diffraction in the hard x-ray beams of third-generation synchrotron radiation sources such as the ESRF, due essentially to the very small angular size of the source. Phase objects can lead to spurious contrast in x-ray diffraction images (topographs) of crystals. It is shown that this contrast can be eliminated through random phase plates, which provide an effective way of tailoring the angular size of the source. The possibilities of this very simple technique for imaging phase objects in the hard x-ray range are explored experimentally and discussed. They appear very promising, as shown in particular by the example of a piece of human vertebra, and could be extended to phase tomography.

X-ray and neutron diffraction in nonideal crystals

Abstract: 1. Distribution of the Scattering Intensity. General Aspects.- 1.1 Diffraction Techniques for Analyzing Imperfections in Crystals.- 1.2 Kinematical Theory of Scattering.- 1.2.1 Dynamical and Kinematical Theories.- 1.2.2 X-Ray Scattering Intensity.- 1.2.3 Scattering Cross Section for Thermal Neutrons.- 1.2.4 Applicability Range for the Kinematic Theory.- 1.3 Scattering by Perfect Crystals of Finite Size.- 1.3.1 Intensity Distribution in Reciprocal Lattice Space: Form Function.- 1.3.2 Intensity Distribution in the Debye Diffraction Pattern.- 1.4 Scattering in Undistorted Crystals Containing Microscopic Cavities or Inclusions.- 1.5 Scattering by Crystals Containing Defects of Arbitrary Type. Classification of Defects.- 1.5.1 Analysis of Scattering by Imperfect Crystals.- 1.5.2 Scattering by Crystals with Randomly Distributed Defects.- 1.5.3 Classification of Defects.- 1.5.4 Diffuse Scattering by Crystals Containing First-Class Defects Under Weak Overlap of the Displacement Fields of Individual Defects.- 1.5.5 Approximation of Smoothly Varying Distortions.- 1.5.6 Scattering Intensity with Correlated Arrangement of Defects.- 1.6 Harmonic Analysis of the X-Ray Line Shapes.- 1.6.1 Fourier Coefficients for the Intensity Distributions of X-Ray Lines.- 1.6.2 Limiting Cases of Nondistorted and Large-Size Crystallites.- 1.6.3 Analysis of Crystallite Size and Distortions.- 2. Static Displacements in Crystals with Bounded Defects.- 2.1 Fluctuation Waves of Defects Concentration and Static Displacements.- 2.1.1 Symmetry of Defects.- 2.1.2 The Defect Distribution in Terms of Static Concentration Waves.- 2.1.3 Static Displacement Waves.- 2.2 Macroscopic Theory for the Static Displacement Waves.- 2.2.1 Long-Wavelength Fluctuation Waves and the Free Energy of the Anisotropic Elastic Continuum.- 2.2.2 Amplitudes of the Fluctuation Waves of Static Displacements.- 2.2.3 Fourier Components of the Static Displacements in the Continuum Description.- 2.2.4 Simplifications Introduced by Symmetry.- 2.2.5 Fluctuation Waves in Thin Films.- 2.3 Microscopic Theory for the Static Displacement Waves.- 2.3.1 Free Energy of Distorted Crystal with Bravais Lattice.- 2.3.2 Transition to the Long-Wave Approximation and the Related Force Constants.- 2.3.3 Crystals of Arbitrary Structure.- 2.4 Static Displacement Fields Around Bounded Defects.- 2.4.1 Atom Displacements Far from Defects.- 2.4.2 Atomic Displacements Near Defects, Green Functions and Mean Squares of Static Displacements.- 2.5 Static Distortions in Quasi-One-Dimensional and Quasi-Two-Dimensional Crystals.- 2.5.1 Discreteness of the Lattice and Spatial Dispersion.- 2.5.2 Static Distortion Fields of Defects in Strongly-Anisotropic Crystals.- 3. Positions and Intensities of Regular Reflection Peaks.- 3.1 Shift of X-Ray Lines in Imperfect Crystals and the Determination of Defect Concentrations.- 3.1.1 Influence of Defects on X-Ray Line Positions and Estimated Crystal Sizes.- 3.1.2 Studies of Vacancies in Crystals.- 3.1.3 Complexes in Solid Solutions and Their Effect on the Lattice Parameters.- 3.1.4 Dilation Effects Caused by Dislocation Loops.- 3.2 Regular Reflection Intensities in Perfect Crystals.- 3.2.1 Intensity Attenuation Factors.- 3.2.2 Debye-Waller Factor in Perfect Harmonic Crystals.- 3.2.3 Chain-Like and Layered Crystals.- 3.2.4 Effect of Anharmonicity on the Debye-Waller Factor.- 3.3 Effect of Static Displacements on Intensities of Regular Reflections.- 3.3.1 Debye-Waller Factor Due to Static Displacements.- 3.3.2 Effects in Crystals Containing Particles of a New Phase or Dislocation Loops.- 3.3.3 Layered and Chain-Like Crystals.- 3.3.4 Concentrated Solutions.- 3.3.5 Experimental Results on Regular Reflection Intensities in Imperfect Crystals.- 3.4 Effect of Thermal Vibrations in Imperfect Crystals.- 3.4.1 Crystals with Low Defect Concentrations.- 3.4.2 Concentrated Solutions.- 3.5 Debye-Waller Factors in Dynamical Diffraction Effects.- 3.5.1 Anomalous Transmission.- 3.5.2 X-Ray Fluorescence.- 3.5.3 Spatial Intensity Oscillations.- 3.5.4 Critical Potentials.- 4. Diffuse Scattering of X-Rays and Neutrons by Crystal Defects.- 4.1 Weakly Distorted Crystals.- 4.1.1 Scattering by Single Defects.- 4.1.2 Scattering Intensity Near Reciprocal Lattice Points: Symmetry of Defects and Force Dipole Tensors.- 4.1.3 Scattering Intensity Distribution at Large Distances from Reciprocal Lattice Points and Determination of the Defect Configuration and the Force Field.- 4.1.4 Diffuse Scattering and the Correlation in Defect Positions.- 4.1.5 Experiments on Scattering by Point Defects in Irradiated Crystals and Dilute Solutions.- 4.1.6 Scattering by Self-localized Electrons.- 4.1.7 Diffuse Scattering Representation in Various Experimental Techniques.- 4.2 Effects of Groups of Point Defects, New-Phase Particles, or Small-Radius Dislocation Loops.- 4.2.1 Scattering by Large Bounded Defects in Weakly Distorted Crystals.- 4.2.2 Diffuse Scattering by Weakly Distorted Crystals with Particles of a Second Phase and Ageing of Solutions.- 4.2.3 Diffuse Scattering by Small-Radius Dislocation Loops in Strained and Irradiated Materials.- 4.3 Intensity Distribution for Scattering by Strongly Distorted Crystals with Finite Defects.- 4.3.1 Change in Scattering Intensity Distribution with Increasing Defect Strength.- 4.3.2 Integrated Intensity from Strongly Distorted Crystals.- 4.3.3 Intensity Distribution in the Reciprocal Space.- 4.3.4 The Debye Diffraction Pattern.- 4.3.5 Experiments on Strongly Distorted Ageing Alloys and Irradiated Materials.- 4.3.6 Nonrandom Arrangement of Finite Defects.- 4.4 Strongly Anisotropic Crystals.- 4.4.1 Quasi-Two-Dimensional Crystals.- 4.4.2 Quasi-One-Dimensional Crystals.- 4.5 Effect of Finite Defects in Thin Films and Surface Layers on X-Ray Scattering.- 4.5.1 Scattering Intensity for Imperfect Finite Crystals.- 4.5.2 Diffuse Scattering by Defects in Thin Films.- 4.5.3 Broadening of Regular Reflection Peaks in Free Films with a Large Surface Area.- 4.5.4 Diffuse Scattering by Defects in a Thin Surface Layer.- 5. Scattering of X-Ray and Neutrons in Crystals with Dislocations.- 5.1 Broadening of Peaks by Randomly Distributed Defects of the Second Class.- 5.1.1 Linear Dislocations.- 5.1.2 Large-Radius Dislocation Loops.- 5.1.3 Dislocation Dipoles.- 5.1.4 Stacking Faults and Split Dislocations.- 5.2 Effect of Nonrandom Dislocation Arrangement on Scattering Intensity Distribution.- 5.2.1 Scattering by Crystals with Dislocation Walls and a Dislocation Description for the Effects Caused by Blocks and Cells.- 5.2.2 Correlation in the Uniform Dislocation Ensemble and in Crystals with Nonuniform Dislocation Arrangement.- 5.3 Diffraction Methods of Investigation of Dislocation Ensembles.- 5.3.1 Determination of Dislocation Density.- 5.3.2 Correlation and Inhomogeneity in Dislocation Arrangement.- 5.3.3 Dislocations in Narrow Small-Angle Walls (Boundaries) and Excess Dislocations of a Given Sign.- 5.3.4 Diffraction Techniques for Analyzing the Grain Boundaries.- Appendices.- A. Cumulant Expansion.- B. Equations for Amplitudes of Static Displacement Waves for Various Crystal and Defect Symmetries.- D. Mean Squares of Static Displacements in fee Crystals.- for Strongly Deformed Crystals Containing Limited-Size Defects.- F. Calculation of T(?) for Homogeneous Dislocation Ensemble.- References.

Self-Trapping of Partially Spatially Incoherent Light

Abstract: We report the first observation of self-trapping of a spatially incoherent optical beam in a nonlinear medium. Self-trapping occurs in both transverse dimensions, when diffraction is exactly balanced by photorefractive self-focusing.

Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization

Abstract: A new implementation of the coupled-wave method for TM polarization is proposed. We use a second-order differential operator established by Neviere together with a scattering-matrix approach. Thus we obtain for metallic gratings a convergence rate as quick as that in TE polarization.

X-ray scattering and absorption by magnetic materials

Abstract: 1. Introductory survey 2. Non-resonant magentic X-ray diffraction from antiferromagnets 3. Non-resonant magnetic diffraction from ferromagnets 4. Magnetic X-ray dichroism 5. Resonant X-ray diffraction from antiferromagnets 6. Resonant magnetic X-ray diffraction from ferromagnets 7. Compton scattering 8. Theoretical framework Appendix Index

X-ray holography with atomic resolution

Abstract: DIFFRACTION methods for crystallographic structure determination suffer from the so-called 'phase problem'; a diffraction pattern provides intensity but not phase information for the scattered beams, and therefore cannot be uniquely inverted to obtain the crystal structure of a sample. Holographic methods1, on the other hand, offer a means of extracting both intensity and phase information. To be useful for crystallographic applications, holography must be implemented with radiation of sufficiently small wavelength to resolve atomic-scale features2. One method, electron-emission holography3–9, uses electron waves and is a powerful tool for studying surface structure; but it cannot image the internal structure of solids because of complications arising from the highly anisotropic nature of electron scattering processes. A proposed alternative method uses X-rays2,10–13, which scatter more isotropically than electrons. Here we demonstrate the efficacy of atomic-scale X-ray holography by obtaining direct images of the three-dimensional arrangement of strontium atoms in the cubic perovskite SrTiO3. With more intense synchrotron sources for illumination, and with the development of improved X-ray detectors, X-ray holography should become a powerful general technique for unambiguous structure determination in condensed matter systems.

Resonant scattering from two-dimensional gratings

Abstract: A theoretical investigation of resonant scattering from two-dimensional gratings is presented. Abrupt changes of diffraction efficiency over a small parameter range have been observed by rigorous coupled-wave analysis. The peak reflection or transmission efficiencies can approach unity. This phenomenon is explained in terms of the coupling between the incident plane wave and guided modes that can be supported by the two-dimensional-grating waveguide structure. Because of the double periodicity, the incident field can be coupled into any direction in the grating plane. The guided modes supported by two-dimensional gratings are found by rigorous solution of the homogeneous problem associated with the scattering (inhomogeneous) problem. The complex propagation constants for the guided modes provide estimates of both the resonance angle and width. In addition, to illustrate the implication of the radical change in the phase and amplitude of the propagating waves, we report a study of finite-beam diffraction in the resonant scattering region. Applications for the structures include polarization-independent narrow-band filters and bandwidth-tunable filters. It is shown that, because of the double resonance, the polarization-independent narrow-band filters have a large angular tolerance.

Resonant Exchange Scattering: Polarization Dependence and Correlation Function

Abstract: The cross section for X-ray resonant exchange scattering is reformulated in terms of linear polarization states perpendicular and parallel to the scattering plane, a basis particularly well suited to synchrotron X-ray diffraction experiments. The explicit polarization dependence of the terms is calculated for the electric dipole and quadrupole contributions. This expression, in turn, is rewritten in an orthonormal basis to highlight the dependence of the cross section on each component of the magnetic moment. This has the benefit of providing an empirically useful expression for the cross section. Diffraction patterns from a few simple magnetic structures are calculated. Finally, the correlation function measured at each resonant harmonic is derived.

A boundary element solution for a mode conversion study on the edge reflection of Lamb waves

Abstract: The boundary element method, well known for bulk wave scattering, is extended to study the mode conversion phenomena of Lamb waves from a free edge. The elastodynamic interior boundary value problem is formulated as a hybrid boundary integral equation in conjunction with the normal mode expansion technique based on the Lamb wave dispersion equation. The present approach has the potential of easily handling the geometrical complexity of general guided wave scattering with improved computational efficiency due to the advantage of the boundary‐type integral method. To check the accuracy of the boundary element program, vertical shear wave diffraction, due to a circular hole, is solved and compared with previous analytical solutions. Edge reflection factors for the multibackscattered modes in a steel plate are satisfied quite well with the principle of energy conservation. In the cases of A0, A1, and S0 incidence, the variations of the multireflection factors show similar tendencies to the existing results fo...

System and method for optically measuring a structure

Abstract: A system and method for measuring the dimensions of a small (e.g., microelectronic) structure. The present invention is an optical system and method that uses a polarized light beam, reflected off or transmitted through, a structure, to measure the structural parameters, such as the lateral dimensions, vertical dimensions, height, or the type of structural material. The system employs a light source to generate a light beam that is polarized and focused onto the structure to be measured. The structure is illuminated with TE and TM polarized light. The structure is dimensioned such that the TM and TE fields are affected differently by the diffraction off the structure. As a result, either the TE or TM field can be used as a reference to analyze the phase and amplitude changes in the other field. Differences between the diffracted TE and TM far fields allow a comparison of the relationship between the amplitude and phase of those fields to determine the structural parameters of a structure.

Strong effects of photonic band structures on the diffraction of colloidal crystals

Abstract: The influence of photonic band structures on optical diffraction has been studied with colloidal crystals with large refractive index ratios up to 1.45 and polarizibilities per volume as large as 0.6. It is found that the apparent Bragg spacings are strongly dependent on the wavelength of light. The dynamical diffraction theory that correctly describes weak photonic effects encountered in x-ray diffraction also breaks down. Two simple models are presented that give a much better description of the diffraction of photonic crystals. @S01631829~96!06523-X#

Experimental demonstration of resonant anomalies in diffraction from two-dimensional gratings.

Abstract: Resonant effects in diffraction from two-dimensional dielectric gratings is demonstrated experimentally. A two-layer structure, which consists of a uniform guiding layer and a grating layer, yielded symmetric, low-sideband resonance that is suitable for narrow-band filter applications. Excellent agreement between measured and calculated spectral and angular dependence is obtained.

Cluster size determination from diffractive He atom scattering

Abstract: In a crossed molecular beam arrangement helium atoms are scattered from argon clusters which are produced in an averaged size range of n=6 to n=90 by adiabatic expansion through sonic and conical nozzles. The diffraction oscillations in the total differential cross section are used to derive information on the size distribution of the clusters by comparison with quantum mechanical calculations based on a model potential. In the size range covered by the measurements, the average cluster size is given by n=38.4(Γ*/1000)1.64, where Γ* is the scaling parameter of the source conditions introduced by Hagena [Z. Phys. D 4, 291 (1987)]. The results are in agreement with recent measurements of corrected mass spectra but disagree with the results obtained from electron diffraction. General relations are recommended which connect the scaling parameter with the averaged size.

Atomic Wave Diffraction and Interference Using Temporal Slits.

Abstract: We measure the energy distribution of a slow Cesium atomic beam when it is chopped into a short pulse and we find results which agree well with the time-energy uncertainty principle. The chopper consists in an atomic mirror formed by a laser evanescent wave whose intensity is pulsed. We use the temporally diffracted beam to design a Young-slit-type interferometer, in which the interfering paths consist of atomic trajectories bouncing at two different times on the mirror. By changing the mirror intensity, we can scan the atomic phase difference between the two arms. [S0031-9007(96)00519-4] When a beam of particles with a well defined energy is chopped into a short pulse, the outcoming energy distribution is broadened according to the time-energy uncertainty relation. This effect is very well known for photons, and it is at the basis of spectroscopy with ultrashort pulses of light. For matter waves, the phenomenon of diffraction by a time slit has been studied theoretically by several authors [1]. Its observation constitutes a test of time-dependent quantum mechanics, while usual diffraction phenomena can be described using the stationary formulation of the Schrodinger equation. We report here the observation of this temporal diffraction effect for de Broglie atomic waves, and we show that our results are in good agreement with the quantum mechanics prediction. We also use the coherence of the diffracted pulse to realize a Young interferometer using temporal slits. This interferometer is a very flexible device in which the temporal positions of the diffracting slits can

Interdigital cantilevers for atomic force microscopy

Abstract: We present a sensor for the atomic force microscope (AFM) where a silicon cantilever is micromachined into the shape of interdigitated fingers that form a diffraction grating. When detecting a force, alternating fingers are displaced while remaining fingers are held fixed. This creates a phase sensitive diffraction grating, allowing the cantilever displacement to be determined by measuring the intensity of diffracted modes. This cantilever can be used with a standard AFM without modification while achieving the sensitivity of the interferometer and maintaining the simplicity of the optical lever. Since optical interference occurs between alternating fingers that are fabricated on the cantilever, laser intensity rather than position can be measured by crudely positioning a photodiode. We estimate that the rms noise of this sensor in a 10 hz–1 kHz bandwidth is ∼0.02 A and present images of graphite with atomic resolution.

Polarization holographic gratings in side-chain azobenzene polyesters with linear and circular photoanisotropy.

Abstract: We investigate thin phase polarization holographic gratings recorded with two waves with orthogonal linear polarizations in materials in which illumination with linearly/circularly polarized light gives rise to linear/circular birefringence. The theoretical analysis shows that the presence of circular photoanisotropy changes significantly the diffraction characteristics of the gratings. The intensities of the waves diffracted in the +1 and −1 orders of diffraction and their ratio depend substantially on the reconstructing-wave polarization. Experiments with films of side-chain liquid-crystalline azobenzene polyester that is a photoanisotropic material of the considered type confirm the unusual polarization properties. It is shown that polarization holography may be used for real-time simultaneous measurement of photoinduced linear and circular birefringence.

Effect of three‐dimensional topography on seismic motion

Abstract: We present a semianalytical, seminumerical method to calculate the diffraction of elastic waves by an irregular topography of arbitrary shape. The method is a straightforward extension to three dimensions of the approach originally developed to study the diffraction of SH waves [Bouchon, 1985] and P-SV waves [Gaffet and Bouchon, 1989] by two-dimensional topographies. It relies on a boundary integral equation scheme formulated in the frequency domain where the Green functions are evaluated by the discrete wavenumber method. The principle of the method is simple. The diffracted wave field is represented as the integral over the topographic surface of an unknown source density function times the medium Green functions. The Green functions are expressed as integrals over the horizontal wavenumbers. The introduction of a spatial periodicity of thc topography combined with the discretization of the surface at equal intervals results in a discretization of the wavenumber integrals and in a periodicity in the horizontal wavenumber space. As a result, the Green functions are expressed as finite sums of analytical terms. The writing of the boundary conditions of free stress at the surface yields a linear system of equations where the unknowns are the source density functions representing the diffracted wave field. Finally, this system is solved iteratively using the conjugate gradient approach. We use this method to investigate the effect of a hill on the ground motion produced during an earthquake. The hill considered is 120 m high and has an elliptical base and ratios of height-to-half-width of 0.2 and 0.4 along its major and minor axes. The results obtained show that amplification occurs at and near the top of the hill over a broad range of frequencies. For incident shear waves polarized along the short dimension of the hill the amplification at the top reaches 100% around 10 Hz and stays above 50% for frequencies between 1.5 Hz and 20 Hz. For incident shear waves polarized along the direction of elongation of the topography, the maximum amplification occurs between 2 Hz and 5 Hz with values ranging from 50% to 75%. The results also show that the geometry of the topography exerts a very strong directivity on the wave field diffracted away from the hill and that at some distance from the hill this diffracted wave field consists mostly of Rayleigh waves.

Chain Length Dependence of the Striped Phases of Alkanethiol Monolayers Self-Assembled on Au(111): An Atomic Beam Diffraction Study

Abstract: Low-energy helium atom diffraction measurements of the surface structure of n-alkanethiol films deposited from a molecular beam on to the (111) face of gold single crystals (at an impingement rate ...

Wave fields in three dimensions: analysis and synthesis

Abstract: Distributions of wave fields in three-dimensional domains are analyzed, synthesized, and generated experimentally. Fundamental limits are discussed and sampling conditions are derived for their generation, with use of a single diffractive element. A general design procedure, based on optimization algorithms, is developed and implemented. Experimental results show that special three-dimensional light distributions can be achieved with low-information-content elements in on-axis configurations.

Bond angle distribution in amorphous germania and silica

Abstract: The distribution of Ge-O-Ge and Si-O-Si bond angles α in amorphous germania and silica is re-determined on the basis of diffraction experiments. The bond angle α joining adjacent tetrahedra is the central parameter of any continuous random network description (CRN) of these glasses. New high energy photon diffraction experiments on amorphous germania (at photon energies of 97 and 149 keV) are presented, covering the momentum transfer 0.6-33.5 A -1 . In photon diffraction experiments on GeO 2 the contribution of the OO pairs is very small. To obtain a similar information for amorphous SiO 2 , high energy photon diffraction experiments [1] have been combined with neutron diffraction data [2, 3] on amorphous silica in order to eliminate the OO-partial structure factor. With this technique it is shown that the Si-O-Si angle distribution is fairly narrow (σ = 7.5°) and in fact comparable in width to the Ge-O-Ge angle distribution (σ = 8.3°), a result which differs from current opinion. The narrower distribution found in this study are in much better agreement to the determinations based on 29 Si-MAS-NMR. Among the various models relating the chemical shift to the bond angle, best agreement is found with those models based on the secant model. Sharp components in the bond angle distribution can be excluded within the reached real space resolution of 0.09 A

The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation

Abstract: A model problem in the scattering of a time-harmonic wave by an obstacle coated with a thin penetrable shell is examined. In previous studies, the contrast coefficients of the thin shell are assumed to tend to infinity in order to compensate for the thickness considered. In this paper, these coefficients are assumed to remain finite. Such a treatment leads to a singular perturbation term that creates a typical difficulty for the asymptotic analysis of the problem with respect to the thickness of the coating. As a result, the asymptotic analysis is essentially based on a suitable handling of the stability of the solution relative to the thickness. As a consequence, it is shown how effective boundary conditions which can be substituted to the thin shell can then be obtained and analyzed in a simple way.

Light guide plates and light guide plate assembly utilizing diffraction grating

Abstract: A light guide plate is provided which utilizes the phenomenon of diffraction based on wave optics of light, and which can provide much higher and more uniform brightness over an entire illuminated surface than the brightness level achievable by the prior art and can assure longer battery life through reduced power consumption for a light source. The light guide plate consists of a transparent plate, at least on one end of which light rays from the light source fall. The light guide plate has a diffraction grating printed or worked on a bottom surface thereof such that at least one of a grating part width/non-grating part width ratio in unit-width or a sectional configuration of the diffraction grating is varied so as to enhance and uniform light intensity on a top surface of the light guide plate.

A physical model of sound diffraction and reflections in the human concha

Abstract: An approximated physical model of the frequency transfer function of the human concha is developed in this paper. This formulation includes diffraction, reflection, and interference phenomena in the concha cavity. The performance of the proposed diffraction/reflection model is compared with that of the single‐delay‐and‐add approximation by checking their predictions against the experimental transfer function of a metal spiral‐shaped diffracting/reflecting system. Results show that the diffraction/reflection model performs considerably better at predicting both the absolute center frequency of spectral minima and the relative frequency spacing between them. The diffraction/reflection model is then applied to a realistic concha shape and its predictions are compared with experimental head‐related transfer functions for azimuth‐ and elevation‐varying sound sources. In this case, the model predicts the elevation‐dependent spectral features related to the transverse dimensions of the concha. Additionally, the diffraction/reflection model predicts that, because of sound diffraction, similar spectral features must be generated in the concha for sources at all azimuths within the frontal part of the ipsilateral hemisphere. Experimental and theoretical evidence supporting this prediction is presented.

Modal transmission-line theory of multilayered grating structures

Abstract: Solutions to problems involving the scattering and guiding of waves by multilayered grating configurations can be phrased in rigorous modal terms. We show that such a modal solution can be represented by electrical transmission-line networks, which are generalized forms of simpler conventional circuits. This approach brings considerable physical insight into the grating diffraction process and facilitates the derivation of the fields everywhere. In particular, the transmission-line representation can serve as a template for computational algorithms that systematically evaluate dispersion properties, radiation effects, wave coupling and other characteristics that are not readily obtained by other methods. Examples illustrating the application of the present approach are given for waves guided by grating configurations encountered in optoelectronic devices.

Diffuse scattering of X-rays and neutrons by fluctuations

Abstract: 1. Fluctuation Waves of the Composition and Order Parameters.- 1.1 Order in Solid Solutions and Fluctuations.- 1.2 Thermodynamic Theory for Fluctuation Waves of Concentration and Long-Range Order Parameters in Undistorted Crystals.- 1.2.1 Concentration Fluctuations.- 1.2.2 Fluctuations of Long-Range Order Parameters in One-Component Solutions.- 1.2.3 Fluctuations of Long-Range Order Parameters and Concentration in Solid Solutions.- 1.3 Microscopic Semiphenomenological Theory of Fluctuation Waves in Solid Solutions.- 1.4 Fluctuations of the Order Parameters in Solid Solutions.- 1.5 Static Displacements Caused by Fluctuation Waves of Composition, Order and Correlation Parameters.- 1.5.1 Long-Wavelength Limiting Case.- 1.5.2 Fluctuation Waves of Static Displacements in Concentrated Solutions.- 2. Effects of Long-Range Forces on Fluctuations in Crystals and the Production of Heterogeneous States.- 2.1 Effects Caused by Elastic Interaction.- 2.1.1 Effect of the Elastic Interaction on Fluctuations of Concentration and Order Parameters in Crystals.- 2.1.2 Effect of Elastic Interaction on the Shape of Second-Phase Particles and Metastable Heterogeneous Structures in Two-Phase Systems.- 2.2 Effects of Dipole-Dipole Interaction on Polarization Fluctuations.- 2.3 Fluctuations of the Charged Defect Concentration.- 2.4 Effects of Long-Range Forces on Fluctuation Waves in Metal Alloys.- 2.5 Equilibrium Heterogeneous States with Long-Range Forces.- 2.5.1 Crystal Structures with Large Parameters.- 2.5.2 Heterogenenous States in Metal Systems.- 2.5.3 Heterogeneous States in Semiconductor Systems.- 3. Diffuse Scattering of X-Rays and Neutrons in Solid Solutions and One-Component Ordered Crystals.- 3.1 Diffuse Scattering Intensity in Kinematieal Theory.- 3.2 Diffuse Scattering by Solid Solutions: General Analysis.- 3.3 Diffuse Scattering in Undistorted Solid Solutions.- 3.3.1 Scattering by Homogeneous Solutions, Determination of the Correlation Parameters, Ordering Energies and the Fermi Surface Diameters.- 3.3.2 Scattering by Inhomogeneous Solutions.- 3.4 Diffuse Scattering in Distorted Solid Solutions.- 3.4.1 Scattering Caused by Concentration Fluctuations.- 3.4.2 Diffuse Scattering by Fluctuations of the Correlation Parameters.- 3.5 Analysis of Solid Solutions with Diffraction Techniques Employing Diffuse Scattering.- 3.5.1 Correlation Parameters.- 3.5.2 Ordering Energies and Thermodynamic Properties of a Solution.- 3.5.3 Diffraction Studies of the Kinetics of Diffusion Processes.- 3.5.4 Diffraction Studies of the Fermi Surface in Alloys.- 3.5.5 Analysis of Short-Range Order in Alloys.- 3.6 Diffuse Scattering by Long-Range Order Fluctuations.- 3.6.1 One-Component Crystals.- 3.6.2 Solid Solutions.- 3.6.3 Intrinsic Ferroelectrics.- 3.6.4 Incommensurate Structures.- 3.7 Diffuse Scattering by Ionic Crystals with Charged Defects or Impurities.- 4. Anomalous Scattering Near Second-Order Phase Transitions and Critical Points.- 4.1 Thermodynamic Parameters and Fluctuation Waves Near Second-Order Phase Transitions and Critical Points.- 4.1.1 Landau Theory.- 4.1.2 Fluctuation Range.- 4.2 Diffuse Scattering by Critical Fluctuations in Perfect Crystals...- 4.3 Effects Produced by Dislocations on Second-Order Phase Transitions and Anomalous Scattering.- 4.3.1 Phase Transitions in Crystals with Dislocations.- 4.3.2 Scattering by Long-Range Order Inhomogeneities Produced by Dislocations Near a Second-Order Phase Transition.- Appendix: Calculation of the Mean Squares of the Fourier Components in the Microscopy Theory.- References.

Introduction to Optics and Lasers in Engineering

Abstract: 1. Radiometry 2. Geometrical optics 3. Maxwell's equations 4. Properties of electromagnetic waves 5. Propagation and applications of polarized light 6. Interference effects and their applications 7. Diffraction effects and their applications 8. Introduction to the principles of quantum mechanics 9. Atomic and molecular energy levels 10. Radiative transfer between quantum states 11. Spectroscopical techniques for thermodynamical measurements 12. Optical gain and lasers 13. Propagation of laser beams.