Showing papers on "Diffraction published in 1990"

Electromagnetic Wave Propagation, Radiation, and Scattering

Abstract: Fundamental field equations waves in homogeneous and layered media waveguides and cavities Green's functions radiation from apertures and beam waves periodic structures and coupled mode theory dispersion and anisotropic media antennas, apertures and arrays scattering of waves by conducting and di-electric objects waves in cylindrical structures, spheres and wedges scattering of complex objects geometric theory of diffraction and low fequency techniques planar layers, strip lines, patches and apertures radiation from a dipole on the conducting earth, inverse scattering radiometry, noise temperature and interferometry numerical techniques.

Inverse theory applied to multi‐source cross‐hole tomography.: part 1: acoustic wave‐equation method1

Abstract: Frequency-domain methods are well suited to the imaging of wide-aperture cross-hole data. However, although the combination of the frequency domain with the wavenumber domain has facilitated the development of rapid algorithms, such as diffraction tomography, this has also required linearization with respect to homogeneous reference media. This restriction, and association restrictions on source-receiver geometries, are overcome by applying inverse techniques that operate in the frequency-space domain. In order to incorporate the rigorous modelling technique of finite differences into the inverse procedure a nonlinear approach is used. To reduce computational costs the method of finite differences is applied directly to the frequency-domain wave equation. The use of high speed, high capacity vector computers allow the resultant finite-difference equations to be factored in-place. In this way wavefields can be computed for additional source positions at minimal extra cost, allowing inversions to be generated using data from a very large number of source positions. Synthetic studies show that where weak scatter approximations are valid, diffraction tomography performs slightly better than a single iteration of non-linear inversion. However, if the background velocities increase systematically with depth, diffraction tomography is ineffective whereas non-linear inversion yields useful images from one frequency component of the data after a single iteration. Further synthetic studies indicate the efficacy of the method in the time-lapse monitoring of injection fluids in tertiary hydrocarbon recovery projects.

Guided-mode resonances in planar dielectric-layer diffraction gratings

Abstract: The guided-mode resonance behavior of the evanescent and propagating fields associated with an unslanted, planar diffraction grating is studied by means of the rigorous coupled-wave theory. For weakly modulated gratings, the condition on the guided-mode wave number of the corresponding unmodulated dielectric-layer waveguide may be used to predict the range of the incident angle or wavelength within which the resonances can be excited. Furthermore, the locations of the resonances are predicted approximately by the eigenvalue equation of the waveguide. As the modulation amplitude increases, the location and shape of the resonances are described in detail by the rigorous coupled-wave theory. The results presented demonstrate that the resonances can cause rapid variations in the intensity of the external propagating diffracted waves.

Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell's equations

Abstract: We examine the propagation of electromagnetic waves in periodic dielectric structures by solving the vector Maxwell equations with the plane-wave method. Contrary to experimental reports, as well as results of scalar-wave calculations, we do not find a true gap extending throughout the Brillouin zone in the fcc structure. However, there is a depletion in the photon density of states, seemingly a remnant of the Mie resonance, giving rise to a pseudogap in the spectrum that is quite strong for dielectric-sphere packing fraction \ensuremath{\beta}\ensuremath{\sim}0.3--0.4. An effect analogous to the Borrmann effect in x-ray diffraction is predicted, where certain photon modes will propagate an anomalously long distance before getting absorbed.

Cryo-protection of protein crystals against radiation damage in electron and X-ray diffraction

Abstract: By using the fading of electron diffraction patterns during electron irradiation of protein or other organic crystals as a benchmark to measure destruction of the crystalline atomic arrangement by ionizing radiation, calculations suggest that protein crystals in laboratory X-ray beams might last for about five years when the specimen is cooled to liquid nitrogen temperatures or below. It is suggested that all crystals should be equally stable to X-irradiation at this temperature, as they are to electron irradiation. The calculation, which depends on the assumption that electrons and X-rays are more or less equally damaging to the structure giving rise to the diffraction at very low temperature, supports experimental observations that X-ray diffraction from protein crystals seems to last indefinitely at liquid nitrogen temperatures, even in the most powerful beams available at synchrotron X-ray sources. An attempt is made to explain the relation between the present analysis and other ways of viewing radiation damage.

Efficient beam propagation techniques

Abstract: It is shown that suitable modifications of the free-space-propagation operator in the standard fast-Fourier-transform beam propagation procedure yield a far more rapid code in the context of semiconductor rib waveguide calculations. The procedure curtails the diffraction experienced by the high-order Fourier components of the electric field and mirrors the structure of the recently introduced finite-difference beam propagation algorithm. It is used to investigate the propagation losses of a Y-junction composed of single-mode rib waveguides and illuminated by its normalized guided mode. >

Reflection high energy electron diffraction characteristic absences in GaAs(100) (2×4)–As: A tool for determining the surface stoichiometry

Abstract: In general, techniques that monitor the in situ growth of semiconductor materials with electron diffraction [such as reflection high energy electron diffraction (RHEED)] provide no quantitative information about surface stoichiometry. However, sophisticated materials problems, such as heteroepitaxial systems, require such information. Here we demonstrate that the use of characteristic absences in the fractional order diffraction features in RHEED patterns provide detailed quantitative information for the molecular beam epitaxial growth of materials such as GaAs. It is expected that this approach will lead to the improvement of growth for such interface‐sensitive systems as resonant tunneling devices.

The complete second-order diffraction solution for an axisymmetric body Part 2. Bichromatic incident waves and body motions

Abstract: In Part 1 (Kim & Yue 1989), we considered the second-order diffraction of a plane monochromatic incident wave by an axisymmetric body. A ring-source integral equation method in conjunction with a novel analytic free-surface integration in the entire local-wave-free domain was developed. To generalize the second-order theory to irregular waves, say described by a continuous spectrum, we consider in this paper the general second-order wave–body interactions in the presence of bichromatic incident waves and the resulting sum- and difference-frequency problems. For completeness, we also include the radiation problem and second-order motions of freely floating or elastically moored bodies. As in Part 1, the second-order sum- and difference-frequency potentials are obtained explicitly, revealing a number of interesting local behaviours of the second-order pressure. For illustration, the quadratic transfer functions (QTF's) for the sum- and difference-frequency wave excitation and body response obtained from the present complete theory are compared to those of existing approximation methods for a number of simple geometries. It is found that contributions from the second-order potentials, typically neglected, can dominate the total load in many cases.

Energy-dispersive X-ray diffraction tomography

Abstract: A novel tomographic imaging technique is described based on the energy analysis, at fixed angle, of coherent X-ray scatter excited in an object by polychromatic radiation. The authors term their technique 'energy-dispersive X-ray diffraction tomography' (EXDT). It permits the X-ray diffraction properties of small voxels of an extended object to be measured in vivo. Tomographic information is obtained directly without the need to reconstruct from projections. EXDT images of a simple test object comprising water and various plastic materials are presented to illustrate the feasibility of the technique. Potential applications of EXDT in bone imaging are discussed.

Optical element and optical pickup device comprising it

Abstract: An optical element comprises a polarization diffraction element that is provided with diffraction gratings that are respectively mounted on different faces of a transparent substrate of a flat plate shape, which grating pitches are equal to each other and approximately equal to the wavelength of an incident light, and which grating lines are parallel. The thickness of the substrate is set such that the difference that occurs between the phases of the P and S polarizations of a light due to the grating, and the difference that occurs between the phases of the two polarizations when the light propagates through the substrate cancel out. The optical pickup device comprising the optical element includes a polarized light detecting unit provided with a diffraction grating which grating pitch is approximately equal to the wavelength of an incident light; a first photodetector that is mounted integrally and virtually in parallel with the substrate, and that receives a zero-order diffracted light produced by the diffraction grating; and a second photodetector that is located in the same plane as the first photodetector and mounted integrally with the first photodetector and the substrate, and that receives a first-order diffracted light produced by the diffraction grating.

Aztec surface-relief volume diffractive structure

Abstract: Surface-relief diffractive optical elements made interferometrically typically are recorded with the off-axis technique, for which the fringe maxima lie on planes that are predominantly perpendicular to the recording surface and with an intensity variation that is sinusoidal. Such a structure can be readily replicated by mechanical means. Volume diffractive elements, on the other hand, which result from beams propagating in opposite directions, have fringe planes that are predominantly parallel to the surface and, as such, cannot be mechanically replicated. A new type of surface-relief diffractive structure called Aztec is discussed here; it combines features of both off-axis and volume recording geometries, with the result being a phase-quantized, or terraced, surface-relief pattern. The groove profile, instead of being sinusoidal, resembles a stepped pyramid. This structure has been replicated by metal mastering and molding into plastic in the same manner as conventional embossed surface-relief elements, but the diffraction characteristics are typical of volume phase reflective structures. Light of a given wavelength is resonantly diffracted from steps that are a half-wavelength apart and with a bandwidth that is inversely proportional to the number of steps. Color control has been achieved by overcoating the step structure with a clear dielectric that shifts the resonant wavelength to a new value, depending on the index of refraction of the dielectric. Information content is less for the single-layered, but stepped, Aztec structure than for the usual multilayered volume diffractive element. Deep Aztec stepped gratings have also been fabricated by optical lithography, using multiple-mask techniques.

Calculation of universal scaling function for free-electron-laser gain.

Abstract: We present a variational calculation of free-electron-laser gain the exponential regime before saturation using a dispersion relation incorporating the energy spread, emittance, and focusing of the electron beam, and the diffraction and guiding of the radiation Rapid computation facilitates free-electron-laser design optimization Results are expressed in a universal scaled form

Lasers with super-Gaussian mirrors

Abstract: A systematic theoretical and experimental investigation of unstable resonators with variable reflectivity mirrors of a super-Gaussian profile is presented. The validity of a geometrical optics formalism for an algebraic mode calculation is discussed in comparison to the diffraction theory. A new method for the calculation of the output energy by means of a closed-form relationship that accounts for the effects of the transverse mode profile on gain saturation is presented. Various dielectric super-Gaussian mirrors have been fabricated, characterized, and tested in a pulsed Nd:YAG laser. Super-Gaussian resonators can provide even higher output energies than those of traditional unstable resonators and with better beam-focusing properties. >

Wander of an optical beam in the turbulent atmosphere.

Abstract: A simple, analytic, geometrical optics expression for the variance of the beam displacements caused by propagation through weak refractive turbulence described by the Kolmogorov spectrum is presented. The analytical formula includes the effect of the divergence or convergence of the initial beam. The formula is compared with numerical results obtained from a more complicated expression including effects of diffraction and strong path-integrated turbulence. The simple geometrical optics expression holds for apertures larger than the Fresnel zone size and larger than the ratio of the square of the Fresnel zone to the phase coherence length.

Analysis of grating surface emitting lasers

Abstract: An approach to the analysis of grating-coupled semiconductor lasers is presented. It is shown that there are only two resonant solutions when the grating has infinite extent. The solutions are either symmetric or antisymmetric about the center of the longitudinal coordinate system where the antisymmetric solution is nonradiating. The field in the grating layer is expressed in terms of grating eigenfunctions and rigorously matched to the boundary conditions at the waveguide interface. Solutions to the finite-length grating problem are expressed as linear combinations of the infinite-length solutions. It is shown that the two diffraction parameters in the coupled-wave equations are composed of sums and differences of the eigenvalues from the infinite-length problem. >

Anomalous reflection of a shock wave at a fluid interface

Abstract: Several wave patterns can be produced by the interaction of a shock wave with a fluid interface. We focus on the case when the shock passes from a medium of high to low acoustic impedance. Curvature of either the shock front or contact causes the flow to bifurcate from a locally self-similar quasi-stationary shock diffraction, to an unsteady anomalous reflection. This process is analogous to the transition from a regular to a Mach reflection when the reflected wave is a rarefaction instead of a shock. These bifurcations have been incorporated into a front tracking code that provides an accurate description of wave interactions. Numerical results for two illustrative cases are described; a planar shock passing over a bubble, and an expanding shock impacting a planar contact.

Three-dimensional (vector) rigorous coupled-wave analysis of anisotropic grating diffraction

Abstract: The rigorous coupled-wave analysis of diffraction by grating(s) formed in general anisotropic media is reviewed and extended. The method is first applied to a single slanted phase and/or amplitude grating with general three-dimensional incidence of a plane wave. The regions external to the grating can be isotropic, uniaxial, or biaxial anisotropic. The cases of gratings in isotropic media and of the grating vector lying in the plane of incidence (scalar analysis) are obtained as limiting cases of this general analysis. Coupling between the two orthogonal polarizations vanishes in these limiting cases. The Bragg conditions for various combinations of ordinary (for isotropic and uniaxial) and extraordinary (for uniaxial) polarized waves are quantified. The analysis is then extended to multiple cascaded gratings and to volume-superposed gratings. Sample calculations are presented for single anisotropic gratings (a lithium niobate photorefractive hologram in air and an interdigitated-electrode-induced grating in an electro-optic crystal), for multiple cascaded gratings (a lithium niobate hologram with grating strength varying with thickness), and for superposed gratings (multiplexed hologram storage). Applications for this analysis include optical storage, switching, modulation, deflection, optical interconnects, beam splitting, beam combining, and data processing.

Investigation of a millimeter-wavelength-range relativistic diffraction generator

Abstract: A theoretical and experimental study has been made of the operation of a millimeter-wavelength-range sectional relativistic diffraction generator (RDG). Microwave power transported into the atmosphere with the peak parameters of 3.5 and 4.5 GW at the wavelengths of 6.5 to 6.8 mm and 9 to 11.3 mm, respectively, has been obtained. The power at the generator output, up to a horn antenna, has reached 7 and 9 GW for each of the regimes, respectively, the electronic efficiency being equal to approximately 30%. Plasma formed in a slow-wave structure of the RDG is shown to be of considerable importance for radiation pulse duration limitation. Experiments aimed at increasing the pulse duration up to 0.7 mu s have been performed. Theoretical investigation of the beam interaction with a slow-wave structure field has shown that the generation frequency may be determined by the resonance features due to the transverse motion of beam electrons. >

Diffraction from Polymerized Membranes

Abstract: Flexible polymerized membranes in a good solvent are expected to exhibit a remarkable low-temperature flat phase, characterized by a diverging bending rigidity, vanishing elastic constants, and large fluctuations both parallel and perpendicular to the surface. A theory of the equilibrium structure factor provides a good fit to extensive molecular dynamics simulations of simplified "tethered surface" models of these materials. These results show how information about the size, thickness, and internal structure of polymerized membranes can be extracted from diffraction experiments.

Wave diffraction through offshore breakwaters

Abstract: The interaction of water waves with a long linear array of offshore breakwaters is examined to determine the reflection and transmission coefficients for these structures, providing data on the sheltering afforded by these structures. Two variational methods and an eigenfunction expansion method are used to determine the reflection coefficients for waves with wavelengths longer than the distance from gap to gap in the breakwater array. The eigenfunction method is also used for breakwaters, where the spacing between the gaps is longer than the water wavelength. For this case, analogous to scattering of light by a grating, numerous monochromatic directional wave trains can be generated in the region behind (and in front of) these breakwaters, which can lead to the generation of rip currents, beach cusps, and other periodic phenomena on beaches behind the structures.

Modeling of inverse Čerenkov laser acceleration with axicon laser-beam focusing

Abstract: Acceleration of free electrons by the inverse \ifmmode \check{C}\else \v{C}\fi{}erenkov effect using radially polarized laser light focused through an axicon [J. P. Fontana and R. H. Pantell, J. Appl. Phys. 54, 4285 (1983)] has been studied utilizing a Monte Carlo computer simulation and further theoretical analysis. The model includes effects, such as scattering of the electrons by the gas, and diffraction and interference effects of the axicon laser beam, that were not included in the original analysis of Fontana and Pantell. Its accuracy is validated using available experimental data. The model results show that effective acceleration is possible even with the effects of scattering. Sample results are given. The analysis includes examining the issues of axicon focusing, phase errors, energy gain, phase slippage, focusing of the $e$ beam, and emittance growth.

A review of the geometrical fundamentals of reflection high‐energy electron diffraction with application to silicon surfaces

Abstract: Reflection high‐energy electron diffraction (RHEED) is an experimentally simple technique, and yet a powerful one for examining the structure of a substrate surface and for monitoring the surface crystal structure and the crystallographic orientation of thin films during their growth. However, it can be difficult to learn to interpret the RHEED patterns of new materials, because a practical and adequately detailed introduction to the technique is not generally available. To address this need, we develop the geometrical principles of RHEED; using the kinematic approximation, we show how a particular point of the sample surface’s reciprocal net gives rise to a diffraction maximum at a particular location on the RHEED viewing screen. We explain the origins of ‘‘reciprocal lattice rods,’’ RHEED streaks, and Laue rings. We show how to calculate the streak spacing, and clarify the basic effect on the RHEED pattern of using a nonzero angle of incidence for the incident beam. Crystalline nets, reciprocal nets, an...

A new spherical-wave approximation for photoelectron diffraction, EXAFS and MEED

Abstract: An exact formula for the expansion of an outgoing spherical electron wave around another centre is presented from which new approximation for spherical-wave scattering are derived. These expressions allow a considerably higher accuracy in high-speed numerical multiple-scattering calculations than methods existing hitherto. This is demonstrated for tungsten in the energy range from 50 to 5000 eV. The improvements of the given formulae over earlier approaches are greater the higher the energy. In particular the errors in the forward scattering direction are very small.

Observation of {111} ordering and [110] modulation in molecular beam epitaxial GaAs1−ySby layers: Possible relationship to surface reconstruction occurring during layer growth

Abstract: Transmission electron diffraction (TED) was used to observe extra diffraction spots in the TED patterns of molecular beam epitaxial GaAs1−y Sby layers with y=0.25, 0.50, and 0.71 grown at 520 °C on (001) GaAs substrates. Half‐order diffraction spots in the TED patterns indicated ordering on the (111) and (111) planes of the Group V sublattice, and streaks with subsidiary spots indicated a modulation in the [110] direction with a periodicity of ∼4d110 . Streaks in the [001] direction indicated monolayer disruptions of the {111} ordering and the [110] modulation in the [001] direction. As the composition parameter y varied, there were progressive changes in the {111} ordering, the [110] modulation, and the [001] disruptions, and these correlated with corresponding changes in the reconstruction of the dangling bonds at the growing layer surface, as determined by reflection high‐energy electron diffraction. A model is proposed to explain the observed effects in terms of ordered atomic arrangements of the Gr...

Particle detection on a patterned or bare wafer surface

Abstract: A method and apparatus for predicting the number of contaminant particles in circuit area of a patterned semiconductor wafer having a number of reflective circuit areas. The method includes forming on a wafer in specified areas, a grating test pattern, such as a line grating. The grating patterns are formed at the same time and in the same manner that repetitive circuit patterns are formed on the wafer. The wafer is then scanned by a light beam. Since the diffraction pattern caused by the grating test patterns is known, it is possible to detect when the light beam is scanning one of the known grating patterns. The diffraction pattern may be inspected for fabrication derived variations. In response to detecting a known grating pattern, a detection mechanism is activated. Since the diffraction pattern is known it may be spatially separated. In this way only light scattered by particles or defects in the pattern are collected and detected. From the scattered light that is collected and detected, a particle count may be determined for the grating pattern area. From this particle count an accurate prediction of the number of particles in the circuit patterns may be made. The apparatus may also inspect bare areas. In this manner real time inspection may be performed on patterned wafers.