Showing papers on "Plane wave published in 2002"

New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope.

Abstract: We first obtain a frequency-space equation of diffraction tomography for the electric field vector, within the first-order Born approximation, using a simplified formalism resulting from using three-dimensional spatial frequencies and replacing outgoing waves by linear combinations of homogeneous plane waves. A coherent optical diffraction tomographic microscope is then described, in which a sample is successively illuminated by a series of plane waves having different directions, each scattered wave is recorded by phase-shifting interferometry, and the object is then reconstructed from these recorded waves. The measurement process in this device is analysed taking into account the illuminating wave, the wave scattered by the sample, the reference wave, and the phase relations between these waves. This analysis yields appropriate equations that take into account the characteristics of the reference wave and compensate random phase shifts. It makes it possible to obtain a high-resolution three-dimensional frequency representation in full conformity with theory. The experimentally obtained representations show index and absorptivity with a resolution limit of about a quarter of a wavelength, and have a depth of field of about 40 microm.

Electromagnetic and absorption properties of some microwave absorbers

Abstract: Electromagnetic properties of a thermoplastic natural rubber (TPNR), a lithium–nickel–zinc (Li–Ni–Zn) ferrite and a TPNR–ferrite composite subjected to transverse electromagnetic (TEM) wave propagation were investigated. The incorporation of the ferrite into the matrix of the TPNR was found to reduce the dielectric loss but the magnetic loss increased. The absorption characteristics of all the samples subjected to a normal incidence of TEM wave were investigated based on a model of a single-layered plane wave absorber backed by a perfect conductor. It is evident from a computer simulation that the ferrite is a narrowband absorber, whereas the polymeric samples show broadband absorption characteristics. Minimal reflection of the microwave power or matching condition occurs when the thickness of the absorbers approximates an odd number multiple of a quarter of the propagating wavelength. This is discussed as due to cancellation of the incident and reflected waves at the surface of the absorbers. The Li–Ni–Z...

Ultrafast compound imaging for 2-D motion vector estimation: application to transient elastography

Abstract: This paper describes a new technique for two-dimensional (2-D) imaging of the motion vector at a very high frame rate with ultrasound. Its potential is experimentally demonstrated for transient elastography. But, beyond this application, it also could be promising for color flow and reflectivity imaging. To date, only axial displacements induced in human tissues by low-frequency vibrators were measured during transient elastography. The proposed technique allows us to follow both axial and lateral displacements during the shear wave propagation and thus should improve Young's modulus image reconstruction. The process is a combination of several ideas well-known in ultrasonic imaging: ultra-fast imaging, multisynthetic aperture beamforming, 1-D speckle tracking, and compound imaging. Classical beamforming in the transmit mode is replaced here by a single plane wave insonification increasing the frame rate by at least a factor of 128. The beamforming is achieved only in the receive mode on two independent subapertures. Comparison of successive frames by a classical 1-D speckle tracking algorithm allows estimation of displacements along two different directions linked to the subapertures beams. The variance of the estimates is finally improved by tilting the emitting plane wave at each insonification, thus allowing reception of successive decorrelated speckle patterns.

INTERNAL GRAVITY WAVES: From Instabilities to Turbulence

Abstract: ▪ Abstract We review the mechanisms of steepening and breaking for internal gravity waves in a continuous density stratification. After discussing the instability of a plane wave of arbitrary amplitude in an infinite medium at rest, we consider the steepening effects of wave reflection on a sloping boundary and propagation in a shear flow. The final process of breaking into small-scale turbulence is then presented. The influence of those processes upon the fluid medium by mean flow changes is discussed. The specific properties of wave turbulence, induced by wave-wave interactions and breaking, are illustrated by comparative studies of oceanic and atmospheric observations, as well as laboratory and numerical experiments. We then review the different attempts at a statistical description of internal gravity wave fields, whether weakly or strongly interacting.

Reflection Coefficients and Azimuthal Avo Analysis in Anisotropic Media

Abstract: Reflection and transmission of plane waves at a plane boundary between two isotropic media are two of the most fundamental subjects in wave propagation. Zoeppritz (1919) w as among the first to investigate and publish their analytic solutions. Given the medium properties on both sides of a reflector and invoking continuity of stress and displacement across the interface, he came up with a set of equations to describe the amplitudes of the scattered (i.e., reflected and transmitted) waves. Chapter [2][1] provides an overview of the reflection and transmission problem in isotropic media. It also introduces the notation that is used throughout the text and contains a review of the basic physical principles that lead to the boundary conditions for media in welded contact. Because of the algebraic complexity of the Zoeppritz equations, the inverse problem of esti-mating medium properties from the reflection signature is based mostly on approximate analytic expressions for reflection coefficients. Several approximations for isotropic models have been described in the literature (Richards and Frasier, 1976; Aki and Richards, 1980; Shuey, 1985; Thomsen, 1990). As described in Chapter [2][1], they differ in their assumptions, as well as in the choice of medium parameters. [1]: /gswbk/9781560801764/9781560801764/SEC2.atom

Dispersion and Reflection Properties of Artificial Media Formed By Regular Lattices of Ideally Conducting Wires

Abstract: An analytical theory of electromagnetic waves in artificial media formed by a rectangular lattice of thin ideally conducting cylinders using the local field approach is developed. As a result, the transcendental dispersion equation is obtained in closed form and solved numerically. Typical dispersion curves are calculated. Using these results, the reflection problem from an interface between a half space of wire medium and free space is solved for plane-wave excitation. In the low-frequency approximation a simple analytical formula for the frequency dependent effective dielectric permittivity is established.

Extracting Angle Domain Information From Migrated Wavefield

Abstract: The recent development of wave equation based migration methods provided accurate propagators for seismic wave extrapolation. These propagators brought the possibility that many analysis and inversion can be made at the depth using migrated wavefield. In this study, we propose an approach for extracting angle domain information from migrated wavefield. The method is based on localized plane wave analysis and can be used for almost any migration method. Then, using the concept of the local image matrix, useful information (angle domain image gathers, reflector dips, etc.) can be further extracted from this angle related information. Numerical examples are conducted to demonstrate the applications of this method.

Plane-wave pseudopotential study on mechanical and electronic properties for IV and III-V crystalline phases with zinc-blende structure

Abstract: Norm conserving pseudopotentials have been generated for the light actinides (Th-Np) and the plane waves + pseudopotential formalism has been used to study their crystal structures at zero temperature as a function of pressure. The often complex alpha phases of these elements have been fully relaxed, and we have used a thorough treatment of spin-orbit coupling. The zero-pressure zero-temperature equilibrium volumes and bulk moduli are consistent with previous all-electron full-potential calculations, and, up to uranium, in excellent agreement with experiment. This is also the case for cell parameters and pressure-induced phase transitions. It is likely that, from neptunium on, a more careful treatment of electronic correlations and/or relativistic effects is necessary to reproduce the experimental data with the same precision.

Spiral wave generation in heterogeneous excitable media.

Abstract: As the coupling in a heterogeneous excitable medium is reduced, three different types of behavior are encountered: plane waves propagate without breaking up, plane waves break up into spiral waves, and plane waves block. We illustrate these phenomena in monolayers of chick embryonic heart cells using calcium sensitive fluorescent dyes. Following the addition of heptanol, an agent that reduces the electrical coupling between cells, we observe breakup of spiral waves. These results are modeled in a heterogeneous cellular automaton model in which the neighborhood of interaction is modified.

Crystallography of color superconductivity

Abstract: We develop the Ginzburg-Landau approach to comparing different possible crystal structures for the crystalline color superconducting phase of QCD, the QCD incarnation of the Larkin-Ovchinnikov-Fulde-Ferrell phase. In this phase, quarks of different flavor with differing Fermi momenta form Cooper pairs with nonzero total momentum, yielding a condensate that varies in space like a sum of plane waves. We work at zero temperature, as is relevant for compact star physics. The Ginzburg-Landau approach predicts a strong first-order phase transition (as a function of the chemical potential difference between quarks) and for this reason is not under quantitative control. Nevertheless, by organizing the comparison between different possible arrangements of plane waves (i.e., different crystal structures) it provides considerable qualitative insight into what makes a crystal structure favorable. Together, the qualitative insights and the quantitative, but not controlled, calculations make a compelling case that the favored pairing pattern yields a condensate which is a sum of eight plane waves forming a face-centered cubic structure. They also predict that the phase is quite robust, with gaps comparable in magnitude to the BCS gap that would form if the Fermi momenta were degenerate. These predictions may be tested in ultracold gases made of fermionic atoms. In a QCD context, our results lay the foundation for a calculation of vortex pinning in a crystalline color superconductor, and thus for the analysis of pulsar glitches that may originate within the core of a compact star.

Large fully nonlinear internal solitary waves: The effect of background current

Abstract: In this paper we consider what effect the presence of a nonconstant background current has on the properties of large, fully nonlinear solitary internal waves in a shallow, stratified ocean. In particular, we discuss how the amplitude of the largest nonbreaking wave that it is possible to calculate depends on the background current as well as the nature of the upper bound. We find that the maximum wave amplitude is given by one of three possibilities: The onset of wave breaking, the conjugate flow amplitude or a failure of the wave calculating algorithm to converge (associated with shear instability). We also discuss how wave properties such as propagation speed, half-width, etc. vary with background current amplitude.

Effective velocities in fractured media : A numerical study using the rotated staggered finite-difference grid

Abstract: The modelling of elastic waves in fractured media with an explicit finite-difference scheme causes instability problems on a staggered grid when the medium possesses high-contrast discontinuities (strong heterogeneities). For the present study we apply the rotated staggered grid. Using this modified grid it is possible to simulate the propagation of elastic waves in a 2D or 3D medium containing cracks, pores or free surfaces without hard-coded boundary conditions. Therefore it allows an efficient and precise numerical study of effective velocities in fractured structures. We model the propagation of plane waves through a set of different, randomly cracked media. In these numerical experiments we vary the wavelength of the plane waves, the crack porosity and the crack density. The synthetic results are compared with several static theories that predict the effective P- and S-wave velocities in fractured materials in the long wavelength limit. For randomly distributed and randomly orientated, rectilinear, non-intersecting, thin, dry cracks, the numerical simulations of velocities of P-, SV- and SH-waves are in excellent agreement with the results of the modified (or differential) self-consistent theory. On the other hand for intersecting cracks, the critical crack-density (porosity) concept must be taken into account. To describe the wave velocities in media with intersecting cracks, we propose introducing the critical crack-density concept into the modified self-consistent theory. Numerical simulations show that this new formulation predicts effective elastic properties accurately for such a case.

Modelling of short wave diffraction problems using approximating systems of plane waves

Abstract: This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed.

Statistical theory for incoherent light propagation in nonlinear media.

Abstract: A statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrodinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can stabilize the modulational instability. In the limit of the geometrical optics approximation, incoherent, localized, and stationary wave fields are shown to exist for a wide class of nonlinear media.

Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations.

Abstract: The analysis of many systems in optical communications and metrology utilizing Gaussian beams, such as free-space propagation from single-mode fibers, point diffraction interferometers, and interference lithography, would benefit from an accurate analytical model of Gaussian beam propagation. We present a full vector analysis of Gaussian beam propagation by using the well-known method of the angular spectrum of plane waves. A Gaussian beam is assumed to traverse a charge-free, homogeneous, isotropic, linear, and nonmagnetic dielectric medium. The angular spectrum representation, in its vector form, is applied to a problem with a Gaussian intensity boundary condition. After some mathematical manipulation, each nonzero propagating electric field component is expressed in terms of a power-series expansion. Previous analytical work derived a power series for the transverse field, where the first term (zero order) in the expansion corresponds to the usual scalar paraxial approximation. We confirm this result and derive a corresponding longitudinal power series. We show that the leading longitudinal term is comparable in magnitude with the first transverse term above the scalar paraxial term, thus indicating that a full vector theory is required when going beyond the scalar paraxial approximation. In spite of the advantages of a compact analytical formalism, enabling rapid and accurate modeling of Gaussian beam systems, this approach has a notable drawback. The higher-order terms diverge at locations that are sufficiently far from the initial boundary, yielding unphysical results. Hence any meaningful use of the expansion approach calls for a careful study of its range of applicability. By considering the transition of a Gaussian wave from the paraxial to the spherical regime, we are able to derive a simple expression for the range within which the series produce numerically satisfying answers.

Plane wave scattering from frequency-selective surfaces by the finite-element method

Abstract: This paper presents the application of the finite-element method (FEM) to the analysis of reflection and transmission coefficients, effective permittivity, and permeability of periodic structures to incident plane waves. The problem domain is reduced to a unit cell by using linked boundary conditions (LBCs) and the accuracy and efficiency of the procedure is improved by using the scattered field formulation and perfectly matched layers (PMLs). Examples of the analysis of frequency-selective surfaces (FSSs) derived from photonic bandgap materials (PBGs) and composite materials with negative effective permeability and permittivity are presented.

Spatial-correlation functions of fields and energy density in a reverberation chamber

Abstract: A plane-wave integral representation is used to derive spatial-correlation functions for the complex electric and magnetic field components, and the results agree with previously published results derived by volume averaging of a mode sum. Results are also presented for the correlation functions of squared electric and magnetic field components and electric, magnetic, and total energy densities. The theory for the spatial correlation function of the squared transverse electric field is shown to agree well with published measurements of the power received by transverse monopole antennas.

Strings in the near plane wave background and AdS / CFT

Abstract: We study the AdS/CFT correspondence for string states which flow into plane wave states in the Penrose limit. Leading finite radius corrections to the string spectrum are compared with scaling dimensions of finite R-charge BMN-like operators. We find agreement between string and gauge theory results.

D-brane interactions in type IIB plane-wave background

Abstract: The cylinder diagrams that determine the static interactions between pairs of Dp-branes in the type IIB plane wave background are evaluated. The resulting expressions are elegant generalizations of the flat-space formulae that depend on the value of the Ramond-Ramond flux of the background in a non-trivial manner. The closed-string and open-string descriptions consistently transform into each other under a modular transformation only when each of the interacting D-branes separately preserves half the supersymmetries. These results are derived for configurations of euclidean signature D(p+1)-instantons but also generalize to lorentzian signature Dp-branes.

Envelope broadening of spherically outgoing waves in three‐dimensional random media having power law spectra

Abstract: [1] High-frequency S wave seismogram envelopes are broadened with increasing travel distance due to diffraction and scattering. The basic mechanism of the broadening has been studied on the basis of the scattering theory with the parabolic approximation for the scalar wave equation in random media. However, conventional models are not realistic enough since the plane wave modeling is too simple and the Gaussian autocorrelation function (ACF) is far from the reality to represent the inhomogeneity in the Earth. Focusing on the early part of envelopes, we formulated the envelope broadening of spherically outgoing scalar waves in three-dimensional von Karman-type random media, of which the spectra decay according to a power law at large wave numbers. Random media are characterized by three parameters: RMS fractional velocity fluctuation e, correlation distance a, and order κ that controls the gradient of the power law spectra. This model predicts that the envelope duration increases with both travel distance and frequency when short-wavelength components are rich in random media, while the duration is independent of frequency when short-wavelength components are poor. Introducing phenomenological attenuation Q, we developed a method for estimating the parameters of inhomogeneity and attenuation from the envelope duration. Applying this method to S wave seismogram envelopes for the frequency range from 2 to 32 Hz in northeastern Honshu Japan, we estimated the random inhomogeneity parameters as κ = 0.6, e2.2a−1 ≈ 10−3.6 [km−1] and f/Q = 0.0095 [s−1], where f is frequency. The power law portion of the estimated power spectral density function is P(m) ≈ 0.01 m−4.2 [km3], where m is wave number.

Analysis of the electromagnetic scattering from a cavity

Abstract: Consider a time-harmonic electromagnetic plane wave incident on a cavity in a ground plane. Inside the cavity, the medium may beinhomogeneous. In this paper, variational formulations in TE and TM polarizations are studied. Existence and uniqueness of the solutions for the model problems are established. The variational approach also forms a basis for numerical solution of the model problems.

Design, development, and testing of X-band amplifying reflectarrays

Abstract: The design and development of two X-band amplifying reflectarrays is presented. The arrays use dual-polarized aperture coupled patch antennas with FET transistors and phasing circuits to amplify a microwave signal and to radiate it in a chosen direction. Two cases are considered, one when a reflectarray converts a spherical wave due to a feed horn into a plane wave radiated into a boresight direction, and the other when the reflectarray converts a spherical wave due to a dual-polarized four-element feed array into a co-focal spherical wave. This amplified signal is received in an orthogonal port of the feed array so that the entire structure acts as a spatial power combiner. The two amplifying arrays are tested in the near-field zone for phase distribution over their apertures to achieve the required beam formation. Alternatively, their radiation patterns or gains are investigated.

The LISA response function

Abstract: The orbital motion of the Laser Interferometer Space Antenna (LISA) introduces modulations into the observed gravitational wave signal. These modulations can be used to determine the location and orientation of a gravitational wave source. The complete LISA response to an arbitary gravitational wave is derived using a coordinate free approach in the transverse-traceless gauge. The general response function reduces to that found by Cutler (PRD 57, 7089 1998) for low frequency, monochromatic plane waves. Estimates of the noise in the detector are found to be complicated by the time variation of the interferometer arm lengths.

Accurate molecular integrals and energies using combined plane wave and Gaussian basis sets in molecular electronic structure theory

Abstract: This paper introduces two developments for the application of plane wave basis sets for accurate molecular calculations (1) An analytical formula is introduced for the momentum space representation of a Coulomb operator truncated to a finite range Using this operator, interactions between the molecule and its periodic replicas can be exactly eliminated Examples demonstrating the accuracy of our scheme are given Calculations using a good-quality plane wave basis yield variational total SCF energies which are lower than those obtained with the cc-pvQZ basis for simple two-electron systems (2) A new mixed-basis augmented plane wave all-electron method, the plane wave core Gaussian method has been developed which expands the valence part of the molecular orbitals in plane waves, and the corelike part in nonoverlapping compact Gaussians Analytic equations have been derived for the necessary mixed Gaussian/plane wave electron repulsion integrals Using such augmented basis set, we were able to reproduce the Gaussian-basis Hartree energies of small molecules to within a few μE h

Strings in the near plane wave background and AdS/CFT

Abstract: We study the AdS/CFT correspondence for string states which flow into plane wave states in the Penrose limit. Leading finite radius corrections to the string spectrum are compared with scaling dimensions of finite R-charge BMN-like operators. We find agreement between string and gauge theory results.

X-ray Standing Wave Studies of Minerals and Mineral Surfaces: Principles and Applications

Abstract: With a penetration depth ranging from microns to millimeters, Angstrom-wavelength X-rays are an ideal probe for studying atomic-scale buried structures found in the natural environment, such as impurities in minerals and adsorbed ions at mineral-water interfaces. But this penetration depth also makes an X-ray beam inherently less useful as a spatially localized probe. Using the superposition of two coherently coupled X-ray beams, however, makes it possible to localize the X-ray intensity into interference fringes of an X-ray standing wave (XSW) field, as illustrated in Figure 1⇓, and thereby attain a spatially localized periodic probe with a length scale equivalent to the XSW period. The XSW period is Figure 1. Top: A standing wave field formed from the superposition of two traveling plane waves of wavelength λ and intersection angle (scattering angle) 2𝛉. The standing wave period is D as defined in Equation (1). Bottom: The two traveling planes waves are represented in reciprocal space by wave vectors K and K R . K = K R = 1/λ. The standing wave is defined by standing-wave vector Q defined in Equation (2). \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\mathit{D}\ =\ \frac{{\lambda}}{2\ sin\ {\theta}}\ =\ \frac{1}{\mathit{Q}}\] \end{document}(1) where λ is the X-ray wavelength and 2𝛉 is the scattering angle or angle separation between the two coherently coupled wave vectors K R and K . In reciprocal space, the scattering vector, or wave vector transfer, is defined as \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\mathbf{\mathit{Q}}\ =\ \mathbf{\mathit{K}}\_{\mathit{R}}\ {-}\ \mathbf{\mathit{K}}\_{0}\] \end{document}(2) Q is in the direction perpendicular to the equal-intensity planes of the XSW and has a magnitude that is the reciprocal of D . Thus, Q is also referred to as the standing wave vector. An X-ray standing wave can be used as an atom-specific probe via the photoelectric effect, which can be observed by photoelectron emission, fluorescence, or Auger electron emission. There are a number of mechanisms for generating an XSW. The simplest …

Plane waves: to infinity and beyond!

Abstract: We describe the asymptotic boundary of the general homogeneous plane wave spacetime, using a construction of the 'points at infinity' from the causal structure of the spacetime as introduced by Geroch, Kronheimer and Penrose. We show that this construction agrees with the conformal boundary obtained by Berenstein and Nastase for the maximally supersymmetric ten-dimensional plane wave. We see in detail how the possibility of going beyond (or around) infinity arises from the structure of light cones. We also discuss the extension of the construction to time-dependent plane wave solutions, focusing on the examples obtained from the Penrose limit of Dp-branes.