Showing papers on "Plane wave published in 1989"

Diffusion of light in turbid material

Abstract: This paper discusses some of the present knowledge of the mathematical techniques used to describe light diffusion in turbid material such as tissues. Attention will be paid to the usefulness and limitations of various techniques. First, we review the transport theory, radiance, radiant energy fluence rate, phase functions, boundary conditions, and measurement techniques. We then discuss the first-order solution, multiple scattering, diffusion approximation, and their limitations. The plane wave, spherical wave, beam wave, and pulse wave excitations are discussed followed by a brief review of the surface scattering effects due to rough interfaces.

An efficient boundary element method for nonlinear water waves

Abstract: The paper presents a computational model for highly nonlinear 2-D water waves in which a high order Boundary Element Method is coupled with a high order explicit time stepping technique for the temporal evolution of the waves. The choice of the numerical procedures is justified from a review of the literature. Problems of the wave generation and absorption are investigated. The present method operates in the physical space and applications to four different wave problems are presented and discussed (space periodic wave propagation and breaking, solitary wave propagation, run-up and radiation, transient wave generation). Emphasis in the paper is given to describing the numerical methods used in the computation.

Plane wave coupling to multiple conductor transmission lines above a lossy earth

Abstract: The current induced on an infinite multiple conductor transmission line located above a lossy homogeneous medium due to a transient plane wave is discussed. An exact solution is formulated in the frequency domain using a spatial transform technique. The widely utilized quasi-TEM approximation is derived directly from the exact solution with emphasis on the physical consequences of the assumptions made. Both frequency domain and time domain numerical results are presented for typical transmission structures and documented electromagnetic pulse (EMP) excitations. Comparison of the quasi-TEM approximation to the exact solution is made in order to study the validity of its application in EMP coupling problems. The modeling of the EMP source as an incident plane wave is examined by comparing the induced current due to a dipole source with its steepest-descent contribution. >

Diffraction of elastic waves by three-dimensional surface irregularities. Part II

Abstract: A boundary method is applied to study the seismic response of axisymmetric three-dimensional alluvial valleys on the surface of an elastic half-space. The excitation is given by incident plane waves. The method makes use of the completeness of a family of wave functions in order to construct the scattered and refracted fields. An azimuthal decomposition allows to “split” the problem in several two-dimensional problems, one for each azimuthal number. Boundary conditions are satisfied in the least-squares sense. Numerical results are reported in time domain as an extension of previous work.

A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation

Abstract: A new decomposition of exact solutions to the scalar wave equation into bidirectional, forward and backward, traveling plane wave solutions is described. The resulting representation is a natural basis for synthesizing pulse solutions that can be tailored to give directed energy transfer in space. The development of known free‐space solutions, such as the focus wave modes, the electromagnetic directed energy pulse trains, the spinor splash pulses, and the Bessel beams, in terms of this decomposition will be given. The efficacy of this representation in geometries with boundaries, such as a propagation in a circular waveguide, will also be demonstrated.

Certain computational aspects of vector diffraction problems

Abstract: Fourier decomposition of a given amplitude distribution into plane waves and the subsequent superposition of these waves after propagation is a powerful yet simple approach to diffraction problems. Many vector diffraction problems can be formulated in this way, and the classical results are usually the consequence of a stationary-phase approximation to the resulting integrals. For situations in which the approximation does not apply, a factorization technique is developed that substantially reduces the required computational resources. Numerical computations are based on the fast-Fourier-transform algorithm, and the practicality of this method is shown with several examples.

Elastic Wave Field Extrapolation: Redatuming of Single- and Multi-Component Seismic Data

Abstract: Introduction. I. Acoustic Waves. Introduction. Acoustic wave equation. Spherical wave solutions of the acoustic two-way wave equation. Plane wave solutions of the acoustic two-way wave equation. References. II. Elastic Waves. Introduction. Elastic wave equation. Spherical wave solutions of the elastic two-way wave equation. Plane wave solutions of the elastic two-way wave equation. References. III. Acoustic Two-Way and One-Way Wave Equations. Introduction. Acoustic wave equations for horizontally layered media. Acoustic wave equations for arbitrarily inhomogeneous media. References. IV. Elastic Two-Way and One-Way Wave Equations. Introduction. Elastic wave equations for horizontally layered media. Elastic wave equations for arbitrarily inhomogeneous media. References. V. Acoustic Forward Wave Field Extrapolation. Introduction. Acoustic reciprocity theorems. Acoustic representation theorems. Acoustic two-way and one-way Rayleigh integrals. Acoustic forward wave field extrapolation operators. References. VI. Elastic Forward Wave Field Extrapolation. Introduction. Elastic reciprocity theorems. Elastic representation theorems. Elastic two-way and one-way Rayleigh integrals. Elastic forward wave extrapolation operators. References. VII. Acoustic Inverse Wave Field Extrapolation in Low Contrast Media. Introduction. Acoustic inverse wave field extrapolation in laterally invariant media. Acoustic inverse wave field extrapolation in arbitrarily inhomogeneous media. References. VIII. Elastic Inverse Wave Field Extrapolation in Low Contrast Media. Introduction. Elastic inverse wave field extrapolation in homogeneous isotropic media. Elastic inverse wave field extrapolation in arbitrarily inhomogeneous anisotropic media. References. IX. Acoustic Inverse Wave Field Extrapolation in High Contrast Media. Introduction. Recursive acoustic inverse wave field extrapolation. Iterative acoustic inverse wave field extrapolation. X. Elastic Wave Field Extrapolation in High Contrast Media. Introduction. Recursive elastic inverse wave field extrapolation. Iterative elastic inverse wave field extrapolation. XI. Acoustic Redatuming of Single-Component Seismic Data. Introduction. Forward model for single-component seismic data. Surface related acoustic pre-processing. Acoustic redatuming. References. XII. Elastic Redatuming of Multi-Component Seismic Data. Introduction. Forward model for multi-component seismic data. Surface related elastic pre-processing. Elastic redatuming. References. Appendices. A. Matrix Notation. B. Interactions of One-Way Acoustic Wave Fields. C. Interactions of One-Way Elastic Wave Fields. Index.

Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence

Abstract: First a rigorous formulation is presented for the scattering of a uniform plane wave by an infinite dielectric grating waveguide, under the most general condition of oblique incidence. The results are then applied to the analysis of the guidance of waves by the dielectric grating waveguide. By using a simple coordinate rotation, the TE and TM Floquet mode functions determined previously for the special case of principal-plane incidence are combined to treat the general case of oblique incidence. In terms of the coupling between the known Floquet mode functions of both polarizations, the general case of oblique incidence is formulated in an exact fashion, as a three-dimensional boundary-value problem, so that the hybrid nature of waves supported by the structure can be investigated rigorously.

Light scattering by randomly oriented crystals.

Abstract: The scattering phase function and the degree of linear polarization for small crystals oriented randomly in space have been computed using the geometric ray tracing theory and assuming that the crystals are homogeneous and isotropic. Calculations have been carried out for the main crystal geometries. Detection of halos from crystals other than hexagonal water ice is briefly discussed. The crystal size and shape parameters have also been averaged over some simple distributions in order to examine general light scattering properties of sharp-edged particles. A scalar physical optics correction has been developed for the geometric optics phase functions. Results can be applied to light scattering from regoliths and planetary rings, and possibly also to atmospheric halos. Retroreflecting crystals in the regolith would cause an opposition spike, a phenomenon observed for many bright satellites.

Far-field patterns for acoustic waves in an inhomogeneous medium

Abstract: This paper is concerned with the class of far-field patterns corresponding to the scattering of time-harmonic acoustic plane waves by an inhomogeneous medium of compact support. This class is shown to be complete in $L^2 (\partial \Omega )$ (where $\partial \Omega $ is the unit sphere) for any positive value of the wave number, with the possible exception of a discrete set of wave numbers called transmission eigenvalues. The existence of a unique weak solution to the interior transmission problem (which plays a basic role in a new method for solving the inverse scattering problem) is also established for any positive value of the wave number provided the wave number is not a transmission eigenvalue.

A new approach to modeling the electromagnetic response of conductive media

Abstract: We introduce a new and potentially useful method for computing electromagnetic (EM) responses of arbitrary conductivity distributions in the earth. The diffusive EM field is known to have a unique integral representation in terms of a fictitious wave field that satisfies a wave equation. We show that this integral transform can be extended to include vector fields. Our algorithm takes advantage of this relationship between the wave field and the actual EM field. Specifically, numerical computation is carried out for the wave field, and the result is transformed back to the EM field in the time domain. The proposed approach has been successfully demonstrated using two‐dimensional (2‐D) models. The appropriate TE‐mode diffusion equation in the time domain for the electric field is initially transformed into a scalar wave equation in an imaginary q domain, where q is a time‐like variable. The corresponding scalar wave field is computed numerically using an explicit q‐stepping technique. Standard finite‐diffe...

First-principles phonon calculations for La2CuO4.

Abstract: Full potential, linearized, augmented plane wave, total-energy calculations predict that the breathing mode in ${\mathrm{La}}_{2}$Cu${\mathrm{O}}_{4}$ is a high-frequency mode, in agreement with experiment and contrary to previously published results We also find the experimentally observed tilt mode to be unstable within the local-density approximation Eight other modes were studied, and excellent agreement with experiment was found, indicating that the local-density approximation gives accurate total energies and static density response for the high-temperature superconductors

A numerical technique for analyzing electromagnetic wave scattering from moving surfaces in one and two dimensions

Abstract: The electromagnetic wave scattering properties of a moving, perfectly conducting mirror are analyzed using a numerical technique based on the finite-difference time domain (FD-TD) method. This numerical technique does not require a system transformation where the object is at rest, but gives a solution to the problem directly in the laboratory frame. Two canonical one-dimensional cases are considered, the uniformly moving and the uniformly vibrating mirror. Numerical results for the scattered field spectrum are compared to available analytical results, and an excellent agreement is demonstrated. The ability of the FD-TD model to obtain the physics of the double-Doppler effect (for the uniform translation case), and frequency-modulation-like reflected spectrum (for the uniform vibration case) is highlighted. The method is then extended to two-dimensions where a plane wave at oblique incidence on an infinite vibrating mirror is considered. A good agreement with published results is demonstrated for this case. >

Transducer characterization using the angular spectrum method

Abstract: A measurement technique for analyzing the surface velocity patterns of ultrasonic transmitters is presented. The technique is based on the angular spectrum method of wave field analysis. In this approach, acoustic propagation between parallel planar surfaces is modeled using the two‐dimensional (2‐D) Fourier transform of the wave field, with each element in the spatial frequency domain multiplied by the appropriate phase factor. The technique was extended from the basic monochromatic model to the wideband pulsed case. An experimental system was built to measure the acoustic fields from various transducers, including single‐element and multielement phased arrays. Backpropagation results are shown for circular planar, circular focused, and rectangular phase steered transducers. The results demonstrate the ability of the extended angular spectrum method to reconstruct the surface velocity distribution of complex acoustic radiators.

Simple formula for the atomic forces in the augmented-plane-wave method.

Abstract: We present a simple and explicit method for the computation of atomic forces in ab initio total-energy calculations using a basis of augmented plane waves (APW) and the local-density approximation for exchange and correlation. The force on an atom is given by integrals over its muffin-tin sphere only, which can be obtained easily in existing implementations of the linear APW method, for example. The extra computational cost of calculating the forces on all the atoms is negligible compared with that of performing one single self-consistency iteration step.

Wave Propagation in Transversely Isotropic Elastic Media. I. Homogeneous Plane Waves

Abstract: In relation to transversely isotropic media, this paper presents a detailed study of those aspects of the propagation of homogeneous plane elastic waves which are essential to a basic understanding of the behaviour of surface waves. It is first shown how the ordering of the speeds of plane waves provides, directly and simply, a means of classifying the chosen materials, with the class label specifying the broad structure of the slowness surface and the location of its singular points. An examination of the shape of the outer sheet of the slowness surface follows, providing inter alia a complete account of the incidence of the various types of transonic states. The discussion turns next to exceptional waves, that is homogeneous plane waves which leave free of traction some family of parallel planes. The subset of the plane waves possessing this property is determined, after which the subset of the exceptional waves serving as limiting waves for an exceptional transonic state is picked out. Exceptional transonic states occur only when the axis of material symmetry lies either in the reference plane or at right angles to the reference vector and these orientations of the axis are referred to as $\alpha$ and $\beta$ configurations respectively. The exceptional states are arranged in a threefold classification, one class consisting of a continuous set of $\alpha$ configurations and the others discrete $\beta$ configurations. The paper ends with calculations of the limiting speed of the transonic state for the totality of $\alpha$ and $\beta$ configurations.

A paraxial theory for the propagation of ultrasonic beams in anisotropic solids

Abstract: The necessity of nondestructively inspecting cast steels, weldments, composites, and other inherently anisotropic materials has stimulated considerable interest in wave propagation in anisotropic media. Here, the problem of an ultrasonic beam traveling in an anisotropic medium is formulated in terms of an angular spectrum of plane waves. Through the use of small angle approximations, the integral representation is reduced to a summation of Gauss–Hermite eigensolutions. The anisotropic effects of beam skew and excess beam divergence enter into the solution through parameters that are simply interpreted in terms of the slowness surface. Both time harmonic and pulsed solutions are discussed. Formulas are also presented for transmission of a beam through a curved interface between two media. Examples are given illustrating how this method may be applied to predicting beam patterns during ultrasonic inspections.

Multimode network description of a planar periodic metal-strip grating at a dielectric interface. I. Rigorous network formulations

Abstract: The problem of a plane wave incident at an arbitrary angle on a metal strip grating of arbitrary period located at an air-dielectric interface is formulated rigorously in terms of a pair of static integral equations, from which equivalent multimode network descriptions are derived. Both aperture and obstacle approaches are treated, and both TE and TM polarizations are considered explicitly. >

High-frequency scattering from a wedge with impedance faces illuminated by a line source. I. Diffraction

Abstract: The canonical problem of evaluating the scattered field at a finite distance from the edge of an impedance wedge which is illuminated by a line source is considered. The presentation of the results is divided into two parts. In this first part, reciprocity and superposition of plane wave spectra are applied to the left far-field response of the wedge to a plane wave, to obtain exact expression for the diffracted field and the surface wave contributions. In addition, a high-frequency solution is given for the diffracted field contribution. Its expression, derived via a rigorous asymptotic procedure, has the same structure as that of the uniform geometrical theory of diffraction (UTD) solution for the field diffracted by a perfectly conducting wedge. This solution for the diffracted field explicitly exhibits reciprocity with respect to the direction of incidence and scattering. >

Spatial modifications of Gaussian beams diffracted by reflection gratings

Abstract: By using an angular spectral representation, we show that the fields of Gaussian beams scattered by reflection gratings differ markedly from those predicted by geometrical considerations. We find that, in general, each diffracted beam exhibits a lateral displacement, a focal shift, and an angular deflection; in addition, the size of the beam width is enlarged or reduced. The beam changes are largest if the incidence angle is phase matched to a leaky wave that may be supported by the grating. This phase condition is identical to that for which Wood’s anomalies of the resonant variety occur if plane waves, instead of bounded beams, are incident. By evaluating the spatial modifications of beams diffracted at a canonic grating structure consisting of a sinusoidal reactance plane, we show that the magnitudes of the beam effects can be considerably large. We also examine the special case of blazed diffracted orders and find that their corresponding beams are not extinguished completely but appear with reduced intensity and strong profile distortion.

Insights into the hydrodynamics of free falling wavy films

Abstract: On selectionne trois ondes isolees de differentes amplitudes et formes a partir de mesures sur un film liquide tombant. On calcule les champs de vitesse et de pression ainsi que la vitesse de l'onde

L-shaped array for estimating 2-D directions of wave arrival

Abstract: An L-shaped array of sensors to improve the estimation accuracy of two-dimensional directions of plane wave arrival is proposed. The Cramer-Rao bounds for several two-dimensional array configuration are shown. An efficient least-squares algorithm based on the L-shaped array is presented to achieve its theoretical limit. >

Numerical analysis and validation of the combined field surface integral equations for electromagnetic scattering by arbitrary shaped two-dimensional anisotropic objects

Abstract: The numerical solution of coupled integral equations for arbitrarily shaped two-dimensional, homogeneous anisotropic scatterers is presented. The combined theoretical and numerical approach utilized in the solution of the integral equations is based on the combined field formulation and is specialized to both transverse electric (TE) and transverse magnetic (TM) polarizations. As opposed to the currently available methods for anisotropic scatterers, the present approach involves integration over the surface of the scatterer in order to determine the unknown surface electric and magnetic current distributions. The solution is facilitated by developing a numerical approach employing the method of moments. The various difficulties involved in the numerical effort are pointed out, and ways of overcoming them are discussed in detail. The results obtained for two canonical anisotropic structures, namely, a circular cylinder and a square cylinder, are given and validated by results obtained by alternative methods. >

Critical size and curvature of wave formation in an excitable chemical medium

Abstract: The critical radius for the outward propagation of waves in an excitable solution of the Belousov—Zhabotinskii reaction was experimentally analyzed and found to be ≈20 μm, being in a range predicted by theory Thus, the wave initiation depends on the critical radius in an all-or-none fashion For waves having high positive curvature of wave fronts, a linear relationship between the curvature and their normal velocity was established, allowing computation of a diffusion coefficient of 19 × 10-5 cm2/s for the autocatalytic species, which agrees well with results previously obtained for negatively curved wave fronts The analysis of the dispersion of wave velocity yielded the decrease of wave velocity for small initiation periods as predicted theoretically

Gravitational waves in general relativity XIII. Caustic property of plane waves

Abstract: We study the effect of a plane gravitational wave of limited duration (‘sandwich wave’) on an infinite set of test particles at relative rest. We prove, at least for waves of fixed polarization, that all the particles strung out in a certain direction will collide after a finite time that is independent of how far apart they were originally. This we call the caustic property. The effect of the wave on null geodesics is such that this phenomenon does not require any particle to move faster than light. Indeed, an observer who has passed through such a wave will within a finite time have seen an infinite spatial volume lying in a space-like half­ hyperplane on the other side of the wave. For a certain (‘bicaustic’) type of wave the whole of that half-hyperplane will have become visible.

On the rotational components of seismic motion

Abstract: The surface motion during an earthquake is different from point to point depending on the propagation properties of the seismic waves. Rocking and torsion are thus present in the free field, in proportion to the spatial derivatives of the surface motion with respect to a given direction. These derivatives are inversely proportional to the apparent wave velocity in that direction, so the smaller the wave apparent velocity, the more important its contribution to the rotations. In this respect, a marked contribution to surface rotations from surface waves is expected. A mathematical model is presented, based on a detailed representation of soil impedance, an approximate identification of surface waves and a deconvolution of body waves in P and SV contributions. Through this model the surface motion obtained from the records of strong-motion accelerometers can be expressed as a superposition of plane waves of known wavelengths. Rocking response spectra are computed and results are compared with previously published spectra. A sensitivity analysis is performed on some parameters of the model.

Electron wave optics in semiconductors

Abstract: Starting from fundamental principles, quantitative analogies between quantum mechanical electron waves in semiconductor materials and electromagnetic optical waves in dielectrics are presented. This, in turn, suggests many new classes of electron wave optical devices such as narrow‐band superlattice interference filters. Phase effects associated with an electron wave are incorporated using an ‘‘electron wave phase refractive index’’ that is proportional to the square root of the product of the electron effective mass and the electron kinetic energy. It is shown that the amplitude of an electron wave is analogous to the electric field of a TE polarized electromagnetic wave (or to the magnetic field of a TM polarized electromagnetic wave) in a dielectric. Amplitude effects associated with an electron wave are incorporated using an ‘‘electron wave amplitude refractive index’’ that is proportional to the square root of the ratio of the kinetic energy to the effective mass. A simple expression for the critical...