Showing papers on "Plane wave published in 1988"

Intensity images and statistics from numerical simulation of wave propagation in 3-D random media

Abstract: An extended random medium is modeled by a set of 2-D thin Gaussian phase-changing screens with phase power spectral densities appropriate to the natural medium being modeled. Details of the algorithm and limitations on its application to experimental conditions are discussed, concentrating on power-law spectra describing refractive-index fluctuations of the neutral atmosphere. Inner and outer scale effects on intensity scintillation spectra and intensity variance are also included. Images of single realizations of the intensity field at the observing plane are presented, showing that under weak scattering the small-scale Fresnel length structure of the medium dominates the intensity scattering pattern. As the strength of scattering increases, caustics and interference fringes around focal regions begin to form. Finally, in still stronger scatter, the clustering of bright regions begins to reflect the large-scale structure of the medium. For plane waves incident on the medium, physically reasonable inner scales do not produce the large values of intensity variance observed in the focusing region during laser propagation experiments over kilometer paths in the atmosphere. Values as large as experimental observations have been produced in the simulations, but they require inner scales of the order of 10 cm. Inclusion of an outer scale depresses the low-frequency end of the intensity spectrum and reduces the maximum of the intensity variance. Increasing the steepness of the power law also slightly increases the maximum value of intensity variance.

Electromagnetic wave scattering from some vegetation samples

Abstract: For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite length. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements. >

Dark-pulse propagation in optical fibers.

Abstract: We report measurements of the reshaping of 0.3-psec dark pulses due to their passage through 10 m of single-mode optical fiber. The measurements were performed as a function of intensity and the observed strong reshaping agrees qualitatively with the predictions of the nonlinear Schr\"odinger equation which suggest that we have observed the formation of dark-pulse solitons.

An examination of the theory and practices of planar near-field measurement

Abstract: Using computer simulation, several fundamental issues in planar near-field measurement are examined. The results indicate that some of the prevailing views of practices regarding the evanescent modes, the sampling and filtering of data, and the selection of the location and directivity of the probe are incomplete or misleading. In particular, the merits of using smaller low-directivity probes in conjunction with a closer probe-to-antenna distance have been found to be unduly overlooked. >

Scattering from black holes

Abstract: This book investigates the propagation of waves in the presence of black holes Astrophysical black holes may eventually be probed by these techniques The authors emphasise intuitive physical thinking in their treatment of the techniques of analysis of scattering, but alternate this with chapters on the rigourous mathematical development of the subject High and low energy limiting cases are treated extensively and semi-classical results are also obtained The analogy between Newtonian gravitational scattering and Coulomb quantum mechanical scattering is fully exploited The book introduces the concepts of scattering by considering the simplest, scalar wave case of scattering by a spherical black hole It then develops the formalism of spin-weighted spheroidal harmonics and of plane wave representations for neutrino, electromagnetic and gravitational scattering Research workers and graduate and advanced undergraduate students in scattering theory, wave propagation and relativity will find this a comprehensive treatment of the topic

Sound scattering by cylinders of finite length. II. Elastic cylinders

Abstract: There are many different finite length scatterers in the ocean such as marine biota in the water column and protuberances (or ‘‘bosses’’) on the seafloor, sea surface, and underside of sea ice. Since it is impossible to describe scattering from the exact shape of most objects, one must use simple geometrical objects such as spheres, spheroids, or finite cylinders as the approximate shape. In this article, the scattering of an incident plane wave by a fluid finite circular cylinder is described for all frequencies. By neglecting end effects, the volume flow per unit length of the scattered field of the finite cylinder is approximated by that of the infinite cylinder. The solution is obtained by integrating this volume flow along the length of the cylinder. This approximation restricts the solution to geometries where the incident waves are normal or near normal to the axis of the cylinder. The solution is adapted to describe the scattering of sound by shrimp, which are elongated fluid‐saturated marine organisms. There was excellent agreement between the adapted solution and shrimp backscatter data.

Coupled-Wave Analysis Of Two-Dimensional Dielectric Gratings

Abstract: Diffraction by two-dimensional surface-relief dielectric gratings are analyzed using rigorous three-dimensional vector coupled-wave approach. The method applies to arbitrary plane wave angle of incidence, wavelength, and polarization. In the resulting conical diffraction, the input TE and TM polarization are coupled and the diffracted orders are, in general, elliptically polarized. Diffraction characteristics of two-dimensional binary gratings are presented. Ultrahigh spatial-frequency gratings (grating period less light wavelength) are shown to exhibit polarization independent antireflection behavior (zero-reflectivity).

SAFARI: Seismo-Acoustic Fast Field Algorithm for Range-Independent Environments. User's Guide

Abstract: : An efficient algorithm has been developed for solving the depth- separated wave equation in general fluid/solid horizontally stratified media. The algorithm has been built into a general-purpose packages of computer codes called SAFARI. The package consists of three modules providing plane wave reflection coefficients, continuous wave transmission losses, and broadband pulse response. This document describes the mathematical model for seismo- acoustic propagation in stratified media. Then the numerical solution technique is outlined followed by a description of the three different SAFARI modules and their implementation. The actual use of the different modules is described, including a detailed discussion on the numerical considerations that are crucial for successful use of this type of numerical model. SAFARI is applicable to a wide range of problems in many disciplines, from seismology to ultrasonics. Here its use is illustrated by a series of examples from underwater acoustics. Keywords: Attenuation; Beam propagation; Fast field program; Green's function; Normal mode propagation; Numerical modelling; Pulse propagation; Reflection coefficient; Seismic interface wave; Seismo-acoustic propagation; Wave equations; Wave propagation; NATO-furnished. edc

Acoustic radiation force experienced by a solid cylinder in a plane progressive sound field

Abstract: The acoustic radiation force experienced by a solid cylinder suspended freely in a plane progressive sound field is calculated, taking into account the elasticity of the cylinder. The results of numerical calculations are presented, indicating the ways in which the form of the frequency dependence of the radiation force function YP for cylindrical targets is affected by variations in the material parameters of the cylinder. The results are compared with those for solid spherical targets.

Duct propagation of hydromagnetic waves in the upper ionosphere, 1, Electromagnetic field disturbances in high latitudes associated with localized incidence of a shear Alfvén wave

Abstract: Mode conversion to the fast magnetosonic wave by anisotropic ionospheric currents from a localized incident shear Alfven wave is studied in detail, based on a simple layered model inclusive of an anisotropic conducting sheet (the ionospheric E layer) and an upper ionospheric ducting layer under vertical, uniform ambient magnetic field lines. A horizontal profile of electromagnetic field intensity at the E layer shows a wider spread than that of the incident wave due to trapping of the fast magnetosonic wave in the ducting layer. Since electrostatic electric field intensity of the incident Alfven wave is dominant in the central region, the eddy Hall current associated with the Alfven wave generates the ground magnetic field variations. On the other hand, since electromagnetic electric field intensity of the trapped fast magnetosonic wave exceeds to that of the incident Alfven wave in the region surrounding the central region, both the magnetic field of the fast magnetosonic wave and the secondary field due to the eddy Pedersen current contribute to the ground magnetic field variations.

Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance faces

Abstract: A uniform asymptotic solution is presented for the electromagnetic diffraction by a wedge with impedance faces and with included angles equal to 0 (half-plane), pi /2 (right-angled wedge), pi (two-part plane) and 3 pi /2 (right-angled wedge). The incident field is a plane wave of arbitrary polarization, obliquely incident to the axis of the wedge. The formal solution, which is expressed in terms of an integral, was obtained by the generalized reflection method. A careful study of the singularities of the integrand is made before the asymptotic evaluation of the integral is carried out. The asymptotic evaluation of the integral is performed taking into account the presence of the surface wave poles in addition to the geometrical optics poles near the saddle points. This results in a uniform solution which is continuous acros the shadow boundaries of the geometrical optics fields as well as the surface wave fields. >

Application of a conjugate gradient FFT method to scattering from thin planar material plates

Abstract: The backscatter cross section is calculated for thin material plates with finite electric permittivity, conductivity, and magnetic permeability illuminated by a plane wave. The plates are assumed to be planar with an arbitrary perimeter. The integral equations are formed and solved by a combined conjugate gradient-fast Fourier transform (CG-FFT) method. The CG-FFT method was tested for several geometrics and materials measured and computed backscatter results are compared for a perfectly conducting equilateral triangle plate, a square dielectric and magnetic plate, and a circular dielectric plate. The agreement between measured and computed data is generally good except toward edge-on incidence where several factors cause discrepancies. Accurate approximations to the geometry and far-field integrals become critical near edge-on incidence and, it is postulated that as the incidence angle approaches edge-on, the sampling interval and tolerance should be decreased. >

Electromagnetic scattering by pyramidal and wedge absorber

Abstract: Electromagnetic scattering from pyramidal and wedge absorbers used to line the walls of modern anechoic chambers is measured and compared with theoretically predicted values. The theoretical performance for various angles of incidence is studied. It is shown that a pyramidal absorber scatters electromagnetic energy more as a random rough surface does. The apparent reflection coefficient from an absorber wall illuminated by a plane wave can be much less than the normal absorber specifications quoted by the manufacturer. For angles near grazing incidence, pyramidal absorbers give a large backscattered field from the pyramid side-faces or edges. The wedge absorber was found to give small backscattered fields for nuclear-grazing incidence. Based on this study, some new guidelines for the design of anechoic chambers are advocated because the specular scattering models used at present do not appear valid for pyramids that are large compared to the wavelength. >

Electromagnetic scattering from a dielectric cylinder of finite length

Abstract: The dyadic scattering amplitude is determined for a planar electromagnetic wave incident on a dielectric cylinder of finite length and circular cross section under the assumption that the internal fields induced within the finite-length cylinder can be approximated by those within an infinite-length cylinder. These internal fields are then used to calculate the dyadic scattering amplitude in terms of the cylinder's physical dimensions, orientation, and dielectric properties. The theoretical development is complemented by numerical calculations, and its validity assessed by comparison with experiment. >

Relative phases of electromagnetic waves diffracted by a perfectly conducting rectangular-grooved grating.

Abstract: A complete solution of plane-wave scattering from a groove-corrugated surface of infinite extent for arbitrary incidence is presented. The electromagnetic wave is decomposed into fast and slow modal representation, and the solution is accomplished through the use of the mode-matching method. We solved for the zero-order diffraction efficiency and the phase of each polarization component for arbitrary incident angles. Our results have verified special cases previously published by others and have illustrated the phase shift between polarizations associated with the diffraction process as a function of the incident angles.

Resonant Mie scattering from a layered sphere

Abstract: The theory of Aden and Kerker is used to compute the resonant response of large layered spheres to an incident linearly polarized plane wave. Cases considered include hollow spheres and those with transparent and absorbing cores whose diameters range from zero up to that of the particle. Both core and layer resonances are studied. The results are presented as partial wave amplitudes, energy densities, and scattered light intensities for a typical resonant mode, TE39.

Theory of Bernstein wave coupling with loop antennas

Abstract: Coupling to ion Bernstein waves near the first harmonic of the ion cyclotron resonance with coil antennas is investigated by using a plane layered model of a tokamak plasma. The boundary conditions in vacuum are solved analytically for arbitrary orientation of the antenna and Faraday screen conductors, in terms of the surface impedance matrix of the plasma for plane waves. The latter is evaluated by solving the wave equations in the plasma by taking into account finite Larmor radius and finite electron inertia effects, cyclotron and harmonic damping by the ions, and Landau and collisional damping by the electrons. – Applications to the Alcator C tokamak give reasonable agreement between the calculated and measured radiation resistance when the first ion cyclotron harmonic is just behind the antenna; outside this range, the calculated resistance is lower than the experimental one. In general, the coupling efficiency is found to be very sensitive to the edge plasma density, good coupling requiring a low density plasma layer in the vicinity of the Faraday screen. Coupling also improves with increasing ion temperature in the scrape-off layer and is appreciably better for antennas with antisymmetric than with symmetric current distribution in the toroidal direction.

Models for very wide-angle water waves and wave diffraction

Abstract: \For a bathymetry consisting of parallel bottom contours, wide-angle parabolic models are developed to describe the diffraction of linear water waves. The first model, developed by operator correspondence, extends the validity of conventional forms of the parabolic model for wave angles up to 70" from the assumed wave direction. Through the use of Fourier decomposition, wave models valid to 90" are developed for three different lateral boundary conditions. By application, it is shown that the diffraction of waves through gaps or around structures is governed by the initial wave condition at the structure, which can be expanded into progressive and evanescent wave modes. Away from the structure, the wave field consists of only the progressive wave modes, which disperse according to their direction of propagation, the water depth and Snell's Law. Examples are shown for oblique waves through a gap, directional seas past a breakwater, a plane wave with varying crest amplitude, and finally for the diffraction of waves into a channel.

Reverse-time wave-field extrapolation, imaging, and inversion

Abstract: The scattered wave field propagated backward in time into an arbitrary background medium is related via a volume integral to perturbations in velocity about the background, which are expressed as a scattering potential. In general, there is no closed-form expression for the kernel of this integral representation, although it can be expressed asymptotically as a superposition of plane waves backpropagated from the receiver array. When the receiver array completely surrounds the scatterer, the kernel reduces to the imaginary part of the Green's function for the background medium.This integral representation is used to relate the images obtained by imaging algorithms to the actual scattering potential. Two such relations are given: (1) for the migrated image, obtained by deconvolving the extrapolated field with the incident field; and (2) for the reconstructed image, obtained by applying a one-way wave operator to the extrapolated field and then deconvolving by the incident field. The migrated image high-lights rapid changes in the scattering potential (interfaces), whereas the reconstructed image can, under ideal conditions, be a perfect reconstruction of the scattering potential. 'Ideal' conditions correspond to (1) weak scattering about a smoothly varying background medium, (2) a receiver array with full angular aperture, and (3) data of infinite bandwidth.Images obtained from a multioffset vertical seismic profile (VSP) illustrate some of the practical differences between the two imaging algorithms. The reconstructed image shows a much clearer picture of the target (a reef structure), in part because the one-way imaging operator eliminates artifacts caused by the limited aperture of the receiver array.

Bandpass grids with annular apertures

Abstract: A rigorous theory is developed for describing the diffraction of a plane wave by a doubly periodic array of annular apertures in a thick, perfectly conducting screen. Coaxial waveguide modes are used to describe the fields within each aperture, while the fields above and below the grid are written as plane wave expansions. Appropriate boundary conditions are applied at the upper and lower surfaces of the screen, and the method of moments is used to determine mode and wave amplitudes. Such a structure was found to exhibit excellent bandpass characteristics which can be adjusted by changing the size of the apertures and the thickness of the screen. >

Acoustics of solids

Abstract: I Elements of Material Structure and Solid Dynamics.- 1.1 Dynamic response of solids.- 1.2 Structure of materials.- 1.3 Continuum and microstructure.- 1.4 Deformations.- 1.5 Stresses.- 1.6 Conservation laws.- 1.7 Hooke's law.- 1.8 Absorption and viscoelasticity.- 1.9 Piezoelectricity and other coupled phenomena.- 1.10 Variational theorems.- 1.11 Wave front and wave classification.- 1.12 Conditions across discontinuity.- 1.13 Characteristics and hyperbolicity.- 1.14 Energy flux.- 1.15 Basic concepts of waves. Debye's frequency.- 1.16 Group and signal velocities.- 1.17 Causality and general relations for linear systems.- Problems.- References and additional reading.- II Bulk Waves in Isotropic Media.- 2.1 Modes and velocities of elastic waves.- 2.2 Vector representation and wave potentials.- 2.3 Wave motion in curvilinear coordinates and separability.- 2.4 Plane waves.- 2.5 Cylindrical waves.- 2.6 Spherical waves.- 2.7 Radiation from a cylindrical cavity.- 2.8 Radiation from a rigid embedded cylinder. Radiation damping.- 2.9 Radiation from a spherical cavity. Remarks on radiation conditions.- 2.10 Radiation from a rigid embedded sphere. Imperfect bonding.- 2.11 Multipoles, resonances, and related considerations.- 2.12 Green's dynamic tensor.- 2.13 Energy transport in harmonic waves.- 2.14 Viscoelastic waves. Spatial and temporal attenuation.- 2.15 Viscoelastic pulse propagation. Wavefront velocity.- 2.16 Radiation from a moving dislocation.- 2.17 Creation of a dislocation dipole. Non-uniform motion.- 2.18 Limitations of the linear theory. Shock waves.- Problems.- References and additional reading.- III Bulk Waves in Anisotropie Media.- 3.1 Plane waves.- 3.2 Effects of symmetry.- 3.3 Pure modes in cubic systems.- 3.4 General modes in cubic systems.- 3.5 Energy velocity.- 3.6 Waves in piezoelectric media.- 3.7 Quasi-electrostatic approximation of piezoelectricity.- 3.8 Modes in a piezoelectric cubic system.- 3.9 Bulk wave piezoelectric transducer.- 3.10 Generation of harmonic waves. Resonators.- 3.11 Improved analysis of resonators.- 3.12 Characteristic surfaces.- Problems.- References and additional reading.- IV Boundary Effects and Waveguides.- 4.1 Reflection and mode conversion at free boundary.- 4.2 Reflection at interface. Impedance matching.- 4.3 Rayleigh waves in isotropic half-space.- 4.4 Rayleigh waves in anisotropic half-space.- 4.5 Love waves.- 4.6 Interdigital transducer.- 4.7 Waves in a plate. Cut-off frequencies.- 4.8 Frequency spectrum of a plate.- 4.9 Torsional waves in a cylinder.- 4.10 Longitudinal waves in a cylinder.- 4.11 Flexural waves in a cylinder.- 4.12 Timoshenko beam theory.- 4.13 Mindlin plate theory.- 4.14 Normal modes of waveguides.- 4.15 Forced motions via modal superpositions.- 4.16 Acoustic emission in a rod.- 4.17 Radiation from a moving load.- Problems.- References and additional reading.- V Wave-Obstacle Interactions. Waves in Composites.- 5.1 Wave-obstacle interactions.- 5.2 Dynamic stress concentrations.- 5.3 Scattering cross-sections.- 5.4 Diffraction by a sphere.- 5.5 Response of random composites.- 5.6 Effective scatterer approach.- 5.7 Composite sphere assemblage.- 5.8 A differential scheme.- 5.9 Response of polycrystals.- 5.10 Rigorous definitions of the effective response.- 5.11 Bounds for static moduli.- 5.12 Wave propagation in random composites.- 5.13 Causal approach of independent scatterers.- 5.14 Causal differential media.- 5.15 Waves in fiber composites. Typical dispersion curves.- 5.16 Waves in ordered systems. Atomic lattice.- 5.17 Waves in layered composites.- Problems.- References and additional reading.- Comments on Selected Problems.- References.- Author Index.

Parametrically excited, standing cross-waves

Abstract: Luke's (1967) variational formulation for surface waves is extended to incorporate the motion of a wavemaker and applied to the cross-wave problem. Whitham's average-Lagrangian method then is invoked to obtain the evolution equations for the slowly varying complex amplitude of the parametrically excited cross-wave that is associated with symmetric excitation of standing waves in a rectangular tank of width π/ k , length l and depth d for which kl = O (1) and kd [Gt ] 1. These evolution equations are Hamiltonian and isomorphic to those for parametric excitation of surface waves in a cylinder that is subjected to a vertical oscillation, for which phase-plane trajectories, stability criteria and the effects of damping are known (Miles 1984 a ). The formulation and results differ from those of Garrett (1970) in consequence of his linearization of the boundary condition at the wavemaker and his neglect of self-interaction of the cross-waves in the free-surface conditions (although Garrett does incorporate self-interaction in his calculation of the equilibrium amplitude of the cross-waves). These differences have only a small effect on the criterion for the stability of plane waves, but the self-interaction is crucial for the determination of the stability of the cross-waves.

Low-frequency low-impedance electromagnetic shielding

Abstract: The problem of low-frequency shielding of a loop that is axially perpendicular to a plane shield of infinite extent is analyzed by the thin shield work of S. Levy (1936), solution of the vector wave equation, and application of S.A. Schelkunoff's (1934) transmission theory of shielding. Experimental data are obtained and compared with results of using the Levy and the Schelkunoff methods in the frequency range 100-50 kHz. The first analytical technique is not general, and the limits of applicability of the results are discussed. In the second solution, which is general, expressions are derived for the total electric and magnetic fields on both sides of and within the shield. The resulting expression for shielding effectiveness is shown to agree with experimental data. The final expression for shielding effectiveness shows independence of shielding with source-to-shield spacing, a results which is shown to be consistent with experimentally obtained data. >

Scattering by two penetrable cylinders at oblique incidence. I. The analytical solution

Abstract: The Mueller scattering matrix elements (Sij) and the cross sections for the scattering of an electromagnetic plane wave from two infinitely long, parallel, circular cylinders at oblique incidence are derived. Each cylinder can be of arbitrary materials (any refractive index). The incident wave can be in any polarization state. To find the scattering coefficients needed for calculating Sij and the cross sections, the multiple scatterings are taken into account for all orders. The formal solutions of the scalar wave equation are obtained for the three regions concerned (the region outside the two cylinders and the region inside each cylinder), and the scattering coefficients are found by satisfying the boundary conditions. The scattering coefficients for some special cases (normal incidence, small radii, perfectly conducting cylinders, and a single cylinder) are given and discussed. The results for these special cases are compared (numerically or analytically) with those obtained in other published works. To our knowledge, this is the first comprehensive study of the two-cylinder problem. Applications of this formalism, including calculations of Sij and the cross sections, will be presented in part II of this series [ J. Opt. Soc. Am. A5, 1097 ( 1988)].

Electromagnetic Penetration into a Conducting Circular Cylinder through a Narrow Slot, TM Case

Abstract: A procedure is presented for calculating the electromagnetic field in the vicinity of an infinitesimally thin conducting circular cylindrical shell with an infinitely long slot illuminated by a TE plane wave. This field is the short-circuit field plus the field due to the slot. The short-circuit field is the field that would exist if there were no slot. The field due to the slot stems from the Φ -component of the electric field in the slot. Approximated by a linear combination of expansion functions that satisfy the edge conditions, this field component is determined by testing the equation of continuity of the axial magnetic field in the slot with non-negative powers of Φ where |Φ| is the angular distance from the center of the slot. Alternative expansion functions are introduced to preserve the accuracy of the solution in the vicinity of an internal resonance. Containing the resonant electric field, the first alternative expansion function is normalized so that its axial magnetic field remains finite as...

Ultrasonic reflection by a planar distribution of cracks

Abstract: Ultrasonic wave reflection and transmission by planar crack distributions is considered. General expressions for the reflection and transmission coefficients are derived for incident longitudinal and transverse time harmonic plane waves. For low frequencies, closed-form algebraic expressions are given in terms of the geometrical parameters, the material constants, and the incident wavefield. The results have been extended to statistical distributions, and reflection coefficients for equivalent statistical and deterministic distributions of penny-shaped cracks are compared. It is also shown that the Mode-I stress-intensity factor for a distribution of equal-sized cracks can be directly related to reflection data.

Wiener-Hopf analysis of the EM diffraction by an impedance discontinuity in a planar surface and by an impedance half-plane

Abstract: The Wiener-Hopf technique is used to solve two canonical problems. The first problem considered is the electromagnetic (EM) diffraction, by a planar surface with an impedance discontinuity (two-part surface), of an arbitrarily polarized plane wave obliquely incident to the axis of the two-dimensional objects. The second problem considers the EM diffraction by a half-plane with equal impedances on both sides. The solutions obtained are cast in a matrix notation which is useful for diffraction problems. The exact formal solutions are expressed in terms of integrals which can be asymptotically evaluated. Uniform asymptotic expressions are obtained where the presence of the geometrical optics (GO) poles as well as the surface-wave poles near the saddle point are fully taken into account. Several numerical examples are presented and it is shown that the solutions are continuous across the shadow boundaries of the GO and surface-wave fields. >