Showing papers on "Plane wave published in 1987"

Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

Abstract: The interaction of a plane weak shock wave with a single discrete gaseous inhomogeneity is studied as a model of the mechanisms by which finite-amplitude waves in random media generate turbulence and intensify mixing. The experiments are treated as an example of the shock-induced Rayleigh-Taylor instability. or Richtmyer-Meshkov instability, with large initial distortions of the gas interfaces. The inhomogeneities are made by filling large soap bubbles and cylindrical refraction cells (5 cm diameter) whose walls are thin plastic membranes with gases both lighter and heavier than the ambient air in a square (8.9 cm side shock-tube text section. The wavefront geometry and the deformation of the gas volume are visualized by shadowgraph photography. Wave configurations predicted by geometrical acoustics, including the effects of refraction, reflection and diffraction, are compared to the observations. Departures from the predictions of acoustic theory are discussed in terms of gasdynamic nonlinearity. The pressure field on the axis of symmetry downstream of the inhomogeneity is measured by piezoelectric pressure transducers. In the case of a cylindrical or spherical volume filled with heavy low-sound-speed gas the wave which passes through the interior focuses just behind the cylinder. On the other hand, the wave which passes through the light high-sound-speed volume strongly diverges. Visualization of the wavefronts reflected from and diffracted around the inhomogeneities exhibit many features known in optical and acoustic scattering. Rayleigh-Taylor instability induced by shock acceleration deforms the initially circular cross-section of the volume. In the case of the high-sound-speed sphere, a strong vortex ring forms and separates from the main volume of gas. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Rayleigh-Taylor instability. The circulation and Reynolds number of the vortical structures are calculated from the measured velocities by modeling a piston vortex generator. The results of the flow visualization are also compared with contemporary numerical simulations.

Calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavity

Abstract: An efficient numerical technique is presented for the calculation of induced electric currents on coupled wires and multiconductor bundles placed in an arbitrary shaped cavity and excited by an external incident plane wave. The method is based upon the finite-difference time-domain (FD-TD) formulation. The concept of equivalent radius is used to replace wire bundles with single wires in the FD-TD model. Then, the radius of the equivalent wire is accounted by a modified FD-TD time-stepping expression (based on a Faraday's law contour-path formulation) for the looping magnetic fields adjacent to the wire. FD-TD computed fields at a virtual surface fully enclosing the equivalent wire are then obtained, permitting calculation of the currents on the wires of the original bundle using a standard electric field integral equation (EFIE). Substantial analytical and experimental validations are reported for both time-harmonic and broad-band excitations of wires in free space and in a high- Q metal cavity.

The wave structure of monochromatic electromagnetic radiation

Abstract: The paper considers a general field of electromagnetic waves of a single frequency and identifies the salient structurally stable features of the three-dimensional pattern of polarization. The approach is geometrical rather than analytical, and it differs from previous treatments of this kind by being applicable even when the constituent plane waves are travelling in all directions. Lines and surfaces exist where the electric or magnetic vibration ellipse is singular. The field is divided into right-handed and left-handed regions by \`T surfaces', the electric and magnetic T surfaces not being coincident. Lying in the T surfaces are \`L$^T$ lines' where the vibration is linear, and cutting through the T surfaces are `C$^T$ lines' where the vibration is circular. Both kinds of lines are surrounded by characteristic patterns of vibration ellipses, which provide a singularity index, $\pm$ 1 for L$^T$ and $\pm \frac{1}{2}$ for C$^T$. The analysis is applicable in a cavity, but a loss-free resonating cavity represents a highly degenerate case.

Ultrasound Doppler Probing of Flows Transverse with Respect to Beam Axis

Abstract: It is an accepted fact that transverse Doppler effects of the first order in v/c are nonexistent for all physical wave phenomena, including acoustics, i.e., the Doppler effect is zero for radiation normal to the direction of motion. However, this statement assumes that the incident field is a plane wave, which is not true in general for finite aperture sources. Consequently, the probing of flows transverse to the axis of finite diameter beams, particularly focused beams, is feasible. This geometry will be advantageous in many applications where the classical orientation of the sound beam, oblique to the flow, is not possible. With this motivation in mind, the theory and experimental feasibility of measuring Doppler spectra in transverse geometries is presently investigated.

Scattering from a microstrip patch

Abstract: A solution to the problem of plane wave scattering by a rectangular microstrip patch on a grounded dielectric substrate is presented. The model does not include the microstrip feed, and thus does not include the so-called "antenna mode" component of the scattering. The solution begins by formulating an electric field integral equation for the surface current density on the microstrip patch. The integral equation is solved using the method of moments. Computed data for the patch radar cross section (RCS) is found to be in close agreement with measurements over a broad frequency range. The microstrip RCS versus frequency consists of a number of large peaks which are identified as impedance or pattern factor resonance peaks.

Electromagnetic theory of diffraction by a circular aperture in a thick, perfectly conducting screen

Abstract: A rigorous electromagnetic theory of the diffraction of radiation by a circular aperture in a thick screen is developed. In particular, the case of an incident plane wave is considered, and the effects of varying the thickness of the screen and of varying the wavelength, polarization, and angle of incidence of the incident wave on the reflection and transmission properties of the screen are investigated.

Millimeter-Wave Characteristics of Phase-Correcting Fresnel Zone Plates

Abstract: A focusing element called the phase-correcting Fresnel zone plate is described, and its characteristics are given when used in the millimeter-wave region for imaging or frequency filtering in place of a lens. Two versions are discussed, one where alternate concentric annular grooves are cut in a single piece of low-loss dielectric, and a second where two (or more) dielectrics are used in alternate concentric rings. For the latter case, an appropriate choice of parameters produces a design of constant thickness (i.e., a flat disk), named the "planar lens." Design formulas and curves, as well as measured results, are given for both types, and an analytical description is derived for the far-field patterns. Compared with lenses, zone plates are simpler to construct and have lower absorption loss, thickness, and weight.

Surface and near-surface effects on seismic waves—theory and borehole seismometer results

Abstract: A simple plane wave model is adequate to explain many surface versus borehole seismometer data sets. Using such a model, we present a series of examples which demonstrate the effects of the free-surface, near-surface velocity gradients, and low impedance surface layers on the amplitudes of upcoming body waves. In some cases, these amplitudes are predictable from simple free-surface and impedance contrast expressions. However, in other cases these expressions are an unreliable guide to the complete response, and the full plane wave calculation must be performed. Large surface amplifications are possible, even without focusing due to lateral heterogeneities or nonlinear effects. Both surface and borehole seismometer site responses are almost always frequency-dependent. Ocean bottom versus borehole seismic data from the 1983 Ngendei Seismic Experiment in the southwest Pacific are consistent with both a simple plane wave model and a more complete synthetic seismogram calculation. The borehole seismic response to upcoming P waves is reduced at high frequencies because of interference between the upgoing P wave and downgoing P and SV waves reflected from the sediment-basement interface. However, because of much lower borehole noise levels, the borehole seismometer enjoys a P -wave signal-to-noise advantage of 3 to 7 dB over nearby ocean bottom instruments.

Applied seismic wave theory

Abstract: Introduction. I. Capita Selecta from Vector Analysis. Scalar product, gradient, curl and divergence. Theorem of Stokes, theorem of Gauss and Green's theorem. II. One-Dimensional Discrete Spectral Analysis. The delta pulse and discrete functions. Fourier series of periodic time functions. Fourier integral of transients. Relationship between the discrete property and periodicity. Sampling and aliasing in time and frequency. Matrix formulations. Decomposition of a broad band experiment into monochromatic simulations. III. Multi-Dimensional Discrete Spectral Analysis. Basic theory. Spatial aliasing. Two-dimensional spectral analysis and plane wave decomposition. Extensions to three dimensions. IV. Vibrations. Basic concepts. Free vibrations. Forced vibrations. Coupled systems. From vibrations to waves. V. Acoustic Waves. Derivation of the acoustic wave equation. One-way versions of the acoustic wave equation. Plane waves. Spherical waves. Cylindrical waves. Principle of numerical modeling with the acoustic wave equation. VI. Elastic Waves. Compressional waves in homogeneous isotropic solids. Shear waves in homogeneous isotropic solids. Derivation of the elastic wave equation. One-way versions of the elastic wave equation. Principle of numerical modeling with the elastic wave equation. VII. Boundary Conditions. Reflection and transmission coefficients for acoustic boundaries. Reflection in terms of convolution. The fluid-solid boundary. Reflection and transmission coefficients for elastic boundaries. Summary. VIII. Kirchhoff and Rayleigh Integrals. Derivation of the Kirchhoff integral for homogeneous media. Derivation of the Rayleigh integrals for homogeneous media. Rayleigh integrals in terms of convolution. Transformation of Rayleigh integrals to the wave number domain. Kirchhoff and Rayleigh integrals for inhomogeneous fluid-like media. Rayleigh integrals as one-way versions of the Kirchhoff integral. Discrete version of the Kirchhoff integral. Discrete versions of the Rayleigh integrals. Summary. IX. Directivity Properties of Wave Fields. Fraunhofer approximations in terms of the Fourier integral. Directivity patterns. Far field expressions of scattered wave fields. Summary. X. Forward and Inverse Problems. Principle of one-way forward wave field extrapolation. Principle of one-way inverse wave field extrapolation. Principle of two-way techniques. Example. Summary. (Each chapter includes an introduction and references). Appendices. Subject Index.

Linear plane waves in dissipative relativistic fluids.

Abstract: This paper analyzes the dispersion relations for linear plane waves in the Eckart and the Israel-Stewart theories of dissipative relativistic hydrodynamics. We show that in the long-wavelength (compared to a typical mean-free-path-length) limit the complicated dynamical structure of the Israel-Stewart theory reduces to the familiar dynamics of classical fluids: 9 of the 14 modes of an Israel-Stewart fluid are strongly damped in this limit, two propagate at the adiabatic sound speed (with appropriate viscous and thermal damping), two transverse shear modes decay at the classical viscous damping rate, and the final longitudinal mode is damped at the classical thermal diffusion rate. The short-wavelength limit of these dispersion relations is also examined. We demonstrate that the phase and group velocities of these waves must approach the characteristic velocities in the short-wavelength limit. Finally, we show how some of the perturbations of an Eckart fluid violate causality.

Analytical method of a multilayered meander-line polarizer plate with normal and oblique plane-wave incidence

Abstract: Simple empirical formulas for perpendicular and parallel polarization susceptances for a meander-line grating plate are given. The numerical results compared favorably with experimental data and published data. Simple transmission-line model in terms of E -type mode and H -type mode for multilayered meander-line polarizer plate is presented for plane wave incidence at normal and oblique angles. Numerical results for design examples are given for practical application.

Scattering from cavity-backed apertures: The generalized dual series solution of the concentrically loaded E -pol slit cylinder problem

Abstract: The generalized dual series solution to the scattering of an E -polarized ( E -pol) plane wave from an infinite circular cylinder having an infinite axial slot and enclosing an infinite concentric impedance cylinder is presented. This solution explicitly exhibits the correct edge behavior, and it can handle cylinders that are either electrically small or large without special considerations. The angle of incidence is arbitrary. A variety of current, field, and cross-section results are presented. These are compared with the corresponding H -pol problem results to establish the polarization dependencies of the aperture coupling. It is also shown that effects corresponding to the presence of the interior cavity dominate all of the scattering data. In particular, the bistatic cross sections in either case and the current induced along an interior wire in the E -pol case exhibit new resonance features that are due to the cavity-backed nature of the aperture.

Electromagnetic scattering by stratified inhomogeneous anisotropic media

Abstract: An analytical formulation is presented for the computation of scattering and transmission by general anisotropic stratified material. This method employs a first-order state-vector differential equation representation of Maxwell's equations whose solution is given in terms of a 4 \times 4 transition matrix relating the tangential field components at the input and output planes of the anisotropic region. The complete diffraction problem is solved by combining impedance boundary conditions at these interfaces with the transition matrix relationship. A numerical algorithm is described which solves the state-vector equation using finite differences. The validation of the resultant computer program is discussed along with example calculations.

Spectral analysis of focus wave modes

Abstract: The focus wave mode (FWM), which is a time-dependent beam field that propagates at the speed of light without dispersion and retains its shape in space, is an interesting wave object with possible implications for synthesizing focused fields under transient conditions. To explore this potential, it is necessary to understand fully the properties of this wave field. It is already known that the FWM is a homogeneous solution of the wave equation, which is related in a special way to the field of a source moving on a complex trajectory parallel to the real axis of propagation. This suggests that there may be a connection between the FWM and the conventional free-space Green’s function. It is shown here that the FWM is related, in fact, to a source-free combination of causal and anticausal free-space Green’s functions and that one can formulate a bilateral transform pair relating these solutions. This new representation is then analyzed by using the spectral theory of transients to establish the properties of the FWM in terms of a distribution of transient plane waves. The spectral decomposition in the spatial wave-number domain reveals that the FWM is synthesized by both forward- and backward-propagating plane waves that are restricted to the visible spectrum. Asymptotic considerations show that the dominant mechanism is constructive interference of the backward-propagating waves. Taken together, the Green’s-function and spectral approaches grant further insight into the physical and spectral properties of the FWM. The conclusions cast doubt on the possibility of embedding the FWM within a causal excitation scheme.

Weakly dispersive spectral theory of transients, part I: Formulation and interpretation

Abstract: Dispersive effects in transient propagation and scattering are usually negligible over the high frequency portion of the signal spectrum, and for certain configurations, they may be neglected altogether. The source-excited field may then be expressed as a continuous spatial spectrum of nondispersive time-harmonic local plane waves, which can be inverted in closed form into the time domain to yield a fundamental field representation in terms of a spatial spectrum of transient local plane waves. By exploiting its analytic properties, one may evaluate the basic spectral integral in terms of its singularities-real and complex, time dependent and time independent-in the complex spectral plane. These singularities describe distinct features of the propagation and scattering process appropriate to a given environment. The theory is developed in detail for the generic local plane wave spectra representative of a broad class of two-dimensional propagation and diffraction problems, with emphasis on physical interpretation of the various spectral contributions. Moreover, the theory is compared with a similar approach that restricts all spectra to be real, thereby forcing certain wave processes into a spectral mold less natural than that admitting complex spectra. Finally, application of the theory is illustrated by specific examples. The presentation is divided into three parts. Part I, in this paper, deals with the formulation of the theory and the classification of the singularities. Parts II and III, to appear subsequently, contain the evaluation and interpretation of the spectral integral and the applications, respectively.

Radiative Wave Equations for Vector Electromagnetic Propagation in Dense Nontenuous Media

Abstract: A set of radiative wave equations including all four Stokes parameters is derived for vector electromagnetic wave propagation in dense nontenuous media. The derivation is based on the quasi-crystalline approximation with coherent potential on the first moment of the field, and the modified ladder approximation on the second moment of the field. These two approximations are shown to be energetically consistent for dense nontenuous media. To simplify the derivation of the radiative wave equations, the model of small spherical scatterers is used. The derived radiative wave equations assume the same form as the classical radiative transfer equations. However, the relations of the extinction rate, the albedo and the phase matrix to the physical parameters of the media include the effects of dense media and can be different from the classical relations of independent scattering.

Dipole radiation in a multilayer geometry

Abstract: There are several kinds of experiments that can be done with multilayer stacks of dielectric media which require an understanding of light emission by sources within the stack for their analysis. These experiments may involve, for example, light-emitting tunnel junctions, Raman scattering in Kretschmann and other multilayered geometries, and Rayleigh scattering by small amounts of surface or interface roughness, either alone or in combination with other processes. A set of electromagnetic Green's functions for a multilayer stack of isotropic dielectric media [D. L. Mills and A. A. Maradudin, Phys. Rev. B 12, 2943 (1975)] gives the electric fields produced everywhere by a point source of current oscillating at a frequency f. These Green's functions can thus be used to solve this type of problem. In this paper we show how these Green's functions can be written in terms of 2\ifmmode\times\else\texttimes\fi{}2 transfer matrices of the type commonly used to find the fields in a dielectric stack due to an incident plane wave. With this simplification we can easily evaluate the Green's functions for a stack with an arbitrary number of layers. We further show that, when the electric fields generated by a point source within the stack are evaluated far away, they can be written directly in terms of the electric fields that would be generated at the location of the current source by plane waves incident from the direction of the observation point. We show that this follows from the Lorentz reciprocity theorem. Thus, in this case the formalism of Green's functions is not needed.

Scattering of a plane wave by a radially stratified tilted cylinder

Abstract: We calculate the intensity of the light scattered by an infinite, radially stratified cylinder. The incident light is a plane wave having an arbitrary angle of incidence and an arbitrary polarization. The Hertz potentials of the scattered wave are represented as superpositions of conical waves, and the boundary-value method is used to derive an infinite set of systems of linear equations for the expansion coefficients. The intensity and the polarization of the far-field scattered wave is expressed in terms of these expansion coefficients. Numerical results showing the angular distribution of the scattered intensity corresponding to different angles of incidence are also presented for the case of a doubly clad image-transmitting fiber illuminated by a He–Ne laser.

A numerical method for an inverse scattering problem

Abstract: Publisher Summary This chapter discusses an approach to solve an inverse problem in time harmonic acoustic or electromagnetic scattering. The chapter describes a time harmonic acoustic wave propagation in a homogeneous isotropic medium in ℝ2. The wave motion can be described by a velocity potential U{x, t) = u(x)e-iwt. The velocity field v is obtained by the gradient of U and the pressure by p = p0 - From the full time-dependent wave equation, the reduced wave equation or Helmholtz equation is obtained for the space dependent part u with a positive wave number k = ω/c. Here, ω denotes the frequency, and c denotes the speed of sound. The chapter also presents the case where Maxwell's equations reduce to the two-dimensional Helmholtz equation for u.

On the collision of gravitational plane waves: a class of soliton solutions

Abstract: The inverse scattering method is used to obtain a class of solutions of the vacuum Einstein equations describing the space-time following the collision of two gravitational plane waves. The general features of these solutions are analyzed in terms of the behavior of the Weyl scalars, and some degenerate cases are discussed.

Inverse scattering method for one-dimensional inhomogeneous layered media

Abstract: An inverse scattering method to reconstruct simultaneously the permittivity profile and the conductivity profile of one-dimensional inhomogeneons medium which makes use of the transverse electric (TE) wave and/or transverse magnetic (TM) wave, is proposed. The medium is illuminated by the TE and/or TM plane wave at oblique incidence, and the data are taken as the reflection coefficients for a set of discrete frequencies and/or a finite number of incident angles. Furthermore, the reflection coefficient data contain the Gaussian noise. The nonlinear integral equation relating the unknown constitutive parameter of the medium to the reflection coefficient for TE wave and/or TM wave is solved by the Newton iteration method. The inverse operator in the Newton method is determined by the regularization method. It is demonstrated in terms of the numerical examples that this method utilizing both polarizations and the incident angle of the incident plane wave is very effective even if the reflection coefficient contains the practical measurement error, or the phase of the reflection coefficient is unknown. Moreover, the relationships between the errors of reconstructed profile and the measured reflection coefficient are also discussed.

Two-dimensional beam diffraction by a half-plane and wide slit

Abstract: The far field of a two-dimensional beam resulting from an electric line source at a complex position is described, its half-power beamwidth determined, and its validity as an antenna beam indicated. Farfield diffraction by a half-plane is then determined from an exact uniform solution for an isotropic line source by making the source position complex. The same basic solution and technique are used for beam diffraction by a wide slit, with first-order interaction between the slit edges included. Numerical results for normal incidence illustrate the evolution of the diffraction patterns from those for an omnidirectional source to those for a highly directive beam. Results for plane wave incidence by a slit also come out of this solution. The remarkable simplicity and convenience of this method relative to alternative asymptotic procedures is discussed.

High‐frequency expression for the field in the caustic region of a cylindrical reflector using Maslov's method

Abstract: High-frequency expressions in the caustic region are derived for the wave reflected by a circular and a parabolic cylindrical reflector using Maslov's method when a plane wave is incident obliquely. Maslov's method is a systematic procedure for predicting the field in the caustic region combining the simplicity of ray and generality of the transform method. Numerical computations are made for the field pattern around the caustic or cusp region and the variation of peak positions of the reflected field with respect to the incident angle.

Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: A spectral approach

Abstract: A set of two coupled integral equations based on a plane wave representation Of the fields in a simply connected and anisotropic medium has been derived in order to handle the problem of scattering by a homogeneous anisotropic cylinder for an obliquely incident plane wave of arbitrary linear polarization. The unknowns are scalar, the range of integration is finite, and the kernels are not singular. Numerical results are presented and discussed in detail. The gyrotropic type case is emphasized, and it is found that as in the isotropic case, the depolarization is the same for transverse electric (TE) and transverse magnetic (TM) incident waves.

Principle of prestack migration based on the full elastic two-way wave equation

Abstract: The acoustic approximation in seismic migration is not allowed when the effects of wave conversion cannot be neglected, as is often the case in data with large offsets. Hence, seismic migration should ideally be founded on the full elastic wave equation, which describes compressional as well as shear waves in solid media (such as rock layers, in which shear stresses may play an important role). In order to cope with conversions between those wave types, the full elastic wave equation should be expressed in terms of the particle velocity and the traction, because these field quantities are continuous across layer boundaries where the main interaction takes place. Therefore, the full elastic wave equation should be expressed as a matrix differential equation, in which a matrix operator acts on a full wave vector which contains both the particle velocity and the traction. The solution of this equation yields another matrix operator. This full elastic two‐way wave field extrapolation operator describes the re...

Reflection and transmission coefficients of a thin strip grating for antenna application

Abstract: Reflection and transmission coefficients of thin strip gratings are discussed for plane wave incidence from arbitrary direction. Upon use of the low-frequency approximation, simple closed-form expressions are obtained. They are applicable for the analysis of grid reflector antennas. Physical interpretations of the phenomena are also given and interesting characteristics of the gratings are pointed out. The validity and the applicability of our results is examined numerically by making use of the point matching method (PMM). It is shown that the accuracy is excellent provided the period of gratings is smaller than about 0.3 wavelength.

Numerical Results for the Symmetrical Condensed TLM Node

Abstract: Numerical calculations have been made in order to test the accuracy of the recently derived three-dimensional symmetrical condensed TLM node for electromagnetic. Demonstrations of its use in these areas are given. Analysis of dispersion characteristics shows that the velocity error bound for the new symmetrical condensed node is likely to be less than that for the expanded node. Predictions of the surface currents on an F-111 aircraft due to the scattering of an incident plane wave are in good agreement with other computed codes and measurements. Lastly, the introduction of, stubs into tbe scattering node allows generalization to a cylindrical mesh, which is tested by finding coaxial cavity modes.

Elastic Wave Scattering from an Interface Crack: Antiplane Strain

Abstract: The two-dimensional scalar problem of scattering of elastic waves under antiplane strain from an interface crack between two elastic half-spaces is considered. The method used is a direct integral equation method with the crack-opening displacement as the unknown. Chebyshev polynomials are used as expansion functions and the matrix in the resulting equations is simplified by contour integration techniques. The scattered far field is expressed explicitly in simple functions and the expansion coefficients. The consequences of energy conservation are explored and are used as a check in the numerical implementation. For incoming plane waves numerical results are given for the total scattered energy and the far field amplitude.