Showing papers on "Plane wave published in 1970"
TL;DR: In this article, it was shown that for a wide class of conservative systems in fluid dymamics changes in amplitude along the rays may be computed from conservation of wave action, defined as the wave energy divided by the intrinsic frequency.
Abstract: When a slowly varying wavetrain of small amplitude propagates in a general medium, changes of frequency and wavenumber are determined along definite paths known as rays. It is shown that, for a wide class of conservative systems in fluid dymamics changes in amplitude along the rays may be computed from conservation of wave action, which is defined as the wave energy divided by the intrinsic frequency. The intrinsic frequency is the frequency which would be measured by an observer moving with the local mean velocity of the medium. This result is the analogue for continuous systems of the adiabatic invariant for a classical simple harmonic oscillator.
590 citations
TL;DR: Thomson theory of arbitrarily intense elliptically polarized plane electromagnetic wave scattering by free electrons, solving electron equations of motion as discussed by the authors, solving electron equation of motion (EoMOM).
Abstract: Thomson theory of arbitrarily intense elliptically polarized plane electromagnetic wave scattering by free electrons, solving electron equations of motion
452 citations
TL;DR: In this article, the elastic wave field in a layer-over-half-space medium with an irregular interface was calculated for the M discontinuity, and the results were compared with those derived from the flat layer theory and from the ray theory.
Abstract: A practical method is devised to calculate the elastic wave field in a layer-over-half-space medium with an irregular interface, when plane waves are incident from below. This method may be used for studying the interface shape of the M discontinuity, for example, using the observed spectral amplitude and phase-delay anomalies due to teleseismic body waves. The method is also useful for the engineering-seismological study of earthquake motions of soft superficial layers of various cross sections. The scattered field is described as a superposition of plane waves, and application of the continuity conditions at the interface yields coupled integral equations in the spectral coefficients. The equations are satisfied in the wave-number domain when the interface shape is made periodic and the equations are Fourier transformed and truncated. Frequency smoothing by using complex frequencies reduces lateral interferences associated with the periodic interface shape and permits comparison of computed results with those obtained from finite bandwidth observations. Analyses of the residuals in the interface stress and displacement, performed for each computed solution, provided estimates of the errors. The relative root-mean-square residual errors were generally less than 5% and often less than 1% for problems in which the amplitude of the interface irregularity and the shortest wavelength were comparable. The method is applied to several models of ‘soft basins’ ‘dented M discontinuity’ and ‘stepped M discontinuity’ The results are compared with those derived from the flat-layer theory and from the ray theory. In addition to vertical interference effects familiar in the flat-layer theory, we observe the effects of lateral interference as well as those of ray geometry on the motion at the surface.
372 citations
TL;DR: In this article, a prism-film coupler was proposed for a laser beam coupled with high efficiency into a light-guiding thin film by means of a prism reflecting prism.
Abstract: A laser beam can be coupled with high efficiency into a light-guiding thin film by means of a prism–film coupler. Basically this device is a totally reflecting prism, the light-guiding film being separated from the reflecting prism face by a narrow gap of reduced refractive index. This coupling scheme is analyzed in detail by the method of plane-wave expansion. It is shown how the coupling efficiency is determined by the competition between the desired coupling effect and the reverse effect of leakage. A general condition is derived under which the transverse profile of the input beam continues undistorted into the guide. The theory is illustrated for a gaussian beam, which allows a maximum coupling efficiency of 0.80.
354 citations
TL;DR: In this article, a general solution to the problem of determining first the aperture field distribution and then the transmission and reflection coefficients of an infinite planar conducting sheet perforated periodically with apertures has been formulated.
Abstract: A general solution to the problem of determining first the aperture field distribution and then the transmission and reflection coefficients of an infinite planar conducting sheet perforated periodically with apertures has been formulated. The excitation is considered to be a plane wave incident at any arbitrary angle. The aperture dimensions and array element spacings were assumed to be comparable with the wavelength of the incident electromagnetic field. The solution given can include the effect of a dielectric slab used to support the thin conducting sheet. The solution is obtained by matching the tangential field components at the surface of the screen. The resulting integral equation is solved by the method of moments which reduces the integral equation to a system of linear algebraic equations that can be solved with the use of a digital computer. Accurate results for both the magnitude and phase of the aperture field distribution and the transmission coefficients for the propagating modes are determined explicitly for a specific example of slots arranged in an equilateral triangular lattice. The balance of power flow between the reflected and the transmitted waves has been checked with satisfactory results. The solution can be applied to the problem of scattering from a conducting screen with periodic apertures and to the complementary problem of scattering from a set of conducting plates by the use of Babinet's principle.
265 citations
TL;DR: In this article, the boundary value problem of an infinite array of thin plates arranged in a doubly periodic grid along any two coordinates is formulated in a general form for an arbitrarily polarized plane wave incident from any oblique angle.
Abstract: The boundary value problem of an infinite array of thin plates arranged in a doubly periodic grid along any two coordinates is formulated in a general form for an arbitrarily polarized plane wave incident from any oblique angle. The induced current on the plate, the near-field distribution, and the distant reflected waves can be obtained to a very close accuracy. Both magnitudes and phases of the reflection coefficients for some specific examples are determined explicitly. For the case of a wave incident normally on a rectangular lattice array of narrow rectangular plates, the calculated values are in excellent agreement with the measurements in a previously published paper.
210 citations
TL;DR: In this article, the multidimensional scalar wave equation at a single frequency is split into two equations, one controlling the downgoing transmitted wave; the other controlling the upcoming reflected wave.
Abstract: The multidimensional scalar wave equation at a single frequency is split into two equations. One controls the downgoing transmitted wave; the other controls the upcoming reflected wave. The equations are coupled, but in many reflection seismology situations the transmitted wave may be calculated without consideration of the reflected wave. The reflected wave is then calculated from the transmitted wave and the assumed velocity field. The waves are described by a modulation on up‐ or downgoing plane waves. This modulation function is calculated by difference equations on a grid. Despite complicated velocity models (steep faults, buried focus, etc.), the grid may be quite coarse if waves of interest do not propagate at large angles from the vertical. A one‐dimensional grid may be used for a two‐dimensional velocity model. With approximations, a point source emitting waves spreading in three dimensions may be included on the one‐dimensional grid. Calculation time for representative models is a few seconds. P...
195 citations
TL;DR: In this paper, it was shown that plane stress waves in solids or fluids exhibit two phase velocities associated with the stress profile of the wave and the mass velocity profile.
Abstract: This paper shows that in general, plane stress waves in solids or fluids exhibit two phase velocities. One of these is associated with the stress profile of the wave and the other with the mass‐velocity profile. These velocities are distinct except for isentropic simple waves, steady flow, or discontinuous fronts, As a result, the determination of time‐dependent constitutive relations from shock‐wave experiments requires more measurements than has heretofore been recognized.
174 citations
TL;DR: In this paper, the authors demonstrate the deflection of an optical film-guided wave by a surface acoustic wave by measuring the depletion of the incident optical guided wave, and show that when Bragg conditions are satisfied, 0.18 W acoustic power gives rise to 66% deflection efficiency.
Abstract: The experimental demonstration of deflection of an optical film‐guided wave by a surface acoustic wave is reported. When Bragg conditions are satisfied, 0.18 W acoustic power gives rise to 66% deflection efficiency as measured by the depletion of the incident optical guided wave.
153 citations
TL;DR: In this article, a thin vertical plate makes small, simple harmonic rolling oscillations beneath the surface of an incompressible, irrotational liquid, and a train of plane waves of frequency equal to the frequency of oscillation of the plate, is normally incident on the plate.
Abstract: A thin vertical plate makes small, simple harmonic rolling oscillations beneath the surface of an incompressible, irrotational liquid. The plate is assumed to be so wide that the resulting equations may be regarded as two-dimensional. In addition, a train of plane waves of frequency equal to the frequency of oscillation of the plate, is normally incident on the plate. The resulting linearized boundary-value problem is solved in closed form for the velocity potential everywhere in the fluid and on the plate. Expressions are derived for the first- and second-order forces and moments on the plate, and for the wave amplitudes at a large distance either side of the plate. Numerical results are obtained for the case of the plate held fixed in an incident wave-train. It is shown how these results, in the special case when the plate intersects the free surface, agree, with one exception, with results obtained by Ursell (1947) and Haskind (1959) for this problem.
TL;DR: In this article, multiple wave propagation in acoustic duct with winds, using perturbation Lagrangian for ideal fluid flow was performed using multiple wave propagators and perturbations.
Abstract: Multiple wave propagation in acoustic duct with winds, using perturbation Lagrangian for ideal fluid flow
TL;DR: By assuming that a plane atmospheric wave acts on a plane-stratified F layer in the presence of a constant geomagnetic field, this paper derived an expression for the resulting perturbations in total columnar electron content as a function of wave and ionospheric-layer parameters and of the orientation of the column through the ionosphere.
Abstract: By assuming that a plane atmospheric wave acts on a plane-stratified F layer in the presence of a constant geomagnetic field, we derive an expression for the resulting perturbations in total columnar electron content as a function of wave and ionospheric-layer parameters and of the orientation of the column through the ionosphere. Although idealized, the model not only correctly predicts the order of magnitude of the observed perturbations but also makes visible much of the physics that determines the magnitude of wave-induced total-content fluctuations observed by using satellite transmissions through the ionosphere. Geomagnetic constraints on ion motion and a tendency for total-content fluctuation to be greatest when the ground-satellite path lies in a surface of constant atmospheric wave phase combine to introduce strong experimental biases that favor the observation of some waves and prevent the observation of others. The effects of these biases must be fully removed before total-content measurements can yield the statistical properties of atmospheric waves at ionospheric heights that may be useful in locating wave sources or in characterizing the dynamic state of the ionosphere.
TL;DR: In this article, the collisionless damping of shear Alfven waves in the limit of low frequency and small but finite Larmor radius is discussed, and the normalized damping rate (Im´ω)/(Re´ω) has been computed for both wave modes.
Abstract: The collisionless damping of shear Alfven waves in the limit of low frequency and small but finite Larmor radius is discussed. Because the averaging of the wave electric field over the Larmor circle (the so‐called finite cyclotron radius effect) creates a small difference in the transverse velocities of the ions and electrons, a longitudinal electric field appears in the Alfven wave which is responsible for the transfer of the wave energy into the thermal motion of the “resonant” particles Vz = ω/kz. Numerical solutions (in the complex ω plane) of the dispersion relation for two wave modes have been obtained: the shear Alfven mode and the least damped Fried and Gould ion acoustic mode. The normalized damping rate (Im ω)/(Re ω) has been computed for both waves, and it is shown that the damping factor for the Alfven wave is maximal when the Alfven velocity is equal to the real part of the phase velocity of the ion acoustic wave. Moreover, there exists a particular direction of propagation with respect to th...
TL;DR: In this paper, the forward problem of calculating the waves in a medium of plane, homogeneous, isotropic layers is extended to P and SV body waves at nonnormal incidence, where the horizontal phase velocity of each wave is greater than the shear and compressional velocities of each layer.
Abstract: For plane waves at normal incidence to a layered elastic medium, both the forward and inverse discrete time problems have been previously solved. In this paper the forward problem of calculating the waves in a medium of plane, homogeneous, isotropic layers is extended to P and SV body waves at nonnormal incidence, where the horizontal phase velocity of each wave is greater than the shear and compressional velocities of each layer. Vertical traveltimes for P and SV waves through each layer are rounded off to unequal integer multiples of a small time increment Δτ. This gives a 4×4 layer matrix analogous to the 2×2 layer matrix for normal incidence obtained by previous authors. Reflection and transmission responses recorded at the free surface of a layered half space are derived as matrix series in integer powers of the Fourier transform variable z=e-iωΔτ. These responses are generated recursively by polynomial division and include all multiply reflected P and SV waves with mode conversions. It is shown that...
TL;DR: The centrovelocity as mentioned in this paper is a new velocity which was introduced for the description of the transport of electromagnetic radiation since it does not have any of the short comings of the standard definitions of the group velocity or the velocity of energy transport.
Abstract: The definitions, the physical significances, the interrelationships, and the observability of seven velocities of light are discussed. One of the seven, the centrovelocity, is a new velocity which is introduced here. It is suggested that this velocity can be used for the description of the transport of electromagnetic radiation since it does not have any of the short comings of the standard definitions of the group velocity or the velocity of energy transport.
TL;DR: In this paper, for a plane wave normally incident on a slab-region distribution, the authors obtained more complete results for the flux into a detecting cone at an arbitrary angle of observation, in terms of one-particle scattering functions, scatterer concentration, and distribution thickness.
Abstract: Earlier approximations for multiple scattering by uncorrelated random distributions of large, low-refracting, absorbing particles are generalized by retaining the internal backscattered flux for the case of negligible coherent reflection. For a plane wave normally incident on a slab-region distribution, we obtain more complete results for the flux into a detecting cone at an arbitrary angle of observation, in terms of one-particle scattering functions, scatterer concentration, and distribution thickness. The approximations cover the full range of concentration; although the results near full packing are in general physically unrealizable, they are shown to be in accord with elementary physical considerations. The special forms for the total transmitted flux and total backscattered flux are similar to forms obtained by the diffusion-equation approach. However, the present development, based on averaging the absolute square of the solution of the wave equation for a large number of particles, provides approximations for the bulk parameters and for the flux in terms of results for an isolated scatterer.
TL;DR: In this paper, the waveform distortion of an impulse-excited plane wave as it decays and spreads on passing through large distances of a solid has been studied and theoretical expressions for waveform distortions have been obtained.
Abstract: Under the assumption of almost constant‐Q behavior of solids over a wide range of frequencies, together with some meaningful assumptions about the linear frequency behavior of the attenuation function, we have been able to obtain theoretical expressions describing the waveform distortion of an impulse‐excited plane wave as it decays and spreads on passing through large distances of the solid. When typical values for the parameters (as obtained from laboratory model or short range field experiments) for a solid having a mechanical Q of about 50 are used, the resulting waveforms at first glance appear to have a simple and not unexpected behavior. The peak amplitude of the waveform in the time domain varies roughly with the inverse of the square of the travel distance (this includes an inverse first power due to geometrical spreading). Also, a spreading of the waveform occurs that varies roughly linearly with the travel distance. This spreading is such that a positive impulse simply broadens as it travels wi...
TL;DR: In this paper, the authors derived expressions for the field induced in a thin-film waveguide by plane waves incident upon an adjacent frustrated total reflecting interface, and deduced an expression for the coupling coefficient for a Gaussian TEM 00 beam into such a guide as a function of the guide and beam parameters.
Abstract: We have derived expressions for the field induced in a thin-film waveguide by plane waves incident upon an adjacent frustrated total reflecting interface. From these, we have deduced an expression for the coupling coefficient for a Gaussian TEM 00 beam into such a guide as a function of the guide and beam parameters.
TL;DR: In this article, a modified Babinet's principle is formulated, and this is used to find the diffraction of sound by an acoustically soft circular disk, and the spheroidal wave functions are described and applied to diffraction theory.
Abstract: The three-dimensional diffraction of a scalar plane wave through a circular aperture in an infinite plane screen is analyzed and numerically computed for the case of normal incidence. A modified Babinet's principle is formulated, and this is used to find the diffraction of sound by an acoustically soft circular disk. The spheroidal wave functions are described and applied to the diffraction theory. Numerical values of the rigorous diffraction functions are computed, and these are compared to the approximation obtained by the Huygen-Kirchhoff formulation.
TL;DR: In this article, the authors decompose the magnetic field into two orthogonal components and define separate transmission functions for each polarization, and then compute the diffracted field and the efficiency of the magnetic grating from these transmission functions.
Abstract: Reconstruction effects in a magnetic hologram can easily be interpreted if one assumes a linearly polarized plane wave readout beam. The field transmitted through or reflected off the hologram is rotated via the Faraday or Kerr effect. By decomposing the emerging field into two orthogonal components, one can define separate transmission functions for each polarization. The diffracted field and the efficiency of the magnetic grating are readily computed from these transmission functions. For a binary magnetic grating all diffraction orders, with the exception of zeroth order, are polarized orthogonally to the incoming polarization. For a sinusoidal magnetic grating, the various diffraction orders alternate in polarization with the zeroth order polarized in the same direction as the incoming polarization.
TL;DR: Perturbation method to obtain analytical expressions for attenuation of plane wave sound propagation in lined ducts is presented in this article, where it is shown that attenuation attenuates plane wave propagation in line ducts.
TL;DR: In this article, an extension of Fermat's principle, in which the complex phase refractive index is used instead of only the real part, expresses both of these criteria and leads to a corresponding extension of Snell's law or of Haselgrove's equations to calculate the ray path.
Abstract: Standard ray-tracing programs do not calculate satisfactorily the reflection of LF radio waves from the ionosphere because they do not take losses into account. In lossy media, requiring the ray path to have a minimum attenuation in addition to a minimum wave interference gives a more accurate approximation to the full-wave solution. An extension of Fermat's principle, in which the complex phase refractive index is used instead of only the real part, expresses both of these criteria and leads to a corresponding extension of Snell's law or of Haselgrove's equations to calculate the ray path. Although such a path can have complex coordinates, only those with end points in real space are physically significant. An approximation, in which plane waves in the neighborhood of the receiver are assumed, solves the common ray-tracing problem of homing in on the receiver, a problem that is worse for ray tracing in complex space. Applying ray tracing in complex space to a plane wave incident on a plane stratified medium gives a result that agrees exactly with the result obtained by the phase integral method and that agrees satisfactorily with full-wave solutions above 30 kHz for all results shown.
TL;DR: The effective ion-ion interaction for sodium was calculated from a fundamental basis, using a one-orthogonalized plane wave (OPW) bare electron ion matrix element, and the Geldart and Taylor elect... as discussed by the authors.
Abstract: The effective ion–ion interaction for sodium is calculated from a fundamental basis, using a one-orthogonalized plane wave (OPW) bare electron – ion matrix element, and the Geldart and Taylor elect...
TL;DR: An integral representation of the displacement for problems of transient propagation of horizontally polarized shear waves is employed to investigate the diffraction of a plane wave by a crack of finite length in this article.
TL;DR: In this article, the wave functions for conduction electrons in dysprosium metal have been constructed following the APW formalism to see how much they differ from the plane wave description in pure earth metals.