Showing papers on "Plane wave published in 1975"
TL;DR: In this article, a model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth, and numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.
Abstract: A model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth. Numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.
266 citations
TL;DR: In this article, a computer algorithm is presented which allows simultaneous consideration of selfphase modulation and dispersion for predicting temporal shape changes during the propagation of plane-wave intense light pulses.
Abstract: A computer algorithm is presented which allows simultaneous consideration of self‐phase modulation and dispersion for predicting temporal shape changes during the propagation of plane‐wave intense light pulses. The algorithm entails considering propagation alternately in regions where only one of the two above effects is operative. It is shown for clear materials that the parameters characterizing propagation are the nonlinear index change, the wavelength λ, the relaxation time of the nonlinearity, and the disperison parameter λ3(d2n/dλ2). The thickness of material over which a pulse will significantly reshape is found to be √λ times the geometric length of the pulse divided by the square root of the product of the dispersion parameter and the maximum nonlinear index. It is demonstrated that dispersion significantly modifies the self‐steepening concept of DeMartini, Townes, Gustafson, and Kelley. Numerical simulations of propagation in CS2 indicate that, after sufficient travel, a shock can form on the le...
180 citations
TL;DR: In this article, the problem of scattering of a plane wave by an infinite periodic array of thin conductors on a dielectric slab is formulated, and numerical results are given as well as a comparison of this theory with experimental data.
Abstract: The solution to the problem of scattering of a plane wave by an infinite periodic array of thin conductors on a dielectric slab is formulated in this paper. Numerical results are given as well as a comparison of this theory with experimental data.
165 citations
TL;DR: In this article, the theoretical scattering solution for a plane wave incident normally on a lossy dielectric multilayer circular cylinder of infinite length is outlined, and numerical values of the modal scattering coefficient for TE and TM modes are given for several single and multi-layer cylinders.
Abstract: The theoretical scattering solution for a plane wave incident normally on a lossy dielectric multilayer circular cylinder of infinite length is outlined. Numerical values of the modal scattering coefficient for TE and TM modes are given for several single and multilayer cylinders. Verifications of the results are described. The values may serve as reference data.
122 citations
TL;DR: In this article, the spectrum of refractive index fluctuations is taken to be an unmodified power law of arbitrary strength, with exponent α, 2 30, it represents essentially all of the intensity fluctuations and shows that m saturates at unity for a plane wave as U → ∞.
Abstract: The spatial spectrum of intensity fluctuations due to a concentrated layer of turbulence is derived from the parabolic wave equation. The spectrum of refractive index fluctuations is taken to be an unmodified power law of arbitrary strength, with exponent α, 2 30, it represents essentially all of the intensity fluctuations and shows that m saturates at unity for a plane wave as U → ∞. Simple formulas for m when the source has finite angular extent show that m decreases with increasing turbulence as Uα−2 for U ≫ 1. These results are confirmed by exact calculations for the case α = 3 and by extensive observations of interplanetary scintillations.
109 citations
TL;DR: In this paper, the condition of the Weber number of order one for the free surface is computed to the third-order accuracy of the shallow water parameter, and the development of a long monochromatic wave is analyzed by use of this equation.
Abstract: Long nonlinear waves on a thin fluid layer flowing down an inclined plane are investigated. For the condition of the Weber number of order one, the equation for the free surface is computed to the third‐order accuracy of the shallow water parameter. The development of a long monochromatic wave is analyzed by use of this equation. Near the upper branch of the neutral curve, the original steady flow is found to be supercritically stable and the amplitude of the monochromatic wave is determined. The stretching of the eigenfrequency by nonlinearity has no definite sign. For a comparatively large wavenumber, the wave velocity can be smaller than that of the linear wave. The nonexistence of the periodic wave in the region far from the upper branch of the neutral curve is discussed in connection with the temporally growing solution of the equation in order to determine the second harmonic.
106 citations
TL;DR: In this article, a solution for the diffraction of a plane wave sound source by a semi-infinite half plane was obtained for the problem of diffraction in the shadow region, where the absorbing lining is on the side of the screen which makes the smallest angle to the source or the receiver from the edge.
Abstract: A solution is obtained for the problem of the diffraction of a plane wave sound source by a semi-infinite half plane. One surface of the half plane has a soft (pressure release) boundary condition, and the other surface a rigid boundary condition. Two unusual features arise in this boundary value problem. The first is the edge field singularity. It is found to be more singular than that associated with either a completely rigid or a completely soft semi-infinite half plane. The second is that the normal Wiener-Hopf method (which is the standard technique to solve half plane problems) has to be modified to give the solution to the present mixed boundary value problem. The mathematical problem which is solved is an approximate model for a rigid noise barrier, one face of which is treated with an absorbing fining. It is shown that the optimum attenuation in the shadow region is obtained when the absorbing lining is on the side of the screen which makes the smallest angle to the source or the receiver from the edge.
104 citations
TL;DR: In this article, the propagation and radiation of electromagnetic waves from oscillating sources in a suddenly created plasma are studied in detail and field expressions are derived through the use of Laplace transformations.
Abstract: Propagation and radiation of electromagnetic waves from oscillating sources in a suddenly created plasma are studied in this investigation. Field expressions are derived through the use of Laplace transformations. The spatial distribution of sources is taken to be arbitrary but confined. Two cases are considered in detail: 1) plane wave propagation in a source-free region and 2) electric point dipole radiation. In the case of plane wave propagation, various aspects such as wave split, frequency shift, phase and group velocities, amplitude changes, power flows, and energy relations are discussed. In the case of electric dipole radiation, the electromagnetic fields and instantaneous radiated power are calculated and expressed in terms of Lommel functions of two variables. Asymptotic expressions and graphical results of numerical calculations of these quantities are presented. Many interesting properties of the spherical waves and power radiation are discussed.
89 citations
Abstract: The reflection of a locally plane wave from a curved interface between two nonabsorbing dielectric media is investigated. Our analysis is applicable to an interface of general shape, defined at each point by the two principal radii of curvature. When the wave is incident from the denser medium at angles greater than the critical angle it is only partially reflected, due to a form of electromagnetic tunneling. Generalized Fresnel transmission coefficients and an extension of Snell's law are derived to account for this transmission into the less dense medium. Ray tracing can then be applied to determine such phenomena as the bending losses in optical slab waveguides, and the curvature loss of skew rays within straight optical waveguides of circular cross section.
86 citations
01 Oct 1975
TL;DR: In this paper, the relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativists Alfven waves, linearly polarized transverse waves propagating in zero magnetic field and the extraordinary mode propagating at an arbitrary angle to magnetic field.
Abstract: Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.
85 citations
TL;DR: In this paper, the dynamical processes affecting the evolution of a random internal wave field are considered and the source function describing these changes is determined by the superposition of all processes governing the generation, transfer, and dissipation of wave energy.
Abstract: The dynamical processes affecting the evolution of a random internal wave field are considered. If the statistical properties of the internal wave field vary slowly with space and time, these dynamical processes can be treated as small perturbations about the local steady state of the free linear field. The time evolution of the wave field is then governed by a radiative transfer equation describing changes in the action density spectrum of the wave field along wave group trajectories. The source function describing these changes is determined by the superposition of all processes governing the generation, transfer, and dissipation of wave energy. Some terms of the source function, those corresponding to expansible processes, can be derived rigorously by using weak interaction concepts. Other terms, corresponding to nonexpansible processes which are governed locally by strongly nonlinear dynamics, cannot be determined completely. For the case where the internal wave field can adequately be described in the WKBJ approximation, a rather complete list of source terms is presented. The evaluation of these source terms is difficult partly because of their complicated functional structure and partly because the geophysical fields involved are not sufficiently known. Those source terms which have been evaluated in detail are briefly reviewed, and their implications on the energy balance of the internal wave field are discussed.
01 Jan 1975
TL;DR: Gravitational plane waves, like their electromagnetic and Yang-Mills counterparts, are undistorted by vacuum polarization effects to all loop orders, if no cosmological term is induced.
Abstract: Gravitational plane waves, like their electromagnetic and Yang-Mills counterparts, are undistorted by vacuum polarization effects to all loop orders, if no cosmological term is induced.
TL;DR: In this paper, the absorbed power of a prolate spheroid being irradiated by a plane wave when the waveIength is long compared to the dimensions of the model was investigated.
Abstract: An electromagnetic (EM) field perturbation technique is used to find internal electrical fields and the absorbed power of a prolate spheroid being irradiated by a plane wave when the waveIength is long compared to the dimensions of the spheroid. The results show significant differences in the power absorption patterns with changes in the orientation of the spheroid with respect to the incident EM fields. Calculations of the power absorbed by a prolate spheroid model of man are given.
TL;DR: In this paper, a nonlinear upper hybrid wave with negative dispersion propagates across a magnetic field as a soliton, when its pulse speed exceeds the magnetosonic speed.
Abstract: A nonlinear upper hybrid wave with negative dispersion propagates across a magnetic field as a soliton, when its pulse speed exceeds the magnetosonic speed.
TL;DR: In this paper, a power law spectrum with index α = 3 was assumed for the turbulence or refractive index spectrum, and the intensity spectra were found to duplicate the Born approximation for weak scattering and the high frequency approximation for strong scattering.
Abstract: Spectra of intensity fluctuations resulting from the propagation of a plane wave through a thin but arbitrarily strong layer of refractive index variations are computed using the theory in a companion paper [Rumsey, 1975]. A power law spectrum with index α = 3 was assumed for the turbulence or refractive index spectrum. The intensity spectra were found to duplicate the Born approximation for weak scattering and the high frequency approximation for strong scattering. The scintillation index, or the rms intensity fluctuation, saturates at unity for a plane wave. The scintillation index has been computed for sources of various sizes. The results of the computation are in remarkable agreement with the results of radio star scintillation measurements.
01 Oct 1975
TL;DR: In this article, general expressions for estimating the errors in the sum or difference far-field pattern of electrically large aperture antennas which measured by planar near-field scanning technique are derived.
Abstract: General expressions are derived for estimating the errors in the sum or difference far-field pattern of electrically large aperture antennas which measured by planar near-field scanning technique. Upper bounds are determined for the far-field errors produced by 1) the nonzero fields outside the finite scan area, 2) the inaccuracies in the positioning of the probe, 3) the distortion and non-linearities of the instrumentation which measures the amplitude and phase of the probe output, and 4) the multiple refractions. Computational errors, uncertainties in the receiving characteristics of the probe, and errors involved with measuring the input power to the test antenna are briefly discussed.
TL;DR: In this paper, the decay of a circularly polarized electromagnetic wave propagating parallel to an external magnetic field into another LME and an ion acoustic wave in a homogeneous plasma is considered.
Abstract: The decay of a circularly polarized electromagnetic wave propagating parallel to an external magnetic field into another circularly polarized electromagnetic wave and an ion acoustic wave in a homogeneous plasma is considered.
TL;DR: In this paper, the laser wave is considered as an external prescribed field and its interaction with the electron-positron field is treated without reference to perturbation theory, and the vacuum polarization tensor is computed to second order in the fine structure constant in the form of a double integral.
Abstract: According to quantum electrodynamics the vacuum shows polarization properties because of the presence of virtual electron-positron pairs. These properties are investigated in the presence of an intense plane wave field, such as is produced by a laser. The laser wave is considered as an external prescribed field and its interaction with the electron-positron field is treated without reference to perturbation theory. The vacuum polarization tensor is computed to second order in the fine structure constant in the form of a double integral. For a Dyson equation for the photon propagator is solved by an eigenfunction expansion. For a plane laser wave of infinite extent and circular polarization the results are relatively simple and explicit. Analytical properties of the photon propagator are discussed. The effects of vacuum polarization on an additional weak wave field (a non-laser photon) can be described approximately by two complex indices of refraction.
TL;DR: In this article, integral and differential equations for the two-frequency mutual coherence function in a random distribution of stationary and moving particles are derived for a plane wave case, and the coherent bandwidth is obtained for both the weak and strong fluctuation cases.
Abstract: In this paper, integral and differential equations are derived for the two-frequency mutual coherence function in a random distribution of stationary and moving particles. The differential equation is then solved for a plane wave case, and the coherent bandwidth is obtained for both the weak and strong fluctuation cases. Using the two-frequency correlation function, the output pulse shape is calculated for different particle densities. When the optical distance is small compared with unity, the pulse shape is substantially unchanged, but a long tail develops. When the optical distance is large, the coherent bandwidth is reduced and considerable pulse spread and delay occur. Numerical calculations are given for a nanosecond optical pulse propagating through cloud. It is shown that in dense cloud (density 0.5 × 10
9
m
−3
), the pulse delay and spread are 3 and 1.28 μsec respectively over a distance of 5 km. This agrees with available experimental data.
TL;DR: In this article, the conductivity of (SN)/sub x/ does not undergo a Peirels Frohlich transition, but increases with decreasing temperature, and alternative hypotheses to account for this anomaly are described, and calculations of the orthogonalized plane wave band structure, and one-electron state densities carried out in order to test these hypotheses.
Abstract: The conductivity of (SN)/sub x/ does not undergo a Peirels Frohlich transition, but increases with decreasing temperature. Alternative hypotheses to account for this anomaly are described, and calculations of the orthogonalized plane wave band structure, and one-electron state densities carried out in order to test these hypotheses. The low temperature conductivity is believed to be due to closed Fermi surfaces produced by electronic coupling between chains. The orthogonalized plane wave structure is compared with the Lyon and Penn crystal structures, but no definite conclusion reached. 24 references.
TL;DR: In this article, the wave orthogonals and the wave heights are presented for depth refraction of regular, long-crested, small amplitude surface gravity waves over an arbitrary bottom, using time as the independent variable.
Abstract: The equations for the wave orthogonals and the wave heights are presented for depth refraction of regular, long-crested, small amplitude surface gravity waves over an arbitrary bottom, using time as the independent variable. The effect of turbulent bottom friction on the wave height is included. The computer outputs are in the form of automatically plotted wave orthogonals with the wave heights written at discrete points along these paths. Systematic tests are presented for water areas with straight and parallel bottom contours. The errors inherently connected with the introduction of a grid plus a set of formulas for the differentiation and interpolation are examined for a horizontal bottom with an infinite long sinusoidal threshold. For one plane sloping bottom, information is given for the influence of the initial curvature of the wave front, bottom roughness, and initial wave height.
TL;DR: In this paper, an improved matrix method of calculating the solutions of wave equations in a horizontally stratified anisotropic medium is described, where an inhomogeneous medium is divided into a number of thin horizontal and homogeneous slabs.
Abstract: An improved matrix method of calculating the solutions of wave equations in a horizontally stratified anisotropic medium is described. An inhomogeneous medium is divided into a number of thin horizontal and homogeneous slabs. The solutions of a differential equation with constant coefficients in each slab are connected by applying the boundary conditions, and the wave fields are given as the power series expansion of wave fields. In calculating the wave fields, a matrix is divided into two matrices for two independent solutions and Gram-Schmidt orthogonalizing process is applied to prevent numerical swamping. Comparisons are made between this and other full wave methods regarding step size and computer time, and this method is found to be more efficient than the full wave method especially at high frequency wave fields. The magnetoionic modes separated from the resultant wave are shown for a model ionosphere.
TL;DR: In this paper, the Fourier methods widely used in treating fluctuations associated with second-order phase transitions are extended to first-order structural phase transitions, where the fluctuations, which represent dynamical plane waves of small amplitude for secondorder transitions, must be interpreted as large amplitude, quasi-static wave packets.
TL;DR: In this article, the reflection of electromagnetic waves from a smooth conducting surface at high frequencies is studied and the incident and reflected fields are expanded in asymptotic series of the form E = exp [iks(r)]\Sigma\min{m=0}max{\infty}(ik)^{-m}e_{m}(r), where s is the phase function, and e is the amplitude vector.
Abstract: The reflection of electromagnetic waves from a smooth conducting surface at high frequencies is studied in this paper. Both the incident and reflected fields are expanded in asymptotic series of the form E = exp [iks(r)]\Sigma\min{m=0}\max{\infty}(ik)^{-m}e_{m}(r) , where s is the phase function, and { e_{m} } are amplitude vectors. Explicit formulas based on a ray technique are given for calculating the first two orders of the electric field, magnetic field, and surface current. When the conducting surface is a paraboloid (or a sphere) and the incident field is a plane wave in its axial direction, our solution recovers the exact solution (or the first two orders of the exact asymptotic solution), As a special case, our result is compared with the work of Schensted. It appears that the latter is only partially correct.
TL;DR: In this article, specular reflection and transmission of an acoustic plane wave at a randomly rough two-fluid interface is studied and the perturbation method of Bass is used to derive a new set of boundary conditions to replace the unperturbed boundary conditions.
Abstract: The specular reflection and transmission of an acoustic plane wave at a randomly rough two‐fluid interface is studied. The perturbation method of Bass is used to derive a new set of boundary conditions to replace the unperturbed boundary conditions. The new conditions are valid for surfaces characterized by arbitrary anisotropic correlation functions. Using these new boundary conditions, reflection and transmission coefficients are derived. It is shown that in the Kirchhoff approximation, the reflection and transmission coefficients reduce to those obtained earlier by Eckhart, Clay, Medwin, and Hagy. In the limit of the density of one of the fluids going to zero, the reflection coefficient for a rough pressure release surface is obtained. Results are presented using ocean surface models in terms of wind speed and direction.Subject Classification: 30.40, 30.30, 30.25,30.20.
TL;DR: In this paper, the authors proposed a method to measure the magnetic field strength above an ocean surface by measuring the wave spectra of a progressive ocean wave in a horizontally stratified ocean, which is a summation of a transverse electric type field, transverse magnetic type field and an electrostatic type field.
Abstract: The electromagnetic field generated by a progressive ocean wave in a horizontally stratified ocean is a sum of a transverse electric type field, a transverse magnetic type field, and an electrostatic type field. Seawater velocity components in a vertical plane containing the direction of wave propagation generate the transverse electric part of the field, and the velocity component normal to the plane generates the transverse magnetic part of the field, which vanishes above an ocean surface. The electrostatic part of the field results from surface charges that halt vertical electric currents at an ocean surface. Gradients of magnetic fields generated at the surface by both surface and internal waves provide sensible signals for recently developed magnetic gradiometers based on the Josephson effect, provided surface speeds exceed 1 cm/s or so. Vertically spaced measurements of noise spectra of magnetic field gradients above an ocean surface offer a unique and promising means of obtaining a measure of surface and internal wave spectra for three reasons: (1) magnetic field strengths above the surface are proportional to a weighted average of seawater speed over an ocean depth, which provides a response depending on the mode structure of internal waves; (2) field strengths decrease exponentially with height above the surface as e−kh, where k denotes wave number, which provides means of wave number discrimination and, together with frequency discrimination, offers means of resolving internal wave spectra mode by mode; and (3) noise spectra of magnetic field gradients are effectively cross spectra and so provide directional information on wave spectra from an effective point measurement.
TL;DR: In this article, the energy flow in the case of plane wave transmission across a shear discontinuity is analyzed and this problem serves as a convenient test for conservation, and the energy principle developed by Blokhintsev is shown to be applicable.
TL;DR: In this paper, the theoretical analysis of the scattering of a beam by a spherical object centered on the propagation axis is treated exactly, and for both conducting and dielectric bodies, those cases of sphere radii smaller than, equal to, and larger than that of the beam are analyzed numerically and the power radiated in the far zone is obtained.
Abstract: The theoretical analysis of the scattering of a beam by a spherical object centered on the propagation axis is treated exactly. For both conducting and dielectric bodies, those cases of sphere radii smaller than, equal to, and larger than that of the beam are analyzed numerically and the power radiated in the far zone is obtained. The difference between the scattering of a beam wave and that of a plane wave is discussed.
TL;DR: In this paper, a simple physical theory was used to calculate the variation of wave amplitudes and the wave refraction in a schematic model for a high-speed solar wind stream, and the results indicated that nonlinear effects may be more important in the rarefaction region.
Abstract: We use a simple physical theory to calculate the variation of Alfven wave amplitudes and the wave refraction in a schematic model for a high-speed solar wind stream. The results are as follows. (1) The wave amplitudes 〈δB²〉1/2 are larger in the compression region of the stream than in the rarefaction region. (2) The relative amplitudes 〈δB²〉1/2/B0 are larger in the rarefaction region than in the compression region, this result indicating that nonlinear effects may be more important in the rarefaction region. (3) The azimuthal velocity gradient in the stream leads to the result that k is no longer nearly radial at 1 AU, in contrast to predictions based on a spherically symmetric solar wind structure. In the rarefaction region, k turns into the direction of B0, whereas in the compression region, k turns away from the direction of B0. This predicted result in the rarefaction region agrees with direct in situ observations at 1 AU. (4) Waves that start near the sun with different k all tend to be refracted into the same direction by the time that they reach 0.5 AU. This result indicates that plane wave analyses will be appropriate beyond 0.5 AU.