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Showing papers on "Plane wave published in 1984"


Journal ArticleDOI
TL;DR: In this paper, a 2 × 2 matrix method is applied to planar multilayer optical waveguides to satisfy substrate-to-cover field transfer equations that reduce to the equation 0 for bound modes and leaky waves.
Abstract: A standard 2 × 2 matrix method-used in thin-film optics is applied to planar multilayer optical waveguides. All modes are required to satisfy substrate-to-cover field-transfer equations that reduce to the equation γcm11 + γcγsm12 + m21 + γsm22 = 0 for bound modes and leaky waves. Expressions are derived for the field profiles and the power in each medium. A first-order perturbation theory is developed and applied to absorbing multilayer guides and to the reflection of plane waves from the prism-loaded lossy multilayer guide. The latter leads to experimental arrangements for measuring losses in which the gap thickness and propagation constant are accessible parameters.

419 citations


Journal ArticleDOI
TL;DR: In this paper, the three-dimensional resonant interaction of a plane Tollmien-Schlichting wave, having a frequency f 1, with a pair of oblique waves having frequencies ½ f 1 was observed and studied experimentally.
Abstract: The three-dimensional resonant interaction of a plane Tollmien-Schlichting wave, having a frequency f1, with a pair of oblique waves having frequencies ½ f1, was observed and studied experimentally. In the initial stages, the interaction proved to be a parametric resonance, resulting in the amplification of small random priming (background) oscillations of frequency ½ f1, and of a packet of low-frequency oscillations. The resonant interaction of waves in a boundary layer was investigated also by introducing a priming oscillation with frequency f’ = ½ f1 + Δf for different values of the frequency detuning Δf. The importance of the discovered wave interaction in boundary-layer transition is demonstrated. Causes of realization of different types of laminar-flow breakdown are discussed.

394 citations


Journal ArticleDOI
TL;DR: In this paper, the transverse plane wave dispersion in linear, non-local micropolar elastic solids is derived by equating the frequency of the Transverse Acoustical (TA) branch at the end of the Brillouin zone.

278 citations


Journal ArticleDOI
TL;DR: In this article, a second-order multiple-scattering theory of discrete particles is proposed to explain the angular width of backscattering from a random distribution of discrete scatterers.
Abstract: A recent laboratory-controlled optical experiment demonstrates that a sharp peak of small but finite angular width is exhibited in backscattering from a random distribution of discrete scatterers. In this paper the phenomenon is explained by using a second-order multiple-scattering theory of discrete particles. The theory gives an angular width of the order of the attenuation rate divided by the wave number and is in agreement with experimental observations. The relations of the present results to past theories on backscattering enhancements are also discussed.

185 citations


Journal ArticleDOI
TL;DR: For homogeneous regions of space, however, this wave equation becomes identical to the full acoustic wave equation as discussed by the authors, and possible applications of the wave equation for forward modeling and for migration are illustrated with simple models.
Abstract: Highly reduced reflection coefficients for transmission across material boundaries. For homogeneous regions of space, however, this wave equation becomes identical to the full acoustic wave equation. Possible applications of this wave equation for forward modeling and for migration are illustrated with simple models.--Modified journal abstract.

142 citations


Journal ArticleDOI
TL;DR: In this paper, an approximate method for the estimation of wave forces on groups of fixed vertical cylinders is presented based upon a large spacing approximation and involves replacing scattered diverging waves by plane waves.

139 citations


Journal ArticleDOI
TL;DR: In this paper, an analytical description of the scattered field of a harmonic sound wave coming out of an open ended annular duct (a semi-infinite cylinder inside of which, coaxially, is a doubly infinite hub), submerged in a subsonic, coaxial, uniform mean flow, was derived by using a Wiener-Hopf approach.

130 citations


Journal ArticleDOI
TL;DR: In this article, the authors used OCO 5 triaxial search coil magnetometer data to determine the wave propagation directions of postmidnight chorus in the near-equatorial region at L shells of 6 to 7.
Abstract: OGO 5 triaxial search coil magnetometer data are used to determine the wave propagation directions of postmidnight chorus in the near-equatorial region at L shells of 6 to 7. The methods used to estimate the wave normal directions involved minimum variance, the imaginary part of the cross-spectral matrix, the eigenvector of the Hermitian cross-spectral matrix, and a fitting of dispersion relations for one-wave and two-wave models to the cross-spectral matrix. Wave propagation at all frequencies within chorus tones is found to occur most frequently along the magnetic field with median and average cone angles of 9.1 deg and 12.2 deg, respectively. It is concluded that for waves propagating parallel to B, wave growth is maximum.

122 citations


Journal ArticleDOI
TL;DR: In this paper, a systematic procedure of V. P. Maslov that makes use of a representation of the geometrical optics field in the phase space M = X × K, where a point m = (x, k) is a pair of a position vector x e X and a wave vector k e K, is presented.
Abstract: It is well known that the geometrical optics approximation, generally valid for high-frequency fields, fails in the vicinity of a caustic. A systematic procedure of V. P. Maslov that remedies this situation will be reviewed in this paper. Maslov's method makes use of a representation of the geometrical optics field in the phase space M = X × K, where a point m = (x, k) is a pair of a position vector x e X and a wave vector k e K. A Lagrangian submanifold of M, Λ, that lies in the dispersion surface and is a union of the phase space trajectories selected by the initial conditions is constructed. It can be considered as a global representation of the phase. The phase space amplitudes (half densities) satisfy transport equations defined along those trajectories in Λ. Since trajectories in M never form a caustic, a globally defined amplitude can be established on Λ. The field on X is related to the resultant field on Λ by the “canonical operator,” an operator introduced by Maslov. It generates an integral form of the solution near a caustic that can be evaluated analytically, numerically, or with uniform asymptotic techniques. Away from the caustic it recovers the geometrical optics field. Alternatively, the phase space field can be projected on a hybrid space Y where some of the space coordinates have been replaced by the corresponding wave vector components. For any caustic point in X, one such hybrid space Y where this projection does not encounter a caustic exists. A geometrical optics field results in Y that is related to the original in X by an asymptotic Fourier transform. The solution in X near a caustic can be represented as the Fourier transform to X of that hybrid space geometrical optics solution. These techniques are illustrated with two simple but revealing problems: continuation of the field through a fold caustic in a linear layer medium and through a caustic with a cusp point in a homogeneous medium.

103 citations


Journal ArticleDOI
TL;DR: In this paper, the S-Matrix was constructed using the Rayleigh-Bloch wave expansion and the reduced Grating Propagator (GRP) for the Scattered Fields problem.
Abstract: 1. Physical Theory.- 1. The Physical Problem.- 2. The Mathematical Formulation.- 3. Solution of the Initial-Boundary Value Problem.- 4. The Reference Problem and Its Eigenfunctions.- 5. Rayleigh-Bloch Diffracted Plane Waves for Gratings.- 6. Rayleigh-Bloch Surface Waves for Gratings.- 7. Rayleigh-Bloch Wave Expansions.- 8. Wave and Scattering Operators for Gratings.- 9. Asymptotic Wave Functions for Gratings.- 10. The Scattering of Signals from Remote Sources.- 2. Mathematical Theory.- 1. Grating Domains and Grating Propagators.- 2. Rayleigh-Bloch Waves.- 3. The Reduced Grating Propagator Ap.- 4. Analytic Continuation of the Resolvent of Ap.- 5. Proofs of the Results of 4.- 6. The Eigenfunction Expansion for Ap.- 7. Proofs of the Results of 6.- 8. The Rayleigh-Bloch Wave Expansions for A.- 9. Proofs of the Results of 8.- 10. The Initial-Boundary Value Problems for the Scattered Fields.- 11. Construction of the Wave Operators for AP and Ao,p.- 12. Construction of the Wave Operators for A and Ao.- 13. Asymptotic Wave Functions and Energy Distributions.- 14. Construction and Structure of the S-Matrix.- 15. The Scattering of Signals by Diffraction Gratings.- References.

87 citations


Journal ArticleDOI
TL;DR: In this paper, a study of the propagation of plane electromagneto-thermo-elastic harmonic waves in an unbounded isotropic conducting medium permeated by a primary uniform magnetic field when the entire medium rotates with a uniform angular velocity is made.

Journal ArticleDOI
TL;DR: In this paper, a radar cross-section measurement system using a Scientific Atlanta compact range reflector (an offset parabolic reflector) to generate a far-field plane wave in the confines of a 40 \times 20 \times 60 ft anechoic chamber is described.
Abstract: The ElectroScience Laboratory at The Ohio State University has recently installed a new radar cross-section measurement system. The system uses a Scientific Atlanta compact range reflector (an offset parabolic reflector) to generate a far-field plane wave in the confines of a 40 \times 20 \times 60 ft anechoic chamber. The system uses a computer controlled microwave frequency synthesizer and a multichannel computer controlled receiver. The target support/positioning system and an optical target alignment system are also interfaced to the computer. The parameters of the system are 1) operation from 1 to 30 GHz (eventual operation to 96 GHz has been confirmed by field probing); 2) a plane wave volume (test area volume) of 1.3 m diameter; and 3) a sensitivity of -50 dBsm. Of particular importance is the ability of the system to measure phase as well as amplitude. This permits vector subtraction of the background and system calibration using a reference (sphere) target. The development of this system and the performance characteristics obtained so far will be discussed. Some results which demonstrate the system performance will be shown. Of particular interest is the broad-band measurement of both amplitude and phase. This permits conversion of the results to the time domain. Examples will be shown in which the various system components (antennas, reflector, walls, ceiling, etc.) are separated in the time domain by this technique. The development of the range is continuing and planned future improvements will also be discussed.

Journal ArticleDOI
TL;DR: In this paper, the theory of diffraction tomography for two-dimensional objects within the Born approximation is presented for cases where the scattered field is measured over arbitrarily shaped boundaries surrounding the object.

Journal ArticleDOI
TL;DR: In this paper, the azimuthal current induced by an H-polarized plane wave with an arbitrary angle of incidence on an infinite cylinder with an infinite axial slot is considered.
Abstract: The azimuthal current induced by an H-polarized plane wave with an arbitrary angle of incidence on an infinite cylinder with an infinite axial slot is considered. A system of dual series equations is derived from the modal expansions of the tangential field components by enforcing the electromagnetic boundary conditions. This dual series system is then solved for the modal coefficients with techniques borrowed from the Riemann-Hilbert problem of complex variable theory. The resulting infinite system of linear equations for the modal coefficients can be handled in an efficient manner. A comparison of the generalized dual series solution with a purely numerical method of moments solution based upon vector and scalar potentials is made. In contrast to this method of moments solution, it explicitly contains the behavior of the solution near the aperture rim and can generate the current values in a shadow region for small to large ratios of cylinder radius to wavelength without additional special considerations.

Journal ArticleDOI
TL;DR: An analog feedback control system for instruments which use synchrotron X-radiation and double cyrstal arrangements in a parallel setting as monochromator or plane wave generators is described in this article.

Journal ArticleDOI
TL;DR: In this paper, the Ricatti-Bessel functions were used to obtain expressions for the location and width of each spike in the backscattering from large dielectric spheres, where each spike can be allocated to two patterns, which are described in terms of sequences of two integers and whose repetition period is a function only of the refractive index m.
Abstract: Each spike that is observed in the backscattering from large dielectric spheres arises from just one term in the Mie series. By approximating the Ricatti–Bessel functions involved, one obtains expressions for the location and width of each spike. Every single spike can be allocated to just two patterns, which are described in terms of sequences of two integers and whose repetition period is a function only of the refractive index m. The physical process involved is shown to be a resonance inside the sphere of the electric or magnetic field, in which the appropriate field increases rapidly to a large value at a radial distance r/a ~ 1/m, whereas the other field remains small. As the sphere surface is approached, they combine to form a simple, spherical electromagnetic standing-wave pattern of large amplitude.

Journal ArticleDOI
TL;DR: In this article, the propagation of elliptically polarised inhomogeneous, time-harmonic plane waves is studied and a simple direct formulation of the eigenvalue problem for these waves is given.
Abstract: This paper deals with the propagation of elliptically polarised inhomogeneous, time-harmonic plane waves. Such waves arise in many areas. Examples include Rayleigh, Love and Stoneley waves in classical linear isotropic elasticity theory, gravity waves in ideal fluids, TE and TM waves in electromagnetism, and viscoelastic waves. For the most part even though the applications given here are in the theory of isotropic and anisotropic elastic bodies, it should be apparent that the results have application in other areas, such as electromagnetism. The purpose of the paper is to show how the theory of complex vectors, or “bivectors”as Hamilton and Gibbs called them, may be used to give results on the polarisations of inhomogeneous plane waves. Also, the use of bivectors leads to a simple direct formulation of the eigenvalue problem for these waves.

Journal ArticleDOI
TL;DR: Polarization characteristics of polarizers are evaluated for a general incident wave front using the plane-wave spectral representation and it is shown that even an ideal polarizer will transmit part of a cross-polarized wave if it does not coincide with the wave front.
Abstract: The action of a polarizer is conventionally determined only for a normally incident plane wave. In this work polarization characteristics of polarizers are evaluated for a general incident wave front using the plane-wave spectral representation. It is shown that even an ideal polarizer will transmit part of a cross-polarized wave if it does not coincide with the wave front. Some interesting polarization effects are demonstrated by application of the theoretical analysis to polarized spherical waves.

Journal ArticleDOI
TL;DR: In this paper, the partial reflection of a planar ion-acoustic soliton from a plane rigid boundary with sharp density gradients is studied, where the reflected wave attenuates rapidly, forming a spherical wave front apart from a small reflector.
Abstract: Experimental observations on the partial reflection of a planar ion‐acoustic soliton from a plane rigid boundary with sharp density gradients are presented. The reflected wave attenuates rapidly, forming a spherical wave front apart from a small reflector. The reflection coefficient of about 25% at the boundary has no apparent dependence on the incident wave amplitude and the sheath thickness in front of the reflector in the case of the disk reflector, while it has a dependence in the case of the mesh reflector, having even larger values of up to about 50%.

Journal ArticleDOI
TL;DR: In this article, the exact series solutions of the mixed boundary value problem for incident P, SV, SH and SH waves are presented, and the ground motion on or near the valley has been studied.

Journal ArticleDOI
P. Mciver1
TL;DR: In this paper, a large spacing approximation where diverging waves are replaced by plane waves is used to calculate the added mass and damping coefficients for an array of floating axisymmetric bodies.
Abstract: Previous work on the scattering of an incident wave field by an array of fixed vertical cylinders is extended to calculate the added-mass and damping coefficients for an array of floating axisymmetric bodies. The method is based upon a large spacing approximation where diverging waves are replaced by plane waves. It is shown that, given the scattering and radiation properties of a single body, the interaction effects within an array can be calculated both simply and accurately.

Journal ArticleDOI
TL;DR: In this paper, two stability criteria for discretization of the source type integrals are formulated to guarantee that the instability can be controlled by reducing the discretisation step, if they are met, and analyzed the solution of two two-dimensional electromagnetic scattering problems.
Abstract: The transient scattering of two-dimensional electromagnetic fields by an obstacle of finite extent is investigated with the aid of the time domain integral equation technique. In solving such equations with the marching-on-in-time method, numerical instabilities form a major problem. These instabilities can be attributed to errors in the discretization of the source type integrals that occur in the equations. In this paper, we formulate two so-called stability criteria for such a discretization that, if they are met, guarantee that the instability can be controlled by reducing the discretization step. With the aid of these criteria, we analyze the solution of two two-dimensional electromagnetic scattering problems, namely the scattering of a pulsed plane wave by a perfectly conducting and an inhomogeneous, lossy dielectric cylinder. Numerical results are presented and discussed.

Journal ArticleDOI
TL;DR: In this paper, the probability of transitions induced by the variation of the interaction potential between quantum states corresponding to the two sheets of the dispersion surface is calculated and the predictions of this theory are found to be in agreement with direct solutions of the Takagi-Taupin equations as well as with the experimental results.
Abstract: The propagation of neutron waves in a deformed crystal is considered from the point of view of quantum mechanics. Instead of solving the Takagi-Taupin equations the probability of transitions, induced by the variation of the interaction potential, between quantum states corresponding to the two sheets of the dispersion surface is calculated. In this way transmission and reflection coefficients for an incident plane wave are obtained after a simple analytical calculation for a wide class of crystal deformations. The predictions of this theory are found to be in agreement with direct solutions of the Takagi-Taupin equations as well as with the experimental results.

Journal ArticleDOI
TL;DR: An anomolous diffraction theory is presented to describe the scattering of plane waves by circular cylinders for the general case of oblique incidence and for both real and complex values of particle refractive index in terms of a single Bessel-like function.
Abstract: An anomolous diffraction theory is presented to describe the scattering of plane waves by circular cylinders for the general case of oblique incidence and for both real and complex values of particle refractive index in terms of a single Bessel-like function. By comparison with the formal solution of Maxwell’s equations, it is demonstrated that the simple theory well approximates the extinction and absorption efficiencies, particularly for a normally incident wave on a nonabsorbing or weakly to moderately absorbing particle. It is also shown that the simple theory provides the correct small (i.e., x → 0) and large (i.e., x → ∞) particle limits for extinction and absorption efficiencies despite the original premise that the theory requires x ≫ 1. The simple theory is particularly useful for those types of practical problem that require integration over all particle orientations or integration over a distribution of particle sizes, since these integrations tend to smear out the errors associated with the single particle theory.

Journal ArticleDOI
TL;DR: In this article, the effects of electric fields on the front wave propagation in the iodate-arsenous acid reaction system were reported, and the mechanism of the electric field action was discussed.

Journal ArticleDOI
TL;DR: In this paper, an exact closed-form solution for the propagation characteristics of an arbitrarily polarized optical beam in an isotropic medium which is subjected to a dc electric field is presented.
Abstract: An exact, closed-form solution is presented for the propagation characteristics of an intense, arbitrarily polarized optical beam in an isotropic medium which is subjected to a dc electric field. The related phenomena of dc-electric-field-induced optical rectification and second-harmonic generation are examined as well as the propagation characteristics of a weak beam in an isotropic medium in the presence of both the intense optical and dc fields. One fundamental and noteworthy aspect of the results presented here is that both the formalism and the resulting solutions for these third-order nonlinear optical phenomena are given explicitly and entirely in terms of the set of real, observable Stokes parameters rather than in terms of the electric field amplitudes and phases.

Journal ArticleDOI
TL;DR: In this paper, the problem of the propagation of a slow high-frequency ionising electromagnetic wave along a thin plasma cylinder surrounded by a dielectric tube is considered, assuming that the characteristic diffusion and thermal conductivity lengths are small in comparison with the discharge length.
Abstract: The problem of the propagation of a slow high-frequency ionising electromagnetic wave along a thin plasma cylinder surrounded by a dielectric tube is considered, assuming that the characteristic diffusion and thermal conductivity lengths are small in comparison with the discharge length. The wave phase characteristics as well as the radial and axial profiles of the wave field and of the plasma electron temperature and density are determined. The obtained results suggest an approach for explanation of the experimental data.

Journal ArticleDOI
TL;DR: In this article, the authors calculate the time dependent wave function and energy spectrum resulting from the passage of a monoenergetic (plane wave) neutron beam through a chopper consisting of a slit with time dependent width.
Abstract: We calculate the time dependent wave function and energy spectrum resulting from the passage of a monoenergetic (plane wave) neutron beam through a chopper consisting of a slit with time dependent width. Experimental possibilities of observing the predicted effects are discussed. A new type of inelastic scattering spectrometer involving the use of frame overlap in a time of flight instrument is proposed.

Journal ArticleDOI
TL;DR: In this article, the propagation of longitudinal waves in isotropic homogeneous elastic plates is studied in the context of the linear theory of nonlocal continuum mechanics, and the dispersion equation obtained for the plane longitudinal wave in an infinite medium is matched with the parallel equation derived in the theory of atomic lattice dynamics.
Abstract: Propagation of longitudinal waves in isotropic homogeneous elastic plates is studied in the context of the linear theory of nonlocal continuum mechanics. To determine the nonlocal moduli, the dispersion equation obtained for the plane longitudinal waves in an infinite medium is matched with the parallel equation derived in the theory of atomic lattice dynamics. Using the integroalgebraic representation of the stress tensor and the Fourier transform, the system of two coupled differential field equations is solved in the standard manner giving the frequency equations for the symmetric and antisymmetric wave modes. It is found that the short wave speed in the Poisson medium differs by about 13 percent from the speed established in the classical theory. A numerical example is given.

Journal ArticleDOI
TL;DR: In this article, the effects of anelasticity on wave propagation, such as absorption and dispersion, are often described using one-dimensional (1-D) plane waves of the form exp[i(ωt-kx)] with k complex and frequency-dependent.
Abstract: The mathematical theory which is typically used to model the intrinsic anelasticity of the earth is the linear theory of viscoelasticity. The effects of anelasticity on wave propagation, such as absorption and dispersion, are often described using one‐dimensional (1-D) plane waves of the form exp[i(ωt-kx)] with k complex and frequency‐dependent. These waves are solutions of the 1-D viscoelastic wave equation. The reflection and transmission of plane waves in a layered viscoelastic medium is, however, a 2-D or 3-D problem. The solutions to the 2-D or 3-D viscoelastic wave equation are the so‐called general plane waves, which are classified as homogeneous or inhomogeneous depending upon whether or not the planes of constant phase, i.e., wavefronts, coincide with the planes of constant amplitude (the 1-D plane waves mentioned above are strictly homogeneous).