Showing papers on "Plane wave published in 1977"
TL;DR: In this paper, a surface integral equation (SIE) technique is developed to analyze the scattering properties of arbitrarily-shaped lossy dielectric bodies of revolution, and the unknown surface currents (both electric and magnetic) are calculated by first, Fourier decomposition, and then, the moment method, Galerkin's procedure.
Abstract: A surface integral equation (SIE) technique is developed to analyze the scattering properties of arbitrarily-shaped lossy dielectric bodies of revolution. Two coupled vector integral equations formulated via Maxwell's equations, Green's theorem, and the boundary conditions are used. The unknown surface currents (both electric and magnetic) are calculated by, first, Fourier decomposition, and then, the moment method, Galerkin's procedure. The far scattered field and radar cross section (RCS) are then readily determined from the reciprocity theorem and the measurement matrix concept. For a dielectric sphere good agreement is obtained between the SIE and exact solutions. Solutions of a thick dielectric cylinder are next used to demonstrate the arbitrary geometry capability of the SIE method. This method is suitable for homogeneous dielectric bodies and only the axially incident plane wave is considered here. The method also applies for a wide range of dielectric parameters (with ∈r from 1.44 to 80 and conductivity σ from 0 to 103 mho/m).
344 citations
01 Jun 1977
327 citations
TL;DR: In this paper, an integral equation is used to derive formal expressions for the scattering of a plane wave from a single homogeneous flaw embedded in an isotropic elastic medium, and an optical theorem is also derived.
Abstract: An integral equation is used to derive formal expressions for the scattering of a plane wave from a single homogeneous flaw embedded in an isotropic elastic medium. Expressions are found for the scattered amplitudes and differential cross sections. An optical theorem is also derived.
233 citations
TL;DR: In this paper, an inviscid, incompressible, stably stratified fluid occupies a horizontal channel, along which an internal gravity-wave packet is propagating and the wave induced mean motions are calculated, and the equations describing the evolution of the wave amplitude derived.
Abstract: An inviscid, incompressible, stably stratified fluid occupies a horizontal channel, along which an internal gravity-wave packet is propagating. The wave induced mean motions are calculated, and the equations describing the evolution of the wave amplitude derived. When the group velocity of the wave packet coincides with a long-wave speed there is a resonance, and the equations describing this resonance are derived.
181 citations
169 citations
TL;DR: In this article, the authors derived new regions of modulational instabilities in directions oblique to the initial wave propagation with growth rates much greater than in the case of parallel self-modulation.
Abstract: Two-dimensional nonlinear self-modulations of a high-frequency whistler wave propagating along an applied magnetic field in a plasma are investigated. We derive new, fairly broad, regions of modulational instabilities in directions oblique to the initial wave propagation with growth rates much greater than in the case of ‘parallel’ self-modulation. The largest growth rate appears to be for the angles corresponding to the parametric instabilities. Nonlinear solutions describing the envelope solitons propagating obliquely to the initial wave are also discussed. Our results are in qualitative agreement with recent experiments.
141 citations
TL;DR: In this article, the wave equation is solved to determine the transmission and reflection coefficients for plane waves at oblique incidence on a system of n layers of plane parallel plates, and both shear and longitudinal wave properties of the materials are included in the derivation.
Abstract: The wave equation is solved to determine the transmission and reflection coefficients for plane waves at oblique incidence on a system of n layers of plane parallel plates. Both shear‐ and longitudinal‐wave properties of the materials are included in the derivation. Equations are presented in a form which will facilitate adaptation to a digital computer. Data measured in the frequency range 100–700 kHz for one, two, and three solid layers immersed in water compare favorable with computer results.
131 citations
116 citations
TL;DR: In this article, reaction-diffusion equations which, locally in space and time, are close to plane wave trains are investigated and the structure of these layers, which are mathematically analogous to gas-dynamic shocks, is investigated on the basis of the full equations.
Abstract: Solutions of reaction-diffusion equations which, locally in space and time, are close to plane wave trains are investigated Apart from certain exceptional (and localized) regions, such solutions are approximately described by solutions of a Hamilton-Jacobi equation obtained from the properties of ideal plane waves This provides a fairly simple description of many features of the initial value problem, but implies that transition layers in which the approximate description is invalid will generally arise The structure of these layers, which are mathematically analogous to gas-dynamic shocks, is investigated on the basis of the full equations
113 citations
TL;DR: In this article, frustrated total reflection was used to optically excite electromagnetic surface plasma waves (SPW) in two different layered structures, where the surface roughness of the evaporated Mg${\mathrm{F}}_{2}$ films was found to increase with film thickness and this roughness has a pronounced effect on the SPW resonances.
Abstract: The method of frustrated total reflection is used to optically excite electromagnetic surface plasma waves (SPW) in two different layered structures. The first system studied has two films (Mg${\mathrm{F}}_{2}$-Ag) between glass and air, and the second has three films (Ag-Mg${\mathrm{F}}_{2}$-Ag) between glass and air. Surface roughness of the evaporated Mg${\mathrm{F}}_{2}$ films is found to increase with film thickness and this roughness has a pronounced effect on the SPW resonances. A cermet is imagined to form at the Mg${\mathrm{F}}_{2}$-Ag interface, and its effective optical constants can be evaluated using the Maxwell Garnett theory. If this cermet is treated as a separate layer in the structure, then good agreement is found with the experimentally observed resonances. A calculation of the Poynting vector field, current distributions, and surface charge densities, resulting from an incident monochromatic plane wave, shows the different modes of oscillation corresponding to each resonance.
106 citations
TL;DR: In this paper, the fluorescence lifetime of an excited molecule described as a classical oscillating dipole in front of a partially reflecting plane interface is studied theoretically, the lifetime being inversely proportional to the radiated power.
TL;DR: In this paper, the modulational instability of the ion wave is observed experimentally and the result of the quasi-monochromatic wave packet is qualitatively explained by the modified nonlinear Schrodinger equation taking account of the waveparticle interaction at the group velocity.
Abstract: The modulational instability of the ion wave is observed experimentally. Two kinds of wave packets are launched in the plasma by means of a grid. One is a broad-band wave packet excited by a positive step voltage. The other is a quasi-monochromatic wave packet modulated by a pulse. For the step voltage response, we observe a large oscillation in the wave front which evolves to Korteveg–de Vries solitons and a small amplitude wave packet in the tail. The wave packet becomes modulationally unstable and divides into smaller wave packets. Whenever the wave packet is modulated, the spread of the packet is suppressed and is much smaller than is expected from linear dispersion. For the quasi-monochromatic wave packet, we also observe the modulational instability if the carrier frequency is high. The frequency of the carrier is shifted by the instability. The result of the quasi-monochromatic wave packet is qualitatively explained by the modified nonlinear Schrodinger equation taking account of the wave-particle interaction at the group velocity.
TL;DR: In this paper, the shear wave field generated in a linear viscoelastic medium confined between parallel plates (one fixed, the other oscillating sinusoidally in its own plane) has been evaluated and presented in a graphical form convenient for determination of the role of wave propagation effects in dynamic rheological measurements.
Abstract: The shear‐wave field generated in a linear viscoelastic medium confined between parallel plates (one fixed, the other oscillating sinusoidally in its own plane) has been evaluated and presented in a graphical form convenient for determination of the role of wave propagation effects in dynamic rheological measurements. The transition from closely spaced planes (“gap loading”) to the freely propagating plane wave (“surface loading”) limit is examined; the importance of deviations in magnitude and phase of the gradient profile from the gap loading limit is discussed in terms of high precision dynamic rheological experiments; significant deviations occur for shear wavelength to gap width ratios of 30 or less.
TL;DR: In this paper, a representation of a finite set of plane waves with a set of Bloch tight-binding functions is described, whose basis functions combine the important physical aspects of the plane wave wave with those of a subset of tight binding functions, and the chosen combination has a particularly simple dependence on the wave vector within the Brillouin zone.
Abstract: A representation is described whose basis functions combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding functions. The chosen combination has a particularly simple dependence on the wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ within the Brillouin zone, and its use in reducing the standard oneelectron band-structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker, augmented-plane-wave, and orthogonalized-plane-wave methods are difficult to use, the present method leads to results with satisfactory accuracy and convergence. It is applied here to the case of compressed molecular hydrogen taken in a $\mathrm{Pa}3$ ($\ensuremath{\alpha}\ensuremath{-}\mathrm{nitrogen}$) structure for various densities but with mean interproton distance held fixed. The bands show a marked free-electron character above 5 to 6 times the normal density, and the overall energy gap is found to vanish at 9.15 times normal density. Within the approximations made, this represents an upper bound for the molecular density in the transition to the metallic state from an $\ensuremath{\alpha}\ensuremath{-}\mathrm{nitrogen}$ structure.
TL;DR: In this paper, the results of an experimental study of nonlinear electrical transport at low temperatures are described for the one-dimensional organic conductors TTF-TCNQ (tetrathiafulvalene-tetracyanoquinodimethane) and TSeF-TTE (tetraselenaful-valene)-Tetracyanion-to-niquera-toquera-nique (TTE-NQ) for low temperatures.
Abstract: The results of an experimental study of nonlinear electrical transport at low temperatures are described for the one-dimensional organic conductors TTF-TCNQ (tetrathiafulvalene-tetracyanoquinodimethane) and TSeF-TCNQ (tetraselenafulvalene-tetracyanoquinodimethane). The $b$-axis conductivity is nonlinear in both compounds with the onset of nonlinearity at applied electric fields of a few V/cm. Measurements along different crystallographic directions show that the nonlinear transport is directly related to the one-dimensional nature of the electronic system. Traditional single-particle mechanisms of nonlinearity in semiconductors are ruled out through direct experimental study. The experimental results are discussed in terms of nonlinear phase-kink solitons of the pinned charge-density wave condensate at low fields, and field-induced depinning at high fields.
TL;DR: In this article, an exact formulation for the scattering by a conducting prolate spheroid of a plane electromagnetic wave of arbitrary polarization and incidence angle is presented, which depends only on the scatterer.
Abstract: Using modal expansions of electromagnetic fields in terms of prolate spheroidal wave functions, an exact formulation is presented for the scattering by a conducting prolate spheroid of a plane electromagnetic wave of arbitrary polarization and incidence angle. In this formulation the column vector of the series coefficients of the scattered field is obtained from the column vector of the series coefficients of the incident field by means of a matrix transformation. The matrix depends only on the scatterer; hence the scattered field for a new direction of incidence is obtained without repeatedly solving a new set of simultaneous equations. The exact curves numerically obtained for the monostatic radar cross section and relative phase of the scattered field as a function of aspect angle (angle of incidence) for both principal polarizations are given for a variety of prolate spheroids in the resonance region.
TL;DR: An enclosing "box" calorimeter has been used to measure the polarization and angular dependence of 1.06-m laser-light absorption under experimental conditions approximating those assumed by Estabrook, Valeo, and Kruer in their simulations as mentioned in this paper.
Abstract: An enclosing "box" calorimeter has been used to measure the polarization and angular dependence of 1.06-\ensuremath{\mu}m laser-light absorption under experimental conditions approximating those assumed by Estabrook, Valeo, and Kruer in their simulations; i.e., \ensuremath{\sim}${10}^{16}$ W/${\mathrm{cm}}^{2}$ plane waves incident on a planar plasma. A clear resonance absorption maximum was observed for $p$-but not for $s$-polarized incident radiation as predicted.
TL;DR: In this paper, the electromagnetic field coupling through small apertures illuminated by an arbitrary incident plane wave is discussed for general aperture shapes and a set of new integral equations in a form highly amenable to numerical solution techniques is derived.
Abstract: The electromagnetic field coupling through small apertures illuminated by an arbitrary incident plane wave is discussed for general aperture shapes. A set of new integral equations in a form highly amenable to numerical solution techniques is derived. Based on the application of the Rayleigh series method, an analytical solution is obtained for the first few terms of the expansion of the aperture E - field of a circular aperture. Numerical results are also constructed for the aperture field and the diffracted field of small rectangular apertures and compared with those of the circular apertures.
01 Jan 1977
TL;DR: In this paper, the authors analyzed the continuity and Poisson's equations using the multiple time and length scale technique to emphasize the wide separation of scales between those of chemical wave propagation and the tendency toward electroneutrality.
Abstract: In the best known example of chemical wave propagation, the Belusov–Zaikin–Zhabotinsky) reaction, most important species are ionic yet all theoretical studies that proport to describe wave porpagation in this media neglect the importance of charge neutrality coupling in ionic transport. In this paper we analyze the continuity and Poisson’s equations using the multiple time and length scale technique to emphasize the wide separation of scales between those of chemical wave propagation and the tendency toward electroneutrality. We derive a new equation for chemical waves in ionic systems and show that a coupling term due to the presence of a Planck liquid junction potential must be added to the neutral species equation to guarantee charge neutrality. It is pointed out that chemical waves in these systems are accompanied by propagating liquid junction potentials and that applied electric fields may significantly alter wave propagation, thus serving as a new experimental probe of chemical waves.
01 Mar 1977
TL;DR: In this paper, H-field, E-field and combined field solutions are developed for the electric surface current and far scattered fields of a perfectly conducting body of revolution excited by an incident plane wave.
Abstract: : H-field, E-field, and combined field solutions are developed for the electric surface current and far scattered fields of a perfectly conducting body of revolution excited by an incident plane wave. These solutions are obtained by applying the method of moments to the H-field, E-field, and combined field integral equations, respectively. The H-field integral equation is obtained by requiring the tangential magnetic field to be zero just inside the surface S of the body of revolution. The E-field integral equation is obtained by requiring the tangential electric field to be zero on S. The combined field integral equation is a linear combination of the H-field and E-field integral equations. Computations show that both the H-field and the E-field solutions deteriorate near internal resonances of the conducting surface S, but that the combined field solution does not. The computer program subroutines used to perform these computations will appear in a forthcoming report.
TL;DR: A set of miniature isotropic probes has been used experimentally to map electric fields within two small spheres of simulated muscle tissue (3.3 cm and 8 cm radii) that were irradiated by 450-, 915-, and 2450-MHz plane waves as discussed by the authors.
Abstract: A set of miniature isotropic probes has been used experimentally to map electric fields within two small spheres of simulated muscle tissue (3.3-cm and 8-cm radii) that were irradiated by 450-, 915-, and 2450-MHz plane waves. Good agreement was obtained with the theoretically predicted spatial distribution of fields in both spheres, even in the immediate proximity of the boundaries. The absolute calibrations of the probes were found to be moderately to significantly dependent upon the dielectric constant of the medium (1 ≤ ∈r ≤ 50) in which the probe was implanted, with the least dependence occurring at 2450 MHz (±2.25 dB), and the greatest dependence occurring at 450 MHz (±4.25 dB). A set of design criteria is presented that are necessary for proper performance of such a dipole/diode probe. Of particular importance are the thickness of the insulation surrounding the dipole antenna, and the dimensions of the dipole. Both must be small compared to the wavelength of the field in the biological media. The validity of the design criteria has been experimentally demonstrated, illustrating the feasibility of producing an improved probe whose response to an electric field of given strength would be relatively constant regardless of the dielectric constant of the media and independent of boundary-proximity effects. Preliminary results of in vivo measurements are presented; improved, biologically compatible designs are discussed.
TL;DR: In this article, a formal theory of magneto-acoustic wave propagation and dissipation in a compressible fluid subjected to a magnetic field is presented. But the authors do not consider the effects of the magnetic field on wave propagation.
Abstract: The generation, and thence the dissipation, propagation and radiation, of waves in a compressible fluid subjected to a magnetic field is studied as an extension of the ‘acoustic analogy’ (Lighthill 1952) to magneto-acoustics. A formal theory of magneto-acoustic waves introduces (i) a single differential operator describing propagation, (ii) a dynamic and a magnetic tensor modelling generation and (iii) a dissipation tensor to complete the wave equation. The interpretation of these tensors indicates the magnitude of the physical processes of wave generation, by turbulence and inhomogeneities, and of wave dissipation, by viscous and electrical resistance and heat conduction. The total quadrupole components are classified according to the mode of emission. If the magnetic field or compressibility is neglected we obtain, respectively, ‘aerodynamic acoustics’ and a corresponding theory for Alfven waves. These hydrodynamic and hydromagnetic results contrast with magnetodynamics, when the magnetic field is dominant. The magneto-acoustic far field implies a law of directivity and intensity of radiation. The main results have been collected in three summary tables (see appendix).
TL;DR: In this article, the induced eletric fields in an ellipsoidal model of man and experimental animals irradiated by an electromagnetic (EM) plane wave when the wavelength is long compared to the dimensions of the ellipseid were derived.
Abstract: Expressions are derived for the induced eletric fields in an ellipsoidal model of man, and experimental animals irradiated by an electromagnetic (EM) plane wave when the wavelength is long compared to the dimensions of the ellipsoid. Calculations of the power absorbed by an ellipsoidal model of man are given for six different orientations of the ellipsoid with respect to the incident plane wave field vectors. The results show that the induced fields and the absorbed power in the ellipsoid are strong functions of frequency, size, and orientation with respect to the incident EM field vectors. The results for the ellipsoidal model of man are also compared with those of the prolate spheroidal model.
TL;DR: Results obtained from calculating the integrated scattered signal indicate a strong dependence upon the following physical parameters: particle size, index of refraction, cross beam angle, and collection solid angle.
Abstract: The Mie scattering properties of a homogeneous, isotropic spherical particle, moving at a constant velocity and illuminated by two intersecting coherent plane waves having the same polarization direction, have been analyzed based upon an exact solution to Maxwell's equations. The solutions are in a form suitable for the calculation of the time varying scattered signal integrated across a detector aperture of variable size that is centered on either the forward or backward scattering direction. This problem is of importance in defining the scattered signal in a cross beam laser Doppler velocimeter (LDV). Results obtained from calculating the integrated scattered signal indicate a strong dependence upon the following physical parameters: particle size, index of refraction, cross beam angle, and collection solid angle.
TL;DR: In this paper, a non-linear Schrodinger equation for Langmuir waves is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics.
Abstract: A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially in the expressions concerning the modulation instability of a plane Langmuir wave. When the Vlasov equation for the ions is applied, a Langmuir wave is modulationally unstable for arbitrary perturbations independent of the unperturbed wave amplitude, in contrast to what is found for fluid ions. A simple analogy with negative energy waves explaining the different features of the two cases is outlined.
TL;DR: The theory and performance of a two beam differential interferometer for measurement of both surface and bulk waves are described in this article, which is insensitive to small errors (< 1 mm) in focus or in specimen flatness.
Abstract: The theory and performance of a two beam differential interferometer for measurement of both surface and bulk waves are described. The system is insensitive to small errors (<1 mm) in focus or in specimen flatness. Both amplitude and phase measurements are demonstrated. The system has been absolutely calibrated and can detect 6 × 10−4 A surface wave displacements on glass.
01 Aug 1977
TL;DR: In this paper, the kinetic properties of the Alfven wave, which originates from the finite perpendicular wavelength effects, have been shown for both linear and nonlinear regime, and the wave can be excited in a plasma either by drift wave instability or resonant mode conversion of surface magnetohydrodynamic wave.
Abstract: Kinetic properties of the Alfven wave, which originate from the finite perpendicular wavelength effects, are shown for both linear and nonlinear regime. The wave accompanies a parallel electric field and can propagate in the direction perpendicular to the ambient magnetic field. The kinetic Alfven wave can be excited in a plasma either by drift wave instability or resonant mode conversion of a surface magnetohydrodynamic wave.