Showing papers on "Plane wave published in 1979"

Combined wave and current interaction with a rough bottom

Abstract: An analytical theory is presented to describe the combined motion of waves and currents in the vicinity of a rough bottom and the associated boundary shear stress. Characteristic shear velocities are defined for the respective wave and current boundary layer regions by using a combined wave-current friction factor, and turbulent closure is accomplished by employing a time invariant turbulent eddy viscosity model which increases linearly with height above the seabed. The resulting linearized governing equations are solved for the wave and current kinematics both inside and outside the wave boundary layer region. For the current velocity profile above the wave boundary layer, the concept of an apparent bottom roughness is introduced, which depends on the physical bottom roughness as well as the wave characteristics. The net result is that the current above the wave boundary layer feels a larger resistance due to the presence of the wave. The wave-current friction factor and the apparent roughness are found as a function of the velocity of the current relative to the wave orbital velocity, the relative bottom roughness, and the angle between the currents and the waves. In the limiting case of a pure wave motion the predictions of the velocity profile and wave friction factor from the theory have been shown to give good agreement with experimental results. The reasonable nature of the concept of the apparent bottom roughness is demonstrated by comparison with field observations of very large bottom roughnesses by previous investigators. The implications of the behavior predicted by the model on sediment transport and shelf circulation models are discussed.

Theory of electromagnetic beams

Abstract: A relatively simple method for calculating the properties of a paraxial beam of electromagnetic radiation propagating in vacuum is presented. The central idea of the paper is that the vector potential field is assumed to be plane-polarized. The nonvanishing component of the vector potential obeys a scalar wave equation. A formal solution employing an expansion in powers of $\frac{{w}_{0}}{l}$ is obtained, where ${w}_{0}$ is the beam waist and $l$ the diffraction length. This gives the same result for the lowest-order components of the transverse and longitudinal electric field of a Gaussian beam that was derived by Lax, Louisell, and McKnight using a more complicated approach. We derive explicit expressions for the second-order transverse electric field and the third-order longitudinal field corrections.

On the parabolic equation method for water-wave propagation

Abstract: A parabolic approximation to the reduced wave equation is investigated for the propagation of periodic surface waves in shoaling water. The approximation is derived from splitting the wave field into transmitted and reflected components.In the case of an area with straight and parallel bottom contour lines, the asymptotic form of the solution for high frequencies is compared with the geometrical optics approximation.Two numerical solution techniques are applied to the propagation of an incident plane wave over a circular shoal.

Discrete wave number representation of elastic wave fields in three-space dimensions

Abstract: We present the generalization to three dimensions of the discrete wave number representation method of Bouchon and Aki (1977). The method is developed to study the near field of a three-dimensional seismic source embedded in a layered medium. The elastic wave fields are represented by a superposition of plane waves propagating in discrete directions. The discretization is exact and results from a periodic two-dimensional arrangement of sources. The accuracy of the method is checked, in the case of a rectangular dislocation source radiating in an infinite medium, by comparing the results obtained with Madariaga's (1978) exact solution. Examples of the calculation of strong ground motion produced by a thrust fault and a strike slip fault are presented.

Self-consistent mixed-basis approach to the electronic structure of solids

Abstract: A mixed-basis method is developed for the calculation of the electronic structure of solids. The method is shown to be capable of treating crystals with large complex unit cells. A combined set of plane waves and Bloch sums of localized functions is employed as basis functions, thus leading to a very efficient representation of systems which contain both highly localized (atomiclike) and delocalized (plane-wave-like) electrons. The crystalline potential is determined in a fully self-consistent manner with no approximations made to its shape. The present method has the flexibility of being easily applicable to the study of many different systems (e.g., surface calculations with supercells). Specific application is made to bulk Nb and Pd to demonstrate the efficiency and accuracy of the method. Very good agreement with experimental results and with band structures calculated using other methods is obtained. It is found that, with a mixed basis, only a relatively small set of functions is needed to obtain convergent wave functions for the electrons.

Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy half-space

Abstract: An infinite array of arbitrarily oriented identical elements with arbitrary identical currents is considered. The field from this array is expanded into plane inhomogeneous waves, and the mutual impedance between the array elements and an exterior arbitrarily oriented element is derived. The formulation is particularly useful when the array is located adjacent to a dielectric interface. Numerical examples are given and the relationship to earlier formulations pointed out. It is further shown that the impedance of a single element can be obtained as the average of the scan impedance taken over the entire hemisphere (called the array scanning method (ASM)). This technique has a clear physical interpretation which greatly facilitates its uses, which include the moment method solutions of wire antennas as applied to the Sommerfeld integral. Numerical evaluation is straightforward when the dipole is in the lossy half-space, and the utility of the method is demonstrated by the presentation of results for the input impedance of dipoles in a variety of half-space environments. Solution is by Galerkin's method with a piecewise sinusoidal expansion for the current. Computer time is proportional to d^{-1} , where d is the distance of the dipole to the interface. For conducting media and low frequencies an approximation is made to reduce computation time. The moment method solution of a dipole buried at a depth as small as 1/150000 wavelength in the earth is presented.

Matter and Light Wave Interferometry in Gravitational Fields

Abstract: We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism∫ ds. In weak fieldsh μυ this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 ∫h μυ P υ dx μ whereP υ is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the “dragging of the ether frame” by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 ∫h μυ K υ dx μ , whereK υ is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.

Corrugated dielectric waveguides: A numerical study of the second-order stop bands

Abstract: A short description of a rigorous electromagnetic theory based on the numerical integration of a differential system is given. It allows the study of the stop-bands of a corrugated waveguide. Dispersion curves in the first and the second-order stop-bands are computed for various periodic waveguides. A selection rule due to the symmetry of the corrugation is found. The reflection of a plane wave by the guide is examined. It is demonstrated that under peculiar circumstances, the reflection coefficient has a modulus equal to unity.

An asymptotic analysis of the scattering of plane waves by a smooth convex cylinder

Abstract: An approximate asymptotic high-frequency result which is convenient for engineering applications is obtained for the field exterior to a smooth perfectly conducting convex cylinder when it is illuminated by a plane wave. This result is uniform in the sense that it remains valid within the transition regions adjacent to the shadow boundaries where the pure ray optical solution based on the geometrical theory of diffraction (GTD) fails, and it automatically reduces to the GTD solution exterior to the transition regions where the latter solution becomes valid. Furthermore, this result is expressed in the simple format of the GTD, and it employs the same ray paths as in the GTD solution. This uniform result is not valid in the close neighborhood of the cylinder; hence a separate asymptotic result is presented for this special case in a form which is also convenient for applications. The asymptotic results presented here are useful for predicting the patterns of antennas radiating in the presence of convex conducting cylindrical structures.

Direct Solution of Wave Dispersion Equation

Abstract: Approximate solutions for wave speed given by equations reduce the number of arithmetic operations required during a refraction calculation. The precise saving depends on the algorithms presently in use, but a time saving of about half appears typical.

Electromagnetic wave propagation

Abstract: Methods in Electromagnetic Wave Propagation. By D.S. Jones. Pp. 887. (Clarendon/Oxford University Press: Oxford, 1979.) £22.50.

A uniform GTD solution for the diffraction by strips illuminated at grazing incidence

Abstract: An asymptotic solution for the electromagnetic diffraction by a perfectly conducting strip illuminated at grazing incidence is obtained by an extension of the uniform GTD. Uniform expressions for the scattered field are given for plane, cylindrical, and spherical wave illuminations. Outside the transition regions these essentially reduce to results obtained by an ordinary application of the uniform GTD augmented by slope diffraction. In the case of plane wave illumination a very simple closed form expression is provided for the scattered far field. Numerical results are presented and compared with those calculated from a moment method solution.

Stimulated scattering of light by ion modes in a homogeneous plasma: Space-time evolution

Abstract: Stimulated Brillouin scattering, filamentation, and induced Thomson scattering are studied for a coherent electromagnetic plane wave propagating in a uniform plasma. A generalized Green’s function is found that describes the impulse response for stimulated scattering by electron and ion modes. Explicit asymptotic Green’s functions are calculated for those parametric instabilities involving ion modes or quasi‐modes. Special attention is given to whether the instabilities are convective or absolute. For a traveling wave pump in a uniform plasma, Brillouin and induced Thomson backscatter can be absolute, but sidescatter is convective; filamentation of traveling waves is always convective. Spatial growth rates are calculated for convectively unstable modes. Finally, the competition of filamentation and stimulated Brillouin scattering is considered for parameters typical of real laser‐fusion experiments.

Linear augmented plane wave method for self-consistent calculations

Abstract: Andersen (1975) has recently introduced a linear augmented plane wave method (LAPW) for the calculation of electronic structure that was shown to be computationally fast. A more general formulation of an LAPW method is presented here. It makes use of a freely disposable number of eigenfunctions of the radial Schrodinger equation. These eigenfunctions can be selected in a self-consistent way. The present formulation also results in a computationally fast method. It is shown that Andersen's LAPW is obtained in a special limit from this formulation. Self-consistent test calculations for copper show the present method to be remarkably accurate. As an application, scalar-relativistic self-consistent calculations are presented for the band structure of FCC lanthanum.

Resonances in electromagnetic scattering by objects with negative absorption

Abstract: This is a numerical study of electromagnetic scattering by particles exhibiting negative absorption, i.e., with refractive index m = n(1 + κi), where the time dependence is exp(+iωt). The particle is a homogeneous circular cylinder. The stimulating incident plane wave travels perpendicularly to the cylinder axis. The scattering, amplification, and extinction cross sections as well as the differential scattering cross sections were evaluated for n = 1.50 over the nκ = 0.001–1 range for the size parameter up to α = 50, where α = 2πa/λ (a is the radius and λ is the wavelength). In some cases results were obtained for much larger values of α. The most remarkable finding was the occurrence of sharp resonances. Not only does this provide for large amplification of the scattered radiation traveling outward as spherical waves (for 3-D objects) or as cylindrical waves (for 2-D objects), but, because of the occurrence of negative extinction cross sections, it may also result in amplification of the incident plane wave. The present formalism (Lorenz-Mie for spheres; Rayleigh for cylinders) implies a particular and highly contrived mechanism for pumping and stimulation. However, the formalism may be extended to other particular mechanisms.

Theoretical reflection seismograms for elastic media

Abstract: Theoretical seismograms for an explosive source in a multilayered elastic medium are constructed by Fourier synthesis and plane wave superposition. The calculation scheme which builds up a reflection matrix layer by layer in the frequency and wave number domain allows the inclusion of attenuation and a choice of the level of internal multiples in each layer. Comparative calculations of theoretical seismograms for an elastic model and in the acoustic approximation, neglecting shear, show that the main differences arise at large offsets. The inclusion of shear waves leads to lower reflected P wave amplitudes at the end of the spread but only small amounts of converted phases.

Numerical solution of wave scattering problems in the parabolic approximation

Abstract: A numerical analysis of two-dimensional wave scattering problems is performed. The treatment relies on the parabolic approximation and provides the forward scattered wave field. Two problems are considered in particular: (i) the scattering of plane waves by a cylindrical inhomogeneity of uniform refraction index, (ii) the scattering of plane waves by a viscous core vortex. The structure of the scattered field is examined in detail and the numerical solutions of the two problems are compared to analytical results obtained in the Born approximation and interpreted according to the method of smooth perturbation.

Scattering by resistive strips

Abstract: For resistive strips of large electrical width kw illuminated by E- or H-polarized plane waves the geometrical theory of diffraction is used to obtain expressions for the far zone scattered field through second-order terms, valid for directions of incidence and observation away from grazing. The results are then cast as products of functions analogous to those appearing in the known (uniform) expansions for perfectly conducting strips. Each function involves the current on the corresponding half plane, and by invoking this connection, far field expressions are produced which are uniform in angle. In particular, for E polarization the backscattered field at edge-on incidence is shown to consist of two terms, each of which is expressible in terms of the half-plane current, and for all resistivities the resulting values of the field are in excellent agreement with those found by numerical solution of the integral equation, even for kw as small as unity.

Waveguide launching of lower hybrid waves

Abstract: The theory of launching lower hybrid waves in fusion-oriented plasmas using waveguide arrays (the 'grill') is generalized to allow for the excitation of the fast wave in the outer layers of the plasma. It is found that the reflection coefficient of the antenna and the fraction of power radiated in the 'inaccessible' portion of the parallel-wavenumber spectrum remain essentially the same as those predicted by the simplified theory considering only the slow plasma wave. The most important new feature is that the power radiated in this part of the spectrum is mainly coupled to discrete waveguide-like eigenmodes confined to the outer layers of the plasma, which guide the power away from the antenna in the direction parallel to the wall of the chamber. This fraction of the power is likely to be lost from the point of view of the heating efficiency; therefore, one should make it as small as possible by using arrays of four guides or more.

Ring-Shaped Quasi-Soliton Solutions to the Two- and Three-Dimensional Sine-Gordon Equation

Abstract: Ring-shaped solitary wave solutions to the Sine-Gordon equation in two and three spatial dimensions are investigated by numerical computation. Each expanding wave exhibits a return effect. The reflection of the shrinking wave at the singularity at the center of the wave is investigated in a particular case. Collision experiments in numero for expanding and shrinking concentric ring waves show that the solutions possess quasisoliton properties. A Backlund transformation for the non-symmetric three-dimensional case is given.

Electromagnetic Absorption in Multilayered Cylindrical Models of Man

Abstract: The absorption characteristics of multilayered cylindrical models of man irradiated by a normally incident electromagnetic plane wave are investigated. Numerical calculations for a specific skin-fat-muscle cylindrical model of man predict a layering resonance at 1.2 GHz with an average specific absorption rate (SAR) about double that calculated for the corresponding homogeneous model. The layering resonance frequency is found to be the same for incident waves polarized parallel and perpendicular to the cylinder axis. The effects of layers on whole-body absorption by man are determined by averaging the effects obtained for many combinations of skin and fat thicknesses. Absorption effects due to clothing are also investigated.

Scattering by linearly vibrating objects

Abstract: The scattering problem for a plane wave incident upon a perfectly conducting linearly oscillating object is investigated both theoretically and experimentally. The theoretical analysis, accurate to order v/c where v and c axe the velocities of object and light, respectively, shows that the target oscillation changes the scattered far field of a motionless target only in phase. The oscillation is assumed to be periodic, and this period is shown to be impressed on the scattered field. Spectral analysis of the modulation shows that the power distribution varies with the shape of the motion, wavelength of the incident field, and the magnitude of the projections of the oscillation in the direction of incidence and receiver. Power spectra have been calculated for square, triangular, and sinusoidal target motion and, in general, the power content in the higher harmonics is found to increase with cartier frequency and magnitude of oscillation. For backscattering from an object moving sinusoidally along the direction of incidence, the power in the first harmonic is shown to exceed that at the carrier frequency when d > 0.23\lambda where d is the magnitude of the oscillation. These calculations are shown to agree with experimental measurements of the phase modulation of the field scattered from a vibrating disk at the X -band. Experimental results were obtained with continuous wave backscatter equipment at 10 GHz that utilized separate tunnel antennas for transmitting and receiving. The receiving section of this equipment was modified to separately display phase modulation and amplitude modulation characteristics of the backscattered signal in both time and frequency, as well as characteristics of the overall modulation envelope. Phase modulations introduced by target oscillations as small as \pm 0.001 in were readily detected, as were amplitude modulations of a few percent.

On electromagneto-thermoelastic plane waves

Abstract: The propagation of harmonically time-dependent electromagneto-thermoelastic plane waves of assigned frequency in an unbounded, homogeneous, isotropic, elastic, thermally and electrically conducting medium is considered. The theory of thermoelasticity recently proposed by Green and Lindsay is used to account for the interactions between the elastic and thermal fields. The results pertaining to phase velocity and attenuation coefficient of various types of waves are compared with those of Nayfeh and Nemat-Nasser who have dealt with a theory of thermoelasticity having a thermal relaxation time.

Two-dimensional plane wave theory of strong acousto-optic interaction in isotropic media

Abstract: Strong interaction is the preferred (high-efficiency) mode of operation in acousto-optic devices. Yet most theories of strong interaction use simplifying assumptions, such as sharply bounded sound columns, which are often unrealistic. The theory presented in this paper makes no such assumptions; it describes strong acousto-optic interaction as a multiple scattering of plane waves.

Nonlinear plane waves in the massless Yang-Mills theory

Abstract: A new set of solutions of the Yang-Mills equations, which are nonlinear massive plane waves, is obtained and analyzed.

Electromagnetic ion waves in cold relativistic plasmas

Abstract: The high-energy processes which occur in many astrophysical objects have motivated recent studies (e.g., Tsintsadze and Tsikarishvili, 1976; Ferrariet al., 1978; Sweeney and Stewart, 1978) of large amplitude wave propagation in plasmas. Such investigations are also of interest for laboratory experiments where strong laser radiation interacts with a high-density target. In the present paper we shall show that even rather small amplitude waves in the presence of an external magnetic field can induce particle velocities which are comparable to the velocity of light. In this ultrarelativistic limit we shall demonstrate that two completely new types of circularly polarized waves appear and that under certain conditions, modulational instabilities occur. Finally we look at the possibility to relate the amplitudes and wavelengths of such waves to pulsar data.

Beam wave two-frequency mutual-coherence function and pulse propagation in random media: an analytic solution.

Abstract: Pulse propagation in a random medium is determined by the two-frequency mutual coherence function which satisfies a parabolic equation. In the past, numerical solutions of this equation have been reported for the plane wave case. An exact analytical solution for the plane wave case has also been reported for a Gaussian spectrum of refractive-index fluctuations. Using the same approximation, an exact analytic solution for the more general case of an incident beam wave is presented. The solution so obtained is used to study the propagation characteristics of the beam wave mutual coherence function at a single frequency as well as at two frequencies. Simple expressions are obtained which qualitatively describe the decollimating and defocusing effects of turbulence on a propagating beam wave. The time variation of the received pulse shape, on and away from the beam axis, is studied when the medium is excited with a delta function input. The results are presented for both collimated and focused beams.