Showing papers on "Plane wave published in 1976"

Theory of discommensurations and the commensurate-incommensurate charge-density-wave phase transition

Abstract: The lowest-energy state of the incommensurate charge density wave (CDW) near the lock-in transition is found to be a distorted plane wave. An exact solution is found in the weak-coupling limit and the lock-in phase transition is continuous. A new defect is found in the commensurate CDW, a discommensuration, in which the phase of the CDW slips by $\frac{2\ensuremath{\pi}}{3}$ relative to the perfectly locked in CDW. The lock-in phase transition is interpreted as a defect melting transition with a finite density of discommensurations in the incommensurate state.

On the modulational instability of hydromagnetic waves parallel to the magnetic field

Abstract: The stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. A set of equations for slowly varying waves of arbitrary amplitude is obtained. A discussion of the stability of the waces is based on this set of equations. Earlier results are confirmed; in addition we find that finite amplitude always promotes stability. An amplitude dependent stability condition for long waves, previously obtained by the author, is confirmed.

Nonlinear phenomena in the ionosphere

Abstract: 1. Introduction.- 1.1 Data on the Structure of the Ionosphere.- 1.2 Features of Nonlinear Phenomena in the Ionosphere.- 1.2.1. Nonlinearity Mechanisms.- 1.2.2. Qualitative Character of Nonlinear Phenomena.- 1.2.3. Brief Historical Review.- 2. Plasma Kinetics in an Alternating Electric Field.- 2.1. Homogeneous Alternating Field in a Plasma (Elementary Theory).- 2.1.1.Electron Current-Electronic Conductivity and Dielectric Constant.- 2.1.2.Electron Temperature.- 2.1.3.Ion Current-Heating of Electrons and Ions.- 2.2. The Kinetic Equation.- 2.2.1. Simplification of the Kinetic Equation for Electrons.- 2.2.2. Transformation of the Electron Collision Integral.- 2.2.3. Inelastic Collisions.- 2.3. Electron Distribution Function.- 2.3.1. Strongly Ionized Plasma.- 2.3.2. Weakly Ionized Plasma.- 2.3.3. Arbitrary Degree of lonization-Concerning the Elementary Theory.- 2.4. Ion Distribution Function.- 2.4.1. Simplification of the Kinetic Equation.- 2.4.2. Distribution Function.- 2.4.3. Ion Temperature, Ion Current.- 2.5. Action of Radio Waves on the Ionosphere.- 2.5.1. lonization Balance in the Ionosphere.- 2.5.2. Effective Frequency of Electron and Ion Collisions-Fraction of Lost Energy.- 2.5.3. Electron and Ion Temperatures in the Ionosphere.- 2.5.4. Heating of the Ionosphere in an Alternating Electric Field.- 2.5.5.Perturbations of the Electron and Ion Concentrations.- 2.5.6. Artificial lonization of the Ionosphere-Heating of Neutral Gas.- 3. Self-Action of Plane Radio Waves.- 3.1. Simplification of Initial Equations.- 3.1.1. Nonlinear Wave Equation.- 3.1.2. Nonlinear Geometrical Optics of a Plane Wave.- 3.2. Effect of Nonlinearity on the Amplitude and Phase of the Wave.- 3.2.1. Self-Action of a Weak Wave.- 3.2.2. Self-Action of a Strong Wave.- 3.2.3. Self-Action of Waves in the Case of Artificial lionization.- 3.3. Change of Wave Modulation.- 3.3.1. Weak Wave.- 3.3.2. Change of Amplitude Modulation of Strong Wave.- 3.3.3. Phase Modulation.- 3.3.4. Nonlinear Distortion of Pulse Waveform.- 3.4. Generation of Harmonic Waves and Nonlinear Detection.- 3.4.1. Frequency Tripling.- 3.4.2. Nonlinear Detection.- 3.5. Self-Action of Radio Waves in the Lower Ionosphere.- 4. Interaction of Plane Radio Waves.- 4.1. Cross Modulation.- 4.1.1. Weak Waves.- 4.1.2. Strong Perturbing Wave.- 4.1.3. Resonance Effects near the Electron Gyrofrequency.- 4.2. Interaction of Unmodulated Waves.- 4.2.1. Interaction of Short Pulses.- 4.2.2. Change in the Absorption of a Wave Propagating in a Perturbed Plasma Region.- 4.2.3. Generation of Waves with Combination Frequencies.- 4.3. Radio Wave Interaction in the Lower Ionosphere.- 4.3.1. Cross Modulation.- 4.3.2. Fejer's Method.- 4.3.3. Nonstationary Processes in the Interaction of Strong Radio Waves.- 5. Self-Action and Interaction of Radio Waves in an Inhomogeneous Plasma.- 5.1. Inhomogeneous Electric Field in a Plasma.- 5.1.1. Fundamental Equations.- 5.1.2. Distribution of Density and Temperatures in Plasma.- 5.2. Kinetics of Inhomogeneous Plasma.- 5.2.1. Kinetic Coefficients. Elementary Theory.- 5.2.2. Kinetic Theory.- 5.2.3. Fully Ionized Plasma.- 5.3. Modification of the F Region of the Ionosphere by Radio Waves.- 5.3.1. Modification of the Electron Temperature and of the Plasma Concentration.- 5.3.2. Radio Wave Reflection Region.- 5.3.3. Growth and Relaxation of the Perturbations.- 5.4. Focusing and Defocusing of Radio Wave Beams.- 5.4.1. Nonlinear Geometrical Optics.- 5.4.2. Defocusing of Narrow Beams.- 5.4.3. Mutual Defocusing.- 5.4.4. Thermal Focusing in the Lower Ionosphere.- 6. Excitation of Ionosphere Instability.- 6.1. Self-Focusing Instability.- 6.1.1. Spatial Instability of a Homogeneous Plasma.- 6.1.2. Instability in the Wave-Reflection Region.- 6.2. Resonant Absorption and Resonance Instability.- 6.2.1. Langmuir Oscillations in an Inhomogeneous Plasma.- 6.2.2. Excitation of Plasma Waves.- 6.2.3. Resonance Instability.- 6.2.4. Absorption of Ordinary Radio Waves.- 6.3. Parametric Instability.- 6.3.1. Langmuir Oscillations of a Plasma in an Alternating Field.- 6.3.2. Parametric Excitation of Langmuir Oscillations.- 6.3.3. Parametric Instability in the Ionosphere.- 6.3.4. Dissipative Parametric Instability.

Electromagnetic fields in the presence of rotating bodies

Abstract: Field calculations in the presence of rotating bodies with symmetry of revolution can be performed in the (inertial) laboratory frame of reference. Specific results are presented for a rotating circular cylinder immersed in a plane wave of the E or H type. Particular emphasis is put on the low-frequency limit, but some numerical data are also given for a typical frequency in the "resonance" region. The analysis becomes more complicated in the absence of symmetry of revolution. It is then necessary to solve the problem in a rotating system of coordinates. Maxwell's equations are written in these coordinates, together with the relevant constitutive equations and boundary conditions. The general formalism is applied to a typical two-dimensional configuration, viz., a cylinder immersed in an incident E wave. Considerable simplification obtains if all material velocities are negligible with respect to c, a condition which is always met in practice. Even simpler results are obtained if the cross-sectional dimensions of the cylinder are small with respect to λ. Some numerical results are presented, at low frequencies, for a dielectric cylinder of rectangular cross section.

Propagation of pulses

Abstract: The propagation of pulsed wave fields in a homogeneous medium or in a homogeneous line with known dispersion law and damping can be regarded from the ray, wave, and energy points of view. The review describes the most significant theoretical results on one-dimensional pulse propagation, using all three approaches. Greatest attention is paid to the principal part of a high-frequency pulse, the part governed by frequencies closest to the pulse carrier frequency. Paradoxes pertaining to superluminal and negative "group velocities" are resolved, and questions connected with amplification or attenuation of waves in wave beams and active media are discussed.

Real-time measurement of surface roughness by correlation of speckle patterns

Abstract: In a previous article we have shown that the two speckle patterns produced from the same rough surface illuminated by two coherent plane waves under two different angles of incidence are correlated. The correlation depends on the surface roughness. In this paper a method is described where the rough surface is illuminated simultaneously by the two plane waves. The ensemble-averaged coherence function, that is, the correlation function, of the scattered field is measured by using a two-waves interferometer. This affords a real-time measurement of the surface roughness in the range of large roughness (σ > λ). The theoretical calculations have been performed for a normally distributed surface. The experimental results are in good agreement with theory. We describe the optical arrangement of an instrument based on this principle.

Two-frequency mutual coherence function and pulse propagation in a random medium: An analytic solution to the plane wave case

Abstract: Pulse propagation in a random medium is determined by the two-frequency mutual coherence function which satisfies a parabolic equation. In the past, approximate or numerical solutions of this equation have been reported. This paper presents an exact analytical solution for a plane wave case when the random medium is approximated by A(0) − A(ρ) ∝ ρ2. Analytic expressions for two-frequency mutual coherence function, pulse shape, temporal and angular spectra are presented in universal forms, and should be applicable to a large number of practical problems.

Relativistic nonlinear plasma waves in a 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.

The Momentum of Light in a Refracting Medium

Abstract: It is shown that neither Minkowski's result, according to which the ratio of momentum to energy for a light wave in a medium of refractive index n is n/c, nor that of Abraham, who found 1/nc, is correct. For a broad wave in a uniform medium, the correct answer is given by (2.12) with $\sigma =\frac{1}{5}$. For weak refraction it is approximately equal to the average of the Abraham and Minkowski results. Abraham's formula gives correctly the part of the momentum which resides in the electromagnetic field, but not the mechanical momentum of the medium which travels with the light pulse. Minkowski's formula gives the pseudo-momentum, a quantity of physical interest. The momentum change upon reflexion or transmission usually involves also acoustic transients, these are discussed for some simple cases.

A comparative study of three techniques for using the spectral matrix in wave analysis

Abstract: Digital power spectral analysis and coherency analysis are powerful techniques for studying ultra-low-frequency (ULF) waves in the earth's magnetosphere. Wave polarization parameters provided by these techniques are important in the development of theoretical models for wave generation. Because of this, it is important to understand the capabilities of the digital analysis techniques. Three different techniques of using the spectral matrix to do wave analysis have been presented in the literature. Because data for wave studies involve measurement in arbitrary coordinate systems, it is necessary to transform the spectral matrix to the principal plane of the wave before coherency analysis can be performed. The fundamental differences in the three techniques lie in how they determine the transformation to the principal plane. A comparative study of these three techniques was done using simulated data involving known wave and noise properties and real ULF wave event data from the geosynchronous satellites ATS 1 and ATS 6. In general, the quality of performance of the three different techniques on both simulated and real wave events was approximately the same.

On the adequacy of plane-wave reflection/transmission coefficients in the analysis of seismic body waves

Abstract: In order to estimate the effect (on body waves) of discontinuities within the Earth, it is common practice to use the theory for plane waves incident upon the plane boundary between two homogeneous half-spaces. The resulting reflection/P~ V conversion/transmission coefficients are shown here to he inaccurate for many problems of current interest. Corrected coefficients are needed, in particular, for cases where the discontinuity (upon which boundary conditions are to be applied) is near a turning point of the P- or S-wave rays, or if one of these rays intersects the discontinuity at a near-grazing angle. Adequate corrections, based upon the Langer approximation to a full wave theory, are shown to be easily derived in practice. The method is first to write out the plane-wave coefficients as a rational polynomial, in sines and cosines of the angles of incidence upon the boundary, and second to introduce a multiplicative factor for each cosine. The new factors depart from unity only when the associated cosine tends to zero; i.e., when a turning point is approached. They incorporate all the corrections required for curvature of the boundary, frequency dependence, and Earth structure (velocity gradients) near the boundary.

Two‐frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence

Abstract: Propagation characteristics of pulse waves in rain, fog, and turbulence are determined by a two-frequency mutual coherence function. Parabolic differential equations applicable to strong fluctuation cases are derived for the two-frequency mutual coherence function for randomly distributed scatterers and turbulence. These equations are solved for the plane wave case using the eigenfunction-eigenvalue method. Numerical calculations are given for millimeter waves (100 GHz) and optical waves (0.6943 and 10.6 μm) in rain, fog, and turbulence over the distance of 5 km. The coherence bandwidths are found to be in the range of MHz for millimeter waves (100 GHz) in heavy rain (25 mm/hr) and for optical waves in fog, and considerable distortion of pulse shape may result in these situations. For other cases, the effect on pulse shape distortion may be negligibly small.

Influence of a circularly polarized electromagnetic wave on a magnetized plasma.

Abstract: A dispersion relation is derived for a magnetized plasma in which a large amplitude circularly polarized wave propagates along the external magnetic field. It is shown that new modes, which appear due to relativistic effects, can be unstable.

Asymptotic approximations to angular-spectrum representations

Abstract: Under rather general conditiosn a time‐harmonic wave field u (x,y,z) can be represented in a half‐space z≳0 by a double integral known as the angular spectrum of plane waves. The representation divides naturally into the sum of two double integrals, one of which (uH) is a superposition of homogeneous plane waves and the other (ui) is a superposition of inhomogeneous plane waves. We obtain asymptotic approximations to u (x,y,z), uH, and UI valid when the point of observation of the field recedes towards infinity in a fixed direction through a fixed point. The results apply when the spectral amplitude of the plane waves belongs to a specific class which arises frequently in applications. Our approach is based on the method of stationary phase, which we extend in order to permit the presence of inhomogeneous waves in the integrand. Although the analysis of u requires that we distinguish the directions that are perpendicular to the z axis from the directions pointing into the half‐space z≳0, the results for t...

Radiation of electromagnetic fields in uniaxially anisotropic media

Abstract: The angular spectrum of plane-waves representation is obtained for the electromagnetic field radiated by a localized current source in a biaxially anisotropic medium. The linear medium is homogeneous throughout all space. It may be absorbing and temporally dispersive but is not spatially dispersive. The conductivity and the permeability are scalar constants. The time behavior of the current is arbitrary except that its magnitude is always bounded and it is zero prior to a fixed finite time. The representation of monochromatic fields radiated by time-harmonic sources is included also in the results. The radiated field is expressed as a superposition of monochromatic extraordinary plane waves propagating in various directions. The spectral amplitudes of the plane waves are determined explicitly in terms of the source. The guide axis of the representation coincides with one of the principal axes of the medium. The form of the solution is particularly appropriate for the study of diffraction, reflection, and refraction at plane boundaries normal to one of the principal axes of the medium.

Self-modulation and filamentation of electromagnetic waves in a plasma

Abstract: Self-modulation and filamentation of an electromagnetic wave is considered as a problem of the nonlinear interaction between electromagnetic and ion waves. A new electro-magnetic modulational instability is obtained, whose threshold is the same as that of the oscillating two-stream instability. A simple geometrical model is given of filamentation when the non-linearity is due to the ponderomotive force. The relationship between the filamentation and electromagnetic modulational instabilities and other parametric instabilities is considered. In particular, it is shown that both electromagnetic modulational and filamentation instabilities can occur at the critical density where they have the same threshold as the modulational instability of a Langmuir wave. Finally, a conservation relation (a generalization of the Manley-Rowe relation) for the wave action density is obtained for the filamentation instability. This shows clearly that this instability results from a four wave interaction.

Spherical-wave theory of the zero-absorption LLL X-ray or neutron interferometer

Abstract: Amplitude and intensity distributions within the outgoing beams of the triple-Laue-case (LLL) interferometer have been calculated for the case of zero absorption, which in practice is predominantly encountered with thermal neutrons. The type-1 wavefield with antinodes on the atomic sites, which with X-rays is quite frequently anomalously attenuated in the lattice, is here fully taken into account together with the type-2 wavefield of anomalous low absorption. After the combined diffraction by beam splitter, mirror, and analyser crystal of the interferometer for an incident plane wave has been solved, the solution for an incident spherical wave is developed by Fourier expansion, by a similar method to that first given by Kato [Acta Cryst. (1961), 14, 526–532] for just one diffracting crystal plate. In order to optimize the interferometer geometry spatial intensity profiles as functions of the geometric dimensions of the interferometer and of the phase shift between the interfering beams are calculated. The influence of deviations from the ideal geometry is investigated. Deviations of the order of the extinction length can result in a drastic reduction of interference contrast. Very good energy-converging and contrast properties are found if tM = 2tS= 2tA where tM, tS, tA are the thicknesses of mirror, beam splitter, and analyser respectively. The calculated intensity profiles are in agreement with preliminary experimental profiles obtained recently with a silicon interferometer at the HFR in Grenoble.

Electromagnetic Field Penetration into a Cylindrical Cavity

Abstract: For an E-polarized plane wave incident on a perfectly conducting cylindrical shell having a longitudinal slit aperture, the fields inside the cavity are determined by a numerical solution of the E-field integral equation. Selected data are presented and the first few complex frequency (SEM) singularities are determined for a variety of aperture sizes.

Multiple-plane wave calculation of the electron–phonon interaction in Al

Abstract: We have computed from first principles the electron–phonon spectral weight αk2(ω)Fk(ω) for many points k on the aluminum Fermi surface (FS). According to Migdal's theorem this spectral weight completely determines the self-energy of the electrons. The calculations involve an integral over final states on the Fermi surface which we calculate from Ashcroft's 4-plane wave pseudopotential model fit to the de Haas–van Alphen data. For the electron–phonon matrix element 15 plane waves are included. The phonons are taken from a Born–von Karman model fit to the measured dispersion curves. From the spectral weights we compute the Fermi surface variation of the electron–phonon effective mass and the quasiparticle lifetimes at various temperatures.

Exact theory of te-wave scattering from blazed dielectric gratings

Abstract: We present an exact description of scattering of an incident plane wave with te-polarization at an interface between two dielectric media that is deformed by a grating with triangularly shaped teeth. The theory employs an expansion in plane waves outside of the grating region and describes the field in the grating region as a double Fourier series expansion. The results of this theory are represented graphically. That blazing provides substantial discrimination of the scattering process in favor of beams scattered into one or the other of the two media is shown. The exact theory is used to check an approximation for the effective reflection plane that is useful for future applications of the theory to scattering by gratings of guided waves in thin-film waveguides.

Magnetoelastic surface waves in a magnetic film-piezoelectric substrate configuration

Abstract: This paper treats the propagation characteristics of magnetoelastic surface waves in a delay line consisting of a ferromagnetic film deposited on a piezoelectric substrate Magnetoelastic coupling within the film and mechanical coupling between the film and substrate enables the acoustic velocity to be varied by changing the magnetic bias field A theory to predict the dependence of the surface wave velocity upon applied dc magnetic field, material constants, and frequency is presented The velocity change occurs predominantly in a bias field range where the static magnetization vectors are undergoing a rotation The two orientations of the magnetic field in the sagittal plane considered exhibit significantly different characteristics With the field parallel to the direction of propagation the velocity first decreases, attains a minimum, and then increases toward a saturation value as the external field is increased With the field normal to the plane of the film, the velocity increases monotonically toward a saturation value with an increase in field The calculated velocity changes are in good agreement with changes measured on a Ni‐LiNbO3 delay line

Formation of hologram

Abstract: PURPOSE: To eliminate astigmatism and image distorsion, even if the wave fronts are made different upon formation and reproduction of FZP (Fresnel Zone Plate), by making plane waves incident at an angle upon the surface of a photosensitive material while fixing the angle between the plane waves and spherical waves COPYRIGHT: (C)1978,JPO&Japio

Differential cross sections for weak-field gravitational scattering

Abstract: Differential cross sections are presented for the scattering of plane scalar, electromagnetic, and gravitational waves from the gravitational field of sources in the weak-field approximation. Comparison is made with the long- wavelength limit of analogous scattering off of spherical black holes. (AIP)

Electromagnetic scattering of an arbitrary plane wave by a wire mesh with bonded junctions

Abstract: A doubly infinite set of linear equations for the currents has been found valid for a wire mesh with bonded junctions without imposing any junction conditions. However, the convergence of the solution is greatly improved by building junction discontinuity conditions into the current representation. Using such a modified solution, numerical results are generated to illustrate the dependence of reflection and transmission coefficients on various parameters.

e-He atoms elastic scattering at intermediate energies

Abstract: The differential cross section obtained in the plane wave approximation for the elastic scattering of electrons of energy equal to and greater than 200 eV by helium atoms are in good agreement (within about 10%) with recent experimental data.