Showing papers on "Plane wave published in 1995"
Book•
31 May 1995
TL;DR: This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.
Abstract: Part 1 Reinventing electromagnetics: background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology. Part 2 The one-dimensional scalar wave equation: propagating wave solutions finite-difference approximation of the scalar wave equation dispersion relations for the one-dimensional wave equation numerical group velocity numerical stability. Part 3 Introduction to Maxwell's equations and the Yee algorithm: Maxwell's equations in three dimensions reduction to two dimensions equivalence to the wave equation in one dimension. Part 4 Numerical stability: TM mode time eigenvalue problem space eigenvalue problem extension to the full three-dimensional Yee algorithm. Part 5 Numerical dispersion: comparison with the ideal dispersion case reduction to the ideal dispersion case for special grid conditions dispersion-optimized basic Yee algorithm dispersion-optimized Yee algorithm with fourth-order accurate spatial differences. Part 6 Incident wave source conditions for free space and waveguides: requirements for the plane wave source condition the hard source total-field/scattered field formulation pure scattered field formulation choice of incident plane wave formulation. Part 7 Absorbing boundary conditions for free space and waveguides: Bayliss-Turkel scattered-wave annihilating operators Engquist-Majda one-way wave equations Higdon operator Liao extrapolation Mei-Fang superabsorption Berenger perfectly-matched layer (PML) absorbing boundary conditions for waveguides. Part 8 Near-to-far field transformation: obtaining phasor quantities via discrete fourier transformation surface equivalence theorem extension to three dimensions phasor domain. Part 9 Dispersive, nonlinear, and gain materials: linear isotropic case recursive convolution method linear gyrontropic case linear isotropic case auxiliary differential equation method, Lorentz gain media. Part 10 Local subcell models of the fine geometrical features: basis of contour-path FD-TD modelling the simplest contour-path subcell models the thin wire conformal modelling of curved surfaces the thin material sheet relativistic motion of PEC boundaries. Part 11 Explicit time-domain solution of Maxwell's equations using non-orthogonal and unstructured grids, Stephen Gedney and Faiza Lansing: nonuniform, orthogonal grids globally orthogonal global curvilinear co-ordinates irregular non-orthogonal unstructured grids analysis of printed circuit devices using the planar generalized Yee algorithm. Part 12 The body of revolution FD-TD algorithm, Thomas Jurgens and Gregory Saewert: field expansion difference equations for on-axis cells numerical stability PML absorbing boundary condition. Part 13 Modelling of electromagnetic fields in high-speed electronic circuits, Piket-May and Taflove. (part contents).
11,194 citations
TL;DR: In this article, the sensitivity to variations in direction of the primary pseudo-plane beam which occurs on boundaries between media with slight differences in density values is impressive. And two types of contrasts are pointed out: area contrast caused by slight deviation of the beam and boundary contrast.
Abstract: A technique for observation of the inner structure of objects is proposed The sensitivity to variations in direction of the primary pseudo-plane beam which occurs on boundaries between media with slight differences in density values is impressive Two types of contrasts are pointed out: 'area contrast' caused by slight deviation of the primary beam and 'boundary contrast' Basic principles and experimental results are presented
409 citations
TL;DR: In this paper, the projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and the ones based on atomic orbitals.
Abstract: The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and the ones based on atomic orbitals. Given a candidate atomic basis, ({\it i}) its quality is evaluated by its projection into the plane-wave eigenfunctions, ({\it ii}) it is optimized by maximizing that projection, ({\it iii}) the associated tight-binding Hamiltonian and energy bands are obtained, and ({\it iv}) population analysis is performed in a natural way. The proposed method replaces the traditional trial-and-error procedures of finding appropriate atomic bases and the fitting of bands to obtain tight-binding Hamiltonians. Test calculations of some zincblende semiconductors are presented.
349 citations
TL;DR: In this paper, the projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and the ones based on atomic orbitals.
343 citations
DOI•
11 Aug 1995TL;DR: In this article, a solution for combined wave-current turbulent bottom boundary layer flows with the wave motion specified by its near-bottom orbital velocity directional spectrum is obtained based on the linearized governing equations, a bottom roughness specified by the equivalent Nikuradse sand grain roughness, fcjv, and a time invariant eddy viscosity analogous to that of Grant and Madsen (1979 and 1986).
Abstract: Based on the linearized governing equations, a bottom roughness specified by the equivalent Nikuradse sand grain roughness, fcjv, and a timeinvariant eddy viscosity analogous to that of Grant and Madsen (1979 and 1986) the solution is obtained for combined wave-current turbulent bottom boundary layer flows with the wave motion specified by its near-bottom orbital velocity directional spectrum. The solution depends on an a priori unknown shear velocity, u*r, used to scale the eddy viscosity inside the wave boundary layer. Closure is achieved by requiring the spectral wavecurrent model to reduce to the Grant-Madsen model in the limit of simple periodic plane waves. To facilitate application of the spectral wave-current model it is used to define the characteristics (near-bottom orbital velocity amplitude, U(,r, radian frequency, uir, and direction of propagation, 4>wr) of a representative periodic wave which, in the context of combined wavecurrent bottom boundary layer flows, is equivalent to the wave specified by its directional spectrum. Pertinent formulas needed for application of the model are derived and their use is illustrated by outlining efficient computational procedures for the solution of wave-current interaction for typical specifications of the current
342 citations
TL;DR: In this article, the density of a molecule expanded in plane waves is decoupled from its periodic images using a fit to atom-centered Gaussians, which reproduces the long-range electrostatic potential of the original density.
Abstract: The density of a molecule expanded in plane waves is decoupled from its periodic images using a fit to atom‐centered Gaussians, which reproduces the long‐range electrostatic potential of the original density. The interaction energy between the cluster and its periodic images is calculated by an Ewald summation. The method has been applied to self‐consistent ab initio molecular dynamics calculations of charged and polar molecules. An atomic point charge model of the charge density is obtained, which can be used for classical molecular dynamics models and to couple classical and quantum mechanical simulations.
212 citations
TL;DR: In this article, the analytical partial derivatives of the plane wave EXAFS function can be calcalated using cubic spline, which decreases the CPU time needed for a refinement by over 60% for a three shell system compared to a refinement with partial derivaties calculated with the finite difference method.
Abstract: Parameterization of phase and backscattering amplitude with cubic splines is described. Using the cubic spline, the analytical partial derivatives of the plane wave EXAFS function can be calcalated. The use of analytical partial derivatives decreases the CPU time needed for a refinement by over 60% for a three shell system compared to a refinement with partial derivaties calculated with the finite difference method.
198 citations
15 Jun 1995
TL;DR: In this article, an analysis of optical propagation through turbulence which causes fluctuations in the index of refraction is presented. But the authors assume that the index fluctuations are assumed to have spatial power spectra that obey arbitrary power laws and do not obey Kolmogorov's power spectral density model.
Abstract: Several observations of atmospheric turbulence statistics have been reported which do not obey Kolmogorov's power spectral density model. These observations have prompted the study of optical propagation through turbulence described by non-classical power spectra. This paper presents an analysis of optical propagation through turbulence which causes fluctuations in the index of refraction. The index fluctuations are assumed to have spatial power spectra that obey arbitrary power laws. The spherical and plane wave structure functions are derived using Mellin transform techniques. The wave structure function is used to compute the Strehl ratio of a focused plane wave propagating in turbulence as the power law for the spectrum of the index of refraction fluctuations is varied from -3 to -4. The relative contributions of the log amplitude and phase structure functions to the wave structure function are computed. At power laws close to -3, the magnitude of the log amplitude and phase perturbations are determined by the system Fresnel ratio. At power laws approaching -4, phase effects dominate in the form of random tilts.
184 citations
TL;DR: In this article, a Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound-soft or perfectly conducting arc from a knowledge of the far-field pattern for the scattering of time-harmonic plane waves.
Abstract: A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound-soft or perfectly conducting arc from a knowledge of the far-field pattern for the scattering of time-harmonic plane waves. Frechet differentiability with respect to the boundary is shown for the far-field operator, which for a fixed incident wave maps the boundary arc onto the far-field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.
177 citations
TL;DR: It was shown that the uncoupled mode, or the mode that cannot be excited by an external plane wave, which was previously found for the triangular lattice by the numerical calculation of the transmittance, is an antisymmetric mode under the relevant mirror reflection, and this fact is consistent with the observation by Robertson et al.
Abstract: The photonic bands of two-dimensional triangular and square lattices composed of circular rods were classified by means of the group theory based on the symmetry of the lattice structure. According to this classification, it was shown that the uncoupled mode, or the mode that cannot be excited by an external plane wave, which we previously found for the triangular lattice by the numerical calculation of the transmittance, is an antisymmetric mode under the relevant mirror reflection, and this fact is consistent with the observation by Robertson et al. It was also shown that triangular and square lattices with ${\mathit{C}}_{6\mathit{v}}$ or ${\mathit{C}}_{4\mathit{v}}$ symmetry have many other uncoupled modes with relatively low eigenfrequencies and some of them can be easily identified as the spectral ranges of total reflection in spite of their nonzero state density.
164 citations
TL;DR: In this article, the authors derived approximate energy models for infinite and finite plates using three relationships; an energy balance, a loss factor damping model and an approximate energy transmission model, which is analogous to Fourier's law of heat conduction.
TL;DR: In this article, a test electron is trapped in a nonlinear, cold fluid model and the maximum energy gain and the minimum energy required for trapping of the test electron are determined.
Abstract: The trapping and acceleration of a test electron in a nonlinear plasma wave is analyzed in one dimension using Hamiltonian dynamics. The plasma wave is described by a nonlinear, cold fluid model. The maximum energy gain and the minimum energy required for trapping of the test electron are determined. The separatrix is plotted for several values of plasma wave amplitude. In the large wave amplitude limit, the maximum energy of a trapped electron scales as 2γ2pE2z, where γp is the relativistic factor associated with plasma wave phase velocity and Ez is the electric field amplitude of the nonlinear plasma wave. This is in contrast to the well‐known results for a sinusoidal wave, in which the maximum energy scales as 4γ2pEz. As the nonlinear plasma wave approaches wavebreaking, the maximum energy is given by γmax→4γ3p−3γp, where γmax is the relativistic factor of the trapped electron.
TL;DR: In this paper, Hladky-Hennion et al. presented a new extension of the finite element approach to the analysis of the propagation of plane acoustic waves in passive periodic materials without losses and described its application to doubly periodic materials containing different types of inclusions.
Abstract: The finite element approach has been previously used, with the help of the ATILA code, to model the scattering of acoustic waves by single or doubly periodic passive structures [A. C. Hladky‐Hennion et al., J. Acoust. Soc. Am. 90, 3356–3367 (1991)]. This paper presents a new extension of this technique to the analysis of the propagation of plane acoustic waves in passive periodic materials without losses and describes with particular emphasis its application to doubly periodic materials containing different types of inclusions. In the proposed approach, only the unit cell of the periodic material has to be meshed, thanks to Bloch–Floquet relations. The modeling of these materials provides dispersion curves from which results of physical interest can be easily extracted: identification of propagation modes, cutoff frequencies, passbands, stopbands, as well as effective homogeneous properties. In this paper, the general method is first described, and particularly the aspects related to the periodicity. Then a test example is given for which analytical results exist. This example is followed by detailed presentations of finite element results, in the case of periodic materials containing inclusions or cylindrical pores. The homogenized properties of porous materials are determined with the help of an anisotropic model, in the large wavelength limit. A validation has been carried out with periodically perforated plates, the resonance frequencies of which have been measured. The efficiency and the versatility of the method is thus clearly demonstrated.
TL;DR: Cesium atoms prepared in a state of well-defined total energy have been reflected from a vibrating mirror, causing the matter waves to be phase modulated, and the resulting beam consists of a “carrier” plus various sidebands corresponding to de Broglie waves propagating at different velocities.
Abstract: Cesium atoms prepared in a state of well-defined total energy have been reflected from a vibrating mirror, causing the matter waves to be phase modulated. The mirror is an evanescent light wave whose intensity is modulated in time at a frequency $\ensuremath{
u}$ in the range 0 to 2 MHz; the atoms are reflected at normal incidence. The resulting beam consists of a ``carrier'' plus various sidebands corresponding to de Broglie waves propagating at different velocities. The precision and flexibility of this technique make it a promising tool in atom optics.
TL;DR: In this paper, a comparison of light propagation simulation methods in the Fresnel region is presented, based on the Kirchhof scalar theory of diffraction, and the simulated results are verified in an experimental optical setup.
TL;DR: Quantitative error analyses for the simulation of wave propagation in three-dimensional random media, when narrow angular scattering is assumed, are presented for plane-wave and spherical-wave geometry.
Abstract: Quantitative error analyses for the simulation of wave propagation in three-dimensional random media, when narrow angular scattering is assumed, are presented for plane-wave and spherical-wave geometry. This includes the errors that result from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive indices of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared with the spatial spectra of intensity. The numerical requirements for a simulation of given accuracy are determined for realizations of the field. The numerical requirements for accurate estimation of higher moments of the field are less stringent.
TL;DR: The quantized surface mode technique is used to evaluate the interaction V of a ``particle'' (an electron or atom) with two sets of plane parallel walls of arbitrary thicknesses and arbitrary permittivities and shows that it can be treated as a single wall with an effective reflection coefficient scrR.
Abstract: We use the quantized surface mode technique to evaluate the interaction V of a ``particle'' (an electron or atom) with two sets of plane parallel walls of arbitrary thicknesses and arbitrary permittivities; one set is on one side of the particle and the other set is on the other side. It is shown that a set of walls on either side of the particle can be treated as a single wall with an effective reflection coefficient scrR, a function of the frequency and angle of incidence of an incoming plane wave. The two sets of walls have thereby been effectively reduced to one wall on each side. Using a modified version of the standard image technique\char22{}the locations of the images are the usual ones, but the strengths are modified\char22{}one finds that the closed form for V can be reexpressed as a sum of interactions of the set of images on a given side with the wall on the other side. Taking various limits (thin walls, thick walls, metallic walls, dilute media) reproduces many known interactions and also provides a number of results not previously obtained. The latter results enable us to give quantitative estimates of the error incurred in approximating a wall of finite thickness by a wall of semi-infinite thickness, or approximating a wall with large permittivity by a wall of infinite permittivity. In an attempt to make the paper user friendly, we provide a tabulation of many of the short-range (van der Waals-like) and long-range (retardation) interactions now known, with equation references.
TL;DR: In this paper, the dispersion characteristics of sound waves propagating in a tunnel with an array of Helmholtz resonators connected axially are examined. And the validity of the continuum approximation for distribution of the resonators is discussed in terms of dispersion relations, though subjected intrinsically not only to weak damping due to the dissipative effects but also to the weak dispersion due to wall friction.
Abstract: This paper examines dispersion characteristics of sound waves propagating in a tunnel with an array of Helmholtz resonators connected axially. Assuming plane waves over the tunnel’s cross section except a thin boundary layer, weakly dissipative effects due to the wall friction and the thermoviscous diffusivity of sound are taken into account. Sound propagation in such a spatially periodic structure may be termed ‘‘acoustic Bloch waves.’’ The dispersion relation derived exhibits peculiar characteristics marked by emergence of ‘‘stopping bands’’ in the frequency domain. The stopping bands inhibit selectively propagation of sound waves even if no dissipative effects are taken into account, and enhance the damping pronouncedly even in a dissipative case. The stopping bands result from the resonance with the resonators as side branches and also from the Bragg reflection by their periodic arrangements. In the ‘‘passing bands’’ outside of the stopping bands, the sound waves exhibit dispersion, though subjected intrinsically not only to the weak damping due to the dissipative effects but also to the weak dispersion due to the wall friction. Taking a plausible example, the dispersion relation and the Bloch wave functions for the pressure are displayed. Finally the validity of the continuum approximation for distribution of the Helmholtz resonators is discussed in terms of the dispersion relations.
TL;DR: In this paper, a comparison of various time domain numerical techniques to model material dispersion is presented, and the superiority of the new method, in terms of accuracy and computer resources, over four previously published techniques is demonstrated on the problem of a transient electromagnetic plane wave propagating in a dispersive media.
Abstract: A comparison of various time domain numerical techniques to model material dispersion is presented. Methods that model the material dispersion via a convolution integral as well as those that use a differential equation representation are considered. We have shown how the convolution integral arising in the electromagnetic constitutive relation can be approximated by the trapezoidal rule of numerical integration and implemented using a newly derived one-time-step recursion relation. The superiority of the new method, in terms of accuracy and computer resources, over four previously published techniques is demonstrated on the problem of a transient electromagnetic plane wave propagating in a dispersive media. All of the methods considered are easily incorporated into 3-D codes where the requirement for efficiency is very important.
Book•
31 Oct 1995
TL;DR: In this article, the number of evolutionary segments on the Shock Adiabat and their types is shown to be a function of the evolution of Riemann wave properties.
Abstract: Mathematical Introduction Conservation Laws and Related Differential Equations. Hyperbolic Systems. Linear and Linearized Equations. Riemann Invariants. Boundary Conditions and Evolutionary Properties. Riemann Waves. Discontinuities and Relations on Them. Shock Adiabat. Evolutionary Conditions for Discontinuity. Low Intensity Discontinuities. Shock Adiabat Behavior in a Vicinity of the Jouget Point. Conservation Law in the Godunov Form. Entropy. Entropy Production and Entropy Density Change on a Discontinuity. Solutions with Discontinuities as a Limit of Continuous Solutions to Equations of a Complicated Model. Small Perturbations in Dissipative Media. Shock Wave Structure. On Plane Wave Problems in Elastic Media Elastic Medium Model. Governing Equations. Plane Wave Equations. Conditions on a Discontinuity. Shock Adiabat. Entropy Change Along the Shock Adiabat. Wave Isotropy and Anisotropy. Internal Energy of a Medium with Weak Wave Anisotropy. Elastic Potential for a Weakly Nonlinear Medium. Nonlinear Wave Propagation Through Media Interacting with Electromagnetic Fields. Riemann Waves Small Perturbations. Linear Waves. Equations for Riemann Waves. Quasilongitudinal Waves. Quasitransverse Riemann Wave. Parameter Variations in Quasitransverse Waves. Evolution of Quasitransverse Riemann Waves. Riemann Waves in the Case of Wave Isotropy. Shock Waves Relationships on a Weak Shock Wave. Quasilongitudinal Shock Waves. Quasitransverse Waves. Shock Adiabat. Entropy Nondecreasing Condition. Evolutionary Conditions on Shocks. Velocities in Quasitranverse Waves. The Number of Evolutionary Shock Waves and Their Types. Locations of Evolutionary Segments on the Shock Adiabat. Shock Transitions into a Given State. Special Forms of Initial Deformations. Quasitransverse Shock Waves for G/R2
TL;DR: The contributions of homogeneous and evanescent waves to two-dimensional near-field diffraction patterns of scalar optical fields are examined in detail and the total plane-integrated intensities of the two contributions are introduced as convenient measures of their relative importance.
Abstract: The contributions of homogeneous and evanescent waves to two-dimensional near-field diffraction patterns of scalar optical fields are examined in detail. The total plane-integrated intensities of the two contributions are introduced as convenient measures of their relative importance. As an example, the diffraction of a plane wave by a slit is considered.
TL;DR: In this article, a modified version of the Damon-Eshbach theory of magnetostatic waves for in-plane magnetized anisotropic films is presented, relative to the usual backward volume wave, non-reciprocal surface wave, and surface mode critical angle properties for isotropic films.
TL;DR: It is shown that there exist an infinite number of eigenvalues of the far field operator corresponding to the scattering of a time-harmonic plane wave by either an imperfectly conducting obstacle or an absorbing inhomogeneous medium.
Abstract: It is shown that there exist an infinite number of eigenvalues of the far field operator corresponding to the scattering of a time-harmonic plane wave by either an imperfectly conducting obstacle or an absorbing inhomogeneous medium. Regions in the complex plane are found where these eigenvalues must lie and, in the case of obstacle scattering, numerical examples are given showing how precise these regions are.
TL;DR: In this paper, the authors considered the problem of sound scattering by a pair of spheres, which can be strong or weak depending on their separation, compositions, frequency, and directions of observation, and the tools to attack this type of problem are the (forward/backward) addition theorems for the spherical wave functions.
Abstract: If acoustic scattering by a single sphere is the most basic problem of scalar scattering, then sound scattering by a pair of spheres is next in the hierarchy of complexity. The problem has been formulated by several approaches in the past, but no actual detailed studies have been openly published so far. Two spheres insonified by plane waves at arbitrary angles of incidence are considered. The solution of this simplest of multiple‐scattering problems is generated by exactly accounting for the interaction between the two spheres, which can be strong or weak depending on their separation, compositions, frequency, and directions of observation. The tools to attack this type of problem are the (forward/backward) addition theorems for the spherical wave functions, which permit the field expansions—all referred to the center of one of the spheres—by means of Wigner (3‐j) symbols. The fields scattered by each sphere are obtained as pairs of (double) sums in the spherical wave functions, with coefficients that are coupled through an infinite set of two linear, complex, algebraic equations. These are then solved (by truncation) and used to obtain (i) the scattered fields and (ii) the scattering cross section of the pair of spheres. These exact results are illustrated with many plots of the form functions at various relevant incidence angles, separations, frequencies, etc. Finally, some asymptotic approximations for this problem that are analytically simple are obtained. They are displayed and compared to the exact solutions found above, with quite satisfactory results, even for the simple approximations used here. Thus the phenomenon is described, explained, graphically displayed, physically interpreted, and reduced to a simple accurate approximation in some important cases.
TL;DR: In this article, a theoretical understanding of near edge structure calculation in solids is derived from various band theory methods with varying degrees of approximation, and a place for theories based on simple physical ideas as well as large sophisticated calculations.
TL;DR: In this paper, the authors consider the case of a standing wave confined in a bounded (square) domain, a case which can be directly compared with laboratory experiments, using a pseudo-spectral method with symmetries.
Abstract: The evolution of an internal gravity wave is investigated by direct numerical computations. We consider the case of a standing wave confined in a bounded (square) domain, a case which can be directly compared with laboratory experiments. A pseudo-spectral method with symmetries is used. We are interested in the inertial dynamics occurring in the limit of large Reynolds numbers, so a fairly high spatial resolution is used (1292 or 2572), but the computations are limited to a two-dimensional vertical plane. We observe that breaking eventually occurs, whatever the wave amplitude: the energy begins to decrease after a given time because of irreversible transfers of energy towards the dissipative scales. The life time of the coherent wave, before energy dissipation, is found to be proportional to the inverse of the amplitude squared, and we explain this law by a simple theoretical model. The wave breaking itself is preceded by a slow transfer of energy to secondary waves by a mechanism of resonant interactions, and we compare the results with the classical theory of this phenomenon: good agreement is obtained for moderate amplitudes. The nature of the events leading to wave breaking depends on the wave frequency (i.e. on the direction of the wave vector); most of the analysis is restricted to the case of fairly high frequencies. The maximum growth rate of the inviscid wave instability occurs in the limit of high wavenumbers. We observe that a well-organized secondary plane wave packet is excited. Its frequency is half the frequency of the primary wave, corresponding to an excitation by a parametric instability. The mechanism of selection of this remarkable structure, in the limit of small viscosities, is discussed. Once this secondary wave packet has reached a high amplitude, density overturning occurs, as well as unstable shear layers, leading to a rapid transfer of energy towards dissipative scales. Therefore the condition of strong wave steepness leading to wave breaking is locally attained by the development of a single small-scale parametric instability, rather than a cascade of wave interactions. This fact may be important for modelling the dynamics of an internal wave field.
TL;DR: In this article, it was shown that the plane wave spectrum representation of Hill et al. can also be used to provide a simple derivation for the spatial correlation function of the fields.
Abstract: Hill, Crawford, Kanda and Wu (see ibid., vol.35, p.69, 1993) described random fields in a reverberation chamber by an integral representation of plane waves over all real angles. A physical interpretation of the random field in a reverberation chamber is that each member of the ensemble corresponds to a different stirrer (tuner) position. The plane wave spectrum representation has been found useful for providing a mathematical description for the response of a receiving antenna or other test object in a reverberation chamber and for calculating the quality factor (Q) for reverberation chambers of arbitrary geometries. This article shows that the plane wave spectrum representation of Hill et. al. can also be used to provide a simple derivation for the spatial correlation function of the fields. >
TL;DR: Wahtund et al. as mentioned in this paper theoretically explore the relationship of a class of low-frequency nonlinear oblique plasma waves to recent Freja satellite observations of solitary kinetic Alfv6n waves, hereafter called SKAW.
Abstract: One-dimensional models of obliquely propagating nonlinear plasma waves were formulated and solved both analytically and numerically to interpret recent Freja satellite observations of low-frequency plasma waves detected in the low-Mtitude auroral magnetosphere. Analytic calculations revealed four types of steady state waves solutions. Time dependent initial value numerical calculations were compared to the steady state solutions and to Freja observations. One type of steady state wave solution emerged in the long time limit from the initial sinusoidal waves; however, the initial value simulations agreed best with the observations during the nonlinear steepening phase of the initial waveform at a time well before a steady state ws reached. From this result we concluded that many of the low altitudeuroral waves Freja has detected were oblique inertial Alfv6n waves that had nonlinearly steepened due to propagation into a region of lower Alfv6n speed. The nonlinear steepening was found to produce very large parallel currents. The current is sufficiently high to excite prallel electron drift instabilities, which may lead to electronnd ion energiztion and enhanced dissipation of auroral arc energy. 1.1. Scope of Work In this paper we theoretically explore the relationship of a class of low-frequency nonlinear oblique plasma waves to recent Freja satellite observations of solitary kinetic Alfv6n waves, hereafter called SKAW (Wahtund el at., 1994a; Louarn el at., 1994). We investigated low-frequency w < fi and small-scale L_ c/w e one- dimensional plane waves having a phase front oriented at a small angle aV/rolM to the geomagnetic field. These waves are commonly called inertial Alfvdn waves (Lysak and Dum, 1983; $eyter, 1990; Lysak, 1990; Hui and Seyler, 1992) and are widely believed to be a fun- damental aspect of small-scale auroral arcs. We formulated a one-dimensional fluid theory of iner- tial Alfvdn waves which included thermal electron and ion effects. We found analytic steady state solutions and compared the results to numerically determined time dependent initial value solutions. These solutions were then compared to se!ected Freja observations. The excellent agreement we found led us to important con-
TL;DR: The FDTD technique is well suited for calculating the fields scattered by buried objects when the sources are close enough to the air/ground interface so that they can be incorporated into the solution space.
Abstract: The FDTD technique is well suited for calculating the fields scattered by buried objects when the sources are close enough to the air/ground interface so that they can be incorporated into the solution space. Difficulties arise, however, when the sources are far from the interface since the total fields in the solution space are not all outgoing waves. Using well-known formulas for the fields transmitted and reflected by stratified media, this paper discusses a method whereby the fields scattered by a buried object can be easily calculated by the FDTD technique when the incident field is a plane wave. >
TL;DR: In this article, a full wave, formally exact solution for the problem of scattering at the junction of a rectangular waveguide and a larger circular waveguide is obtained for the general case of an arbitrary offset of the waveguide axes.
Abstract: A full wave, formally exact solution is obtained for the problem of scattering at the junction of a rectangular waveguide and a larger circular waveguide. The general case of an arbitrary offset of the waveguide axes is considered. E-field mode matching over the rectangular aperture of the smaller guide is facilitated by a transformation of the circular cylindrical Bessel-Fourier modal fields of the circular guide into a finite series of exponential plane wave functions in rectangular coordinates. This permits an analytical finite series solution for each of the elements of the E-field mode matching matrix [M] from which the scattering matrix [S] of the junction is easily obtained. Numerical evaluation of the S-parameters for the dominant TE/sub 10/ (rectangular) and TE/sub 11/ (circular) modes in the cases of junctions with no offset and with offset is presented. Moreover, the practical case of a circular cavity resonator with smaller input and output rectangular guides is considered and excellent agreement is found between the calculated and measured S-parameters. >