Showing papers on "Plane wave published in 1998"

Plane wave integral representation for fields in reverberation chambers

Abstract: A plane wave integral representation is presented for well-stirred fields in a reverberation chamber. The representation automatically satisfies Maxwell's equations in a source-free region and the statistical properties of the fields are introduced through the angular spectrum, which is taken to be a random variable. Starting with fairly simple and physically appropriate assumptions for the angular spectrum, a number of properties of the electric and magnetic fields and the power received by an antenna or a test object are derived. Many of these properties and test object responses are in agreement with other theories or with measured results. An important result for radiated immunity testing is that the ensemble (stirring) average of received power is equal to the average over plane wave incidence and polarization.

Fundamentals of Polarized Light: A Statistical Optics Approach

Abstract: HISTORIAL SURVEY OF UNDERSTANDING OF POLARIZED LIGHT. First Period: Early Ideas and Observations-from Bartholinus to Stokes. Second Period: The Electromagnetic Nature of Light. Third Period: The Coherence and Quantum Properties of Light. PRELIMINARIES TO A CLASSICAL RADIATION FIELD THEORY. The Basic Differential Equations and Boundary Conditions. Invariance Transformations. Monochromatic Plane Wave. POLARIZATION AND THE RADIATION FIELD. Elementary Concepts and Definitions. Geometric Representations of Partially Polarized Light. Statistics of the Radiation Field. Entropy of the Radiation Field. INTERACTION OF RADIATION WITH LINEAR MEDIA. Jones and Mueller Polarization Transfer Matrix Methods. Polarization Effects at Dielectric Interfaces. Polarized Light and Symmetry Transformations. Random Media. APPLICATIONS TO SELECTED TOPICS. Electromagnetic Propagation in Linear Anisotropic Media. Optical Polarizing Components. Measurement of Stokes Parameters. Measurement of Jones and Mueller Polarization Matrices. Appendices. Indexes.

Geometric wave equations

Abstract: The wave equation Conservation laws Function spaces The linear wave equation Well-posedness Semilinear wave equations Wave maps Wave maps with symmetry Notes Bibliography

Electromagnetic Processes at High Energies in Oriented Single Crystals

Abstract: A Theory of Radiation and Pair Creation in External Field The Quasiclassical Method of Describing the Radiation of High-Energy Particles Pair Production by a Photon in an External Field Radiation of Particles Moving Quasiperiodically and in a Superpositon of a Plane Wave and a Constant Field Fast Particles Penetration in Single Crystals Pair Production in Aligned Single Crystal Emission of Radiation by High-Energy Particles in Oriented Single Crystals Electromagnetic Radiation of Particles in Channelling Some Further Problems of the Theory of Electromagnetic Processes in Aligned Single Crystals. (Part contents).

Electromechanical wave propagation in large electric power systems

Abstract: An electrical power network consisting of generators and transmission lines is treated as a continuum system. The application of the limit of zero generator spacing, with finite rotor inertia and transmission line impedance per unit length, yields a nonlinear partial differential equation in time and two spatial dimensions for the rotor phase angle. The equation is a nonlinear version of the standard second-order wave equation which exhibits an explicit expression for the finite wave phase velocity. The electromechanical wave propagation characteristics, equilibrium solutions, and linear stability are investigated and some potentially important results are presented. Numerical simulations of the usual discrete generator model, based upon the swing equation, are presented and demonstrate the electromechanical wave propagation as having interesting properties. Numerical solutions of the analogous continuum model are compared to the discrete model and are found to be in excellent agreement. A numerical estimate of the wave phase velocity for the U.S. power grid is consistent with observations of the transient wave phenomena during staged fault events. The continuum model enables an array of alternative analytic and simulation methods to be applied to the study of global power system characteristics, such as stability and transient dynamics.

Electromechanical wave propagation in large electric power systems

Abstract: An electrical power network consisting of generators and transmission lines is treated as a continuum system. The application of the limit of zero generator spacing, with finite rotor inertia and transmission line impedance per unit length, yields a nonlinear partial differential equation in time and two spatial dimensions for the rotor phase angle. The equation is a nonlinear version of the standard second-order wave equation which exhibits an explicit expression for the finite wave phase velocity. The electromechanical wave propagation characteristics, equilibrium solutions, and linear stability are investigated and some potentially important results are presented. Numerical simulations of the usual discrete generator model, based upon the swing equation, are presented and demonstrate the electromechanical wave propagation as having interesting properties. Numerical solutions of the analogous continuum model are compared to the discrete model and are found to be in excellent agreement. A numerical estimate of the wave phase velocity for the U.S. power grid is consistent with observations of the transient wave phenomena during staged fault events. The continuum model enables an array of alternative analytic and simulation methods to be applied to the study of global power system characteristics, such as stability and transient dynamics.

Spherical wave near-field imaging and radar cross-section measurement

Abstract: The paper presents a new inverse synthetic aperture radar (ISAR) algorithm intended for radar cross-section (RCS) imaging and measurement from scattered fields. The method, based on a spherical-wave near-field illumination of the target, overcomes the requirement for an expensive compact range facility to produce a plane wave illumination. The formulation and the implementation of the algorithm are described. Some experimental results obtained in an anechoic chamber are presented to show RCS results similar to the conventional plane wave methods.

Diffraction by volume gratings with imaginary potentials

Abstract: A medium described by an imaginary potential (or imaginary (refractive index) 2 ), that varies sinusoidally in one direction, acts as a volume grating for plane waves incident on it obliquely or normally. Two peculiar features are identified. First, if the potential is weak, so that there are only two significant diffracted beams near the Bragg angle, and three for normal incidence, diffraction is strongly affected by degeneracies of the non-Hermitian matrix generating the 'Bloch waves' in the grating; the effect of these degeneracies is very different from that of the Hermitian degeneracies for transparent gratings. Second, if the potential is strong and the grating thick, the asymptotic distribution of intensities among the diffracted beams (momentum distribution) is a rather narrow Gaussian, and dominated by a single set of complex rays; this is very different from the semiclassical limit for transparent gratings, where the rays form families of caustics proliferating with thickness, and with a wider momentum distribution.

Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices

Abstract: We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we reproduce the main features of the spectrum obtained by the plane wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eights and ninth bands if the dielectric constant $\epsilon_s$ of spheres is lower than the dielectric constant $\epsilon_b$ of the background medium. If $\epsilon_s> \epsilon_b$, no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast $\epsilon_b/\epsilon_s$ for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of an fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.

Terminal damping of a solitary wave due to radiation in rotational systems

Abstract: The evolution of a solitary wave under the action of rotation is considered within the framework of the rotation-modified Korteweg–de Vries equation. Using an asymptotic procedure, the solitary wave is shown to be damped due to radiation of a dispersive wave train propagating with the same phase velocity as the solitary wave. Such a synchronism is possible because of the presence of rotational dispersion. The law of damping is found to be “terminal” in the sense that the solitary wave disappears in a finite time. The radiated wave amplitude and the structure of the radiated “tail” in space–time are also found. Some numerical results, which confirm the approximate theory developed here, are given.

Electromagnetic scattering by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate

Abstract: We consider a two-dimensional problem of scattering of a time harmonic electromagnetic plane wave by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate. The magnetic permeability is assumed to be a fixed positive constant in the media. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and a positive constant above the layer corresponding to a homogeneous dielectric medium. In this paper, we only examine the TM (transverse magnetic) polarization case. A radiation condition is introduced and equivalence with a second kind, Lippmann-Schwinger-type integral equation is shown. With additional assumptions on the index of refraction in the layer, uniqueness of solution is proved. Existence of solution is then established by employing a form of Fredholm alternative using a general result on the solvability of integral equations on unbounded domains published earlier by Chandler-Wilde and Zhang. An approximate analytic solution for the case of a thin inhomogeneous layer is obtained from the integral equation formulation and is used to show that, if the index of refraction is appropriately chosen, the scattered field can grow with distance from the plate.

Information content of Born scattered fields: results in the circular cylindrical case

Abstract: In this analysis some limitations of the linear Born approximation in the diffraction tomography problem from far-zone data are pointed out. The analysis is performed by means of singular-value decomposition of the scattering operator in the scalar two-dimensional case of a circular dielectric cylinder illuminated by a TM-polarized plane wave. It is shown that the validity of the Born approximation entails the important condition that the scattering object not present too-fast spatial variations of the permittivity profile. For the rotationally symmetric cylinder, evidence is presented that the imaginary part of the normalized scattered far field has no information content for real permittivity objects. Moreover, for angularly varying cylinders the information content of the scattered far field for a single view is approximately the same as in the multiview case. Examples of singular-value and singular-function behavior and of profile reconstruction are depicted for the considered geometries.

Optical diffusion of continuous-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer

Abstract: We discuss several outstanding theoretical problems in optical diffusion in random media. Specifically, we discuss which of several diffusion theories most closely approximates exact solutions of the equation of transfer. We consider a plane wave impinging upon a plane-parallel slab of a random medium as a model problem to compare the diffusion theories with a numerical solution of the equation of transfer for continuous-wave, pulsed, and photon density waves. In addition, we discuss the validity of the diffusion approximation for a variety of parameter settings to ascertain the diffusion approximation’s applicability to imaging biological media.

Modeling ground‐penetrating radar wave propagation and reflection with the Jonscher parameterization

Abstract: As in seismic surveys, forward modeling is essential to the geological interpretation of georadar data. Because a radar signal is broad band, modeling radar waves in a realistic medium requires knowing the frequency dependence of the effective dielectric permittivity of rocks. Various models can be found in the literature. With the support of laboratory measurements carried out on various rock samples, the complex effective dielectric permittivity describing polarization and conduction effects can be modeled by the Jonscher law. In the megahertz range, the Jonscher parameterization involves only three real, constant parameters that are characteristic of the investigated media. Radar plane waves propagating in 1-D models are generated and compared to field data recorded in transmission mode for different frequencies, distances, and geological formations. The signal distortion from propagation is emphasized. Quality factors are calculated and found to be compatible with the propagation in real media. Reflection coefficients are written using the Jonscher relation. Two cases are illustrated: reflection from a half-space and reflection from a thin layer. From the study of the influence of frequency, reflection modes, electric properties of rocks, and layer thickness, it can be concluded that reflection phenomena, like propagation phenomena, lead to phase shifts and frequency content variations. Thus, processing based on the assumption of stationary wavelets is not suitable for georadar signals, even in low-loss media.

High-frequency backscattering enhancements by thick finite cylindrical shells in water at oblique incidence: Experiments, interpretation, and calculations

Abstract: Impulse response backscattering measurements are presented and interpreted for the scattering of obliquely incident plane waves by air-filled finite cylindrical shells immersed in water. The measurements were carried out to determine the conditions for significant enhancements of the backscattering by thick shells at large tilt angles. The shells investigated are made of stainless steel and are slender and have thickness to radius ratios of 7.6% and 16.3%. A broadband PVDF (polyvinylidene fluoride) sheet source is used to obtain the backscattering spectral magnitude as a function of the tilt angle (measured from broadside incidence) of the cylinder. Results are plotted as a function of frequency and angle. These plots reveal large backscattering enhancements associated with elastic excitations at high tilt angles, which extend to end-on incidence in the coincidence frequency region. Similar features are present in approximate calculations for finite cylindrical shells based on full elasticity theory and the Kirchhoff diffraction integral. One feature is identified as resulting from the axial (meridional ray) propagation of the supersonic a0 leaky Lamb wave. A simple approximation is used to describe circumferential coupling loci in frequency-angle space for several surface waves. The resulting loci are used to identify enhancements due to the helical propagation of the subsonic a0− Lamb wave.

All-Electron Spin-Polarized Relativistic Linearized APW Method: Electronic and Magnetic Properties of BCC Fe, HCP Gd and Uranium Monochalcogenides

Abstract: The linearized-augmented-plane-wave (LAPW) method is generalized to case of an all-electron fully-relativistic spin-polarized self-consistent band calculation based on the relativistic spin-density functional theory. Inside spheres around nuclei, the Bloch function is expanded by spherical-symmetry bases and their energy-derivatives, each of which is solved by the corresponding spin-polarized coupled Dirac equation (SPCDE) including a coupling of j = l- 1/2 with j = l+ 1/2 partial state through the magnetic field. In the interstitial region, the relativistic plane wave is used as a conventional basis function. The core states inside the spheres are treated on the same footing of the SPCDE in all iterative processes. This band theory is applied to BCC Fe, HCP Gd and uranium monochalcogenides US, USe and UTe as an interesting example of the ferromagnetic 3d, 4f and 5f systems, respectively. The electronic band structures are shown together with the spin and orbital moments.

First‐principles determination of elastic properties of CaSiO3 perovskite at lower mantle pressures

Abstract: We investigate the equation of state and elasticity of cubic CaSiO3 perovskite up to 140 GPa using the plane wave pseudopotential method within the local density approximation. The calculated equation of state parameters of the cubic phase are in excellent agreement with those from recent quasi-hydrostatic compression data and from all-electron linearized augmented plane wave calculations. We determine the elastic constant tensor of the mineral from the calculated stress-strain relations. The bulk modulus of CaSiO3 perovskite is similar to that of MgSiO3 perovskite, however, its shear modulus is much higher at pressures corresponding to the lower mantle. This suggests that CaSiO3 perovskite can no longer be considered as an invisible component in modelling the composition of the lower mantle, and even small amounts of the mineral may affect significantly the seismic properties, particularly shear wave velocity, of the generally accepted Mg-rich silicate perovskite dominated composition of this region. Moreover, CaSiO3 perovskite exhibits strong anisotropy (about 30% shear-wave polarization anisotropy) at pressures corresponding to the transition zone and the top of the lower mantle.

Lamb waves as thickness vibrations superimposed on a membrane carrier wave

Abstract: Classical Lamb waves in an homogeneous, isotropic linearly elastic plate are reconsidered. The displacement components are obtained in terms of thickness motions superimposed on a membrane carrier wave which defines the propagation along the plate. The carrier wave can be any solution of the reduced wave equation for a membrane. The analysis of the thickness motions results in the usual Rayleigh–Lamb frequency equation. A number of special cases for the carrier wave are considered.

Effective properties and band structures of lamellar subwavelength crystals: Plane-wave method revisited

Abstract: The plane-wave method used to compute the band structure of photonic crystals is revisited in light of recent mathematical results about the Fourier factorization of products of discontinuous functions. Highly accurate numerical predictions for the effective index and for the band structure are obtained for two- and three-dimensional dielectric lamellar crystals with high dielectric contrasts. At the same time, we clarify some aspects related to the effective properties of multidimensional crystals by establishing clear links between their band structures and their effective indices.

Effects of phase shifts on four-beam interference patterns.

Abstract: An analysis of the effects of relative phase changes on the interference pattern formed by the coherent addition of four plane waves is presented. We focus on the configuration in which four plane waves converge at equal angles along two orthogonal planes, an arrangement that is potentially useful for printing arrays of microstructures in resist. We show that, depending on the set of polarization vectors chosen, the shape of the interference pattern is a strong function of the phase difference between each pair of beams. If all the beams have the same phase constant, an intensity distribution that is perfectly modulated and that exhibits strong contrast is produced. However, if the phase constant of any one of the beams is shifted by pi from this condition, a pattern with degraded modulation and significantly weaker contrast is formed. We discuss the implication of these results on lithographic applications of multiple-beam patterns. Further, we show that the sensitivity to phase is a general property of all interference patterns formed by four or more intersecting coherent wave fronts that have collinear electric-field components.

Electric field intensity variation in the vicinity of a perfectly conducting conical probe: Application to near‐field microscopy

Abstract: A vibrating metallic conical probe has been used in near-field microscopic measurements to obtain optical resolutions much smaller than the wavelength. Numerical simulations of these complex problems have drawn most of the attention in the past. We propose here an analytical expression for the electric field intensity in the near region of a probe situated above the surface of a semi-infinite dielectric medium. It is given as a function of the observation point location, with the cone aperture, the dielectric medium permittivity, and the characteristics of the incident plane wave as parameters. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 18: 120–124, 1998.

Power deposition in the head and neck of an anatomically based human body model for plane wave exposures

Abstract: At certain frequencies, when the human head becomes a resonant structure, the power absorbed by the head and neck, when the body is exposed to a vertically polarized plane wave propagating from front to back, becomes significantly larger than would ordinarily be expected from its shadow cross section. This has possible implications in the study of the biological effects of electromagnetic fields. Additionally the frequencies at which these resonances occur are not readily predicted by simple approximations of the head in isolation. In order to determine these resonant conditions an anatomically based model of the whole human body has been used, with the finite-difference time-domain (FDTD) algorithm to accurately determine field propagation, specific absorption rate (SAR) distributions and power absorption in both the whole body and the head region (head and neck). This paper shows that resonant frequencies can be determined using two methods. The first is by use of the accurate anatomically based model (with heterogeneous tissue properties) and secondly using a model built from parallelepiped sections (for the torso and legs), an ellipsoid for the head and a cylinder for the neck. This approximation to the human body is built from homogeneous tissue the equivalent of two-thirds the conductivity and dielectric constant of that of muscle. An IBM SP-2 supercomputer together with a parallel FDTD code has been used to accommodate the large problem size. We find resonant frequencies for the head and neck at 207 MHz and 193 MHz for the isolated and grounded conditions, with absorption cross sections that are respectively 3.27 and 2.62 times the shadow cross section.

Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space

Abstract: The effect of pre-stress on the propagation and reflection of plane waves in an incompressible isotropic elastic half-space has been examined recently by the authors (Ogden & Sotiropoulos, 1997). In the present paper the corresponding analysis for compressible materials is detailed. In the two-dimensional context considered for incompressible materials the (homogeneous) plane waves were necessarily shear waves. By contrast, in the compressible context pure shear waves can propagate only in specific directions in the considered principal plane and, in a general direction, a quasi-shear wave may be accompanied by a quasi-longitudinal wave, as is the case in the anisotropic linear theory. The dependence of the (in-plane) slowness section on the pre-stress (and finite deformation) and on the choice of constitutive law is elucidated. This information is used to determine the reflection coefficients for reflection of either a (quasi-) shear wave or a (quasi-) longitudinal wave from the boundary of the half-space and to characterize the different cases which arise depending on the geometry of the slowness section. The theoretical results are illustrated by numerical calculations for the range of possible types of behaviour with reference to different forms of strain-energy function and different states of finite deformation and to the question of stability of the half-space.