Showing papers on "Plane wave published in 2000"

Fundamentals of Physical Acoustics

Abstract: Detailed Development of the Acoustical Wave Equation. Reflection and Transmission of Normally Incident Plane Waves of Arbitrary Waveform. Normal Incidence Continued: Steady-State Analysis. Transmission Phenomena: Oblique Incidence. Normal Modes in Cartesian Coordinates: Strings, Membranes, Rooms, and Rectangular Waveguides. Horns. Propagation in Stratified Media. Propagation in Dissipative Fluids: Absorption and Dispersion. Spherical Waves. Cylindrical Waves. Waveguides. Radiation from a Baffled Piston. Diffraction. Arrays. Appendices. Index.

An acoustic wave equation for anisotropic media

Abstract: A wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media. The wavefield solutions obtained using this VTI acoustic wave equation are free of shear waves, which significantly reduces the computation time compared to the elastic wavefield solutions for exploding‐reflector type applications. From this VTI acoustic wave equation, the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a TI medium are derived. These equations, based on the acoustic assumption (shear wave velocity = 0), are much simpler than their elastic counterparts, yet they yield an accurate description of traveltimes and geometrical amplitudes. Numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex TI models.

Plane Wave Limits and T-Duality

Abstract: The Penrose limit is generalized to show that, any leading order solution of the low-energy field equations in any one of the five string theories has a plane wave solution as a limit. This limiting procedure takes into account all the massless fields that may arise and commutes with the T-duality so that any dual solution has again a plane wave limit. The scaling rules used in the limit are unique and stem from the scaling property of the D=11 supergravity action. Although the leading order solutions need not be exact or supersymmetric, their plane wave limits always preserve some portion of the Poincare supersymmetry and solve the relevant field equations in all powers of the string tension parameter. Further properties of the limiting procedure are discussed.

Analysis of transient electromagnetic scattering from closed surfaces using a combined field integral equation

Abstract: In the past, both the time-domain electric and magnetic field integral equations have been applied to the analysis of transient scattering from closed structures. Unfortunately, the solutions to both these equations are often corrupted by the presence of spurious interior cavity modes. In this article, a time-domain combined field integral equation is derived and shown to offer solutions devoid of any resonant components. It is anticipated that stable marching-on-in-time schemes for solving this combined field integral equation supplemented by fast transient evaluation schemes such as the plane wave time-domain algorithm will enable the analysis of scattering from electrically large closed bodies capable of supporting resonant modes.

Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings

Abstract: The concept of polarization freedom is employed to design diffraction gratings that are capable of transforming an electromagnetic plane wave into two or three diffraction orders with an arbitrary efficiency distribution among them, such that the combined efficiency of the signal orders is always equal to 100%. As a special case we consider paraxial-domain duplicators and triplicators with 100% efficiency, which is not possible for illumination by scalar waves: Diffractive elements that are capable of performing the required wave transformation must modulate the state of polarization of the incident field.

Calculated equation of state of al, cu, ta, mo, and W to 1000 GPa

Abstract: Calculated Hugoniots and 293-K isotherms at pressures up to 1 TPa (10 Mbar) for the five reference metals Al, Cu, Ta, Mo, and W are reported using the classical mean-field approach where both the cold and the thermal parts of the Helmholtz free energy are derived entirely from the 0-K total energies and electronic density of states calculated with the full-potential linearized augmented plane wave method within the generalized gradient approximation to exchange correlational functional. Our approach permits efficient computation and invokes no empirical parameters. Both the experimental Hugoniots and 293-K isotherms are reproduced excellently.

Transmission Lines and Wave Propagation

Abstract: INTRODUCTION Transmission Systems The Circuit-Theory Approach to Transmission-Line Analysis Traveling-Wave Fields - Lines and Waveguides Closure References WAVE PROPAGATION ON AN INFINITE LOSSLESS LINE Partial Differential Equations of Lossless Line Traveling-Wave Solutions to the Wave Equation Conclusions Problems References STEP-FUNCTION WAVES ON A TERMINATED LOSSLESS LINE Boundary Conditions and Reflection Process Responses of Single-Section Lines Reflections on Lines with Discontinuities or Branches Conclusions Problems References SINUSOIDAL TRAVELING WAVES ON A LOSSY LINE Mathematical Solution for Traveling-Wave Properties Phasor Notation for Traveling-Wave Functions Propagation Characteristics as Functions of Frequency Conclusions Problems References WAVE DISTORTION ON LOSSY LINES - STEP-FUNCTION SOURCE Transforms of Voltage and Current on a Lossy Line Operational Parameters - First-Order Skin-Effect Approximation Response on Semi-Infinite Line with Zero Source Impedance Semi-Infinite Line, Nonzero Source Resistance Line of Finite Length, Resistively Matched Conclusions Problems References SINUSOIDAL VOLTAGES AND CURRENTS ON A TERMINATED LINE - STANDING WAVES Incident and Reflected Wave Functions Limiting-Case Reflection Situations Standing-Wave Ratio Resultant Standing-Wave Phasors - Hyperbolic Functions Lumped-Impedance Discontinuities Conclusions Problems References IMPEDANCE, ADMITTANCE, AND THE SMITH CHART Input Impedance Limiting-Case Input Impedances Line Parameters as Functions of Open-Circuit and Short-Circuit Impedances Lossless Line: Impedance Function and Standing-Wave Ratio Nomographic Chart for Impedance Calculations Some Applications of the Smith Chart Thevenin Equivalent Circuit for output of Energized Line Conclusions Problems References THE LADDER-NETWORK DELAY LINE OR ARTIFICIAL LINE Symmetrical Networks The Lumped-Parameter Delay Line as a Low-Pass Filter Step-Function Response of Ladder-Network Delay Line Conclusions Problems References COUPLED TRANSMISSION LINES Partial Differential Equations for Coupled Lines Solution for Symmetric Coupled Lines Coupled-Line Directional Coupler Solution for Asymmetric Coupled Lines Crosstalk Between Coupled Lines Conclusions Problems References ELECTROMAGNETIC FIELDS AND MAXWELL'S EQUATIONS An Overview of Classical Electromagnetics Reduction of Field Equations to Differential Form Conclusions Problems References PLANE ELECTROMAGNETIC WAVES Sinusoidal Traveling-Wave Fields in Infinite Medium Reflection and Refraction at Normal Incidence Reflection at Oblique Incidence Plane Waves Traveling Parallel to Highly Conducting Surfaces Conclusions Problems References GUIDED FIELDS: ARRAYS OF TWO OR MORE CONDUCTORS Coaxial Line Circular-Wire Parallel Pair Image-Conductor Analysis of Ground Planes and Shields Transmission Modes of Multiconductor Systems Some Design Considerations for Practical Lines Conclusions Problems References FIELDS IN HOLLOW RECTANGULAR WAVEGUIDES TEm0 Propagating Modes Dominant-Mode Standing Waves-Waveguide Impedances General Solution for TE and TM Modes Evanescent Modes and General Discontinuities Velocities and Signal Propagation Attenuation of TE10 Propagating Mode Conclusions Problems References FIELDS IN CYLINDRICAL WAVEGUIDES Solution of Maxwell's Equations in Cylindrical Coordinates Propagation Modes in Hollow Circular Waveguide Fiber Optic Cables Parasitic Propagating Modes in Coaxial Cable Elliptical Cylindrical Waveguides Conclusions Problems References SKIN EFFECT IN COAXIAL CONDUCTORS Conduction-Current-Density Field Magnetic Field within Conducting Regions Impedance Component Due to Finite Conductivity Thin-Walled Outer Conductor Conclusions Problems References APPENDIX A: VECTOR ANALYSIS - DEFINITIONS AND FORMULAS Vector Operations and Functions Coordinate Systems and Component Resolution References APPENDIX B: BESSEL FUNCTIONS Independent Variable Real Independent Variable Purely Imaginary Independent Variable Complex References APPENDIX C: PARALLEL-SLAB EQUIVALENT OF SLOTTED COAXIAL LINE Slotted Lines: General Conformal Transformations: Basic Properties Transformation Function for Coaxial Line Problems References APPENDIX D: EARTH CURRENTS AND DISTRIBUTED IMPEDANCES Earth-Current Characteristics Distributed Impedances of Ground-Return Circuits Conclusions References APPENDIX E: LOW-TEMPERATURE IMPEDANCE EFFECTS Superconductivity Anomalous Skin Effect References APPENDIX F: TABLE OF PHYSICAL CONSTANTS AUTHOR INDEX SUBJECT INDEX

Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate

Abstract: We present a theory to compute the force due to light upon a particle on a dielectric plane by the coupled dipole method. We show that, with this procedure, two equivalent ways of analysis are possible, both based on Maxwell's stress tensor. The interest in using this method is that the nature and size or shape of the object can be arbitrary. Even more, the presence of a substrate can be incorporated. To validate our theory, we present an analytical expression of the force due to the light acting on a particle either in presence, or not, of a surface. The plane wave illuminating the sphere can be either propagating or evanescent. Both two- and three-dimensional calculations are studied.

Short wave modelling using special finite elements

Abstract: The solutions to the Helmholtz equation in the plane are approximated by systems of plane waves. The aim is to develop finite elements capable of containing many wavelengths and therefore simulating problems with large wave numbers without refining the mesh to satisfy the traditional requirement of about ten nodal points per wavelength. At each node of the meshed domain, the wave potential is written as a combination of plane waves propagating in many possible directions. The resulting element matrices contain oscillatory functions and are evaluated using high order Gauss-Legendre integration. These finite elements are used to solve wave problems such as a diffracted potential from a cylinder. Many wavelengths are contained in a single finite element and the number of parameters in the problem is greatly reduced.

A numerical model for the low frequency diffuse field sound transmission loss of double-wall sound barriers with elastic porous linings

Abstract: This paper discusses the prediction of the low frequency diffuse field transmission loss through double-wall sound barriers with elastic porous linings. The studied sound barriers are made up from a porous-elastic decoupling material sandwiched between an elastic skin and a septum. The prediction approach is based on a finite element model for the different layers of the sound barrier coupled to a variational boundary element method to account for fluid loading. The diffuse field is modeled as a combination of uncorrelated freely propagating plane waves with equal amplitude, no two of which are traveling in the same direction. The corresponding vibroacoustic indicators are calculated efficiently using a Gauss integration scheme. Also, a power balance is presented to explain the dissipation mechanisms in the different layers. Typical results showing the effects on the transmission loss of several parameters such as the septum mass, the decoupling porous layer properties and the multi-layer mounting conditions are presented.

An integral equation method for the electromagnetic scattering from cavities

Abstract: Consider a time-harmonic electromagnetic plane wave incident on a cavity in a ground plane. The physical process is modelled by Maxwell's equations. In this paper, integral representations of the solutions to the model problem in both fundamental polarizations are derived and studied. Existence and uniqueness of the solutions for the integral equations are established. The integral equations approach forms a basis for numerical solution of the model problem. In particular, for each fundamental polarization, an integral formulation with Garding-type estimates is derived. These formulations provide a basis for variational boundary element methods for solving the cavity problem. The Garding-type estimates imply convergence results for conforming boundary element methods. Copyright © 2000 John Wiley & Sons, Ltd

Inversion of ultrasonic, plane-wave transmission data in composite plates to infer viscoelastic material properties

Abstract: Stiffness and damping properties of viscoelastic materials are given by the real and imaginary components, respectively, of the material constants. A new technique is proposed to experimentally measure the real and imaginary components of anisotropic (and isotropic) viscoelastic plates. Main advantage of this technique is that material properties of thin plates can be measured where many other techniques fail. Material properties are obtained by numerically inverting the transmitted ultrasonic fields, obtained for different incident angles. Simplex inversion algorithm is applied to initial estimates of plate thickness and plate properties. By this iterative technique the values of the unknown parameters (material properties and plate thickness) are continuously modified to give better agreement between the experimental and theoretical transmitted fields. After a certain number of iterations the speed of convergence of the Simplex scheme is significantly reduced. To improve the accuracy of convergence the Newton–Raphson inversion technique is adopted at that point. By this technique material properties of different types of plates are measured. These is a glass plate (isotropic plate with no damping), a polymer plate (isotropic plate with damping), and glass fiber reinforced epoxy plates with different fiber orientations (anisotropic plates with damping). Both real and imaginary components are successfully measured for all these plates. In a relative scale the measurement error for the imaginary components is higher. Reliability of the measured material constants of fiber reinforced epoxy plates is verified by the method of invariance. All experiments are carried out in the frequency range that is appropriate for satisfying two conditions—the specimen homogeneity and the plane wave conditions.

Ray-density normalization for ray-optical wave propagation modeling in arbitrarily shaped tunnels

Abstract: This work is concerned with the calculation of natural electromagnetic (EM) wave propagation and the determination of the propagation channel characteristics in highway or railway tunnels in the ultrahigh-frequency (UHF) range and above (>300 MHz). A novel ray-tracing technique based on geometrical optics (GO) is presented. Contrary to classical ray tracing, where the one ray representing a locally plane wave front is searched, the new method requires multiple representatives of each physical EM wave at a time. The contribution of each ray to the total field at the receiver is determined by the proposed ray-density normalization (RBN). This technique has the further advantage of overcoming one of the major disadvantages of GO, the failure at caustics. In contrast to existing techniques, the new approach does not use ray tubes or adaptive reception spheres. Consequently, it does not suffer their restrictions to planar geometries. Therefore, it allows one to predict the propagation of high-frequency EM waves in confined spaces with curved boundaries, like tunnels, with an adequate precision. The approach is verified theoretically with canonical examples and by various measurements at 120 GHz in scaled tunnel models.

Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm

Abstract: A fast algorithm is presented for solving electric, magnetic, and combined field time-domain integral equations pertinent to the analysis of surface scattering phenomena. The proposed two-level plane wave time-domain (PWTD) algorithm permits a numerically rigorous reconstruction of transient near-fields from their far-field expansion and augments classical marching-on in-time (MOT) based solvers. The computational cost of analyzing surface scattering phenomena using PWTD-enhanced MOT schemes scales as O(N/sub i/N/sub s//sup 2/3/ log N/sub s/) as opposed to /spl Oscr/(N/sub t/N/sub s//sup 2/) for classical MOT methods, where N/sub t/ and N/sub s/ are the numbers of temporal and spatial basis functions discretizing the scatterer current. Numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering from electrically large structures and that confirm the above complexity estimate are presented.

Structural Properties of Lanthanide and Actinide Compounds within the Plane Wave Pseudopotential Approach

Abstract: We show that plane wave ultrasoft pseudopotential methods readily extend to the calculation of the structural properties of lanthanide and actinide containing compounds. This is demonstrated through a series of calculations performed on UO, UO2 ,U O 3 ,U 3O8 ,U C 2, a-CeC2, CeB6, CeSe, CeO2, NdB6, TmOI, LaBi, LaTiO3, YbO, and elemental Lu. PACS numbers: 61.50.Ah, 61.66.Fn The plane wave pseudopotential approach has developed steadily in applicability. Initially, empirical pseudopotentials were constructed for the so-called “easy” elements such as silicon and aluminum. These potentials were used mainly in the prediction and understanding of electronic band structures and were found to be particularly accurate for semiconductors. With the subsequent development of ab initio pseudopotentials and expressions for the accurate calculation of forces and stresses, the plane wave pseudopotential approach has come into its own as the method of choice for the first principles prediction of structural parameters. A combination of improved computing resources, algorithms, and pseudopotential formalisms has allowed the plane wave pseudopotential technique to be applied to ever “harder” elements, such as, initially, the first row elements (including carbon and oxygen), and later the transition metal elements. In this paper we will show

Scattering of Internal Waves at Finite Topography in Two Dimensions. Part I: Theory and Case Studies

Abstract: The scattering of internal gravity waves at finite topography in two dimensions is studied theoretically and numerically for a finite depth ocean A formal solution is derived using a mapping function based on ray tracing The solution satisfies radiation conditions Energy is conserved The incoming energy flux is redistributed in physical and modenumber space Numerical solutions are calculated for a single plane wave propagating from the ocean side onto slope–shelf configurations where a flat shallow shelf is connected to a flat deep ocean by linear slopes, staircases, convex or concave parabolic profiles, and half-cosine slopes The fraction of the incoming energy flux transmitted onto the shelf and reflected back to the deep ocean and the distribution of these fluxes in modenumber space are calculated The results depend on the parameters of the incident wave and of the topography Especially important is the distinction between supercritical topography, where the slope of the topography exc

First-principles study of strain-electronic interplay in ZnO: Stress and temperature dependence of the piezoelectric constants

Abstract: We present a first-principles study of the relationship between stress, temperature, and electronic properties in piezoelectric ZnO. Our method is a plane wave pseudopotential implementation of density-functional theory and density-functional linear response within the local-density approximation. We observe marked changes in the piezoelectric and dielectric constants when the material is distorted. This stress dependence is the result of strong, bond-length dependent hybridization between the O $2p$ and Zn $3d$ electrons. Our results indicate that fine tuning of the piezoelectric properties for specific device applications can be achieved by control of the ZnO lattice constant, for example by epitaxial growth on an appropriate substrate.

Free and guided propagation

Abstract: Historical Survey.- Waves, Fluid as a Scalar Model.- Crystal Properties and Their Representation by Tensors.- Elasticity and Piezoelectricity.- Plane Waves in Crystals.- Guided Waves.

Highly localized solutions of the wave equation

Abstract: Simple explicit solutions of the linear wave equation in three dimensions are presented which describe wave packets exponentially localized near a point moving with the wave speed. For large values of a certain free parameter these new solutions are localized in Gaussian manner with respect to longitudinal and transverse variables and time. This agrees with considerations by Babich–Ulin and Ralston who have presented an asymptotic description of solutions exhibiting such local behavior. Global estimates and large-time asymptotics of these solutions are given.

Impedance and Its Time-Domain Extensions

Abstract: The classical concept of impedance as a means to characterize the ree ectivity and absorption of a surface to the incident waves has always been a complex-valued quantity akin to plane harmonic waves and the analysis of their ree ections. A new look at this classical quantity irrespective of the type of incident waves is presented. It points out that a direct operational inversion of impedance into time-domain boundary operators will, in general, lead to an unstable system, whereas the inversion of the corresponding ree ection coefe cient will result in stable, easily implementable boundary operators for time-domain prediction of wave ree ection. It reveals the equivalent, pulselike, causal process of time convoluting the incident wave into the ree ected wave. Excellent agreement with analytical solutions derived here and from other sources supports the validity of the approach and demonstrates the accuracy of the implementations.

Symmetries of cross-polarization diffraction coefficients of gratings

Abstract: In a recent paper [J. Opt. Soc. Am. A16, 1108 (1999)] Logofǎtu et al. demonstrated by experimental and numerical evidence that the 0th-order cross-polarization (s to p and p to s) reflection coefficients of isotropic, symmetrical, surface-relief gratings in conical mount are identical. Here an analytical proof is given to show that the observed identity is merely a manifestation of the electromagnetic reciprocity theorem for the 0th-order diffraction of symmetrical gratings. The above result is further generalized to bianisotropic gratings, to the 0th-order cross-polarization transmission coefficients, and to the mth-order reflection and transmission coefficients when the wave vector of the incident plane wave and the negative of the wave vector of the mth reflected order are symmetrical with respect to the plane perpendicular to the grating grooves.

An experimental investigation of higher-harmonic wave forces on a vertical cylinder

Abstract: First- and higher-harmonic wave loads on a vertical circular cylinder are investigated experimentally in a wave tank of small scale. The incoming waves are (periodic) Stokes waves with wave slope up to 0.24. A large set of waves which are long compared to the cylinder radius is calibrated. The first seven harmonic components of the measured horizontal force on the cylinder are analysed. The higher-harmonic forces are significantly smaller than the first-harmonic force for all wave parameters. The measurements are continued until the wave amplitude is comparable to the cylinder radius, where the second-, third- and fourth-harmonic forces become of comparable size. Comparison with existing perturbation and fully nonlinear models shows, with a few exceptions, an overall good agreement for small and moderate wave amplitude. A fully nonlinear model agrees with the experiments even up to the seventh-harmonic force for part of the amplitude range. For the large amplitudes the models mostly give conservative predictions. It is important that the distance from the wave maker to the cylinder is large in order to avoid parasitic effects in the incoming wave field. The limited width of the wave tank is not important to the results except when close to resonance.

Effect of rotation and relaxation times on plane waves in generalized thermo-visco-elasticity

Abstract: The generalized dynamical theory of thermo-elasticity proposed by Green and Lindsay is applied to study the propagation of harmonically time-dependent thermo-visco- elastic plane waves of assigned frequency in an infinite visco-elastic solid of Kelvin-Voigt type, when the entire medium rotates with a uniform angular velocity A more general dispersion equation is deduced to determine the effects of rotation, visco-elasticity, and relaxation time on the phase-velocity of the coupled waves The solutions for the phase velocity and attenuation coefficient are obtained for small thermo-elastic couplings by the perturbation technique Taking an appropriate material, the numerical values of the phase velocity of the waves are computed and the results are shown graphically to illustrate the

Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure

Abstract: We report measurements of the diffraction pattern of a two-dimensional photonic quasicrystal structure and use the set of plane waves defined by the diffraction pattern as the basis of a theoretical approach to calculate the photonic band structure of the system. An important feature of the model is that it retains the essence of the rotational and inflational properties of the quasicrystal at all levels of approximation: properties lost in approximate models which artificially introduce elements of periodicity. The calculated density of modes of the quasicrystals is found to display a weakly depleted region analogous to the bandgap that occurs in a periodic system. The calculated transmission spectra for different polarizations and directions of propagation show features that correlate with the behaviour of the density of modes.

Tapered wave with dominant polarization state for all angles of incidence

Abstract: Typical applications of the method of moments (MoM) to rough surface three-dimensional (3-D) electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave. It is shown how such a wave can be constructed as a superposition of plane waves, avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence. The proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a least squared error property of the wave. Issues in the application to 3-D scattering from an object over a rough surface are discussed. Approximate 3-D scalar and vector tapered waves which can be evaluated without resorting to any numerical integrations are derived and important limitations to the accuracy and applicability of these approximations are pointed out.