Showing papers on "Plane wave published in 2001"

A Formulation of a Phase-Independent Wave-Activity Flux for Stationary and Migratory Quasigeostrophic Eddies on a Zonally Varying Basic Flow

Abstract: A new formulation of an approximate conservation relation of wave-activity pseudomomentum is derived, which is applicable for either stationary or migratory quasigeostrophic (QG) eddies on a zonally varying basic flow. The authors utilize a combination of a quantity A that is proportional to wave enstrophy and another quantity E that is proportional to wave energy. Both A and E are approximately related to the wave-activity pseudomomentum. It is shown for QG eddies on a slowly varying, unforced nonzonal flow that a particular linear combination of A and E, namely, M ≡ (A + E)/2, is independent of the wave phase, even if unaveraged, in the limit of a small-amplitude plane wave. In the same limit, a flux of M is also free from an oscillatory component on a scale of one-half wavelength even without any averaging. It is shown that M is conserved under steady, unforced, and nondissipative conditions and the flux of M is parallel to the local three-dimensional group velocity in the WKB limit. The autho...

Laser Beam Scintillation with Applications

Abstract: Optical Wave Propagation In Random Media - Background Review Optical Scintillation Modelling Theory Of Scintillation - Plane Wave Model Theory Of Scintillation - Spherical Wave Model Theory Of Scintillation - Gaussian-Beam Wave Model Aperture Averaging Optical Communication Systems Fade Statistics For Lasercom Systems Laser Radar Systems - Scintillation Of Return Waves Laser Radar Systems - Imaging Through Turbulence.

Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media

Abstract: We develop a model for the probability density function (pdf) of the irradiance fluctuations of an optical wave propagating through a turbulent medium. The model is a two-parameter distribution that is based on a doubly stochastic theory of scintillation that assumes that small-scale irradiance fluctuations are modulated by large-scale irradi- ance fluctuations of the propagating wave, both governed by indepen- dent gamma distributions. The resulting irradiance pdf takes the form of a generalized K distribution that we term the gamma-gamma distribution. The two parameters of the gamma-gamma pdf are determined using a recently published theory of scintillation, using only values of the refractive-index structure parameter C n (or Rytov variance) and inner scale l 0 provided with the simulation data. This enables us to directly calculate various log-irradiance moments that are necessary in the scaled plots. We make a number of comparisons with published plane wave and spherical wave simulation data over a wide range of turbu- lence conditions (weak to strong) that includes inner scale effects. The gamma-gamma pdf is found to generally provide a good fit to the simu- lation data in nearly all cases tested. © 2001 Society of Photo-Optical Instrumen-

Wave propagation in media having negative permittivity and permeability

Abstract: Wave propagation in a double negative (DNG) medium, i.e., a medium having negative permittivity and negative permeability, is studied both analytically and numerically. The choices of the square root that leads to the index of refraction and the wave impedance in a DNG medium are determined by imposing analyticity in the complex frequency domain, and the corresponding wave properties associated with each choice are presented. These monochromatic concepts are then tested critically via a one-dimensional finite difference time domain (FDTD) simulation of the propagation of a causal, pulsed plane wave in a matched, lossy Drude model DNG medium. The causal responses of different spectral regimes of the medium with positive or negative refractive indices are studied by varying the carrier frequency of narrowband pulse excitations. The smooth transition of the phenomena associated with a DNG medium from its early-time nondispersive behavior to its late-time monochromatic response is explored with wideband pulse excitations. These FDTD results show conclusively that the square root choice leading to a negative index of refraction and positive wave impedance is the correct one, and that this choice is consistent with the overall causality of the response. An analytical, exact frequency domain solution to the scattering of a wave from a DNG slab is also given and is used to characterize several physical effects. This solution is independent of the choice of the square roots for the index of refraction and the wave impedance, and thus avoids any controversy that may arise in connection with the signs of these constituents. The DNG slab solution is used to critically examine the perfect lens concept suggested recently by Pendry. It is shown that the perfect lens effect exists only under the special case of a DNG medium with $\ensuremath{\epsilon}(\ensuremath{\omega})=\ensuremath{\mu}(\ensuremath{\omega})=\ensuremath{-}1$ that is both lossless and nondispersive. Otherwise, the closed form solutions for the field structure reveal that the DNG slab converts an incident spherical wave into a localized beam field whose parameters depend on the values of $\ensuremath{\epsilon}$ and $\ensuremath{\mu}.$ This beam field is characterized with a paraxial approximation of the exact DNG slab solution. These monochromatic concepts are again explored numerically via a causal two-dimensional FDTD simulation of the scattering of a pulsed cylindrical wave by a matched, lossy Drude model DNG slab. These FDTD results demonstrate conclusively that the monochromatic electromagnetic power flow through the DNG slab is channeled into beams rather then being focused and, hence, the Pendry perfect lens effect is not realizable with any realistic metamaterial.

Dynamical theory of x-ray diffraction

Abstract: This chapter presents the dynamical theory of the diffraction of X-rays by perfect crystals. The most important part is devoted to the case of plane waves (Section 5.1.2). The solutions of the propagation equation of plane waves in crystals are given in Section 5.1.3 using the concept of wavefields introduced by Ewald for X-rays in 1913 and by Bloch for electrons in 1928 (known in solid-state physics as Bloch waves). They are applied to the interpretation of the main properties of dynamical diffraction: anomalous transmission, standing waves and Pendellosung. The expressions for the diffracted intensity are given in both the transmission (Section 5.1.6) and the reflection (Section 5.1.7) cases. The last part (Section 5.1.8) concerns the diffraction of real and spherical waves, which is described in a qualitative way.

BW media—media with negative parameters, capable of supporting backward waves

Abstract: Both isotropic and uniaxially anisotropic media capable of supporting backward waves are reviewed. Such an effect recently has been of great interest, and certain man-made composite media have been introduced under the names “media with negative refraction factor” or “left-handed materials,” effective in a certain band of microwaves. Neither of these names appears to be well founded, and “backward-wave medium” (or BW medium) is suggested instead. It is shown that, at an interface of a regular and a BW medium, Snell's law does not imply a negative refraction factor. However, the refraction is anomalous in the sense that the transmitted plane wave is a backward wave with a Poynting vector and a wave vector pointing in opposite lateral directions. The significance of the Zenneck wave and guided modes in a cylindrical guide made of BW medium is discussed. Finally, the BW property is extended to uniaxially anisotropic media, and its occurrence is studied for different value combinations of its medium parameters. It is shown that a lateral backward wave can arise when a plane wave is transmitted through an interface when one of the four parameters of the uniaxial medium is negative. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 129–133, 2001.

Reproduction of a plane-wave sound field using an array of loudspeakers

Abstract: Reproduction of a sound field is a fundamental problem in acoustic signal processing. In this paper, we use a spherical harmonics analysis to derive performance bounds on how well an array of loudspeakers can recreate a three-dimensional (3-D) plane-wave sound field within a spherical region of space. Specifically, we develop a relationship between the number of loudspeakers, the size of the reproduction sphere, the frequency range, and the desired accuracy. We also provide analogous results for the special case of reproduction of a two-dimensional (2-D) sound field. Results are verified through computer simulations.

Polarization singularities in isotropic random vector waves

Abstract: Following Nye & Hajnal, we explore the geometry of complex vector waves by regarding them as a field of polarization ellipses. Singularities of this field are the C lines and L lines, where the polarization is purely circular and purely linear, respectively. The singularities can be reinterpreted as loci of photon spin 1 (C lines) and 0 (L lines). For Gaussian random superpositions of plane waves equidistributed in direction but with an arbitrary frequency spectrum, we calculate the density (length per unit volume) of C and L lines.

Waves in locally periodic media

Abstract: We review the theory of wave propagation in one dimension through a medium consisting of N identical “cells.” Surprisingly, exact closed-form results can be obtained for arbitrary N. Examples include the vibration of weighted strings, the acoustics of corrugated tubes, the optics of photonic crystals, and, of course, electron wave functions in the quantum theory of solids. As N increases, the band structure characteristic of waves in infinite periodic media emerges.

A k-space method for large-scale models of wave propagation in tissue

Abstract: Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for "slow" (c(x)/spl les/c/sub 0/) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed.

Thermoelastic wave induced by pulsed laser heating

Abstract: In this work, a generalized solution for the thermoelastic plane wave in a semi-infinite solid induced by pulsed laser heating is developed. The solution takes into account the non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, which play significant roles in ultrashort pulsed laser heating. Based on this solution, calculations are conducted to study stress waves induced by nano-, pico-, and femtosecond laser pulses. It is found that with the same maximum surface temperature increase, a shorter pulsed laser induces a much stronger stress wave. The non-Fourier effect causes a higher surface temperature increase, but a weaker stress wave. Also, for the first time, it is found that a second stress wave is formed and propagates with the same speed as the thermal wave. The surface displacement accompanying thermal expansion shows a substantial time delay to the femtosecond laser pulse. On the contrary, surface displacement and heating occur simultaneously in nano- and picosecond laser heating. In femtosecond laser heating, results show that the coupling effect strongly attenuates the stress wave and extends the duration of the stress wave. This may explain the minimal damage in ultrashort laser materials processing.

Study of distributions of modes and plane waves in reverberation chambers for the characterization of antennas in a multipath environment

Abstract: A rectangular metallic cavity is known to support a number of resonant cavity modes. Each of these modes can be described as a sum of eight plane waves incident from different angles. This paper studies how these plane waves are angularly distributed in space, which is of interest when the cavity is used to simulate multipath environment. The results show that the angular distribution in space is uniform provided that the three linear dimensions of the chamber are sufficiently large, and do not deviate too much from each other. As an example, two rectangular cavities with dimensions 1 m×0.8 m×1 m and 5.5 m×2.5 m×3.5 m are analyzed in detail, and are shown to have uniform plane-wave distributions. We also demonstrate how the chamber geometry may be chosen in order to weight the angular plane-wave distribution in the elevation plane. A result of the study is that we detect a 25 MHz frequency band with very few modes in a small chamber designed for use with reduced accuracy in the GSM 900 MHz band. We also propose how this chamber can be modified to obtain uniform mode distribution over this frequency band. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 386–391, 2001.

Multi-directional random wave transformation model based on energy balance equation

Abstract: The purpose of this paper is to develop a prediction model for multi-directional random wave transformation. The wave prediction model is based on an energy balance equation with an energy dissipat...

Micro-mechanical modelling of granular material. Part 1: Derivation of a second-gradient micro-polar constitutive theory

Abstract: This contribution is one in a series of two papers. In the current paper a constitutive law is developed that includes the micro-structural effects by particle displacement as well as particle rotation. Both degrees of freedom can be related to corresponding macroscopic kinematic continuum variables, where the resulting gradients of displacement are selected up to the fourth-order and the gradients of rotation up to the third order. The elastic micro-structural properties for an individual particle are used to derive the macro-level behavior for a fabric of equal-sized spherical particles, leading to a second-gradient micro-polar formulation. In this model, all coefficients are expressed in terms of particle stiffness and particle structure. It is shown that the second-gradient micro-polar model can be reduced to simpler forms, such as the classic linear elastic model, the second-gradient model and the Cosserat model. In the accompanying paper these reduced forms are treated in more detail by analyzing the corresponding dispersion relations for plane body wave propagation.

Lamb and SH waves generated and detected by air-coupled ultrasonic transducers in composite material plates

Abstract: Electrostatic, air-coupled, ultrasonic transducers are used to generate and detect guided waves in anisotropic solid plates. Waves considered in this study are Lamb-type and SH-type, guided modes. If the plane of propagation coincides with a plane of symmetry of the material, then Lamb modes only are launched and detected by the transducers. If the plane of propagation does not coincide with a plane of symmetry of the material, then Lamb modes are still generated and detected, but guided, SH-like modes are, too. The variation of phase velocity with frequency is measured for several modes propagating in different directions along a glass–epoxy composite plate. A numerical model that takes into account the anisotropy of composite materials is developed to predict the dispersion curves (phase velocity, group velocity or wave-number versus frequency) and the displacement fields of plate waves, the plane of propagation being either a plane of symmetry or not. The experimental phase velocities are in good agreement with the predicted dispersion curves, thus showing that the forward problem concerning the propagation of plate waves in anisotropic, homogeneous, composite material plates is properly solved. The dispersion curves associated with the predicted displacement fields show that guided modes in composite plates have different behaviors depending on their direction of propagation.

Complete solution of the Schrödinger equation for the time-dependent linear potential

Abstract: The complete solutions of the Schr\"odinger equation for a particle with time-dependent mass moving in a time-dependent linear potential are presented. One solution is based on the wave function of the plane wave, and the other is in the form of the Airy function. A comparison is made between the present solution and former ones to show the completeness of the present solution.

Experimental observation of vertically polarized transverse dust-lattice wave propagating in a one-dimensional strongly coupled dust chain.

Abstract: Externally driven, vertically polarized transverse dust-lattice waves were observed in a one-dimensional strongly coupled dust chain levitated in the plasma-sheath boundary of a dc argon plasma at low gas pressure around 5 mtorr. Real and imaginary parts of the complex wave number were measured in the experiments. The experimental result clearly shows that the observed transverse dust-lattice wave propagates as a backward wave, which is in good agreement with the theoretical prediction.

Extension of T-matrix to scattering of electromagnetic plane waves by non-axisymmetric dielectric particles: application to hexagonal ice cylinders

Abstract: The calculation of scattering by cirrus particles at intermediate size parameters greater than 20 has not as yet been satisfactorily solved with exact theory. This has made it difficult to represent scattering and absorption of ice clouds in remote sensing retrievals and in modelling radiative forcing. The T-matrix approach applied to ice particles has previously been implemented only for axisymmetric particles, but ice clouds consist of particles which are not axisymmetric. In this paper an implementation of T-matrix which provides exact solutions for scattering and absorption from non-axisymmetric particles is presented. Rigorous tests demonstrate the stability and accuracy of the method. Results for finite hexagonal cylinders are presented. The general T-matrix formulation has major conceptual and practical advantages over other existing methods such as the finite difference time domain (FDTD) and the discrete dipole approximation (DDA). These advantages are due largely to its analytic character, which allows exact fulfillment of the radiation condition. Other advantages are the restriction of calculations to the scatterer's surface, and the exploitation of particle symmetries which considerably simplifies computation. The new T-matrix implementation is tested against existing T-matrix results for the circular cylinder and the cube in terms of differential scattering cross-sections, no differences are found between the T-matrix calculations. Comparisons with a recently improved implementation of FDTD for randomly oriented hexagonal ice columns show good agreement with T-matrix in terms of absorption and extinction efficiencies.

Thermal equation of state of tantalum

Abstract: We have investigated the thermal equation of state of bcc tantalum from first principles using the full-potential linearized augmented plane wave (LAPW) and mixed-basis pseudopotential methods for pressures up to 300 GPa and temperatures up to 10 000 K. The equation of state at zero temperature was computed using LAPW. For finite temperatures, mixed basis pseudopotential computations were performed for 54 atom supercells. The vibrational contributions were obtained by computing the partition function using the particle in a cell model, and the finite-temperature electronic-free energy was obtained from the LAPW band structures. We discuss the behavior of thermal equation of state parameters such as the Gr\"uneisen parameter $\ensuremath{\gamma},$ the thermal expansivity $\ensuremath{\alpha},$ and the Anderson-Gr\"uneisen parameter ${\ensuremath{\delta}}_{T}$ as functions of pressure and temperature. The calculated Hugoniot shows excellent agreement with shock-wave experiments. An electronic topological transition was found at approximately 200 GPa.

Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium

Abstract: A previously developed fast inhomogeneous plane wave algorithm is adapted to the analysis of the scattering from the objects above a multilayered medium. Based on the similarity of the inhomogeneous plane wave expansion of the Green's function encountered in the layered medium study to its free space counterpart, the proper steepest descent path can be defined. By using the interpolation and extrapolation techniques, the translation matrix is diagonalized. The contributions of the pole and branch point, resulting from the deformation of the integration path, can be handled easily. Comparing with the previously developed methods in this area, this algorithm is simpler, more efficient, and more general. The multilevel fast inhomogeneous plane wave algorithm has been implemented and the numerical results show that O(N log N) computational complexity of the algorithm is achieved. The algorithm is validated by comparing the results from a conventional method of moments program.

High-frequency electromagnetic field coupling to long terminated lines

Abstract: We present a theory for the EMC problem of electromagnetic field coupling to a long line with arbitrary terminations The theory is applicable for the high-frequency plane wave electromagnetic field excitations, when the transmission line approximation is no longer valid Analytical expressions are derived for the induced current along the line, and at the two-line terminals The coefficients of these expressions are determined using a procedure based on the exact solutions of the integral equation for two similar line configurations, but having a significantly shorter length The method is, therefore, particularly efficient when considering the electromagnetic field coupling to very long lines The advantage of the proposed approach is that, in contrast with transmission line approximation, it takes into account high-frequency radiation effects Furthermore, it allows a considerable reduction in computation time and storage requirements with respect to conventional numerical solutions based on the thin-wire approximation

Topological Singularities in Wave Fields

Abstract: This thesis is a study of the natural geometric structures, arising through interference, in fields of complex waves (scalars, vectors or tensors), where certain parameters describing the wave are singular. In scalar waves, these are phase singularities (also called wave dislocations), which are also nodes (zeros of amplitude): in two dimensional fields they are points, and in three dimensions, lines. The morphology of dislocation points and lines is studied in detail, and averages of their geometrical properties (such as density, speed, curvature and twistedness) are calculated analytically for isotropically random gaussian ensembles (superpositions of plane waves equidistributed in direction, but with random phases). It is also shown how dislocation lines may be knotted and linked, and a construction of torus knots in monochromatic waves is studied in detail, using experimentally realisable beams. In vector waves, the appropriate fields are described geometrically by an ellipse at each point (the polarization ellipse). Their singularities, occurring along lines in three dimensions, are where the ellipse is circular (C lines) and linear (L lines); in two dimensional fields, possibly representing the transverse plane of paraxial polarized light waves, there are C points, but still L lines. The geometry of these singularities is considered, and analytical calculations for their densities in isotropic gaussian random vector waves are performed. The C and L singularity structures are generalised to fields of spinors using the Majorana sphere (vector fields have spin 1), and singularities in rank two tensor waves (spin 2) are briefly discussed.

Linear Elastic Waves

Abstract: Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers.

One‐ and two‐dimensional simulations of electron beam instability: Generation of electrostatic and electromagnetic 2f p waves

Abstract: We have performed computer simulations of the self-consistent nonlinear evolution of electrostatic and electromagnetic 2f p waves excited by electron beams with electromagnetic particle code. In both one- and two-dimensional periodic systems an electrostatic 2f p wave is generated at twice the wave number of forward propagating Langmuir waves by wave-wave coupling. This wave grows with the forward propagating Langmuir wave in the nonlinear stage of the simulations. The electrostatic 2f p wave in the simulations is saturated at about -20 ∼ -30 dB of that of the Langmuir waves. It is larger than the value expected from observations in the terrestrial electron foreshock. The electromagnetic 2f p wave is only excited in two-dimensional systems. The magnitude of the electromagnetic 2f p wave is correlated with the backward propagating Langmuir wave, not with the electrostatic 2f p wave. This result suggests that the electromagnetic 2f p wave is excited by the wave-wave coupling of forward and backward propagating Langmuir waves. The typical power density estimated from a reasonable amplitude of Langmuir wave is of the same order or much weaker than the value typically observed around the electron foreshock.