Showing papers on "Plane wave published in 2011"

Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the $p$-Version

Abstract: Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Despres, SIAM J. Numer. Anal., 35 (1998), pp. 255-299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121-136], and plane wave approximation theory.

The Optimal Use of Horizontal-to-Vertical Spectral Ratios of Earthquake Motions for Velocity Inversions Based on Diffuse-Field Theory for Plane Waves

Abstract: The coda of earthquake motions and microtremors are sometimes referred to as diffuse-wave fields. They are generated by the multiple scattering due to the complexity of the Earth. It is accepted that the average cross correlation between the diffuse-field motions at pairs of receivers, in the frequency domain, is proportional to the imaginary part of the Green’s function between these locations. The average autocorrelation of a single receiver is also proportional to the imaginary part of the Green’s function when both the source and receiver are the same. In this study we explored the application of diffuse-field concepts to analyze earthquake records at a site when its site effect can be described using a 1D model. We derived a corollary of Claerbout’s result for a 1D layered medium. We found that the imaginary part of the Green’s function at the free surface is proportional to the square of the absolute value of the corresponding transfer function for a plane, vertically incident wave. We considered a set of incoming plane waves (of P , SV , and SH types) with varying azimuths and incidence angles. After summing up a few hundred synthetics with inclined incidences we obtained horizontal-to-vertical (H/V) spectral ratios that match the ratios estimated from the simple theory of diffuse field. By using observed records in Japan, we found that the earthquake H/V ratios are quite stable and converge rapidly regardless of what part of the waveform is used, except the P -wave part. We also found that their spectral characteristics can be reproduced well by the velocity structures estimated in previous studies. However, theory and observation were not in perfect agreement, which in turn means that the inversion of a 1D structure could be accomplished by adopting the proposed theory for earthquake H/V spectral ratios.

Biot-Rayleigh theory of wave propagation in double-porosity media

Abstract: [1] We derive the equations of motion of a double‐porosity medium based on Biot’s theory of poroelasticity and on a generalization of Rayleigh’s theory of fluid collapse to the porous case. Spherical inclusions are imbedded in an unbounded host medium having different porosity, permeability, and compressibility. Wave propagation induces local fluid flow between the inclusions and the host medium because of their dissimilar compressibilities. Following Biot’s approach, Lagrange’s equations are obtained on the basis of the strain and kinetic energies. In particular, the kinetic energy and the dissipation function associated with the local fluid flow motion are described by a generalization of Rayleigh’s theory of liquid collapse of a spherical cavity. We obtain explicit expressions of the six stiffnesses and five density coefficients involved in the equations of motion by performing “gedanken” experiments. A plane wave analysis yields four wave modes, namely, the fast P and S waves and two slow P waves. As an example, we consider a sandstone and compute the phase velocity and quality factor as a function of frequency, which illustrate the effects of the mesoscopic loss mechanism due to wave‐induced fluid flow.

Triggering Rogue Waves in Opposing Currents

Abstract: We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity U(0) and the wave group velocity c(g). We also reveal that an opposing current can force the development of rogue waves in random wave fields, resulting in a substantial change of the statistical properties of the surface elevation. The present results can be directly adopted in any field of physics in which the focusing nonlinear Schrodinger equation with nonconstant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.

Generation of high-energy photons with large orbital angular momentum by compton backscattering

Abstract: Usually, photons are described by plane waves with a definite 4-momentum. In addition to plane-wave photons, ``twisted photons'' have recently entered the field of modern laser optics; these are coherent superpositions of plane waves with a defined projection $\ensuremath{\hbar}m$ of the orbital angular momentum onto the propagation axis, where $m$ is an integer. In this Letter, we show that it is possible to produce high-energy twisted photons by Compton backscattering of twisted laser photons off ultrarelativistic electrons. Such photons may be of interest for experiments related to the excitation and disintegration of atoms and nuclei, and for studying the photoeffect and pair production off nuclei in previously unexplored experimental regimes.

Plane wave approximation of homogeneous Helmholtz solutions

Abstract: In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω2u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.

Material loss influence on the complex band structure and group velocity in phononic crystals

Abstract: The influence of material loss on the complex band structure of two-dimensional phononic crystals is investigated. A viscoelasticity model is added to the extended plane-wave expansion (EPWE) method, with viscosity proportional to the frequency. It is found that losses have a stronger influence on the real than on the imaginary part of Bloch waves, in contrast with propagation in homogeneous media. Flat bands, i.e., bands initially showing low group velocity without losses, acquire an enhanced damping as compared to bands with larger group velocities. Losses are also found to limit the appearance of large group slownesses, or conversely small group velocities.

Asymmetric transmission of linearly polarized waves and polarization angle dependent wave rotation using a chiral metamaterial

Abstract: An electrically thin chiral metamaterial structure composed of four U-shaped split ring resonator pairs is utilized in order to realize polarization rotation that is dependent on the polarization of the incident wave at 6.2 GHz. The structure is optimized such that a plane wave that is linearly polarized at an arbitrary angle is an eigenwave of the system at this frequency. The analytical relation between the incident polarization and the polarization rotation is derived using transmission matrices. Furthermore, the proposed structure exhibits an asymmetric transmission of linearly polarized waves at 6.2 GHz. Plane waves traveling in opposite but perpendicular directions to the material plane are rotated by different angles. On the other hand, four incident polarization angles have been found for the same structure, at which the transmission is symmetric. The experiment results are in good agreement with the numerical results.

Compton Upconversion of Twisted Photons: Backscattering of Particles with Non-Planar Wave Functions

Abstract: Twisted photons are not plane waves, but superpositions of plane waves with a defined projection ℏm of the orbital angular momentum onto the propagation axis (m is integer and may attain values m≫1). Here, we describe in detail the possibility to produce high-energy twisted photons by backward Compton scattering of twisted laser photons on ultra-relativistic electrons with a Lorentz-factor γ=E/(mec2)≫1. When a twisted laser photon with the energy ℏω∼1 eV performs a collision with an electron and scatters backward, the final twisted photon conserves the angular momentum m, but its energy ℏω′ is increased considerably: ω′/ω=4γ2/(1+x), where x=4Eℏω/(mec2)2. The S matrix formalism for the description of scattering processes is particularly simple for plane waves with definite 4-momenta. However, in the considered case, this formalism must be enhanced because the quantum state of twisted particles cannot be reduced to plane waves. This implies that the usual notion of a cross section is inapplicable, and we introduce and calculate an averaged cross section for a quantitative description of the process. The energetic upconversion of twisted photons may be of interest for experiments with the excitation and disintegration of atoms and nuclei, and for studying the photo-effect and pair production off nuclei in previously unexplored regimes.

An expression for the radiation force exerted by an acoustic beam with arbitrary wavefront (L).

Abstract: Most studies investigating the acoustic radiation force upon a target are based on symmetry considerations between the object and the incident beam. Even so, this symmetry condition is not always fulfilled in several cases. An expression for the radiation force is obtained as a function of the beam-shape and the scattering coefficients of an incident wave and the object, respectively. The expression for the radiation force caused by a plane wave on a rigid sphere is used to validate the formula. This method represents a theoretical advance permitting different interpretations and predictions concerned to the acoustic radiation force phenomenon.

From D3-Branes to Lifshitz Space-Times

Abstract: We present a simple embedding of a z=2 Lifshitz space-time into type IIB supergravity. This is obtained by considering a stack of D3-branes in type IIB supergravity and deforming the world-volume by a plane wave. The plane wave is sourced by the type IIB axion. The superposition of the plane wave and the D3-branes is 1/4 BPS. The near horizon geometry of this configuration is a 5-dimensional z=0 Schroedinger space-time times a 5-sphere. This geometry is also 1/4 BPS. Upon compactification along the direction in which the wave is traveling the 5-dimensional z=0 Schroedinger space-time reduces to a 4-dimensional z=2 Lifshitz space-time. The compactification is such that the circle is small for weakly coupled type IIB string theory. This reduction breaks the supersymmetries. Further, we propose a general method to construct analytic z=2 Lifshitz black brane solutions. The method is based on deforming 5-dimensional AdS black strings by an axion wave and reducing to 4-dimensions. We illustrate this method with an example.

Plane-Wave Coupling to a Twisted-Wire Pair Above Ground

Abstract: A transmission-line model is developed for predicting the response of a twisted-wire pair (TWP) circuit in the presence of a ground plane, illuminated by a plane-wave electromagnetic field. The twisted pair is modeled as an ideal bifilar helix, the total coupling is separated into differential- (DM) and common-mode (CM) contributions, and closed-form expressions are derived for the equivalent induced sources. Approximate upper bounds to the terminal response of electrically long lines are obtained, and a simplified low-frequency circuit model is used to explain the mechanism of field-to-wire coupling in a TWP above ground, as well as the role of load balancing on the DM and CM electromagnetic noise induced in the terminal loads.

Scalar Wave Equation Modeling with Time-Space Domain Dispersion-Relation-Based Staggered-Grid Finite-Difference Schemes

Abstract: The staggered-grid finite-difference (SFD) method is widely used in numerical modeling of wave equations. Conventional SFD stencils for spatial derivatives are usually designed in the space domain. However, when they are used to solve wave equations, it becomes difficult to satisfy the dispersion relations exactly. Liu and Sen (2009c) proposed a new SFD scheme for one-dimensional (1D) scalar wave equation based on the time–space domain dispersion relation and plane wave theory, which is made to satisfy the exact dispersion relation. This new SFD scheme has greater accuracy and better stability than a conventional scheme under the same discretizations. In this paper, we develop this new SFD scheme further for numerical solution of 2D and 3D scalar wave equations. We demonstrate that the modeling accuracy is second order when the conventional 2 M -th-order space-domain SFD and the second order time-domain finite-difference stencils are directly used to solve the scalar wave equation. However, under the same discretization, our 1D scheme can reach 2 M -th-order accuracy and is always stable; 2D and 3D schemes can reach 2 M -th-order accuracy along 8 and 48 directions, respectively, and have better stability. The advantages of the new schemes are also demonstrated with dispersion analysis, stability analysis, and numerical modeling.

Magnonic minibands in antidot lattices with large spin-wave propagation velocities

Abstract: Antidot lattices fabricated from permalloy thin films have been investigated by all-electrical spin-wave spectroscopy and Brillouin light scattering. Periodic arrays of 120-nm-diameter nanoholes have been prepared using focused ion beam etching. The periodicity of the square lattices was varied from 300 to 4000 nm. By applying an in-plane field of 40 mT, we discover surprisingly large spin-wave velocities of up to 6 km/s for a periodicity <400 nm. Using micromagnetic modeling and the further-developed plane wave method, we show that edge excitations at neighboring holes couple and form an allowed miniband supporting fast spin waves. By varying the orientation of the magnetic field we control the miniband characteristics. The coupling of edge modes opens interesting perspectives for magnonic crystals. © 2011 American Physical Society.

Electronic structure and optical properties of Sb2S3 crystal

Abstract: The electronic and optical properties of Sb2S3 are studied using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in Wien2k. In this approach, the alternative form of the generalized gradient approximation (GGA) proposed by Engel and Vosko (EV-GGA) was used for the exchange correlation potential. The calculated band structure shows a direct band gap. The contribution of different bands was analyzed from total and partial density of states curves. Moreover, the optical properties, including the dielectric function, absorption spectrum, refractive index, extinction coefficient, reflectivity and energy-loss spectrum are all obtained and analyzed in detail.

Phonon calculations in cubic and tetragonal phases of SrTiO 3 : A comparative LCAO and plane-wave study

Abstract: The atomic, electronic structure and phonon frequencies have been calculated in cubic and low-temperature tetragonal SrTiO${}_{3}$ phases at the ab initio level. We demonstrate that the use of the hybrid exchange-correlation PBE0 functional gives the best agreement with experimental data. The results for the standard generalized gradient approximation (PBE) and hybrid PBE0 functionals are compared for the two types of approaches: a linear combination of atomic orbitals (CRYSTAL09 computer code) and plane waves (VASP5.2 code). The relation between cubic and tetragonal phases and the relevant antiferrodistortive phase transition is discussed in terms of group theory and is illustrated with analysis of calculated soft-mode frequencies at the \ensuremath{\Gamma} and $R$ points in the Brillouin zone. Based on phonon calculations, the temperature dependence of the heat capacity is in good agreement with experiment.

From D3-branes to Lifshitz spacetimes

Abstract: We present a simple embedding of a z = 2 Lifshitz spacetime into type IIB supergravity. This is obtained by considering a stack of D3-branes in type IIB supergravity and deforming the world-volume by a plane wave. The plane wave is sourced by the type IIB axion. The superposition of the plane wave and the D3-branes is 1/4 BPS. The near horizon geometry of this configuration is a five-dimensional z = 0 Schr?dinger spacetime times a 5-sphere. This geometry is also 1/4 BPS. Upon compactification along the direction in which the wave is traveling the five-dimensional z = 0 Schr?dinger spacetime reduces to a four-dimensional z = 2 Lifshitz spacetime. The compactification is such that the circle is small for weakly coupled type IIB string theory. This reduction breaks the supersymmetries. Further, we propose a general method to construct analytic z = 2 Lifshitz black brane solutions. The method is based on deforming AdS5 black strings by an axion wave and reducing to four dimensions. We illustrate this method with an example.

Asymptotic reflection of linear water waves by submerged horizontal porous plates

Abstract: On the basis of linear water-wave theory, an explicit expression is presented for the reflection coefficient R ∞ when a plane wave is obliquely incident upon a semi-infinite porous plate in water of finite depth The expression, which correctly models the singularity in velocity at the edge of the plate, does not rely on knowledge of any of the complex-valued eigenvalues or corresponding vertical eigenfunctions in the region occupied by the plate The solution R ∞ is the asymptotic limit of the reflection coefficient R as a → ∞, for a plate of finite length a bounded by a rigid vertical wall, and forms the basis of a rapidly convergent expansion for R over a wide range of values of a The special case of normal incidence is relevant to the design of submerged wave absorbers in a narrow wave tank Modifications necessary to account for a finite submerged porous plate in a fluid extending to infinity in both horizontal directions are discussed

Mechanical Action of Inhomogeneously Polarized Optical Fields and Detection of the Internal Energy Flows

Abstract: We analyze numerically correspondence between the mechanical action, experienced by a spherical microparticle, and the internal energy flows in the light field incident on the particle. The inhomogeneous incident field is modelled by superposition of two plane waves; the mechanical action is calculated via the Mie theory for dielectric and conducting particles of different sizes and optical properties. It is shown that both spin and orbital components of the field momentum can produce the mechanical action whose value and sign depend on many additional details of the field-particle interaction. Besides, forces that are not associated with any sort of the energy flow (e.g., the gradient force owing to the inhomogeneous intensity and the polarization-dependent dipole force emerging due to inhomogeneous polarization) can strongly modify the observed mechanical action. The polarization-dependent mechanical action on particles can be treated as a form of the spin-orbit interaction of light.

Increasing the structural variety of discrete nondiffracting wave fields

Abstract: We investigate discrete nondiffracting beams (DNBs) being the foundation of periodic and quasiperiodic intensity distributions. Besides the number of interfering plane waves, the phase relation among these waves is decisive to form a particular intensity lattice. In this manner, we systematize different classes of DNBs and present similarities as well as differences. As one prominent instance, we introduce the class of sixfold nondiffracting beams, offering four entirely different transverse intensity distributions: in detail, the hexagonal, kagome, and honeycomb pattern, as well as a hexagonal vortex beam. We further extend our considerations to quasiperiodic structures and show the changeover to Bessel beams. In addition, we introduce a highly flexible implementation of the experimental analog of DNBs, namely discrete pseudo-nondiffracting beams, and present locally resolved intensity and phase measurements, which underline the nondiffracting character of the generated wave fields.

The colours of cloaks

Abstract: We present a survey of results from various research groups under the unifying viewpoint of transformational physics, which has been recently introduced for the design of metamaterials in optics and acoustics. We illustrate the versatility of underlying geometric transforms in order to bridge wave phenomena (the different 'colours' of waves) ranging from transverse electric waves, to linear surface water waves at an air–fluid interface, to pressure waves in fluids and out-of-plane shear waves in elastic media: these waves are all governed by a second order scalar partial differential equation (PDE) invariant under geometric transform. Moreover, flexural waves propagating in thin plates represent a very peculiar situation whereby the displacement field satisfies a fourth order scalar PDE which also retains its form under geometric transform (unlike for the Navier equation in elastodynamics). Control of flexural wave trajectories is illustrated with a multilayered cloak and a carpet. Interestingly, the colours of waves can be revealed through an analysis of the band spectra of invisibility cloaks. In the context of acoustics, this suggests one can hear the shape of a drum. Alternative avenues towards cloaking based upon anomalous resonances of a negatively refracting coating (which can be seen as the result of folding the space back onto itself), and even plasmonic shells reducing the scattering cross-section of nano-objects are also addressed.

Boundary Effects on the Determination of Metamaterial Parameters From Normal Incidence Reflection and Transmission Measurements

Abstract: A method is described for the determination of the effective electromagnetic parameters of a metamaterial based only on external measurements or simulations, taking boundary effects at the interfaces between a conventional material and metamaterial into account. Plane-wave reflection and transmission coefficients at the interfaces are regarded as additional unknowns to be determined, rather than explicitly dependent on the material parameters. Our technique is thus analogous to the line-reflect-line (LRL) calibration method in microwave measurements. The refractive index can be determined from S-parameters for two samples of different thickness. The effective wave impedance requires the additional assumption that generalized sheet transition conditions (GSTCs) account for the boundary effects. Expressions for the bulk permittivity and permeability then follow easily. Our method is validated by comparison with the results using the Nicolson-Ross-Weir (NRW) for determining properties of an ordinary material measured in a coaxial line. Utilizing S-parameters obtained from 3-D full wave simulations, we test the method on magnetodielectric metamaterials. We compare the results from our method and the conventional one that does not consider boundary effects. Moreover, it is shown that results from our method are consistent under changes in reference plane location, whereas the results from other methods are not.

Local geometry of electromagnetic fields and its role in molecular multipole transitions.

Abstract: Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the fields and field gradients at a single point in space. Many configurations cannot be generated from a single plane wave, regardless of polarization, but any allowed configuration can be generated by superposition of multiple plane waves. There is no local configuration of the fields and gradients that requires near-field effects. Second, we derive a set of local electromagnetic quantities, each of which couples to a particular multipole transition. These quantities are small or zero in plane waves, but can be large in regions of certain superpositions of plane waves. Our findings provide a systematic framework for designing far-field and near-field experiments to drive multipole transitions. The proposed experiments provide information on molecular structure that is in...

Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle

Abstract: A vectorial complex ray model is introduced to describe the scattering of a smooth surface object of arbitrary shape. In this model, all waves are considered as vectorial complex rays of four parameters: amplitude, phase, direction of propagation, and polarization. The ray direction and the wave divergence/convergence after each interaction of the wave with a dioptric surface as well as the phase shifts of each ray are determined by the vector Snell law and the wavefront equation according to the curvatures of the surfaces. The total scattered field is the superposition of the complex amplitude of all orders of the rays emergent from the object. Thanks to the simple representation of the wave, this model is very suitable for the description of the interaction of an arbitrary wave with an object of smooth surface and complex shape. The application of the model to two-dimensional scattering of a plane wave by a spheroid particle is presented as a demonstration.

Impact of attenuation on guided mode wavenumber measurement in axial transmission on bone mimicking plates

Abstract: Robust signal processing methods adapted to clinical measurements of guided modes are required to assess bone properties such as cortical thickness and porosity. Recently, an approach based on the singular value decomposition (SVD) of multidimensional signals recorded with an axial transmission array of emitters and receivers has been proposed for materials with negligible absorption, see Minonzio et al. [J. Acoust. Soc. Am. 127, 2913–2919 (2010)]. In presence of absorption, the ability to extract guided mode degrades. The objective of the present study is to extend the method to the case of absorbing media, considering attenuated plane waves (complex wavenumber). The guided mode wavenumber extraction is enhanced and the order of magnitude of the attenuation of the guided mode is estimated. Experiments have been carried out on 2 mm thick plates in the 0.2–2 MHz bandwidth. Two materials are inspected: polymethylacrylate (PMMA) (isotropic with absorption) and artificial composite bones (Sawbones, Pacific Research Laboratory Inc, Vashon, WA) which is a transverse isotropic absorbing medium. Bulk wave velocities and bulk attenuation have been evaluated from transmission measurements. These values were used to compute theoretical Lamb mode wavenumbers which are consistent with the experimental ones obtained with the SVD-based approach.

Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method

Abstract: The propagation of plane waves in fibre-reinforced, rotating thermoelastic half-space proposed by Lord-Shulman is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the coupled theory and the theory of generalized thermoelasticity with one relaxation time in the presence and absence of rotation and reinforcement. It is found that the rotation has a significant effect and the reinforcement has great effect on the distribution of field quantities when the rotation is considered.