Showing papers on "Plane wave published in 2010"

Optical chirality and its interaction with matter.

Abstract: We introduce a measure of the local density of chirality of the electromagnetic field. This optical chirality determines the asymmetry in the rates of excitation between a small chiral molecule and its mirror image, and applies to molecules in electromagnetic fields with arbitrary spatial dependence. A continuity equation for optical chirality in the presence of material currents describes the flow of chirality, in a manner analogous to the Poynting theorem for electromagnetic energy. ``Superchiral'' solutions to Maxwell's equations show larger chiral asymmetry, in some regions of space, than is found in circularly polarized plane waves.

Spin-orbit coupled spinor Bose-Einstein condensates.

Abstract: An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.

Tutorial on seismic interferometry: Part 1 — Basic principles and applications

Abstract: Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green’s function between these receivers. For the simple situation of an impulsive plane wave propagating along the x-axis, the crosscorrelation of the responses at two receivers along the x-axis gives the Green’s function of the direct wave between these receivers. When the source function of the plane wave is a transientas in exploration seismology or a noise signalas in passive seismology, then the crosscorrelation gives the Green’s function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is the retrieval of seismic surface-wave responses from ambient noise and the subsequent tomographic determination of the surfacewave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct- and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.

Reflectionless Transmission Through Dielectrics and Scattering Potentials

Abstract: A complete solution is given for the problem of constructing a plane stratified dielectric medium having that the property that at a fixed frequency and polarization a plane wave at any angle of incidence will be transmitted without reflection by the medium. This problem can also be interpreted quantum‐mechanically. The dielectric medium of the first interpretation becomes, in the second interpretation, a potential for the one‐dimensional Schrodinger equation such that a particle which is sent in from ‐ ∞ is transmitted with probability one of getting through to + ∞, no matter what the initial kinetic energy of the particle may be.In addition, the results can be applied to the problem of finding perfectly matched nonuniform transmission lines.

Ab-initio study of the bandgap engineering of Al(1-x)Ga(x)N for optoelectronic applications

Abstract: A theoretical study of Al(1-x)Ga(x)N, based on full-potential linearized augmented plane wave method, is used to investigate the variations in the bandgap, optical properties and non-linear behavior of the compound with the variation of Ga concentration. It is found that the bandgap decreases with the increase of Ga in Al(1-x)Ga(x)N. A maximum value of 5.5 eV is determined for the bandgap of pure AlN which reaches to minimum value of 3.0 eV when Al is completely replaced by Ga. The static index of refraction and dielectric constant decreases with the increase in bandgap of the material, assigning a high index of refraction to pure GaN when compared to pure AlN. The refractive index drops below 1 for photon energies larger than 14 eV results group velocity of the incident radiation higher than the vacuum velocity of light. This astonishing result shows that at higher energies the optical properties of the material shifts from linear to non-linear. Furthermore, frequency dependent reflectivity and absorption coefficients show that peak value of the absorption coefficient and reflectivity shifts towards lower energy in the UV spectrum with the increase in Ga concentration. This comprehensive theoretical study of the optoelectronic properties of the alloys is presented for the first time which predicts that the material can be effectively used in the optical devices working in the visible and UV spectrum.

Distribution of noise sources for seismic interferometry

Abstract: SUMMARY We demonstrate that the distribution of seismic noise sources affects the accuracy of Green’s function estimates and therefore isotropic and anisotropic tomographic inversions for both velocity and attenuation. We compare three methods for estimating seismic noise source distributions and quantify the potential error in phase velocity, azimuthal anisotropy and attenuation estimates due to inhomogenous source distributions. The methods include: (1) least-squaresinversionofbeamformeroutput,(2)aleast-squaresinversionofyearlongstacked noise correlation functions assuming both a 2-D plane wave source density model and (3) a 3-D plane wave source density model. We use vertical component data from the 190 stations of the Southern California Seismic Network and some US Array stations for 2008. The good agreement between the three models suggests the 2-D plane wave model, with the fewest number of unknown parameters, is generally sufficient to describe the noise density function for tomographic inversions. At higher frequencies, 3-D and beamforming models are required to resolve peaks in energy associated with body waves. We illustrate and assess isotropic and azimuthally anisotropic phase velocity and attenuation uncertainties for the noise source distribution in southern California by inverting isotropic lossless synthetic Fourier transformed noise correlation function predictions from modelled 2-D source distribution. We find that the variation in phase velocity with azimuth from inhomogeneous source distribution yields up to 1 per cent apparent peak-to-peak anisotropy. We predict apparent attenuation coefficients from our lossless synthetics on the same order of magnitude as those previously reported for the region from ambient noise. Since noise source distributions are likely inhomogeneous varying regionally and with time, we recommend that noise correlation studies reporting attenuation and anisotropy incorporate source density information.

Analysis of Blast Wave Interaction with a Rock Joint

Abstract: The interaction between rock joints and blast waves is crucial in rock engineering when rock mass is suffered from artificial or accidental explosions, bursts or weapon attacks. Based on the conservation of momentum at the wave fronts and the displacement discontinuity method, quantitative analysis for the interaction between obliquely incident P- or S-blast wave and a linear elastic rock joint is carried out in the present study, so as to deduce a wave propagation equation. For some special cases, such as normal or tangential incidence, rigid or weak joint, the analytical solution of the stress wave interaction with a rock joint is obtained by simplifying the wave propagation equation. By verification, it is found that the transmission and reflection coefficients from the wave propagation equation agree very well with the existing results. Parametric studies are then conducted to evaluate the effects of the joint stiffness and incident waves on wave transmission and reflection. The wave propagation equation derived in the present study can be straightforwardly extended for different incident waveforms and nonlinear rock joints to calculate the transmitted and reflected waves without mathematical methods such as the Fourier and inverse Fourier transforms.

Acoustic far-field focusing effect for two-dimensional graded negative refractive-index sonic crystals

Abstract: Focusing effect is experimentally observed for acoustic plane wave normally incident onto a two-dimensional sonic crystal with gradient negative refractive index. The gradual refractive-index is achieved by gradual modification of the lattice spacing both along the transverse and longitudinal directions. It is found that the focal length is controllable by modulation of the lattice spacing. The experiment results are in excellent agreement with theoretical calculation by a multiple scattering theory method.

The wave equation and general plane wave solutions in fractional space

Abstract: This work presents the analytical solution of vector wave equation in fractional space. General plane wave solution to the wave equation for flelds in source-free and lossless media is obtained in fractional space. The obtained solution is a generalization of wave equation from integer dimensional space to a non-integer dimensional space. The classical results are recovered when integer-dimensional space is considered.

Nonlinear structure‐enhancing filtering using plane‐wave prediction*

Abstract: Attenuation of random noise and enhancement of structural continuity can significantly improve the quality of seismic interpretation. We present a new technique, which aims at reducing random noise while protecting structural information. The technique is based on combining structure prediction with either similarity-mean filtering or lower-upper-middle filtering. We use structure prediction to form a structural prediction of seismic traces from neighbouring traces. We apply a non-linear similarity-mean filter or an lower-upper-middle filter to select best samples from different predictions. In comparison with other common filters, such as mean or median, the additional parameters of the non-linear filters allow us to better control the balance between eliminating random noise and protecting structural information. Numerical tests using synthetic and field data show the effectiveness of the proposed structure-enhancing filters.

Electroelastic waves in a finitely deformed electroactive material

Abstract: In this paper, the coupling between a finite deformation and an electric field is examined with particular reference to the propagation of small amplitude waves in a non-linear electroelastic material based on the quasi-electrostatic approximation. The general equations governing the linearized response of electroelastic solids superimposed on a state of finite deformation in the presence of an electric field are derived along with incremental forms of the electroelastic constitutive laws and boundary conditions. Both unconstrained and incompressible materials are considered. Without restriction on the electroelastic constitutive law, the theory is first applied to the analysis of plane waves propagating in a homogeneously deformed material with an underlying uniform electric field and illustrated in the case of an isotropic material. The general equations governing 2D incremental motions are then derived and applied to the study of surface waves in a homogeneously deformed half-space of incompressible isotropic material with the electric field normal to the surface of the half-space. The dependence of the wave speed on the deformation, the electric field and the electromechanical coupling parameters is illustrated for a prototype electroelastic constitutive law.

An E-J Collocated 3-D FDTD Model of Electromagnetic Wave Propagation in Magnetized Cold Plasma

Abstract: A new three-dimensional finite-difference time-domain (FDTD) numerical model is proposed herein to simulate electromagnetic wave propagation in an anisotropic magnetized cold plasma medium. Plasma effects contributed by electrons, positive, and negative ions are considered in this model. The current density vectors are collocated at the positions of the electric field vectors, and the complete FDTD algorithm consists of three regular updating equations for the magnetic field intensity components, as well as 12 tightly coupled differential equations for updating the electric field components and current densities. This model has the capability to simulate wave behavior in magnetized cold plasma for an applied magnetic field with arbitrary direction and magnitude. We validate the FDTD algorithm by calculating Faraday rotation of a linearly polarized plane wave. Additional numerical examples of electromagnetic wave propagation in plasma are also provided, all of which demonstrate very good agreement with plasma theory.

Scale effects on the longitudinal wave propagation in nanoplates

Abstract: In this paper, the propagation characteristics of the longitudinal wave in nanoplates with small scale effects are studied. The equation of the longitudinal wave is obtained using the nonlocal elastic theory. The phase velocity and the group velocity are derived, respectively. The dispersion relation is analyzed with different wave numbers and scale coefficients. It can be observed from the results that the dispersion properties of the longitudinal wave are induced by the small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. Furthermore, the characteristics for the group velocity of the longitudinal wave in nanoplates can also be tuned by these factors.

Fusion of the LAPW and LMTO methods: The augmented plane wave plus muffin-tin orbital method

Abstract: We present a full potential linearized method to solve the one-body problem, for example in the local density approximation. A mixed basis of augmented plane waves and generalized muffin-tin orbitals (MTOs) are used for the eigenfunctions. Since MTOs efficiently describe low-energy and localized states, the mixed basis is dramatically more efficient than the linearized augmented plane wave method for a given tolerance. GaAs, MnAs, ${\text{SrTiO}}_{3}$, Cu, and the ${\text{O}}_{2}$ dimer are used as illustrations.

Focusing NLS Equation: Long-Time Dynamics of Step-Like Initial Data

Abstract: We consider the initial value problem for the focusing nonlinear Schrodinger equation with “step-like” initial data: q(x, 0) = 0 for x ≤ 0 and q(x, 0) = Aexp(−2iBx) for x > 0, where A > 0 and B ∈ ℝ are constants. The paper aims at studying the long-time asymptotics of the solution to this problem. We show that there are three regions in the half-plane −∞ 0, where the asymptotics has qualitatively different forms: a slowly decaying self-similar wave of Zakharov–Manakov type for x < −4Bt, a modulated elliptic wave for $-4Bt , and a plane wave for $x > -4(B - A\sqrt{2})t$ . The main tool is the asymptotic analysis of an associated matrix Riemann–Hilbert problem.

Analysis of Wave Propagation Through a Filled Rock Joint

Abstract: An analytical and experimental study on a longitudinal wave (P-wave) transmission normally across a filled rock joint is presented in this paper. The dynamic property of the filling material for the artificial rock joints is derived from a series of modified split Hopkinson pressure bar (SHPB) tests. The incident and transmitted waves in granitic pressure bars are calculated by wave separations of the strain gauge readings. The incident wave is approximated by a series of half-sinusoidal waves, and an analytical model on wave propagation across a filled rock joint is then deduced. The derived wave transmission coefficients across the filled joint agree very well with those from the test results. Both the analytical and test results show that the wave transmission coefficients are influenced by the mechanical properties and the input energy of the incident waves. Analytical parametric studies with respect to pre-compaction of the filling material, the frequency and amplitude of the incident wave have also been conducted.

New wave generation

Abstract: We present the results of a combined experimental and numerical study of the generation of internal waves using the novel internal wave generator design of Gostiaux et al. (Exp. Fluids, vol. 42, 2007, pp. 123–130). This mechanism, which involves a tunable source composed of oscillating plates, has so far been used for a few fundamental studies of internal waves, but its full potential is yet to be realized. Our study reveals that this approach is capable of producing a wide variety of two-dimensional wave fields, including plane waves, wave beams and discrete vertical modes in finite-depth stratifications. The effects of discretization by a finite number of plates, forcing amplitude and angle of propagation are investigated, and it is found that the method is remarkably efficient at generating a complete wave field despite forcing only one velocity component in a controllable manner. We furthermore find that the nature of the radiated wave field is well predicted using Fourier transforms of the spatial structure of the wave generator.

Freak waves in crossing seas

Abstract: We consider the modulational instability in crossing seas as a potential mechanism for the formation of freak waves. The problem is discussed in terms of a system of two coupled Nonlinear Schroedinger equations. The asymptotic validity of such system is discussed. For some specific angles between the two wave trains, the equations reduce to an integrable system. A stability analysis of these equations is discussed. Furthermore, we present an analytical study of the maximum amplification factor for an unstable plane wave solution. Results indicate that angles between 10∘ and 30∘ are the most probable for establishing a freak wave sea. We show that the theoretical expectations are consistent with numerical simulations of the Euler equations.

SAR variation study from 300 to 5000 MHz for 15 voxel models including different postures.

Abstract: An extensive study on specific absorption rate (SAR) covering 720 simulations and 15 voxel models (18–105 kg) has been performed by applying the parallel finite-difference time-domain method. High-resolution whole-body models have been irradiated with plane waves from 300 MHz to 5 GHz by applying various incoming directions and polarizations. Detailed results of whole-body SAR and peak 10 g SAR are reported, and SAR variation in the dB scale is examined. For an adult, the effect of incoming direction on whole-body SAR is larger in the GHz range than at around 300–450 MHz, and the effect is stronger with vertical polarization. For a child (height ~1.2 m), the effect of incoming direction is similar as for an adult, except at 300 MHz for horizontal polarization. The effect of the phantom (18–105 kg) on whole-body SAR is larger at around 2–5 GHz and at vertical 300 MHz (proximity of whole-body resonance for the child) than at around horizontal 300–900 MHz. Body posture has little effect on whole-body SAR in the GHz range, but at around 300–450 MHz, one may even expect a 2 dB rise in whole-body SAR if posture is changed from the standing position. Posture affects peak 10 g SAR much more than whole-body SAR. The polarization of the incident electric field may have an effect of several dB on whole-body SAR. Between 2 and 5 GHz for adults, whole-body SAR is higher for horizontal than for vertical polarization, if the incoming direction is in the azimuth plane. In the GHz range, horizontal polarization gives higher whole-body SAR, especially for irradiation from the lateral direction. A comparison between homogeneous and heterogeneous models was done. A homogenized model underestimates whole-body SAR, especially at ~2 GHz. The basic restriction of whole-body SAR, set by ICNIRP, is exceeded in the smallest models (~20 kg) at the reference level of exposure, but also some adult phantoms are close to the limit. The peak 10 g SAR limits were never exceeded in the studied cases. The present ICNIRP guidelines should be revised by lowering the reference levels, especially at around 2–5 GHz.

Plane-Wave Decomposition of Acoustical Scenes Via Spherical and Cylindrical Microphone Arrays

Abstract: Spherical and cylindrical microphone arrays offer a number of attractive properties such as direction-independent acoustic behavior and ability to reconstruct the sound field in the vicinity of the array. Beamforming and scene analysis for such arrays is typically done using sound field representation in terms of orthogonal basis functions (spherical/cylindrical harmonics). In this paper, an alternative sound field representation in terms of plane waves is described, and a method for estimating it directly from measurements at microphones is proposed. It is shown that representing a field as a collection of plane waves arriving from various directions simplifies source localization, beamforming, and spatial audio playback. A comparison of the new method with the well-known spherical harmonics based beamforming algorithm is done, and it is shown that both algorithms can be expressed in the same framework but with weights computed differently. It is also shown that the proposed method can be extended to cylindrical arrays. A number of features important for the design and operation of spherical microphone arrays in real applications are revealed. Results indicate that it is possible to reconstruct the sound scene up to order p with p2 microphones spherical array.

Electromagnetic Boundary Conditions Defined in Terms of Normal Field Components

Abstract: A set of four scalar conditions involving normal components of the fields D and B and their normal derivatives at a planar surface is introduced, among which different pairs can be chosen to represent possible boundary conditions for the electromagnetic fields. Four such pairs turn out to yield meaningful boundary conditions and their responses for an incident plane wave at a planar boundary are studied. The theory is subsequently generalized to more general boundary surfaces defined by a coordinate function. It is found that two of the pairs correspond to the PEC and PMC conditions while the other two correspond to a mixture of PEC and PMC conditions for fields polarized TE or TM with respect to the coordinate defining the surface.

Wideband Microwave Absorber Based on a Two-Dimensional Periodic Array of Microstrip Lines

Abstract: The modeling and design is presented of a new kind of circuit analogue absorber, which intercepts the electromagnetic waves through a two-dimensional periodic array of microstrip lines loaded with lumped circuit elements. For a plane wave incidence of polarization perpendicular to the strips, virtual magnetic walls are formed between the strips, and the geometry can be divided into many identical unit-cells. We first study the propagation characteristics of the unit-cell using the singular integral equation method. An RC network is then proposed to match this array with the free space and to dissipate the intercepted energy over a wide frequency range. The complete design procedure is explained through a design example that exhibits a bandwidth of 113% while the absorber thickness is less than 10% of the free space wavelength at the lowest operating frequency.

Wave function extended Lagrangian Born-Oppenheimer molecular dynamics

Abstract: Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] has been generalized to the propagation of the electronic wave functions. The technique allows highly efficient first principles molecular dynamics simulations using plane wave pseudopotential electronic structure methods that are stable and energy conserving also under incomplete and approximate self-consistency convergence. An implementation of the method within the plane-wave basis set is presented and the accuracy and efficiency is demonstrated both for semiconductor and metallic materials.

Guided wave structural health monitoring using CLoVER transducers in composite materials

Abstract: The guided wave (GW) fleld excited by piezoelectric wafers and piezocomposite transducers in carbon-flber composite materials is experimentally investigated with applications to structural health monitoring. This investigation supports the characterization of the Composite Long-range Variable-direction Emitting Radar (CLoVER) transducer introduced by the authors. A systematic approach is followed where composite conflgurations with difierent levels of anisotropy are analyzed. In particular, unidirectional, cross-ply [0/90]6S, and quasi-isotropic [0/45/-45/90]4S IM7-based composite plates are employed. A combination of laser vibrometry and flnite element analysis is used to determine the inplane wave speed and peak-to-peak amplitude distribution in each substrate considered. The results illustrate the efiect of the material anisotropy on GW propagation through the steering efiect where the wave packets do not generally travel along the direction in which they are launched. After characterizing the efiect of substrate anisotropy on the GW fleld, the performance of the CLoVER transducer to detect damage in various composite conflgurations is explored. It is found that the directionality and geometry of the device is efiective in detecting the presence and identifying the location of simulated defects in difierent composite layups.

Construction of Green's functions of parallel plates with periodic texture with application to gap waveguides - a plane-wave spectral-domain approach

Abstract: This study presents Green's functions of parallel-plate structures, where one plate has a smooth conducting surface and the other an artificial surface realised by a one-dimensional or two-dimensional periodic metamaterial-type texture. The purpose of the periodic texture is to provide cut-off of the lowest order parallel-plate modes, thereby forcing electromagnetic energy to follow conducting ridges or strips, that is, to form a gap waveguide as recently introduced. The Green's functions are constructed by using the appropriate homogenised ideal or asymptotic boundary conditions in the plane-wave spectral domain, thereby avoiding the complexity of the Floquet-mode expansions. In the special case of a single ridge or strip, an additional numerical search for propagation constants is needed and performed in order to satisfy the boundary condition on the considered ridge or strip in the spatial domain. The results reveal the dispersion characteristics of the quasi-transverse electromagnetic modes that propagate along the ridges or strips, including their lower and upper cut-off frequencies, as well as the theoretical decay of the modal field in the transverse cut-off direction. This lateral decay shows values of 50-100 dB per wavelength for realisable geometries, indicating that the gap waveguide modes are extremely confined. The analytical formulas for the location of the stopband of the lowest order parallel-plate modes obtained by small-argument approximation of the dispersion equation are also shown. To verify the proposed analysis approach, the results are compared with the results obtained with a general electromagnetic solver showing very good agreement.