Djakou, Audrey Kamta; Darmon, Michel; Fradkin, Larissa; Potel, Catherine
2015-11-01
Diffraction phenomena studied in electromagnetism, acoustics, and elastodynamics are often modeled using integrals, such as the well-known Sommerfeld integral. The far field asymptotic evaluation of such integrals obtained using the method of steepest descent leads to the classical Geometrical Theory of Diffraction (GTD). It is well known that the method of steepest descent is inapplicable when the integrand's stationary phase point coalesces with its pole, explaining why GTD fails in zones where edge diffracted waves interfere with incident or reflected waves. To overcome this drawback, the Uniform geometrical Theory of Diffraction (UTD) has been developed previously in electromagnetism, based on a ray theory, which is particularly easy to implement. In this paper, UTD is developed for the canonical elastodynamic problem of the scattering of a plane wave by a half-plane. UTD is then compared to another uniform extension of GTD, the Uniform Asymptotic Theory (UAT) of diffraction, based on a more cumbersome ray theory. A good agreement between the two methods is obtained in the far field. PMID:26627800
Liu, Haigang; Xu, Zijian; Zhang, Xiangzhi; Wu, Yanqing; Guo, Zhi; Tai, Renzhong
2013-04-10
In coherent diffractive imaging (CDI) experiments, a beamstop (BS) is commonly used to extend the exposure time of the charge-coupled detector and obtain high-angle diffraction signals. However, the negative effect of a large BS is also evident, causing low-frequency signals to be missed and making CDI reconstruction unstable or causing it to fail. We performed a systematic simulation investigation of the effects of BSs on the quality of reconstructed images from both plane-wave and ptychographic CDI (PCDI). For the same imaging quality, we found that ptychography can tolerate BSs that are at least 20 times larger than those for plane-wave CDI. For PCDI, a larger overlap ratio and a smaller illumination spot can significantly increase the imaging robustness to the negative influence of BSs. Our results provide guidelines for the usage of BSs in CDI, especially in PCDI experiments, which can help to further improve the spatial resolution of PCDI. PMID:23670772
Plane Wave Diffraction by a Finite Plate with Impedance Boundary Conditions
Nawaz, Rab; Ayub, Muhammad; Javaid, Akmal
2014-01-01
In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier transform and the modified stationary phase method. Detailed graphical analysis was also made for various physical parameters we were interested in. PMID:24755624
Wave diffraction by a half-plane with an obstacle perpendicular to the boundary
NASA Astrophysics Data System (ADS)
Castro, L. P.; Kapanadze, D.
We prove the unique existence of solutions for different types of boundary value problems of wave diffraction by a half-plane with a screen or a crack perpendicular to the boundary. Representations of the solutions are also obtained upon the consideration of some associated operators. This is done in a Bessel potential spaces framework and for complex (non-real) wave numbers. The investigation is mostly based on the construction of explicit operator relations, the potential method, and a factorization technique for a certain class of oscillating Fourier symbols which naturally arise from the problems.
Plane-wave Fresnel diffraction by elliptic apertures: a Fourier-based approach.
Borghi, Riccardo
2014-10-01
A simple theoretical approach to evaluate the scalar wavefield, produced, within paraxial approximation, by the diffraction of monochromatic plane waves impinging on elliptic apertures or obstacles is presented. We find that the diffracted field can be mathematically described in terms of a Fourier series with respect to an angular variable suitably related to the elliptic parametrization of the observation plane. The convergence features of such Fourier series are analyzed, and a priori truncation criterion is also proposed. Two-dimensional maps of the optical intensity diffraction patterns are then numerically generated and compared, at a visual level, with several experimental pictures produced in the past. The last part of this work is devoted to carrying out an analytical investigation of the diffracted field along the ellipse axis. A uniform approximation is derived on applying a method originally developed by Schwarzschild, and an asymptotic estimate, valid in the limit of small eccentricities, is also obtained via the Maggi-Rubinowicz boundary wave theory. PMID:25401234
Depine, Ricardo A; Lakhtakia, Akhlesh
2004-05-01
Considering the diffraction of a plane wave by a periodically corrugated half-space, we show that the transformation of the refracting medium from positive (negative) phase velocity to negative (positive) phase velocity type has an influence on the diffraction efficiencies. This effect increases with increasing corrugation depth, owing to the presence of evanescent waves in the troughs of the corrugated interface. PMID:15244981
NASA Astrophysics Data System (ADS)
Medvedik, M. Yu.; Smirnov, Yu. G.; Tsupak, A. A.
2014-08-01
The scalar problem of plane wave diffraction by a system of bodies and infinitely thin screens is considered in a quasi-classical formulation. The solution is sought in the classical sense but is defined not in the entire space ℝ3 but rather everywhere except for the screen edges. The original boundary value problem for the Helmholtz equation is reduced to a system of weakly singular integral equations in the regions occupied by the bodies and on the screen surfaces. The equivalence of the integral and differential formulations is proven, and the solvability of the system in the Sobolev spaces is established. The integral equations are approximately solved by the Bubnov-Galerkin method. The convergence of the method is proved, its software implementation is described, and numerical results are presented.
Scattering and diffraction of plane SH-waves by periodically distributed canyons
NASA Astrophysics Data System (ADS)
Ba, Zhenning; Liang, Jianwen; Zhang, Yanju
2016-06-01
A new method is presented to study the scattering and diffraction of plane SH-waves by periodically distributed canyons in a layered half-space. This method uses the indirect boundary element method combined with Green's functions of uniformly distributed loads acting on periodically distributed inclined lines. The periodicity feature of the canyons is exploited to limit the discretization effort to a single canyon, which avoids errors induced by the truncation of the infinite boundary, and the computational complexity and the demand on memory can be significantly reduced. Furthermore, the total wave fields are decomposed into the free field and scattered field in the process of calculation, which means that the method has definite physical meaning. The implementation of the method is described in detail and its accuracy is verified. Parametric studies are performed in the frequency domain by taking periodically distributed canyons of semi-circular and semi-elliptic cross-sections as examples. Numerical results show that the dynamic responses of periodically distributed canyons can be quite different from those for a single canyon and significant dynamic interactions exist between the canyons.
NASA Astrophysics Data System (ADS)
Serdyuk, Vladimir M.; Titovitsky, Joseph A.
2014-06-01
An exact solution of two-dimensional problem of plane electromagnetic wave scattering by a perfectly conducting strip in the presence of a parallel plane dielectric layer is presented. The given solution is constructed using the mode-matching technique in the form of diffraction integrals over propagation parameter, i.e. in the form of superposition of a large number of homogeneous and inhomogeneous plane waves with continuous spectrum of spatial frequencies. These integrals have poles, which are caused by the presence of a transparent dielectric layer and correspond to its waveguide modes. Because of this, diffraction integrals need the procedure of regularization with explicit extraction of pole terms and smoothing of integrands, whereupon the residual diffraction integrals are computed using simple numerical methods. They describe usual scattered field of a bounded obstacle, which is determined by regularized diffraction integrals and decreases in all directions from an obstacle. Besides, the total diffraction field contains a discrete finite sum of waveguide fields of guided modes of a plane dielectric layer, which correspond to the extracted pole terms of initial diffraction integrals. These fields correspond to pairs of guided waves, which move apart from the region of their excitation near a strip, propagating parallel to the boundaries of a layer and conserving finite amplitude at infinity.
Solution of the three-dimensional problem of plane wave diffraction by a two-period plane grating
NASA Astrophysics Data System (ADS)
Manenkov, S. A.
2016-03-01
Using the discrete source method, we develop an algorithm for solving the three-dimensional problem of wave scattering by a plane grating consisting of acoustically soft or acoustically stiff bodies. An efficient algorithm is proposed for determining the periodic Green's function of the grating. Numerical results are obtained for different geometries of the grating elements. The fulfillment of the energy conservation law is verified along with the fulfillment of the boundary condition at the surface of the central grating element.
Declercq, Nico F; Degrieck, Joris; Briers, Rudy; Leroy, Oswald
2005-08-01
This paper extends the theory of the diffraction of sound on 1D corrugated surfaces to 2D corrugated surfaces. Such surfaces, that are egg crate shaped, diffract incoming sound into all polar directions, which is fundamentally different from 1D corrugated surfaces. A theoretical justification is given for extending the classical grating equation to the case of incident inhomogeneous waves, for 1D corrugated surfaces as well as for 2D corrugated surfaces. Even though the present paper presents a theory which is valid for all angles of incidence, special attention is given to the particular case of the stimulation of surface waves by normal incident sound. The most interesting conclusion is that, depending on the frequency and the incident inhomogeneity, Scholte-Stoneley waves and leaky Rayleigh waves can be generated in different directions. This effect might be of particular interest in the development of surface acoustic wave devices and the basic idea of this steering effect can be of importance for planar actuators. PMID:15913694
NASA Astrophysics Data System (ADS)
Kyurkchan, A. G.; Manenkov, S. A.
2016-09-01
Two approaches for solving the three-dimensional problem of wave diffraction at a finite grating consisting of bodies of revolution are proposed. An approximate solution is obtained for a grating with small elements. This solution is applied to consider gratings with a large number of elements. The coincidence of the results obtained by the two methods is shown. The reflection and transmission coefficients are compared for finite and infinite gratings.
Takahashi, Yukio; Nishino, Yoshinori; Ishikawa, Tetsuya; Tsutsumi, Ryosuke; Kubo, Hideto; Furukawa, Hayato; Mimura, Hidekazu; Matsuyama, Satoshi; Zettsu, Nobuyuki; Matsubara, Eiichiro; Yamauchi, Kazuto
2009-08-01
X-ray waves in the center of the beam waist of nearly diffraction limited focused x-ray beams can be considered to have amplitude and phase that are both almost uniform, i.e., they are x-ray plane waves. Here we report the results of an experimental demonstration of high-resolution diffraction microscopy using the x-ray plane wave of the synchrotron x-ray beam focused using Kirkpatrik-Baez mirrors. A silver nanocube with an edge length of {approx}100 nm is illuminated with the x-ray beam focused to a {approx}1 {mu}m spot at 12 keV. A high-contrast symmetric diffraction pattern of the nanocube is observed in the forward far field. An image of the nanocube is successfully reconstructed by an iterative phasing method and its half-period resolution is 3.0 nm. This method does not only dramatically improve the spatial resolution of x-ray microscopy but also is a key technology for realizing single-pulse diffractive imaging using x-ray free-electron lasers.
NASA Astrophysics Data System (ADS)
Feshchenko, A. M.; Strikhanov, M. N.
We investigate a possibility of an interference of diffraction radiation with a field, originated from scattering of refracted on a non-uniform surface electromagnetic wave in a case of total internal reflection. An effect of the field from fast charged particle and the refracted field on surface inhomogeneities gives rise to emergence of surface polarization currents. Radiation from these currents can be of use in analysis of surface optical features. The opportunity of studying of surface characteristics by means of diffraction radiation and total internal reflection of the electromagnetic wave is discussed in this paper.
NASA Astrophysics Data System (ADS)
Kotlyar, Victor V.; Kovalev, Alexey A.; Skidanov, Roman V.; Moiseev, Oleg Yu.; Soifer, Victor A.
2007-07-01
We derive what we believe to be new analytical relations to describe the Fraunhofer diffraction of the finite-radius plane wave by a helical axicon (HA) and a spiral phase plate (SPP). The solutions are deduced in the form of a series of the Bessel functions for the HA and a finite sum of the Bessel functions for the SPP. The solution for the HA changes to that for the SPP if the axicon parameter is set equal to zero. We also derive what we believe to be new analytical relations to describe the Fresnel and Fraunhofer diffraction of the Gaussian beam by a HA are derived. The solutions are deduced in the form of a series of the hypergeometric functions. We have fabricated by photolithography a binary diffractive optical element (a HA with number n=10) able to produce in the focal plane of a spherical lens an optical vortex, which was then used to perform rotation of several polystyrene beads of diameter 5 μm.
Marsh, Stanley P.
1988-01-01
An explosive plane-wave air lens which enables a spherical wave form to be converted to a planar wave without the need to specially machine or shape explosive materials is described. A disc-shaped impactor having a greater thickness at its center than around its periphery is used to convert the spherical wave into a plane wave. When the wave reaches the impactor, the center of the impactor moves first because the spherical wave reaches the center of the impactor first. The wave strikes the impactor later in time as one moves radially along the impactor. Because the impactor is thinner as one moves radially outward, the velocity of the impactor is greater at the periphery than at the center. An acceptor explosive is positioned so that the impactor strikes the acceptor simultaneously. Consequently, a plane detonation wave is propagated through the acceptor explosive.
Marsh, S.P.
1988-03-08
An explosive plane-wave air lens which enables a spherical wave form to be converted to a planar wave without the need to specially machine or shape explosive materials is described. A disc-shaped impactor having a greater thickness at its center than around its periphery is used to convert the spherical wave into a plane wave. When the wave reaches the impactor, the center of the impactor moves first because the spherical wave reaches the center of the impactor first. The wave strikes the impactor later in time as one moves radially along the impactor. Because the impactor is thinner as one moves radially outward, the velocity of the impactor is greater at the periphery than at the center. An acceptor explosive is positioned so that the impactor strikes the acceptor simultaneously. Consequently, a plane detonation wave is propagated through the acceptor explosive. 4 figs.
Marsh, S.P.
1987-03-12
An explosive plane-wave air lens which enables a spherical wave form to be converted to a planar wave without the need to specially machine or shape explosive materials is described. A disc-shaped impactor having a greater thickness at its center than around its periphery is used to convert the spherical wave into a plane wave. When the wave reaches the impactor, the center of the impactor moves first because the spherical wave reaches the center of the impactor first. The wave strikes the impactor later in time as one moves radially along the impactor. Because the impactor is thinner as one moves radially outward, the velocity of the impactor is greater at the periphery than at the center. An acceptor explosive is positioned so that the impactor strikes the acceptor simultaneously. Consequently, a plane detonation wave is propagated through the acceptor explosive. 3 figs., 3 tabs.
NASA Astrophysics Data System (ADS)
Khan, Tufail A.; Ayub, M.; Jilani, K.
2014-09-01
The effects of wall impedances with cold plasma permittivity on an E-polarized electromagnetic signal propagating through a parallel-plate waveguide immersed in a cold plasma have been analyzed. The Helmholtz equation in cold plasma is derived from the model equations. The solution of the Helmholtz equation in cold plasma is determined by Wiener-Hopf technique. From the solution it is observed that the amplitude of the diffracted field decreases with increasing permittivity of the plasma (i.e., by decreasing electron number density (or plasma frequency) or by increasing ion number density). The work presented may be of great importance to quantify the effects of ionosphere plasma on the communicating signals between an Earth station and an artificial satellite in Earth's atmosphere.
NASA Astrophysics Data System (ADS)
Forgács, Péter; Lukács, Árpád; Romańczukiewicz, Tomasz
2013-12-01
It is shown that in a large class of systems, plane waves act as tractor beams: i.e., an incident plane wave can exert a pulling force on the scatterer. The underlying physical mechanism for the pulling force is due to the sufficiently strong scattering of the incoming wave into another mode carrying more momentum, in which case excess momentum is created behind the scatterer. This tractor beam or negative radiation pressure (NRP) effect, is found to be generic in systems with multiple scattering channels. In a birefringent medium, electromagnetic plane waves incident on a thin plate exert NRP of the same order of magnitude as optical radiation pressure, while in artificial dielectrics (metamaterials), the magnitude of NRP can even be macroscopic. In two dimensions, we study various scattering situations on vortices, and NRP is shown to occur by the scattering of heavy baryons into light leptons off cosmic strings, and by neutron scattering off vortices in the XY model.
Realizing in-plane surface diffraction by x-ray multiple-beam diffraction with large incidence angle
Huang, Xian-Rong Gog, Thomas; Assoufid, Lahsen; Peng, Ru-Wen; Siddons, D. P.
2014-11-03
Based on rigorous dynamical-theory calculations, we demonstrate the principle of an x-ray multiple-beam diffraction (MBD) scheme that overcomes the long-lasting difficulties of high-resolution in-plane diffraction from crystal surfaces. This scheme only utilizes symmetric reflection geometry with large incident angles but activates the out-of-plane and in-plane diffraction processes simultaneously and separately in the continuous MBD planes. The in-plane diffraction is realized by detoured MBD, where the intermediate diffracted waves propagate parallel to the surface, which corresponds to an absolute Bragg surface diffraction configuration that is extremely sensitive to surface structures. A series of MBD diffraction and imaging techniques may be developed from this principle to study surface/interface (misfit) strains, lateral nanostructures, and phase transitions of a wide range of (pseudo)cubic crystal structures, including ultrathin epitaxial films and multilayers, quantum dots, strain-engineered semiconductor or (multi)ferroic materials, etc.
Plane waves in noncommutative fluids
NASA Astrophysics Data System (ADS)
Abdalla, M. C. B.; Holender, L.; Santos, M. A.; Vancea, I. V.
2013-08-01
We study the dynamics of the noncommutative fluid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear partial differential equations in which the variables are the fluid density and the fluid potentials. We show that these equations admit a set of solutions that are monochromatic plane waves for the fluid density and two of the potentials and a linear function for the third potential. The energy-momentum tensor of the plane waves is calculated.
Plane Wave and Coulomb Asymptotics
NASA Astrophysics Data System (ADS)
Mulligan, P. G.; Crothers, D. S. F.
2004-01-01
A simple plane wave solution of the Schrödinger Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f obeys unitarity and the optical theorem. By closely considering the standard asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J Leech et al, Phys. Rev. Lett. 88 257901 (2002)). The problem is resolved via non-uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.
Mielenz, Klaus D.
2003-01-01
The accuracy and physical significance of the classical Rayleigh-Sommerfeld and Kirchhoff diffraction integrals are assessed in the context of Sommerfeld’s rigorous theory of half-plane diffraction and Maxwell’s equations. It is shown that the Rayleigh-Sommerfeld integrals are in satisfactory agreement with Sommerfeld’s theory in most of the positive near zone, except at sub-wavelength distances from the screen. On account of the bidirectional nature of diffraction by metallic screens the Rayleigh-Sommerfeld integrals themselves cannot be used for irradiance calculations, but must first be resolved into their forward and reverse components and it is found that Kirchhoff’s integral is the appropriate measure of the forward irradiance. Because of the inadequate boundary conditions assumed in their derivation the Rayleigh-Sommerfeld and Kirchhoff integrals do not correctly describe the flow of energy through the aperture.
Electron diffraction by plasmon waves
NASA Astrophysics Data System (ADS)
García de Abajo, F. J.; Barwick, B.; Carbone, F.
2016-07-01
An electron beam traversing a structured plasmonic field is shown to undergo diffraction with characteristic angular patterns of both elastic and inelastic outgoing electron components. In particular, a plasmonic grating (e.g., a standing wave formed by two counterpropagating plasmons in a thin film) produces diffraction orders of the same parity as the net number of exchanged plasmons. Large diffracted beam fractions are predicted to occur for realistic plasmon intensities in attainable geometries due to a combination of phase and amplitude changes locally imprinted on the passing electron wave. Our study opens vistas in the study of multiphoton exchanges between electron beams and evanescent optical fields with unexplored effects related to the transversal component of the electron wave function.
Jach, T.; Zhang, Y.; Colella, R.; de Boissieu, M.; Boudard, M.; Goldman, A.I.; Lograsso, T.A.; Delaney, D.W.; Kycia, S.
1999-04-01
We have observed dynamical diffraction in the
Electromagnetic diffraction efficiencies for plane reflection diffraction gratings
NASA Technical Reports Server (NTRS)
Marathay, A. S.; Shrode, T. E.
1973-01-01
Results are presented of research activities on holographic grating research. A large portion of this work was performed using rigorous vector diffraction theory, therefore, the necessary theory has been included in this report. The diffraction efficiency studies were continued using programs based on a rigorous theory. The simultaneous occurrence of high diffraction efficiencies and the phenomenon of double Wood's anomalies is demonstrated along with a graphic method for determining the necessary grating parameters. Also, an analytical solution for a grating profile that is perfectly blazed is obtained. The performance of the perfectly blazed grating profile is shown to be significantly better than grating profiles previously studied. Finally, a proposed method is described for the analysis of coarse echelle gratings using rigorous vector diffraction that is currently being developed.
Electromagnetic diffraction efficiencies for plane reflection diffraction gratings
NASA Technical Reports Server (NTRS)
Marathay, A. S.; Shrode, T. E.
1974-01-01
The theory and computer programs, based on electromagnetic theory, for the analysis and design of echelle gratings were developed. The gratings are designed for instruments that operate in the ultraviolet portion of the spectrum. The theory was developed so that the resulting computer programs will be able to analyze deep (up to 30 wavelengths) gratings by including as many as 100 real or homogeneous diffraction orders. The program calculates the complex amplitude coefficient for each of the diffracted orders. A check on the numerical method used to solve the integral equations is provided by a conservation of energy calculation.
Photoelectron wave function in photoionization: plane wave or Coulomb wave?
Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I
2015-11-19
The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion. PMID:26509428
Diffraction optics for terahertz waves
NASA Astrophysics Data System (ADS)
Wiltse, James C.
2004-09-01
Conventional lenses are important components for many terahertz applications, but ordinary lenses are very difficult to fabricate for short-focal lengths. Multi-level phase-corrected zoned lens antennas have been investigated with particular application at terahertz wavelengths. These zoned lenses (or diffractive optics) give better performance than ordinary lenses, and because of their planar construction are easier and cheaper to fabricate. The depths of cut needed for a grooved zone plate are quite small, even when materials with low dielectric constants are used. Zoned lenses have been built and tested at various frequencies from 100 GHz to 1.5 THz, with phase correction levels of half-wave, quarter-wave, or eighth-wavelength. The inherent losses in transparent materials increase monotonically over this frequency range. Typical low-loss materials include polystyrene, polyethylene, Teflon, polycarbonate, polystyrene foam, foamed polyethylene, low density polytetrafluoroethylene (PTFE), TPX, quartz, sapphire, and silicon. Low dielectric-constant materials are normally preferred to reduce reflection and attenuation losses. Techniques for cutting or milling the materials to small dimensions are important, because at 1.0 THz an eighth-wavelength correction for silicon is only 15 μm. Another characteristic of zoned diffraction optics is their frequency behavior. Previous investigations have considered their bandwidth dependence and quasi-periodic extended frequency response for a specified focal length. As frequency changes, the focal point moves along the axis of the zoned lens. An analysis is given to explain this effect.
Double plane wave reverse time migration with plane wave Green's function
NASA Astrophysics Data System (ADS)
Zhao, Z.; Sen, M. K.; Stoffa, P. L.
2015-12-01
Reverse time migration (RTM) is effective in obtaining complex subsurface structures from seismic data. By solving the two-way wave equation, RTM can use entire wavefield for imaging. Although powerful computer are becoming available, the conventional pre-stack shot gather RTM is still computationally expensive. Solving forward and backward wavefield propagation for each source location and shot gather is extremely time consuming, especially for large seismic datasets. We present an efficient, accurate and flexible plane wave RTM in the frequency domain where we utilize a compressed plane wave dataset, known as the double plane wave (DPW) dataset. Provided with densely sampled seismic dataset, shot gathers can be decomposed into source and receiver plane wave components with minimal artifacts. The DPW RTM is derived under the Born approximation and utilizes frequency domain plane wave Green's function for imaging. Time dips in the shot profiles can help to estimate the range of plane wave components present in shot gathers. Therefore, a limited number of plane wave Green's functions are needed for imaging. Plane wave Green's functions can be used for imaging both source and receiver plane waves. Source and receiver reciprocity can be used for imaging plane wave components at no cost and save half of the computation time. As a result, the computational burden for migration is substantially reduced. Plane wave components can be migrated independently to recover specific targets with given dips, and ray parameter common image gathers (CIGs) can be generated after migration directly. The ray parameter CIGs can be used to justify the correctness of velocity models. Subsurface anisotropy effects can also be included in our imaging condition, provided with plane wave Green's functions in the anisotropic media.
Aberrations of diffracted wave fields. II. Diffraction gratings.
Mahajan, V N
2000-12-01
The Rayleigh-Sommerfeld theory is applied to diffraction of a spherical wave by a grating. The grating equation is obtained from the aberration-free diffraction pattern, and its aberrations are shown to be the same as the conventional aberrations obtained by using Fermat's principle. These aberrations are shown to be not associated with the diffraction process. Moreover, it is shown that the irradiance distribution of a certain diffraction order is the Fraunhofer diffraction pattern of the grating aperture as a whole aberrated by the aberration of that order. PMID:11140481
Simple Harmonic Motion in Harmonic Plane Waves.
ERIC Educational Resources Information Center
Benumof, Reuben
1980-01-01
Discusses the distribution of kinetic and potential energy in transverse and longitudinal waves and examines the transmission of power and momentum. This discussion is intended to aid in understanding the simple harmonic motion of a particle involved in the propagation of a harmonic mechanical plane wave. (HM)
A scattering approach to sea wave diffraction
NASA Astrophysics Data System (ADS)
Corradini, M. L.; Garbuglia, M.; Maponi, P.; Ruggeri, M.
2016-06-01
This paper intends to show a model for the diffraction of sea waves approaching an OWC device, which converts the sea waves motion into mechanical energy and then electrical energy. This is a preliminary study to the optimisation of the device, in fact the computation of sea waves diffraction around the device allows the estimation of the sea waves energy which enters into the device. The computation of the diffraction phenomenon is the result of a sea waves scattering problem, solved with an integral equation method.
Horizons and plane waves: A review
Hubeny, Veronika E.; Rangamani, Mukund
2003-11-06
We review the attempts to construct black hole/string solutions in asymptotically plane wave spacetimes. First, we demonstrate that geometries admitting a covariantly constant null Killing vector cannot admit event horizons, which implies that pp-waves can't describe black holes. However, relaxing the symmetry requirements allows us to generate solutions which do possess regular event horizons while retaining the requisite asymptotic properties. In particular, we present two solution generating techniques and use them to construct asymptotically plane wave black string/brane geometries.
NASA Technical Reports Server (NTRS)
Rojas, Roberto G.
1985-01-01
A uniform geometrical theory of diffraction (UTD) solution is developed for the problem of the diffraction by a thin dielectric/ferrite half plane when it is excited by a plane, cylindrical, or surface wave field. Both transverse electric and transverse magnetic cases are considered. The solution of this problem is synthesized from the solutions to the related problems of EM diffraction by configurations involving perfectly conducting electric and magnetic walls covered by a dielectric/ferrite half-plane of one half the thickness of the original half-plane.
Plane wave facing technique for ultrasonic elastography
NASA Astrophysics Data System (ADS)
Lee, Mingu; Shim, Hwan; Cheon, Byeong Geun; Jung, Yunsub
2014-03-01
A shear wave generation technique which exploits multiple plane waves facing with each other toward their center line is introduced. On this line, ultrasonic waves interfere constructively resulting two planar shear waves that propagate to the opposite directions parallel to the transducer instead of oblique wave from multiple point focused pushes due to the temporal inconsistency of the pushes. One advantage of the plane wave facing technique over an unfocused push beam is that it generates much larger shear waves because it actively takes advantage of constructive interference between waves and, moreover, a larger number of elements can be used without diffusing the beam pattern. Field II simulated intensity maps of the push beams using the proposed method are presented with those of multiple point focusing and unfocusing techniques for comparison. In the simulation, two plane waves are considered for the simplicity, and the number of elements, apodization, and steering angles for facing are varied as parameters. Also, elasticity images of CIRS 049A phantom are presented using the proposed technique with comb-shaped push beams, i.e. multiple push beams are used simultaneously at different locations. L7-4 transducer is used for the simulation and elasticity imaging.
NASA Technical Reports Server (NTRS)
Kearns, James A.
1989-01-01
Phenomena associated with long range propagation of sound over irregular topography motivated this work, which was to analyze the diffraction effects which would occur near the tops of hills and ridges. The diffraction of a high frequency plane wave due to its grazing of a two-dimensional curved surface of finite impedance was also studied. Laboratory scale models were constructed and measurements were made of the field on, above, and behind either of two curved surfaces possessing distinctly different impedances; that is, one was soft while the other was hard. The experimental technique consisted of simultaneously measuring the pressure at a reference point and at a field point due to a transient pulse generated by an electric spark. The pressure waveforms were digitized and processed. The ratio of the discrete Fourier transforms of the two waveforms provided an estimate of the insertion loss between them. The results of the measurements were compared with the predictions of a theory which was derived by Pierce using the method of Matched Asymptotic Expansions (MAE). The predictions relied upon the experimental evaluation of the impedance of each surface at grazing angles of incidence. This evaluation was achieved by a fairly standard technique involving empirical models of various generic types of surfaces. An example was shown of the important role that the structural intricacies of a surface play in the determination of an appropriate model. The comparison between the measurements and predictions indicated that the theory gives an excellent description of the field anywhere near a curved surface. Further, with a simple modification, the theory was also shown to give nearly as good of a description of the field surrounding a curved surface even at distances far behind the surface yet near the line of sight.
Rayleigh–Bloch waves along elastic diffraction gratings
Colquitt, D. J.; Craster, R. V.; Antonakakis, T.; Guenneau, S.
2015-01-01
Rayleigh–Bloch (RB) waves in elasticity, in contrast to those in scalar wave systems, appear to have had little attention. Despite the importance of RB waves in applications, their connections to trapped modes and the ubiquitous nature of diffraction gratings, there has been no investigation of whether such waves occur within elastic diffraction gratings for the in-plane vector elastic system. We identify boundary conditions that support such waves and numerical simulations confirm their presence. An asymptotic technique is also developed to generate effective medium homogenized equations for the grating that allows us to replace the detailed microstructure by a continuum representation. Further numerical simulations confirm that the asymptotic scheme captures the essential features of these waves. PMID:25568616
Plane gravitational waves in real connection variables
Hinterleitner, Franz; Major, Seth
2011-02-15
We investigate using plane-fronted gravitational wave space-times as model systems to study loop quantization techniques and dispersion relations. In this classical analysis we start with planar symmetric space-times in the real connection formulation. We reduce via Dirac constraint analysis to a final form with one canonical pair and one constraint, equivalent to the metric and Einstein equations of plane-fronted-with-parallel-rays waves. Because of the symmetries and use of special coordinates, general covariance is broken. However, this allows us to simply express the constraints of the consistent system. A recursive construction of Dirac brackets results in nonlocal brackets, analogous to those of self-dual fields, for the triad variables. Not surprisingly, this classical analysis produces no evidence for dispersion, i.e. a variable propagation speed of gravitational plane-fronted-with-parallel-rays waves.
Wave diffraction by a cosmic string
NASA Astrophysics Data System (ADS)
Fernández-Núñez, Isabel; Bulashenko, Oleg
2016-08-01
We show that if a cosmic string exists, it may be identified through characteristic diffraction pattern in the energy spectrum of the observed signal. In particular, if the string is on the line of sight, the wave field is shown to fit the Cornu spiral. We suggest a simple procedure, based on Keller's geometrical theory of diffraction, which allows to explain wave effects in conical spacetime of a cosmic string in terms of interference of four characteristic rays. Our results are supposed to be valid for scalar massless waves, including gravitational waves, electromagnetic waves, or even sound in case of condensed matter systems with analogous topological defects.
Multipole and plane wave expansions of diverging and converging fields.
Hoang, Thanh Xuan; Chen, Xudong; Sheppard, Colin J R
2014-04-21
This paper presents and compares two basis systems, spherical harmonics and plane waves, for studying diverging and converging beams in an optical system. We show a similarity between a converging field and the time reversed field of a radiation field. We present and analyze the differences between the Debye-Wolf diffraction integral and the multipole theory for focusing of polarized light. The Debye-Wolf diffraction integral gives a well-known anomalous behavior on the optical axis and at the edge of the focused beam that can be avoided by using the multipole theory. PMID:24787784
Coded Excitation Plane Wave Imaging for Shear Wave Motion Detection
Song, Pengfei; Urban, Matthew W.; Manduca, Armando; Greenleaf, James F.; Chen, Shigao
2015-01-01
Plane wave imaging has greatly advanced the field of shear wave elastography thanks to its ultrafast imaging frame rate and the large field-of-view (FOV). However, plane wave imaging also has decreased penetration due to lack of transmit focusing, which makes it challenging to use plane waves for shear wave detection in deep tissues and in obese patients. This study investigated the feasibility of implementing coded excitation in plane wave imaging for shear wave detection, with the hypothesis that coded ultrasound signals can provide superior detection penetration and shear wave signal-to-noise-ratio (SNR) compared to conventional ultrasound signals. Both phase encoding (Barker code) and frequency encoding (chirp code) methods were studied. A first phantom experiment showed an approximate penetration gain of 2-4 cm for the coded pulses. Two subsequent phantom studies showed that all coded pulses outperformed the conventional short imaging pulse by providing superior sensitivity to small motion and robustness to weak ultrasound signals. Finally, an in vivo liver case study on an obese subject (Body Mass Index = 40) demonstrated the feasibility of using the proposed method for in vivo applications, and showed that all coded pulses could provide higher SNR shear wave signals than the conventional short pulse. These findings indicate that by using coded excitation shear wave detection, one can benefit from the ultrafast imaging frame rate and large FOV provided by plane wave imaging while preserving good penetration and shear wave signal quality, which is essential for obtaining robust shear elasticity measurements of tissue. PMID:26168181
Polarization of almost-plane waves.
Sheppard, C J
2000-02-01
The general polarization behavior of almost-plane waves, in which the electric field varies slowly over a circular pupil, is considered, on the basis of an axial Hertz potential treatment and expansion in Zernike polynomials. The resultant modes of a circular aperture are compared with the well-known waveguide (or optical fiber) modes and Gaussian beam modes. The wave can be decomposed into partial waves of electric and magnetic types. The modes for a square pupil are also considered. The particular application of the effect on polarization of focusing the waves is discussed. Another application discussed is the Fresnel reflection from a dielectric interface, it being shown that the Fresnel reflection alters the relative strength of the electric and magnetic components. PMID:10680636
Optics in a nonlinear gravitational plane wave
NASA Astrophysics Data System (ADS)
Harte, Abraham I.
2015-09-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Onural, Levent
2011-03-01
The diffraction relation between a plane and another plane that is both tilted and translated with respect to the first one is revisited. The derivation of the result becomes easier when the impulse function over a surface is used as a tool. Such an approach converts the original 2D problem to an intermediate 3D problem and thus allows utilization of easy-to-interpret Fourier transform properties due to rotation and translation. An exact solution for the scalar monochromatic propagating waves case when the propagation direction is restricted to be in the forward direction is presented. PMID:21383808
Plane wave imaging using phased array
NASA Astrophysics Data System (ADS)
Volker, Arno
2014-02-01
Phased arrays are often used for rapid inspections. Phased arrays can be used to synthesize different wave fronts. For imaging, focused wave fronts are frequently used. In order to build an image, the phased array has to be fired multiple times at the same location. Alternatively, different data acquisition configurations can be designed in combination with an imaging algorithm. The objective of this paper is to use the minimal amount of data required to construct an image. If a plane wave is synthesized, the region of interest is illuminated completely. For plane wave synthesis, all elements in the phase array are fired. This ensures a good signal to noise ratio. Imaging can be performed efficiently with a mapping algorithm in the wavenumber domain. The algorithm involves only two Fourier transforms and can therefore be extremely fast. The obtained resolution is comparable to conventional imaging algorithms. This work investigates the potential and limitations of this mapping algorithm on simulated data. With this approach, frame rates of more than 1 kHz can be achieved.
Symmetrically converging plane thermonuclear burn waves
NASA Astrophysics Data System (ADS)
Charakhch'yan, A. A.; Khishchenko, K. V.
2013-10-01
Five variants of a one-dimensional problem on synchronous bilateral action of two identical drivers on opposite surfaces of a plane layer of DT fuel with the normal or five times greater initial density, where the solution includes two thermonuclear burn waves propagating to meet one another at the symmetry plane, are simulated. A laser pulse with total absorption of energy at the critical density (in two variants) and a proton bunch that provides for a nearly isochoric heating (in three variants) are considered as drivers. A wide-range equation of state for the fuel, electron and ion heat conduction, self-radiation of plasma and plasma heating by α-particles are taken into account. In spite of different ways of ignition, various models of α-particle heat, whether the burn wave remains slow or transforms into the detonation wave, and regardless of way of such a transformation, the final value of the burn-up factor depends essentially on the only parameter Hρ0, where H is the half-thickness of the layer and ρ0 is the initial fuel density. This factor is about 0.35 at Hρ0 ≈ 1 g cm-2 and about 0.7 at Hρ0 ≈ 5 g cm-2. The expansion stage of the flow (after reflecting the burn or detonation wave from the symmetry plane) gives the main contribution in forming the final values of the burn-up factor and the gain at Hρ0 ≈ 1 g cm-2 and increases them approximately two times at Hρ0 ≈ 5 g cm-2. In the case of the proton driver, the final value of the gain is about 200 at Hρ0 ≈ 1 g cm-2 and about 2000 at Hρ0 ≈ 5 g cm-2. In the case of the laser driver, the above values are four times less in conformity with the difference between the driver energies.
Synchrotron-radiation plane-wave GID topography (abstract)
NASA Astrophysics Data System (ADS)
Novikov, D. V.; Gog, T.; Griebenow, M.; Materlik, G.
1995-02-01
X-ray-diffraction topography is a traditional tool for investigating the real structure of crystals and provides high sensitivity to lattice constant variations with good space resolution. However, recent advances in technology and the growing importance of surface regions of single-crystal and multilayer systems require new approaches to this method, which are made possible by the high brightness and wide tunability of synchrotron radiation. In this work the SR plane-wave grazing-incidence diffraction (GID) topography is discussed as an effective tool for depth-resolved investigations of near-surface defect structures in single crystals and epitaxial layers. The favorable properties of synchrotron radiation enable one to avoid the usual limitations on applicability of this diffraction geometry and investigate all classes of defects in real materials. The experiments were performed at the beamlines ROEMO1 and CEMO of HASYLAB, using double-crystal Ge/asymmetric Si monochromators. The image formation of near-surface dislocations and the effects of refraction on rough surfaces were investigated. Oblique diffraction planes were used to compare the topography in skew incoplanar and coplanar geometries. The latter is shown to be more effective, as it utilizes the wavelength tunability of SR and allows one to vary the diffraction conditions in a wide range from usual highly asymmetric to grazing incidence below the critical angle of total external reflection (and the penetration depth from hundreds to tens of nanometers) without off-plane rotations and provides pictures free of complicated geometrical distortions. The dislocation images at different diffraction conditions proved to be qualitatively the same for near-surface defects, while the structure distortions, produced by the defects in the underlying layers, become invisible at grazing incidence, due to both depth resolution of the method and inevitable loss of lattice-parameter resolution. This might be a
Boundary diffraction wave integrals for diffraction modeling of external occulters.
Cady, Eric
2012-07-01
An occulter is a large diffracting screen which may be flown in conjunction with a telescope to image extrasolar planets. The edge is shaped to minimize the diffracted light in a region beyond the occulter, and a telescope may be placed in this dark shadow to view an extrasolar system with the starlight removed. Errors in position, orientation, and shape of the occulter will diffract additional light into this region, and a challenge of modeling an occulter system is to accurately and quickly model these effects. We present a fast method for the calculation of electric fields following an occulter, based on the concept of the boundary diffraction wave: the 2D structure of the occulter is reduced to a 1D edge integral which directly incorporates the occulter shape, and which can be easily adjusted to include changes in occulter position and shape, as well as the effects of sources-such as exoplanets-which arrive off-axis to the occulter. The structure of a typical implementation of the algorithm is included. PMID:22772218
Stolt's f-k migration for plane wave ultrasound imaging.
Garcia, Damien; Le Tarnec, Louis; Muth, Stéphan; Montagnon, Emmanuel; Porée, Jonathan; Cloutier, Guy
2013-09-01
Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wave-fronts. As a plane wave reaches a given scatterer, the latter becomes a secondary source emitting upward spherical waves and creating a diffraction hyperbola in the received RF signals. To produce an image of the scatterers, all the hyperbolas must be migrated back to their apexes. To perform beamforming of plane wave echo RFs and return high-quality images at high frame rates, we propose a new migration method carried out in the frequency-wavenumber (f-k) domain. The f-k migration for PWI has been adapted from the Stolt migration for seismic imaging. This migration technique is based on the exploding reflector model (ERM), which consists in assuming that all the scatterers explode in concert and become acoustic sources. The classical ERM model, however, is not appropriate for PWI. We showed that the ERM can be made suitable for PWI by a spatial transformation of the hyperbolic traces present in the RF data. In vitro experiments were performed to outline the advantages of PWI with Stolt's f-k migration over the conventional delay-and-sum (DAS) approach. The Stolt's f-k migration was also compared with the Fourier-based method developed by J.-Y. Lu. Our findings show that multi-angle compounded f-k migrated images are of quality similar to those obtained with a stateof- the-art dynamic focusing mode. This remained true even with a very small number of steering angles, thus ensuring a highly competitive frame rate. In addition, the new FFT-based f-k migration provides comparable or better contrast-to-noise ratio and lateral resolution than the Lu's and DAS migration schemes. Matlab codes for the Stolt's f-k migration for PWI are provided. PMID:24626107
Imafuku, Muneyuki; Suzuki, Hiroshi; Sueyoshi, Kazuyuki; Akita, Koichi; Ohya, Shin-ichi
2008-06-09
Generalized formula of the x-ray stress analysis for a single crystal with unknown stress-free lattice parameter was proposed. This method enables us to evaluate the plane stress states with any combination of diffraction planes. We can choose and combine the appropriate x-ray sources and diffraction plane families, depending on the sample orientation and the apparatus, whenever diffraction condition is satisfied. The analysis of plane stress distributions in an iron single crystal was demonstrated combining with the diffraction data for Fe{l_brace}211{r_brace} and Fe{l_brace}310{r_brace} plane families.
Scalar wave diffraction from a circular aperture
Cerjan, C.
1995-01-25
The scalar wave theory is used to evaluate the expected diffraction patterns from a circular aperture. The standard far-field Kirchhoff approximation is compared to the exact result expressed in terms of oblate spheroidal harmonics. Deviations from an expanding spherical wave are calculated for circular aperture radius and the incident beam wavelength using suggested values for a recently proposed point diffractin interferometer. The Kirchhoff approximation is increasingly reliable in the far-field limit as the aperture radius is increased, although significant errors in amplitude and phase persist.
Counterpropagating Rossby waves in confined plane wakes
Biancofiore, L.; Gallaire, F.
2012-01-01
In the present work, we revisit the temporal and the spatio-temporal stability of confined plane wakes under the perspective of the counterpropagating Rossby waves (CRWs). Within the context of broken line velocity profiles, each vorticity discontinuity can be associated to a counterpropagating Rossby wave. In the case of a wake modeled by a broken line profile, the interaction of two CRWs is shown to originate in a shear instability. Following this description, we first recover the stability results obtained by Juniper [J. Fluid Mech. 590, 163–185 (2007)]10.1017/S0022112007007975 and Biancofiore and Gallaire [Phys. Fluids 23, 034103 (2011)]10.1063/1.3554764 by means of the classical normal mode analysis. In this manner, we propose an explanation of the stabilizing influence of the confinement on the temporal stability properties. The CRW description further allows us to propose a new interpretation of the counterintuitive spatio-temporal destabilization in wake flows at moderate confinement noticed by Juniper [J. Fluid Mech. 565, 171–195 (2006)]10.1017/S0022112006001558: it is well predicted by the mean group velocity of the uncoupled CRWs. PMID:22865998
Counterpropagating Rossby waves in confined plane wakes
NASA Astrophysics Data System (ADS)
Biancofiore, L.; Gallaire, F.
2012-07-01
In the present work, we revisit the temporal and the spatio-temporal stability of confined plane wakes under the perspective of the counterpropagating Rossby waves (CRWs). Within the context of broken line velocity profiles, each vorticity discontinuity can be associated to a counterpropagating Rossby wave. In the case of a wake modeled by a broken line profile, the interaction of two CRWs is shown to originate in a shear instability. Following this description, we first recover the stability results obtained by Juniper [J. Fluid Mech. 590, 163-185 (2007)], 10.1017/S0022112007007975 and Biancofiore and Gallaire [Phys. Fluids 23, 034103 (2011)], 10.1063/1.3554764 by means of the classical normal mode analysis. In this manner, we propose an explanation of the stabilizing influence of the confinement on the temporal stability properties. The CRW description further allows us to propose a new interpretation of the counterintuitive spatio-temporal destabilization in wake flows at moderate confinement noticed by Juniper [J. Fluid Mech. 565, 171-195 (2006)], 10.1017/S0022112006001558: it is well predicted by the mean group velocity of the uncoupled CRWs.
Counterpropagating Rossby waves in confined plane wakes.
Biancofiore, L; Gallaire, F
2012-07-01
In the present work, we revisit the temporal and the spatio-temporal stability of confined plane wakes under the perspective of the counterpropagating Rossby waves (CRWs). Within the context of broken line velocity profiles, each vorticity discontinuity can be associated to a counterpropagating Rossby wave. In the case of a wake modeled by a broken line profile, the interaction of two CRWs is shown to originate in a shear instability. Following this description, we first recover the stability results obtained by Juniper [J. Fluid Mech. 590, 163-185 (2007)]10.1017/S0022112007007975 and Biancofiore and Gallaire [Phys. Fluids 23, 034103 (2011)]10.1063/1.3554764 by means of the classical normal mode analysis. In this manner, we propose an explanation of the stabilizing influence of the confinement on the temporal stability properties. The CRW description further allows us to propose a new interpretation of the counterintuitive spatio-temporal destabilization in wake flows at moderate confinement noticed by Juniper [J. Fluid Mech. 565, 171-195 (2006)]10.1017/S0022112006001558: it is well predicted by the mean group velocity of the uncoupled CRWs. PMID:22865998
NASA Astrophysics Data System (ADS)
Migukin, Artem; Katkovnik, Vladimir; Astola, Jaakko
2010-04-01
The phase retrieval is formulated as an inverse problem, where the forward propagation is defined by Discrete Diffraction Transform (DDT) [1], [2]. This propagation model is precise and aliasing free for pixelwise invariant (pixelated) wave field distributions in the sensor and object planes. Because of finite size of sensors DDT can be ill-conditioned and the regularization is an important component of the inverse. The proposed algorithm is designed for multiple plane observations and can be treated as a generalization of the Gerchberg-Saxton iterative algorithm. The proposed algorithm is studied by numerical experiments produced for phase and amplitude modulated object distributions. Comparison versus the conventional forward propagation models such as the angular spectrum decomposition and the convolutional model used in the algorithm of the same structure shows a clear advantage of DDT enabling better accuracy and better imaging.
Plane wave gravitons, curvature singularities and string physics
Brooks, R. . Center for Theoretical Physics)
1991-03-21
This paper discusses bounded (compactifying) potentials arising from a conspiracy between plane wave graviton and dilaton condensates. So are string propagation and supersymmetry in spacetimes with curvature singularities.
Hydroelastic wave diffraction by a vertical cylinder.
Brocklehurst, Paul; Korobkin, Alexander; Părău, Emilian I
2011-07-28
A linear three-dimensional problem of hydroelastic wave diffraction by a bottom-mounted circular cylinder is analysed. The fluid is of finite depth and is covered by an ice sheet, which is clamped to the cylinder surface. The ice stretches from the cylinder to infinity in all lateral directions. The hydroelastic behaviour of the ice sheet is described by linear elastic plate theory, and the fluid flow by a potential flow model. The two-dimensional incident wave is regular and has small amplitude. An analytical solution of the coupled problem of hydroelasticity is found by using a Weber transform. We determine the ice deflection and the vertical and horizontal forces acting on the cylinder and analyse the strain in the ice sheet caused by the incident wave. PMID:21690136
Scattering of an electromagnetic plane wave by a Luneburg lens. II. Wave theory.
Lock, James A
2008-12-01
The partial wave scattering and interior amplitudes for the interaction of an electromagnetic plane wave with a modified Luneburg lens are derived in terms of the exterior and interior radial functions of the scalar radiation potentials evaluated at the lens surface. A Debye series decomposition of these amplitudes is also performed and discussed. The effective potential inside the lens for the transverse electric polarization is qualitatively examined, and the approximate lens size parameters of morphology-dependent resonances are determined. Finally, the physical optics model is used to calculate wave scattering in the vicinity of the ray theory orbiting condition in order to demonstrate the smoothing of ray theory discontinuities by the diffraction of scattered waves. PMID:19037389
Mielenz, Klaus D.
2002-01-01
In this paper the classical Rayleigh-Sommerfeld and Kirchhoff boundary-value diffraction integrals are solved in closed form for circular apertures and slits illuminated by normally incident plane waves. The mathematical expressions obtained involve no simplifying approximations and are free of singularities, except in the aperture plane itself. Their use for numerical computations was straightforward and provided new insight into the nature of diffraction in the near zone where the Fresnel approximation does not apply. The Rayleigh-Sommerfeld integrals were found to be very similar to each other, so that polarization effects appear to be negligibly small. On the other hand, they differ substantially at sub-wavelength differences from the aperture plane and do not correctly describe the diffracted field as an analytical continuation of the incident geometrical field.
Reflectarray Demonstrated to Transform Spherical Waves into Plane Waves
NASA Technical Reports Server (NTRS)
Zaman, Afrosz J.
1998-01-01
The development of low-cost, high-efficiency array antennas has been the research focus of NASA Lewis Research Center's Communications Technology Division for the past 15 years. One area of current interest is reflectarray development. Reflectarrays have generally been used to replace reflector antennas. In this capacity, different configurations (such as prime focus and offset) and various applications (such as dual frequency and scanning) have been demonstrated with great success. One potential application that has not been explored previously is the use of reflectarrays to compensate for phase errors in space-power-combining applications, such as a space-fed lens and power-combining amplifiers. Recently, we experimentally investigated the feasibility of using a reflectarray as an alternative to a dielectric lens for such applications. The experiment involved transforming the spherical waves from an orthomode horn to plane waves at the horn aperture. The reflectarray consists of square patches terminated in open stubs to provide the necessary phase compensation.
Vacuum plane waves: Cartan invariants and physical interpretation
NASA Astrophysics Data System (ADS)
Coley, A.; McNutt, D.; Milson, R.
2012-12-01
As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an invariant classification of these spacetimes and then study a few notable subcases: the linearly polarized plane waves, the weak-field circularly polarized waves, and another class of plane waves found by imposing conditions on the set of invariants. As we study these spacetimes we relate the invariant structure (i.e., Cartan scalars) to the physical description of these spacetimes using the geodesic deviation equations relative to timelike geodesic observers.
Problems of diffraction and propagation of waves (selected articles)
NASA Astrophysics Data System (ADS)
Makarov, G. I.; Tikhomirov, N. P.; Vyatkin, V. M.
1984-07-01
The first particle presented concerns the Tropospheric Refraction or radio waves, or more specifically, direct and inverse problems of diffraction on the impedance sphere of a large radius. The exponential profile, which is a precise approximation of the regular component of the atmospheric heterogeneity of the Earth, is selected. Concerning tropospheric refraction, different profiles were studied: bilinear; exponential; and the more general profiles. The second article concerns the refinement of Booker's equation for cylindrical layered inhomogeneous anisotropic media. Booker's equation was originally derived for the case of plane layered anisotropic medium. It is necessary to refine Booker's equation considering the final curvature and terrestrial magnetic field of the modified ionosphere. It was found that the values of the roots of Booker's equation decrease in comparison with the flat plane case, and the effect of final curvature of the ionosphere and magnetic bump of the Earth on the height is manifested such that WKB approximation is inapplicable.
The plain truth about forming a plane wave of neutrons
NASA Astrophysics Data System (ADS)
Wagh, Apoorva G.; Abbas, Sohrab; Treimer, Wolfgang
2011-04-01
We have attained the first sub-arcsecond collimation of a monochromatic neutron beam by diffracting neutrons from a Bragg prism, viz. a single crystal prism operating in the vicinity of Bragg incidence. Analytical as well numerical computations based on the dynamical diffraction theory, led to the optimised collimator configuration of a silicon {1 1 1} Bragg prism for 5.26 Å neutrons. We fabricated a Bragg prism to these specifications, tested and operated it at the double diffractometer setup in Helmholtz Zentrum Berlin to produce a 0.58 arcsec wide monochromatic neutron beam. With a similarly optimised Bragg prism analyser of opposite asymmetry, we recorded a 0.62 arcsec wide virgin rocking curve for this ultra-parallel beam. With this nearly plane-wave neutron beam, we have recorded the first ever USANS spectrum in Q˜10-6 Å-1 range with a hydroxyapatite casein protein sample and demonstrated the instrument capability to characterise agglomerates up to 150 μm in size. The super-collimated monochromatic beam has also enabled us to record the first neutron diffraction pattern from a macroscopic grating of 200 μm period. The transverse coherence length of 175 μm (FWHM) of the ultra-parallel beam derived from the analysis of this pattern, is the greatest achieved to date for Å wavelength neutrons.
Polarization and amplitude attributes of reflected plane and spherical waves
NASA Astrophysics Data System (ADS)
Jiang, Jinjun; Baird, Graham; Blair, Dane
1998-03-01
The characteristics of a reflected spherical wave at a free surface are investigated by numerical methods; in particular, the polarization angles and amplitude coefficients of a reflected spherical wave are studied. The classical case of the reflection of a plane P wave from a free surface is revisited in order to establish our terminology, and the classical results are recast in a way which is more suited for the study undertaken. The polarization angle of a plane P wave, for a given angle of incidence, is shown to be 90° minus twice the angle of reflection of the reflected S wave. For a Poisson's ratio less than 1/3, there is a non-normal incident angle for which both amplification coefficients are 2 precisely; for this incident angle the direction of the particle motion at the free surface is also the direction of the incident wave. For a wave emanating from a spherical source, the polarization angle, for all angles of incidence, is always less than, or equal to, the polarization angle of a plane P wave. The vector amplification coefficient of a spherical wave, for all angles of incidence, is always greater than the vector amplification coefficient of a plane P wave. As expected, the results for a spherical wave approach the results for a plane P wave in the far field. Furthermore, there was a good agreement between the theoretical modelling and the numerical modelling using the dynamic finite element method (DFEM).
Automatic decomposition of a complex hologram based on the virtual diffraction plane framework
NASA Astrophysics Data System (ADS)
Jiao, A. S. M.; Tsang, P. W. M.; Poon, T.-C.; Liu, J.-P.; Lee, C.-C.; Lam, Y. K.
2014-07-01
Holography is a technique for capturing the hologram of a three-dimensional scene. In many applications, it is often pertinent to retain specific items of interest in the hologram, rather than retaining the full information, which may cause distraction in the analytical process that follows. For a real optical image that is captured with a camera or scanner, this process can be realized by applying image segmentation algorithms to decompose an image into its constituent entities. However, because it is different from an optical image, classic image segmentation methods cannot be applied directly to a hologram, as each pixel in the hologram carries holistic, rather than local, information of the object scene. In this paper, we propose a method to perform automatic decomposition of a complex hologram based on a recently proposed technique called the virtual diffraction plane (VDP) framework. Briefly, a complex hologram is back-propagated to a hypothetical plane known as the VDP. Next, the image on the VDP is automatically decomposed, through the use of the segmentation on the magnitude of the VDP image, into multiple sub-VDP images, each representing the diffracted waves of an isolated entity in the scene. Finally, each sub-VDP image is reverted back to a hologram. As such, a complex hologram can be decomposed into a plurality of subholograms, each representing a discrete object in the scene. We have demonstrated the successful performance of our proposed method by decomposing a complex hologram that is captured through the optical scanning holography (OSH) technique.
Diffractive wave transmission in dispersive media
NASA Astrophysics Data System (ADS)
Lescarret, Vincent
The aim of this paper is to study the reflection-transmission of diffractive geometrical optic rays described by semi-linear symmetric hyperbolic systems such as the Maxwell-Lorentz equations with the anharmonic model of polarization. The framework is that of P. Donnat's thesis [P. Donnat, Quelques contributions mathématiques en optique non linéaire, chapters 1 and 2, thèse, 1996] and V. Lescarret [V. Lescarret, Wave transmission in dispersive media, M3AS 17 (4) (2007) 485-535]: we consider an infinite WKB expansion of the wave over long times/distances O(1/ɛ) and because of the boundary, we decompose each profile into a hyperbolic (purely oscillating) part and elliptic (evanescent) part as in M. William [M. William, Boundary layers and glancing blow-up in nonlinear geometric optics, Ann. Sci. École Norm. Sup. 33 (2000) 132-209]. Then to get the usual sublinear growth on the hyperbolic part of the profiles, for every corrector, we consider E, the space of bounded functions decomposing into a sum of pure transports and a "quasi compactly" supported part. We make a detailed analysis on the nonlinear interactions on E which leads us to make a restriction on the set of resonant phases. We finally give a convergence result which justifies the use of "quasi compactly" supported profiles.
Spin-dependent diffraction of evanescent waves by subwavelength gratings.
Wu, Kedi; Wang, Guo Ping
2015-08-15
We present a way to observe the spin-to-orbital conversion phenomenon. A spinning evanescent wave can be asymmetrically transformed into propagation waves through one certain diffraction order by a periodical subwavelength grating. By detecting diffraction field distribution behind the grating, we observed spin-dependent diffraction patterns. Furthermore, replacing the periodical grating by a Fibonacci grating, we can simultaneously observe multiple order diffractions of a spin evanescent wave. In this case, the multiple diffraction beams can interfere with each other behind the quasi-periodical grating to form asymmetric interference patterns. Our work provides another way toward the realization of spin-to-orbital conversion of light. PMID:26274640
DLCQ and plane wave matrix Big Bang models
NASA Astrophysics Data System (ADS)
Blau, Matthias; O'Loughlin, Martin
2008-09-01
We study the generalisations of the Craps-Sethi-Verlinde matrix big bang model to curved, in particular plane wave, space-times, beginning with a careful discussion of the DLCQ procedure. Singular homogeneous plane waves are ideal toy-models of realistic space-time singularities since they have been shown to arise universally as their Penrose limits, and we emphasise the role played by the symmetries of these plane waves in implementing the flat space Seiberg-Sen DLCQ prescription for these curved backgrounds. We then analyse various aspects of the resulting matrix string Yang-Mills theories, such as the relation between strong coupling space-time singularities and world-sheet tachyonic mass terms. In order to have concrete examples at hand, in an appendix we determine and analyse the IIA singular homogeneous plane wave - null dilaton backgrounds.
Ohmic Losses During Scattering of a Plane Electromagnetic Wave by a Metal Corrugated Surface
NASA Astrophysics Data System (ADS)
Koposova, E. V.
2015-10-01
We estimate the ohmic losses in the case of scattering of a plane electromagnetic wave by a metal corrugated surface. Comparative analysis of the losses is performed for different regimes of wave incidence and scattering (self-collimation and different incidence angles), and their dependence on the amplitude and shape of the corrugation profile is studied. The study is based on numerical solving of the integral equation which describes the diffraction of a plane electromagnetic wave by a corrugated interface between two dielectrics. Metal is regarded as a dielectric with purely imaginary dielectric permittivity of a great value which is determined by metal conductivity. The waves with E polarization (i.e., the waves with the electric-field vector directed along the grooves), which are used in echelette gyrotron cavities, are studied in detail.
Exact Nonlinear Internal Equatorial Waves in the f-plane
NASA Astrophysics Data System (ADS)
Hsu, Hung-Chu
2016-07-01
We present an explicit exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward above the thermocline in the f-plane approximation near the equator. Moreover, the mass transport velocity induced by this internal equatorial wave is eastward and a westward current occurs in the transition zone between the great depth where the water is still and the thermocline.
An Apparatus for Constructing an Electromagnetic Plane Wave Model
ERIC Educational Resources Information Center
Kneubil, Fabiana Botelho; Loures, Marcus Vinicius Russo; Amado, William
2015-01-01
In this paper we report on an activity aimed at building an electromagnetic wave. This was part of a class on the concept of mass offered to a group of 20 pre-service Brazilian physics teachers. The activity consisted of building a plane wave using an apparatus in which it is possible to fit some rods representing electric and magnetic fields into…
Arrayed Ultrasonic Transducers on Arc Surface for Plane Wave Synthesis
NASA Astrophysics Data System (ADS)
Kim, Jung-Soon; Kim, Jung-Ho; Kim, Moo-Joon; Ha, Kang-Lyeol; Yamada, Akira
2004-05-01
In ultrasonic computed tomography (UCT), it is necessary to synthesize a plane wave using waves emitted from sound sources arranged in the interior surface of a cylinder. In order to transmit a plane wave into a cylindrical surface, an ultrasonic transducer which has many vibrating elements with piezoelectric transverse effect arrayed on an arc surface is proposed. To achieve a wide beam width, the elements should have a small radiation area with a much narrow width. The measured electroacoustic efficiency for the elements was approximately 40% and the beam width defined by -3 dB level from the maximum was as wide as 120 deg. It was confirmed that plane wave synthesis is possible using the proposed transducer array.
Angular beam width of a slit-diffracted wave with noncollinear group and phase velocities
NASA Astrophysics Data System (ADS)
Lock, Edwin H.
2012-12-01
Taking magnetostatic surface wave diffraction as an example, this paper theoretically investigates the 2D diffraction pattern arising in the far-field region of a ferrite slab in the case of a plane wave with noncollinear group and phase velocities incident on a wide, arbitrarily oriented slit in an opaque screen. A universal analytical formula for the angular width of a diffracted beam is derived, which is valid for magnetostatic and other types of waves in anisotropic media and structures (including metamaterials) in 2D geometries. It is shown that the angular width of a diffracted beam in an anisotropic medium can not only take values greater or less than \\lambda _0/D (where \\lambda _0 is the incident wavelength, and D is the slit width), but can also be zero under certain conditions.
Antenna arrays for producing plane whistler waves
NASA Astrophysics Data System (ADS)
Stenzel, Reiner; Urrutia, J. Manuel
2015-11-01
In a large uniform laboratory plasma helicon modes with mode numbers 1 - 8 have been excited. Using a circular phased array it is shown that positive and negative modes can propagate equally well. The phase fronts of helicons form Archimedian screw surfaces. The electromagnetic field carries linear momentum due to the axial propagation and angular momentum due to the azimuthal propagation. Associated with the orbital angular momentum is a transverse Doppler shift. It is demonstrated that a rapidly rotating ``receiver'' observes a different frequency than the wave. This implies that a rotating electron can undergo cyclotron resonance when moving against the field rotation. Analogous to the axial Doppler shift cyclotron damping and cyclotron instabilities are possible due to the field rotation in helicons. Since helicons exist in unbounded laboratory plasma they should also exist in space plasmas. The angular wave-particle interaction may be an alternate approach for the remedial of energetic electrons. Work supported by NSF/DOE.
In-plane vibrations of a rectangular plate: Plane wave expansion modelling and experiment
NASA Astrophysics Data System (ADS)
Arreola-Lucas, A.; Franco-Villafañe, J. A.; Báez, G.; Méndez-Sánchez, R. A.
2015-04-01
Theoretical and experimental results for in-plane vibrations of a uniform rectangular plate with free boundary conditions are obtained. The experimental setup uses electromagnetic-acoustic transducers and a vector network analyzer. The theoretical calculations were obtained using the plane wave expansion method applied to the in-plane thin plate vibration theory. The agreement between theory and experiment is excellent for the lower 95 modes covering a very wide frequency range from DC to 20 kHz. Some measured normal-mode wave amplitudes were compared with the theoretical predictions; very good agreement was observed. The excellent agreement of the classical theory of in-plane vibrations confirms its reliability up to very high frequencies
Diffraction effects of planar transducers using a numerical expression for edge waves.
Mair, H D; Bresse, L; Hutchins, D A
1988-10-01
It is well established that the field from uniformly vibrating piston transducers may be considered as being derived from two components: a plane wave and an edge wave. These have been both predicted and observed in practice, but it would seem that a mathematical expression for the edge-wave component has not yet been developed fully. In this article, expressions are developed for the pressure and particle velocity edge waves that can be used to calculate the field that results when a plane wave is diffracted by an edge. The expressions are used to study a particular example, namely, that of an arbitrarily shaped piston radiator. The results for certain situations are shown to agree with existing solutions for a disk source. PMID:3198874
Inhomogeneous plane wave and the most energetic complex ray.
Deschamps, M; Poncelet, O
2002-05-01
This paper presents a study on the wave surfaces of anisotropic solids. In addition to the classical and real rays, which are defined by the normal to the slowness surfaces, it is obtained complex rays, which are associated to specific inhomogeneous plane waves. Referring to the complex Christoffel's equation and to the Fermat's principle, an intrinsic equation can be associated to these complex rays. Limiting the study to principal planes and plotting the associated complex wave surfaces, it can be shown that four energetic rays always exist in any directions for both quasi-isotropic and anisotropic media (even beyond the cusp). Consequently, it is always possible to define four closed wave surfaces (real or not). PMID:12159950
Colliding gravitational plane waves with noncollinear polarization. II
Ernst, F.J.; Garcia D., A.; Hauser, I.
1987-12-01
A simple criterion for colliding gravitational plane waves is developed. This colliding wave condition is preserved by a new realization of the Geroch group augmented by a Kramer--Neugebauer involution. A three-parameter generalization of a two-parameter family of solutions with noncollinear polarization discovered recently by Ferrari, Ibanez, and Bruni is presented, and two additional solutions are derived that demonstrate that much larger families are likely to be constructed in the near future.
Plane wave scattering by a thick lossy dielectric half-plane
NASA Astrophysics Data System (ADS)
Uchida, K.; Aoki, K.
A solution is obtained for the scattering of a plane wave by a lossy, thick, dielectric half-plane, with a view to applications for calculating the TV electromagnetic wave scattering by a tall building made of concrete. The problem is analytically framed in terms of the incident and scattered electric fields, assuming the polarization in each case to be invariant. Boundary conditions are defined within which Fourier components of the scattered field are calculated. The far-fields were analyzed employing the saddle-point method. Numerical examples for 100 MHz broadcasts are presented, demonstrating a good agreement in the illuminated region between calculations for a lossy dielectric and a perfectly conducting half plane.
Plane shock wave interaction with a cylindrical water column
NASA Astrophysics Data System (ADS)
Sembian, S.; Liverts, M.; Tillmark, N.; Apazidis, N.
2016-05-01
A complex system of waves propagating inside a water column due to the impact of plane shock wave is investigated both experimentally and numerically. Flow features, such as, focusing of expansion waves generating large negative pressure, nucleation of cavitation bubbles, and a re-circulation zone are observed and discussed qualitatively and quantitatively. Experiments are conducted on a 22 mm diametrical water column hit by shock waves with Mach numbers 1.75 and 2.4 in a newly constructed exploding wire facility. A new technique to create a properly shaped, repeatable, large diameter water column with straight walls is presented. Qualitative features of the flow are captured using the shadowgraph technique. With the aid of numerical simulations the wave motions inside the column are analyzed; the spatial location of the expansion wave focusing point and the corresponding negative peak pressures is estimated.
Diffraction model of peristrophic multiplexing with spherical reference wave.
Yoshida, Shuhei; Takahata, Yosuke; Horiuchi, Shuma; Yamamoto, Manabu
2015-02-01
Multiplexing recording is a primary contributor to determining the recording density in holographic data storage. Therefore, many different kinds of recording methods have been proposed. Among them, the method that utilizes spherical waves as reference waves is characterized by the ability to enable multiplexing recording only by moving (shifting or rotating) the recording medium. In our research, we propose a theoretical diffraction model of peristrophic multiplexing with a spherical reference wave and evaluate the diffraction efficiency; this multiplexing recording method has incorporated spherical reference waves in rotation of the media. Additionally, we verify the effectiveness of the model by comparing it with experimental results. PMID:26366593
Colliding gravitational plane waves with noncollinear polarization. I
Ernst, F.J.; Garcia D., A.; Hauser, I.
1987-09-01
An Ehlers transformation on the Ernst potential for the Nutku--Halil solution (Phys. Rev. Lett. 39, 1379 (1977)) provides a new solution of the Einstein field equations describing colliding gravitational plane waves with noncollinear polarization, the first of an infinite sequence of solutions that can be generated using techniques described in this paper.
Comment on ''Collision of plane gravitational waves without singularities''
Nutku, Y.
1981-08-15
An incorrect paper was published by B. J. Stoyanov carrying the title above. Here we shall point out a coordinate transformation whereby ''the new exact solution'' of his paper is recognized as a Kasner universe. Further, we shall show that Stoyanov's interpretation of the Kasner solution as colliding plane gravitational waves runs into the difficulty that the Einstein field equations are not satisfied everywhere.
Colliding gravitational plane waves with noncollinear polarization. I
NASA Astrophysics Data System (ADS)
Ernst, Frederick J.; García D., Alberto; Hauser, Isidore
1987-09-01
An Ehlers transformation on the Ernst potential for the Nutku-Halil solution [Phys. Rev. Lett. 39, 1379 (1977)] provides a new solution of the Einstein field equations describing colliding gravitational plane waves with noncollinear polarization, the first of an infinite sequence of solutions that can be generated using techniques described in this paper.
Metaphysics of colliding self-gravitating plane waves
Matzner, R.A.; Tipler, F.J.
1984-04-15
We discuss certain global features of colliding plane-wave solutions to Einstein's equations. In particular, we show that the apparently local curvature singularities both in the Khan-Penrose solution and in the Bell-Szekeres solution are actually global. These global singularities are associated with the breakdown of nondegenerate planar symmetry in the characteristic initial data sets.
Ultrafast vascular strain compounding using plane wave transmission.
Hansen, H H G; Saris, A E C M; Vaka, N R; Nillesen, M M; de Korte, C L
2014-03-01
Deformations of the atherosclerotic vascular wall induced by the pulsating blood can be estimated using ultrasound strain imaging. Because these deformations indirectly provide information on mechanical plaque composition, strain imaging is a promising technique for differentiating between stable and vulnerable atherosclerotic plaques. This paper first explains 1-D radial strain estimation as applied intravascularly in coronary arteries. Next, recent methods for noninvasive vascular strain estimation in a transverse imaging plane are discussed. Finally, a compounding technique that our group recently developed is explained. This technique combines motion estimates of subsequently acquired focused ultrasound images obtained at various insonification angles. However, because the artery moves and deforms during the multi-angle acquisition, errors are introduced when compounding. Recent advances in computational power have enabled plane wave ultrasound acquisition, which allows 100 times faster image acquisition and thus might resolve the motion artifacts. In this paper the performance of strain imaging using plane wave compounding is investigated using simulations of an artery with a vulnerable plaque and experimental data of a two-layered vessel phantom. The results show that plane wave compounding outperforms 0° focused strain imaging. For the simulations, the root mean squared error reduced by 66% and 50% for radial and circumferential strain, respectively. For the experiments, the elastographic signal-to-noise and contrast-to-noise ratio (SNR(e) and CNR(e)) increased with 2.1 dB and 3.7 dB radially, and 5.6 dB and 16.2dB circumferentially. Because of the high frame rate, the plane wave compounding technique can even be further optimized and extended to 3D in future. PMID:24484646
Gravitational scattering of zero-rest-mass plane waves
NASA Technical Reports Server (NTRS)
De Logi, W. K.; Kovacs, S. J., Jr.
1977-01-01
The Feyman-diagram technique is used to calculate the differential cross sections for the scattering of zero-rest-mass plane waves of spin 0, 1, and 2 by linearized Schwarzschild and Kerr geometries in the long-wavelength weak-field limit. It is found that the polarization of right (or left) circularly polarized electromagnetic waves is unaffected by the scattering process (i.e., helicity is conserved) and that the two helicity (polarization) states of the photon are scattered differently by the Kerr geometry. This coupling between the photon helicity and the angular momentum of the scatterer also leads to a partial polarization of unpolarized incident light. For gravitational waves, on the other hand, there is neither helicity conservation nor helicity-dependent scattering; the angular momentum of the scatterer has no polarizing effect on incident unpolarized gravitational waves.
Predictive GW calculations using plane waves and pseudopotentials
NASA Astrophysics Data System (ADS)
Klimeš, Jiří; Kaltak, Merzuk; Kresse, Georg
2014-08-01
We derive a finite-basis-set correction for quasiparticle (QP) energies in the GW approximation and many-body correlation energies in the random phase approximation. Since the correction requires only knowledge of the ground-state density distribution, it is straightforward to implement in any plane-wave code and significantly improves convergence at negligible computational cost. The expression also indicates that QP energies might converge to the wrong value using the projector augmented wave (PAW) method since the overlap densities of occupied orbitals and high-energy, plane-wave-like orbitals are inaccurately described. The error is shown to be related to the incompleteness of the partial waves inside the atomic spheres. It can be avoided by adopting norm-conserving partial waves. G0W0 and GW0 results based on such norm-conserving PAW potentials are presented for a large set of semiconductors and insulators. Accurate extrapolation procedures to the infinite-basis-set limit and infinite-k-point limit are discussed in detail.
Worldline approach to helicity flip in plane waves
NASA Astrophysics Data System (ADS)
Ilderton, Anton; Torgrimsson, Greger
2016-04-01
We apply worldline methods to the study of vacuum polarization effects in plane wave backgrounds, in both scalar and spinor QED. We calculate helicity-flip probabilities to one loop order and treated exactly in the background field, and provide a toolkit of methods for use in investigations of higher-order processes. We also discuss the connections between the worldline, S-matrix, and lightfront approaches to vacuum polarization effects.
Holography and entropy bounds in the plane wave matrix model
Bousso, Raphael; Mints, Aleksey L.
2006-06-15
As a quantum theory of gravity, matrix theory should provide a realization of the holographic principle, in the sense that a holographic theory should contain one binary degree of freedom per Planck area. We present evidence that Bekenstein's entropy bound, which is related to area differences, is manifest in the plane wave matrix model. If holography is implemented in this way, we predict crossover behavior at strong coupling when the energy exceeds N{sup 2} in units of the mass scale.
Diffraction of dust acoustic waves by a circular cylinder
Kim, S.-H.; Heinrich, J. R.; Merlino, R. L.
2008-09-15
The diffraction of dust acoustic (DA) waves around a long dielectric rod is observed using video imaging methods. The DA waves are spontaneously excited in a dusty plasma produced in a direct current glow discharge plasma. The rod acquires a negative charge that produces a coaxial dust void around it. The diameter of the void is the effective size of the 'obstacle' encountered by the waves. The wavelength of the DA waves is approximately the size of the void. The observations are considered in relation to the classical problem of the diffraction of sound waves from a circular cylinder, a problem first analyzed by Lord Rayleigh [Theory of Sound, 2nd ed. (MacMillan, London, 1896)].
NASA Astrophysics Data System (ADS)
Jeong, Hyunjo; Zhang, Shuzeng; Cho, Sungjong; Li, Xiongbing
2016-04-01
In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave is defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.
Diffracted and head waves associated with waves on nonseparable surfaces
NASA Technical Reports Server (NTRS)
Barger, Raymond L.
1992-01-01
A theory is presented for computing waves radiated from waves on a smooth surface. With the assumption that attention of the surface wave is due only to radiation and not to dissipation in the surface material, the radiation coefficient is derived in terms of the attenuation factor. The excitation coefficient is determined by the reciprocity condition. Formulas for the shape and the spreading of the radiated wave are derived, and some sample calculations are presented. An investigation of resonant phase matching for nonseparable surfaces is presented with a sample calculation. A discussion of how such calculations might be related to resonant frequencies of nonseparable thin shell structures is included. A description is given of nonseparable surfaces that can be modeled in the vector that facilitates use of the appropriate formulas of differential geometry.
Transition operators in electromagnetic-wave diffraction theory - General theory
NASA Technical Reports Server (NTRS)
Hahne, G. E.
1992-01-01
A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.
Decoding the matrix: Coincident membranes on the plane wave
Bousso, Raphael; Mints, Aleksey L.
2006-03-15
At the core of nonperturbative theories of quantum gravity lies the holographic encoding of bulk data in large matrices. At present this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view, one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law constraints. Its validity rests on nontrivial relations in representation theory, which we identify and verify by explicit computation.
Various approximations made in augmented-plane-wave calculations
NASA Astrophysics Data System (ADS)
Bacalis, N. C.; Blathras, K.; Thomaides, P.; Papaconstantopoulos, D. A.
1985-10-01
The effects of various approximations used in performing augmented-plane-wave calculations were studied for elements of the fifth and sixth columns of the Periodic Table, namely V, Nb, Ta, Cr, Mo, and W. Two kinds of approximations have been checked: (i) variation of the number of k points used to iterate to self-consistency, and (ii) approximations for the treatment of the core states. In addition a comparison between relativistic and nonrelativistic calculations is made, and an approximate method of calculating the spin-orbit splitting is given.
Plane shock wave studies of Westerly granite and Nugget sandstone
Larson, D.B.; Anderson, G.D.
1980-12-01
Plane shock wave experiments were performed by using a light-gas gun on dry and water-saturated Westerly granite and dry Nugget sandstone. Changes in the slopes of the shock velocity versus particle velocity curves at 2 to 3 GPa and 1 to 2 GPa for dry granite and for dry sandstone, respectively, are attributed to the onset of pore collapse. However, there is little apparent loss of shear strength in either dry rock over the stress range of the experiments (i.e., 9.3 GPa in Westerly granite and 9.2 GPa in Nugget sandstone). Agreement between the shock wave data and quasistatic, uniaxial strain data for the dry rock implies the absence of rate-dependence in uniaxial strain. The shock data on saturated granite agree well with those for dry granite, thus suggesting there was no loss in shear strength as a result of pore pressure buildup.
Numerical simulation of shock wave diffraction by TVD schemes
NASA Technical Reports Server (NTRS)
Young, Victor Y. C.; Yee, H. C.
1987-01-01
An upwind total variation diminishing (TVD) scheme and a predictor-corrector symmetric TVD scheme were used to numerically simulate the blast wave diffraction on a stationary object. The objective is to help design an optimum configuration so that lateral motion is minimized and at the same time vortex shedding and flow separation are reduced during a blast wave encounter. Results are presented for a generic configuration for both a coarse grid and a fine grid to illustrate the global and local diffraction flow fields. Numerical experiments for the shock wave reflection on a wedge are also included to validate the current approach. Numerical study indicated that these TVD schemes are more stable and produced higher shock resolution than classical shock capturing methods such as the explicit MacCormack scheme.
NASA Astrophysics Data System (ADS)
Oh, Seungtaik; Seo, Hoyong; Hwang, Chi-Young; Lee, Beom-Ryeol; Son, Wookho
2013-05-01
We present a new method to record and reconstruct a diffracted object wave field in all directions. For this, we are going to use spherically-arranged holograms instead of a single spherical hologram. Our spherically-arranged holograms are constructed to store all components of plane waves propagating in all directions. One can use the well-known efficient FFT-based diffraction formulae such as Fresnel transform and angular spectrum method in generation and reconstruction of our spherically-arranged holograms. It is possible to synthesize a new hologram with an arbitrary position and orientation without the geometry of the object. Numerical experiments are presented to show the effectiveness of our method.
Acoustic plane wave preferential orientation of metal oxide superconducting materials
Tolt, Thomas L.; Poeppel, Roger B.
1991-01-01
A polycrystalline metal oxide such as YBa.sub.2 Cu.sub.3 O.sub.7-X (where 0
The implementation of holography in the plane wave matrix model
NASA Astrophysics Data System (ADS)
Mints, Aleksey Leonidovich
It is expected that at the core of nonperturbative theories of quantum gravity, such as M-theory, lies the realization of the holographic principle, in the sense that a holographic theory should contain one binary degree of freedom per Planck area. Present understanding of such theories requires the holographic encoding of bulk data in large matrices. Currently this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law constraints. Its validity rests on nontrivial relations in representation theory, which we identify and verify by explicit computation. Beyond the decoding and partial identification of selected states in large matrices, one would like to get a better understanding of the holographic state counting of these degrees of freedom, i.e., entropy. Contrary to the naive expectation of holography realized in terms of the covariant entropy bound, we present evidence that it is the Bekenstein entropy bound, which is related to area differences, that is manifest in the plane wave matrix model. If holography is implemented in this way, we predict crossover behavior at strong coupling when the energy exceeds N2 in units of the mass scale.
Plane wave based selfconsistent solution of the GW Dyson equation
NASA Astrophysics Data System (ADS)
Wang, Lin-Wang; Cao, Huawei
We have developed a selfconsistent procedure to calculate the full Dyson equation based on plane wave basis set. The whole formalism is based on the Greens function matrix of the plane wave G-vector. There is no truncation of the conduction band when the dielectric function is calculated. The Dyson equation is the variational minimum solution of the total energy in terms of the Greens function. The calculation uses the ''space-time'' method, with special algorithm for imaginary time integration and Fourier transformation. We have tested isolated molecules and periodic systems. The effects of selfconsistency compared to the G0W0 results will be presented. We will also discuss some special techniques used in the k-point summation for the periodic system. Massive parallelization is used to carry out such calculations. This work is supported by the Director, SC/BES/MSED of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, through the Material Theory program at Lawrence Berkeley National Laboratory.
A plane wave generation method by wave number domain point focusing.
Chang, Ji-Ho; Choi, Jung-Woo; Kim, Yang-Hann
2010-11-01
A method for generation of a wave-field that is a plane wave is described. This method uses an array of loudspeakers phased so that the field in the wave-number domain is nearly concentrated at a point, this point being at the wave-number vector of the desired plane wave. The method described here for such a wave-number concentration makes use of an expansion in spherical harmonics, and requires a relatively small number of measurement points for a good approximate achievement of a plane wave. The measurement points are on a spherical surface surrounding the array of loudspeakers. The input signals for the individual loudspeakers can be derived without a matrix inversion or without explicit assumptions about the loudspeakers. The mathematical development involves spherical harmonics and three-dimensional Fourier transforms. Some numerical examples are given, with various assumptions concerning the nature of the loudspeakers, that support the premise that the method described in the present paper may be useful in applications. PMID:21110571
Love wave tomography in southern Africa from a two-plane-wave inversion method
NASA Astrophysics Data System (ADS)
Li, Aibing; Li, Lun
2015-08-01
Array measurements of surface wave phase velocity can be biased by multipath arrivals. A two-plane-wave (TPW) inversion method, in which the incoming wavefield is represented by the interference of two plane waves, is able to account for the multipath effect and solve for laterally varying phase velocity. Despite broad applications of the TPW method, its usage has been limited to Rayleigh waves. In this study, we have modified the TPW approach and applied it to Love waves. Main modifications include decomposing Love wave amplitude on the transverse component to x and y components in a local Cartesian system for each earthquake and using both components in the inversion. Such decomposition is also applied to the two plane waves to predict the incoming wavefield of an earthquake. We utilize fundamental mode Love wave data recorded at 85 broad-band stations from 69 distant earthquakes and solved for phase velocity in nine frequency bands with centre periods ranging from 34 to 100 s. The average phase velocity in southern Africa increases from 4.30 km s-1 at 34 s to 4.87 km s-1 at 100 s. Compared with predicted Love wave phase velocities from the published 1-D SV velocity model and radial anisotropy model in the region, these values are compatible from 34 to 50 s and slightly higher beyond 50 s, indicating radial anisotropy of VSH > VSV in the shallow upper mantle. A high Love wave velocity anomaly is imaged in the central and southern Kaapvaal craton at all periods, reflecting a cold and depleted cratonic lithosphere. A low velocity anomaly appears in the Bushveld Complex from 34 to 50 s, which can be interpreted as being caused by high iron content from an intracratonic magma intrusion. The modified TPW method provides a new way to measure Love wave phase velocities in a regional array, which are essential in developing radial anisotropic models and understanding the Earth structure in the crust and upper mantle.
Microbeam X-Ray Standing Wave and High Resolution Diffraction
Kazimirov, A.; Bilderback, D.H.; Huang, R.; Sirenko, A.
2004-05-12
Post-focusing collimating optics are introduced as a tool to condition X-ray microbeams for the use in high-resolution X-ray diffraction and scattering techniques. As an example, a one-bounce imaging capillary and miniature Si(004) channel-cut crystal were used to produce a microbeam with 10 {mu}m size and an ultimate angular resolution of 2.5 arc sec. This beam was used to measure the strain in semiconductor microstructures by using X-ray high resolution diffraction and standing wave techniques to {delta}d/d < 5x10-4.
NASA Astrophysics Data System (ADS)
Taran, Yu V.; Balagurov, A. M.; Sheverev, S. G.; Schreiber, J.; Korsunsky, A. M.; Vorster, W. J. J.; Bomas, H.; Stoeberl, C.
2008-03-01
Fatigue and fracture under multiaxial stresses are among the most important current research topics aimed at ensuring improved reliability of industrial components. An ex situ in-plane biaxial low cycle fatigued sample of cruciform geometry from austenitic stainless steel AISI 321 H was investigated on the FSD stress-diffractometer at the IBR-2 pulsed nuclear reactor by using the neutron strain scanner and the uniaxial stress rig. The phase composition of fatigued material was determined and the residual macrostresses and phase microstresses were measured. To the best of our knowledge, no neutron diffraction investigations of materials subjected to biaxial loading have been previously carried out. The first results of the neutron diffraction experiment are presented and discussed.
Measuring In-Plane Displacements with Variable Sensitivity Using Diffractive Optic Interferometry
NASA Technical Reports Server (NTRS)
Shepherd, Robert L.; Gilbert, John A.; Cole, Helen J.; Ashley, Paul R.
1998-01-01
This paper introduces a method called diffractive optic interferometry (DOI) which allows in-plane displacement components to be measured with variable sensitivity. DOI relies on binary optical elements fabricated as phase-type Dammann gratings which produce multiple diffraction orders of nearly equal intensity. Sensitivity is varied by combining the different wavefronts produced by a conjugate pair of these binary optical elements; a transmission element is used to produce several illumination beams while a reflective element, replicated on the surface of a specimen, provides the reference for the undeformed state. The steps taken to design and fabricate these binary optical elements are described. The specimen grating is characterized, and tested on a disk subjected to diametrical compression. Overall, the results are excellent, with experimental data agreeing to within a few percent of the theoretical predictions.
Dual series solution to the scattering of plane waves from a binary conducting grating
NASA Astrophysics Data System (ADS)
Kok, Yon-Lin; Gallagher, Neal C., Jr.; Ziolkowski, Richard W.
1989-07-01
The problem of EM-wave scattering from a perfectly conducting grating with a periodic groove structure is considered. A system of dual series equations is derived by enforcing the EM boundary conditions; this leads to a boundary-value problem that is solved. The mathematics leading to the solution of the dual series system is derived from the equivalent Riemann-Hilbert problem in complex-variable theory and its solution. The solution converges absolutely and makes it possible to obtain analytical results, even where other numerical methods, such as the mode-matching method and spectral iteration methods, are numerically unstable. Consideration is also given to the relative phase values for the diffracted fields. The phase differences between the scattered fields resulting from two orthogonally polarized incident plane waves can be explicitly determined for any incidence angles and for any groove dimensions.
Exact solution to plane-wave scattering by an ideal "left-handed" wedge
NASA Astrophysics Data System (ADS)
Monzon, Cesar; Forester, Donald W.; Smith, Douglas; Loschialpo, Peter
2006-02-01
An exact analytical solution to the problem of plane-wave diffraction by a penetrable left-handed medium (LHM) epsilon=µ=-1 wedge of arbitrary angle (subject to valid physical constraints) is presented. Standard analysis involving discontinuous angular eigenfunctions and even/odd symmetry decomposition resulted in a discrete spectrum leading to a series solution resembling the traditional perfect electric conductor wedge solution but exhibiting the expected negative refraction phenomenology. Numerical results are presented, some of which seemed paradoxical but are explainable by classical means. A new type of illusory edge radiation is observed and explained. Also, a novel edge-launched interface standing wave is observed on the directly illuminated side. The exact analytical solution is verified by comparison with finite-difference time-domain simulation on causal LHM materials.
Plane wave method for elastic wave scattering by a heterogeneous fracture
Nakagawa, Seiji; Nihei, Kurt T.; Myer, Larry R.
2003-02-21
A plane-wave method for computing the three-dimensional scattering of propagating elastic waves by a planar fracture with heterogeneous fracture compliance distribution is presented. This method is based upon the spatial Fourier transform of the seismic displacement-discontinuity (SDD) boundary conditions (also called linear slip interface conditions), and therefore, called the wave-number-domain SDD method (wd-SDD method). The resulting boundary conditions explicitly show the coupling between plane waves with an incident wave number component (specular component) and scattered waves which do not follow Snell's law (nonspecular components) if the fracture is viewed as a planar boundary. For a spatially periodic fracture compliance distribution, these boundary conditions can be cast into a linear system of equations that can be solved for the amplitudes of individual wave modes and wave numbers. We demonstrate the developed technique for a simulated fracture with a stochastic (correlated) surface compliance distribution. Low- and high-frequency solutions of the method are also compared to the predictions by low-order Born series in the weak and strong scattering limit.
Diffractive theorems for the wave equation with inverse square potentials
NASA Astrophysics Data System (ADS)
Qian, Randy Zhigang
This dissertation investigates the phenomenon of diffraction resulting from the addition of an inverse square potential term to the wave operator. In particular, it explicitly establishes the existence of diffraction for the solution to the wave operator with an inverse square potential in 2-dimensional euclidean space and proves a propagation of smoothness result in two more general settings. Chapter 2 establishes diffraction in the fundamental solutions to the wave operator plus inverse square potential with a Dirac Delta initial condition in 2-dimensional euclidean space. Following methods as described by Cheeger and Taylor, we separate variables, apply spectral transforms to each variable, and employ contour deformation techniques to establish an explicit form for diffractive front in the fundamental solution. Chapter 3 proves a propagation of smoothness result for a related wave operator with potential, where instead of a constant, we put a smooth bounded function in the numerator of the potential. Microlocal energy estimates are used following the basic propagation methods of Duistermaat and Hormander, and employing the heavy refinements due to Melrose, Vasy, and Wunsch to handle propagation through the radial point at the origin. The potential term is estimated using Hardy's Inequality. Chapter 4 extends the propagation of smoothness result to conic manifolds with an inverse square potential concentrated at their boundary. We state a product decomposition theorem for the conic metric due to Melrose and Wunsch, then use the resulting coordinates to deploy our argument from Chapter 3. New terms with dependence on distance to the boundary arise, and we show how to bound them.
Unsteady relativistic shock-wave diffraction by cylinders and spheres.
Tsai, I-Nan; Huang, Juan-Chen; Tsai, Shang-Shi; Yang, J Y
2012-02-01
The unsteady relativistic shock-wave diffraction patterns generated by a relativistic blast wave impinging on a circular cylinder and a sphere are numerically simulated using some high-resolution relativistic kinetic beam schemes in a general coordinate system for solving the relativistic Euler equations of gas dynamics. The diffraction patterns are followed through about 6 radii of travel of the incident shock past the body. The complete diffraction patterns, including regular reflection, transition from regular to Mach reflection, slip lines, and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the body are reported in detail. Computational results of several incident shock Mach numbers covering the near ultrarelativistic limit are studied. Various contours of flow properties including the Lorentz factor and velocity streamline plots are also presented to add a better understanding of the complex diffraction phenomena. The three-dimensional relieving effects of the sphere cases are evident and can be quantitatively evaluated as compared with the corresponding cylinder cases. PMID:22463327
Unsteady relativistic shock-wave diffraction by cylinders and spheres
NASA Astrophysics Data System (ADS)
Tsai, I.-Nan; Huang, Juan-Chen; Tsai, Shang-Shi; Yang, J. Y.
2012-02-01
The unsteady relativistic shock-wave diffraction patterns generated by a relativistic blast wave impinging on a circular cylinder and a sphere are numerically simulated using some high-resolution relativistic kinetic beam schemes in a general coordinate system for solving the relativistic Euler equations of gas dynamics. The diffraction patterns are followed through about 6 radii of travel of the incident shock past the body. The complete diffraction patterns, including regular reflection, transition from regular to Mach reflection, slip lines, and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the body are reported in detail. Computational results of several incident shock Mach numbers covering the near ultrarelativistic limit are studied. Various contours of flow properties including the Lorentz factor and velocity streamline plots are also presented to add a better understanding of the complex diffraction phenomena. The three-dimensional relieving effects of the sphere cases are evident and can be quantitatively evaluated as compared with the corresponding cylinder cases.
Six-mm, plane-wave shock driver
Frank, A.M.; Chau, H.H.
1993-06-14
A 6-mm-diameter, plane-wave shock generation system has been developed and characterized as a laboratory bench driver for small scale experiments. The driver is based on an exploding-foil-driven slapper used either directly or to initiate an HE pellet. The slapper is driven by a low-inductance fireset with burst currents on the order of 30 kA and burst times of about 250ns, with a time-to-burst jitter under 10ns. Both the slapper impact and the detonation breakout of the pellet have been measured to be flat to within 10ns over a 6-mm diameter. Fabry-Perot velocimetry of impacts with LiF crystals were used to characterize shock pressures and durations. Attenuator plates and flyers driven by the HE were also measured, which provided a variety of available pulse shapes and data for modeling efforts.
The angular apodization in coherent plane-wave compounding.
Rodriguez-Molares, Alfonso; Torp, Hans; Denarie, Bastien; Løvstakken, Lasse
2015-11-01
This article describes the relation between apodization in conventional focused imaging and apodization in coherent plane-wave compounding (CPWC). We pose the hypothesis that equivalent transmit beams can be produced with both methods if the transmit apodization is adequately transformed. We derive a relation between apodization in CPWC and in synthetic transmit aperture imaging (STAI), which we argue to be equivalent to conventional optimal multifocus imaging. We find that under certain conditions, the transformation of the apodization becomes trivial and the same window used in STAI can be applied for CPWC but extended to the whole angle sequence. We test the hypothesis with in silico data and find that the transformed apodization accurately mimics the objective transmit apodization, with differences in the lateral resolution between 3% and 6%. PMID:26559630
Source function and plane waves: Toward complete bader analysis.
Tantardini, Christian; Ceresoli, Davide; Benassi, Enrico
2016-09-01
The source function (SF) is a topological descriptor that was introduced and developed by C. Gatti and R.W. Bader in 1998. The SF describes the contribution of each atom to the total electron density at a given point. To date, this descriptor has only been calculable from electron densities generated by all-electron (AE) methods for the investigation of single molecules or periodic systems. This study broadens the accessibility of the SF, offering its calculation from electron densities generated by plane wave (PW) methods. The new algorithm has been implemented in the open source code, CRITIC2. Our novel approach has been validated on a series of test systems, comparing the results obtained at PW level with those previously obtained through AE methods. © 2016 Wiley Periodicals, Inc. PMID:27364862
Szkudlarek, Krzesimir; Sypek, Maciej; Cywiński, Grzegorz; Suszek, Jarosław; Zagrajek, Przemysław; Feduniewicz-Żmuda, Anna; Yahniuk, Ivan; Yatsunenko, Sergey; Nowakowska-Siwińska, Anna; Coquillat, Dominique; But, Dmytro B; Rachoń, Martyna; Węgrzyńska, Karolina; Skierbiszewski, Czesław; Knap, Wojciech
2016-09-01
We present the concept, the fabrication processes and the experimental results for materials and optics that can be used for terahertz field-effect transistor detector focal plane arrays. More specifically, we propose 3D printed arrays of a new type - diffractive multi-zone lenses of which the performance is superior to that of previously used mono-zone diffractive or refractive elements and evaluate them with GaN/AlGaN field-effect transistor terahertz detectors. Experiments performed in the 300-GHz atmospheric window show that the lens arrays offer both a good efficiency and good uniformity, and may improve the signal-to-noise ratio of the terahertz field-effect transistor detectors by more than one order of magnitude. In practice, we tested 3 × 12 lens linear arrays with printed circuit board THz detector arrays used in postal security scanners and observed significant signal-to-noise improvements. Our results clearly show that the proposed technology provides a way to produce cost-effective, reproducible, flat optics for large-size field-effect transistor THz-detector focal plane arrays. PMID:27607620
Laboratory modeling of edge wave generation over a plane beach by breaking waves
NASA Astrophysics Data System (ADS)
Abcha, Nizar; Ezersky, Alexander; Pelinovsky, Efim
2015-04-01
Edge waves play an important role in coastal hydrodynamics: in sediment transport, in formation of coastline structure and coastal bottom topography. Investigation of physical mechanisms leading to the edge waves generation allows us to determine their effect on the characteristics of spatially periodic patterns like crescent submarine bars and cusps observed in the coastal zone. In the present paper we investigate parametric excitation of edge wave with frequency two times less than the frequency of surface wave propagating perpendicular to the beach. Such mechanism of edge wave generation has been studied previously in a large number of papers using the assumption of non-breaking waves. This assumption was used in theoretical calculations and such conditions were created in laboratory experiments. In the natural conditions, the wave breaking is typical when edge waves are generated at sea beach. We study features of such processes in laboratory experiments. Experiments were performed in the wave flume of the Laboratory of Continental and Coast Morphodynamics (M2C), Caen. The flume is equipment with a wave maker controlled by computer. To model a plane beach, a PVC plate is placed at small angle to the horizontal bottom. Several resistive probes were used to measure characteristics of waves: one of them was used to measure free surface displacement near the wave maker and two probes were glued on the inclined plate. These probes allowed us to measure run-up due to parametrically excited edge waves. Run-up height is determined by processing a movie shot by high-speed camera. Sub-harmonic generation of standing edge waves is observed for definite control parameters: edge waves represent themselves a spatial mode with wavelength equal to double width of the flume; the frequency of edge wave is equal to half of surface wave frequency. Appearance of sub-harmonic mode instability is studied using probes and movie processing. The dependence of edge wave exponential
Dispersive photonic crystals from the plane wave method
NASA Astrophysics Data System (ADS)
Guevara-Cabrera, E.; Palomino-Ovando, M. A.; Flores-Desirena, B.; Gaspar-Armenta, J. A.
2016-03-01
Nowadays photonic crystals are widely used in many different applications. One of the most used methods to compute their band structure is the plane wave method (PWM). However, it can only be applied directly to non-dispersive media and be extended to systems with a few model dielectric functions. We explore an extension of the PWM to photonic crystals containing dispersive materials, that solves an eigenvalue equation for the Bloch wave vectors. First we compare our calculation with analytical results for one dimensional photonic crystals containing Si using experimental values of its optical parameters, and obtainig very well agreement, even for the spectrum region with strong absorption. Then, using the same method, we computed the band structure for a two dimensional photonic crystal without absorption, formed by an square array of MgO cylinders in air. The optical parameters for MgO were modeled with the Lorentz dielectric function. Finally, we studied an array of MgO cylinders in a metal, using Drude model without absorption, for the metal dielectric function. For this last case, we study the gap-midgap ratio as a function of the filling fraction for both the square and triangular lattice. The gap-midgap ratio is larger for the triangular lattice, with a maximum value of 10% for a filling fraction of 0.6. Our results show that the method can be applied to dispersive materials, and then to a wide range of applications where photonic crystals can be used.
NASA Astrophysics Data System (ADS)
Maradudin, A. A.; Simonsen, I.
2016-05-01
By the use of the Rayleigh method we have calculated the angular dependence of the reflectivity and the efficiencies of several other diffracted orders when the periodically corrugated surface of an isotropic elastic medium is illuminated by a volume acoustic wave of shear horizontal polarization. These dependencies display the signatures of Rayleigh and Wood anomalies, usually associated with the diffraction of light from a metallic grating. The Rayleigh anomalies occur at angles of incidence at which a diffracted order appears or disappears; the Wood anomalies here are caused by the excitation of the shear horizontal surface acoustic waves supported by the periodically corrugated surface of an isotropic elastic medium. The dispersion curves of these waves in both the nonradiative and radiative regions of the frequency-wavenumber plane are calculated, and used in predicting the angles of incidence at which the Wood anomalies are expected to occur.
Resonant Enhancement of Charge Density Wave Diffraction in the Rare-Earth Tri-Tellurides
Lee, W.S.; Sorini, A.P.; Yi, M.; Chuang, Y.D.; Moritz, B.; Yang, W.L.; Chu, J.-H.; Kuo, H.H.; Gonzalez, A.G.Cruz; Fisher, I.R.; Hussain, Z.; Devereau, T.P.; Shen, Z.X.
2012-05-15
We performed resonant soft X-ray diffraction on known charge density wave (CDW) compounds, rare earth tri-tellurides. Near the M{sub 5} (3d - 4f) absorption edge of rare earth ions, an intense diffraction peak is detected at a wavevector identical to that of CDW state hosted on Te{sub 2} planes, indicating a CDW-induced modulation on the rare earth ions. Surprisingly, the temperature dependence of the diffraction peak intensity demonstrates an exponential increase at low temperatures, vastly different than that of the CDW order parameter. Assuming 4f multiplet splitting due to the CDW states, we present a model to calculate X-ray absorption spectrum and resonant profile of the diffraction peak, agreeing well with experimental observations. Our results demonstrate a situation where the temperature dependence of resonant X-ray diffraction peak intensity is not directly related to the intrinsic behavior of the order parameter associated with the electronic order, but is dominated by the thermal occupancy of the valence states.
X-ray diffraction study of crystal plane distortion in silicon carbide substrates
NASA Astrophysics Data System (ADS)
Mastro, M. A.; Fatemi, M.; Gaskill, D. K.; Lew, K.-K.; Van Mil, B. L.; Eddy, C. R.; Wood, C. E. C.
2006-11-01
Bulk growth of 4H-SiC is challenging due to the required high growth temperatures and gradients used in sublimation physical vapor transport that are difficult to control, particularly over large diameter boules. We used x-ray diffraction mapping to show concave crystal plane curvature in substrates from five commercial suppliers with two suppliers producing wafers with ⩽2° curvature. The extent of curvature varied little for substrates from any particular supplier. Maps of peak position and full width at half maximum from symmetric and asymmetric reflections were used to identify defective regions in the crystal. Closer examination of the rocking curves in the defective regions found a low density of low angle grain boundaries only in substrates from one supplier.
Skigin, Diana C; Depine, Ricardo A
2008-05-01
We show that the problem of scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane, which was recently studied by Basha et al. [J. Opt. Soc. Am. A24, 1647 (2007)], was solved 11 years ago using the same formulation. This method was further extended to deal with a finite number of grooves and also with complex apertures including several nonlossy and lossy dielectrics, as well as real metals. PMID:18451923
Numerical investigation of diffraction of acoustic waves by phononic crystals
NASA Astrophysics Data System (ADS)
Moiseyenko, Rayisa P.; Declercq, Nico F.; Laude, Vincent
2012-05-01
Diffraction as well as transmission of acoustic waves by two-dimensional phononic crystals (PCs) composed of steel rods in water are investigated in this paper. The finite element simulations were performed in order to compute pressure fields generated by a line source that are incident on a finite size PC. Such field maps are analyzed based on the complex band structure for the infinite periodic PC. Finite size computations indicate that the exponential decrease of the transmission at deaf frequencies is much stronger than that in Bragg band gaps.
Diffraction efficiency of radially-profiled off-plane reflection gratings
NASA Astrophysics Data System (ADS)
Miles, Drew M.; Tutt, James H.; DeRoo, Casey T.; Marlowe, Hannah; Peterson, Thomas J.; McEntaffer, Randall L.; Menz, Benedikt; Burwitz, Vadim; Hartner, Gisela; Laubis, Christian; Scholze, Frank
2015-09-01
Future X-ray missions will require gratings with high throughput and high spectral resolution. Blazed off-plane reflection gratings are capable of meeting these demands. A blazed grating profile optimizes grating efficiency, providing higher throughput to one side of zero-order on the arc of diffraction. This paper presents efficiency measurements made in the 0.3 - 1.5 keV energy band at the Physikalisch-Technische Bundesanstalt (PTB) BESSY II facility for three holographically-ruled gratings, two of which are blazed. Each blazed grating was tested in both the Littrow configuration and anti-Littrow configuration in order to test the alignment sensitivity of these gratings with regard to throughput. This paper outlines the procedure of the grating experiment performed at BESSY II and discuss the resulting efficiency measurements across various energies. Experimental results are generally consistent with theory and demonstrate that the blaze does increase throughput to one side of zero-order. However, the total efficiency of the non-blazed, sinusoidal grating is greater than that of the blazed gratings, which suggests that the method of manufacturing these blazed profiles fails to produce facets with the desired level of precision. Finally, evidence of a successful blaze implementation from first diffraction results of prototype blazed gratings produce via a new fabrication technique at the University of Iowa are presented.
NMR Shielding in Metals Using the Augmented Plane Wave Method
2015-01-01
We present calculations of solid state NMR magnetic shielding in metals, which includes both the orbital and the complete spin response of the system in a consistent way. The latter contains an induced spin-polarization of the core states and needs an all-electron self-consistent treatment. In particular, for transition metals, the spin hyperfine field originates not only from the polarization of the valence s-electrons, but the induced magnetic moment of the d-electrons polarizes the core s-states in opposite direction. The method is based on DFT and the augmented plane wave approach as implemented in the WIEN2k code. A comparison between calculated and measured NMR shifts indicates that first-principle calculations can obtain converged results and are more reliable than initially concluded based on previous publications. Nevertheless large k-meshes (up to 2 000 000 k-points in the full Brillouin-zone) and some Fermi-broadening are necessary. Our results show that, in general, both spin and orbital components of the NMR shielding must be evaluated in order to reproduce experimental shifts, because the orbital part cancels the shift of the usually highly ionic reference compound only for simple sp-elements but not for transition metals. This development paves the way for routine NMR calculations of metallic systems. PMID:26322148
Quasinormal modes in de Sitter space: Plane wave method
NASA Astrophysics Data System (ADS)
Tanhayi, M. Reza
2014-09-01
Recently, in the context of dS/CFT correspondence, quasinormal modes have been put forward to address certain features of this conjecture. In particular, it is argued that the dual states of quasinormal modes are in fact the states of CFT3 which are created by operator insertions. For a scalar field in dS4, quasinormal modes which are singular on the past horizon of the south pole and decay exponentially towards the future have been considered in [G. S. Ng and A. Strominger, Classical Quantum Gravity 30, 104002 (2013); D. L. Jafferis et al., arXiv:1305.5523]; these modes lie in two complex highest-weight representations of the dS4 isometry group. In this work, we present a simple group representation analysis of these modes so that the de Sitter invariance is obviously manifest. By making use of the so-called plane wave method, we will show that the quasinormal modes correspond to one class of the unitary irreducible representation of the de Sitter group. This consideration could be generalized straightforwardly for higher-spin fields and higher dimensions; in particular, we will study the quasinormal modes for gauge and spinor fields, and, in the case of a scalar field, the generalization to higher dimensions is also obtained.
Dynamical representation of the operators for the Dirac particle in the field of a plane wave
NASA Astrophysics Data System (ADS)
Lobanov, A. E.
2015-01-01
We find an explicit form of the integrals of motion for a Dirac particle placed in a plane-wave field. These operators are a realization of the Lie algebra of the Poincaré group in the case where the representation space consists of solutions of the Dirac-Pauli equation for the particle in a plane-wave field.
Unsteady oblique interaction of a shock wave with a plane disturbance
NASA Technical Reports Server (NTRS)
Moore, Franklin K
1954-01-01
Analysis is made of the flow field produced by oblique impingement of weak plane disturbances of arbitrary profile on a plane normal shock. Three types of disturbance are considered: (a) sound wave propagating in the gas at rest into which the shock moves; (b) sound wave overtaking the shock from behind,(The sound wave reflects as a sound wave, and a stationary vorticity wave is produced); (c) an incompressible vorticity wave stationary in the gas ahead of the shock. The incident wave refracts as a stationary vorticity wave, and either a sound wave or attenuating pressure wave is also produced. Computations are presented for the first two types of incident wave, over the range of incidence angles, for shock Mach numbers of 1, 1.5, and infinity.
Generating Damon-Eshbach Spin Waves in Py using a Conducting Diffraction Grating
NASA Astrophysics Data System (ADS)
Sklenar, J.; Bhat, V. S.; Delong, L.; Ketterson, J. B.
2012-02-01
We have patterned silver hole arrays directly on top of uniform permalloy (Py) films. Typical Py and Ag film thicknesses are 25nm and 40 nm respectively; the holes in the Ag have a 500nm diameter and are patterned on a 1 micron lattice constant. We have measured resonant modes arising from a quasi-uniform microwave excitation field, applied in the plane of the sample, as a function of the in-plane external field and the in-plane field orientation relative to the principal axes of the array. Measurements were done using our broadband meanderline-based ferromagnetic resonance (FMR) spectrometer.ootnotetextC. C. Tsai, J. Choi, S. Cho, B. K. Sarma, C. Thompson, O. Chernyashevskyy, I. Nevirkovets, and J. B Ketterson, Rev. of Sci. Instr. 80, 023904 (2009). In addition to a uniform FMR mode we observe satellite modes that correspond to the Damon-Eshbach spin wavesootnotetextR. W. Damon and J. R. Eshbach J. Phys. Chem. Solids 19, 308 (1961). with wave vectors having Fourier components of the reciprocal lattice of the silver array. Hence, in an otherwise uniform magnetic film the silver array acts as a diffraction grating which excites spin waves with k 0 from the dynamic k 0 microwave magnetic field. The observed spin wave angular dispersion is in excellent agreement with a magnon dispersion relation for spin waves in a uniform film given by Kriesel et al.ootnotetextA. Kreisel, F. Sauli, L. Bartosch, and P. Kopietz, Eur. Phys. J. B 71, 59 (2009).
NASA Astrophysics Data System (ADS)
Humeida, Yousif; Pinfield, Valerie J.; Challis, Richard E.
2013-08-01
Ultrasonic arrays have seen increasing use for the characterisation of composite materials. In this paper, ultrasonic wave propagation in multilayer anisotropic materials has been modelled using plane wave and angular spectrum decomposition techniques. Different matrix techniques, such as the stiffness matrix method and the transfer matrix method, are used to calculate the reflection and transmission coefficients of ultrasonic plane waves in the considered media. Then, an angular decomposition technique is used to derive the bounded beams from finite-width ultrasonic array elements from the plane wave responses calculated earlier. This model is considered to be an analytical exact solution for the problem; hence the diffraction of waves in such composite materials can be calculated for different incident angles for a very wide range of frequencies. This model is validated against experimental measurements using the Full-Matrix Capture (FMC) of array data in both a homogeneous isotropic material, i.e. aluminium, and an inhomogeneous multilayer anisotropic material, i.e. a carbon fibre reinforced composite.
X-ray diffraction study of A- plane non-polar InN epilayer grown by MOCVD
NASA Astrophysics Data System (ADS)
Moret, Matthieu; Briot, Olivier; Gil, Bernard
2015-03-01
Strong polarisation-induced electric fields in C-plane oriented nitrides semiconductor layers reduce the performance of devices. Eliminating the polarization fields can be achieved by growing nitrides along non polar direction. We have grown non polar A-plane oriented InN on R-plane (1‾102) nitridated sapphire substrate by MOCVD. We have studied the structural anisotropy observed in these layers by analyzing High Resolution XRay Diffraction rocking curve (RC) experiments as a function of the in-plane beam orientation. A-plane InN epilayer have a unique epitaxial relationship on R-Plane sapphire and show a strong structural anisotropy. Full width at half maximum (FWHM) of the InN(11‾20) XRD RC values are contained between 44 and 81 Arcmin. FWHM is smaller when the diffraction occurs along the [0001] and the largest FWHM values, of the (11‾20) RC, are obtained when the diffraction occurs along the [1‾100] in-plane direction. Atomic Force Microscopy imaging revealed morphologies with well organized crystallites. The grains are structured along a unique crystallographic orientation of InN, leading to larger domains in this direction. This structural anisotropy can be, in first approximation, attributed to the difference in the domain sizes observed. XRD reciprocal space mappings (RSM) were performed in asymmetrical configuration on (13‾40) and (2‾202) diffraction plane. RSM are measured with a beam orientation corresponding to a maximal and a minimal width of the (11‾20) Rocking curves, respectively. A simple theoretical model is exposed to interpret the RSM. We concluded that the dominant contribution to the anisotropy is due to the scattering coherence length anisotropy present in our samples.
Ab initio quantum transport calculations using plane waves
NASA Astrophysics Data System (ADS)
Garcia-Lekue, A.; Vergniory, M. G.; Jiang, X. W.; Wang, L. W.
2015-08-01
We present an ab initio method to calculate elastic quantum transport at the nanoscale. The method is based on a combination of density functional theory using plane wave nonlocal pseudopotentials and the use of auxiliary periodic boundary conditions to obtain the scattering states. The method can be applied to any applied bias voltage and the charge density and potential profile can either be calculated self-consistently, or using an approximated self-consistent field (SCF) approach. Based on the scattering states one can straightforwardly calculate the transmission coefficients and the corresponding electronic current. The overall scheme allows us to obtain accurate and numerically stable solutions for the elastic transport, with a computational time similar to that of a ground state calculation. This method is particularly suitable for calculations of tunneling currents through vacuum, that some of the nonequilibrium Greens function (NEGF) approaches based on atomic basis sets might have difficulty to deal with. Several examples are provided using this method from electron tunneling, to molecular electronics, to electronic devices: (i) On a Au nanojunction, the tunneling current dependence on the electrode-electrode distance is investigated. (ii) The tunneling through field emission resonances (FERs) is studied via an accurate description of the surface vacuum states. (iii) Based on quantum transport calculations, we have designed a molecular conformational switch, which can turn on and off a molecular junction by applying a perpendicular electric field. (iv) Finally, we have used the method to simulate tunnel field-effect transistors (TFETs) based on two-dimensional transition-metal dichalcogenides (TMDCs), where we have studied the performance and scaling limits of such nanodevices and proposed atomic doping to enhance the transistor performance.
Plane wave holonomies in quantum gravity. II. A sine wave solution
NASA Astrophysics Data System (ADS)
Neville, Donald E.
2015-08-01
This paper constructs an approximate sinusoidal wave packet solution to the equations of canonical gravity. The theory uses holonomy-flux variables with support on a lattice (LHF =lattice-holonomy flux ). There is an SU(2) holonomy on each edge of the LHF simplex, and the goal is to study the behavior of these holonomies under the influence of a passing gravitational wave. The equations are solved in a small sine approximation: holonomies are expanded in powers of sines and terms beyond sin2 are dropped; also, fields vary slowly from vertex to vertex. The wave is unidirectional and linearly polarized. The Hilbert space is spanned by a set of coherent states tailored to the symmetry of the plane wave case. Fixing the spatial diffeomorphisms is equivalent to fixing the spatial interval between vertices of the loop quantum gravity lattice. This spacing can be chosen such that the eigenvalues of the triad operators are large, as required in the small sine limit, even though the holonomies are not large. Appendices compute the energy of the wave, estimate the lifetime of the coherent state packet, discuss circular polarization and coarse-graining, and determine the behavior of the spinors used in the U(N) SHO realization of LQG.
Stolt’s f-k migration for plane wave ultrasound imaging
Garcia, Damien; Le Tarnec, Louis; Muth, Stéphan; Montagnon, Emmanuel; Porée, Jonathan; Cloutier, Guy
2013-01-01
Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wavefronts. As a plane wave reaches a given scatterer, the latter becomes a secondary source emitting upward spherical waves and creating a diffraction hyperbola in the received RF (radio-frequency) signals. To produce an image of the scatterers, all the hyperbolas must be migrated back to their apexes. In order to perform beamforming of plane wave echo RFs and return high-quality images at high frame rates, we propose a new migration method carried out in the frequency-wavenumber (f-k) domain. The f-k migration for PWI has been adapted from the Stolt migration for seismic imaging. This migration technique is based on the exploding reflector model (ERM), which consists in assuming that all the scatterers explode in concert and become acoustic sources. The classical ERM model, however, is not appropriate for PWI. We showed that the ERM can be made suitable for PWI by a spatial transformation of the hyperbolic traces present in the RF data. In vitro experiments were performed to sketch the advantages of PWI with Stolt’s f-k migration over the conventional delay-and-sum (DAS) approach. The Stolt’s f-k migration was also compared with the Fourier-based method developed by J-Y Lu. Our findings show that multi-angle compounded f-k migrated images are of quality similar to those obtained with a state-of-the-art dynamic focusing mode. This remained true even with a very small number of steering angles thus ensuring a highly competitive frame rate. In addition, the new FFT-based f-k migration provides comparable or better contrast-to-noise ratio and lateral resolution than the Lu’s and DAS migration schemes. Matlab codes of the Stolt’s f-k migration for PWI are provided. PMID:24626107
Wang, Fang; Qi, Xiang-Dong; Yu, Hong-Zhu; Yu, Hai-Li
2009-02-01
A new-style system that automatically measures the diffraction efficiency of plane reflection grating was designed. The continuous illuminant was adopted for illumination, the duplex grating spectrograph structure was applied, and the linear array NMOS was the receiving component. Wielding relevant principle of the grating spectrograph, theoretical analysis principle was carried out for the testing system. Integrating the aberration theory of geometrical optics, the image quality of this optics system was analyzed. Analysis indicated that the systematic device structure is compact, and electronics system is simplified. The system does not have the problem about wavelength sweep synchronization of the two grating spectrographs, and its wavelength repeatability is very good. So the precision is easy to guarantee. Compared with the former automated scheme, the production cost is reduced, moreover it is easy to operate, and the working efficiency is enhanced. The study showed that this automatic measurement instrument system features a spectral range of 190-1 100 nm and resolution is less than 3 nm, which entirely satisfies the design request. It is an economical and feasible plan. PMID:19445251
NASA Astrophysics Data System (ADS)
Hooseria, S. J.; Skews, B. W.
2016-04-01
A complex interference flowfield consisting of multiple shocks and expansion waves is produced when high-speed slender bodies are placed in close proximity. The disturbances originating from a generator body impinge onto the adjacent receiver body, modifying the local flow conditions over the receiver. This paper aims to uncover the basic gas dynamics produced by two closely spaced slender bodies in a supersonic freestream. Experiments and numerical simulations were used to interpret the flowfield, where good agreement between the predictions and measurements was observed. The numerical data were then used to characterise the attenuation associated with shock wave diffraction, which was found to be interdependent with the bow shock contact perimeter over the receiver bodies. Shock-induced boundary layer separation was observed over the conical and hemispherical receiver bodies. These strong viscous-shock interactions result in double-reflected, as well as double-diffracted shock wave geometries in the interference region, and the diffracting waves progress over the conical and hemispherical receivers' surfaces in "lambda" type configurations. This gives evidence that viscous effects can have a substantial influence on the local bow shock structure surrounding high-speed slender bodies in close proximity.
Plane waves in de Sitter space: Spin-1/2 field
NASA Astrophysics Data System (ADS)
Reza Tanhayi, M.; Mohsenzadeh, M.; Yusofi, E.
2016-06-01
We employ the coordinate-independent plane wave solution in de Sitter space to study the spin-1/2 particle production. The so-called plane waves in the zero-curvature limit reduce to the usual plane waves in flat space. Previously in (Int. J. Mod. Phys. D 24, 1550052 (2015)) we used such modes to study the instability of the de Sitter space, here, by explicit calculation, we study the sipn-1/2 particle creation in de Sitter space caused by mixing modes.
Gauss' law and nonlinear plane waves for Yang-Mills theory
NASA Astrophysics Data System (ADS)
Tsapalis, A.; Politis, E. P.; Maintas, X. N.; Diakonos, F. K.
2016-04-01
We investigate nonlinear plane-wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the SU(3) theory, we derive solutions which consist of Jacobi elliptic functions depending on an enumerable set of elliptic modulus values. The solutions represent periodic anharmonic plane waves which possess arbitrary nonzero mass and are exact extrema of the nonlinear YM action. Among them, a unique harmonic plane wave with a nontrivial pattern in phase, spin, and color is identified. Similar solutions are present in the SU(4) case, while they are absent from the SU(2) theory.
Multi-frame visualization for detonation wave diffraction
NASA Astrophysics Data System (ADS)
Nagura, Y.; Kasahara, J.; Matsuo, A.
2016-05-01
When a detonation wave emerges from a tube into unconfined space filled with a gas mixture, detonation wave diffraction occurs due to abrupt changes in the cross-sectional area. In the present study, we focused on the local explosion in reinitiation and propagation of a transverse detonation wave by performing comprehensive and direct observation with high time resolution visualization in a two-dimensional rectangular channel. Using the visualization methods of shadowgraph and multi-frame, short-time, open-shutter photography, we determined where the wall reflection point is generated, and also determined where the bright point is originated by the local explosion, and investigated the effects of the deviation angle and initial pressure of the gas mixture. We found that the reinitiation of detonation had two modes that were determined by the deviation angle of the channel. If the deviation angle was less than or equal to 30°, the local explosion of reinitiation might occur in the vicinity of the channel wall, and if the deviation angle was greater than or equal to 60°, the local explosion might originate on the upper side of the tube exit. With a deviation angle greater than 60°, the position of the wall reflection point depended on the cell width, so the radial distance of the wall reflection point from the apex of the tube exit was about 12 times the cell width. Similarly, the bright point (local explosion point) was located a distance of about 11 times the cell width from the apex of the tube exit, with a circumferential angle of 48°.
NASA Astrophysics Data System (ADS)
Lee, Vincent W.; Luo, Hao
2014-03-01
A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a flexible wall on a rigid shallow circular foundation embedded in an elastic half-space is presented. This research generalizes the previous solution by Trifunac in 1972, which tackled only the semi-circular foundation, to arbitrary shallow circular-arc foundation cases, and is thus comparatively more realistic. Ground surface displacement spectra at higher frequencies are also obtained. As an analytical series solution, the accuracy and error analysis of the numerical results are also discussed. It was observed from the results that the rise-to-span ratio of the foundation profile, frequency of incident waves, and mass ratios of different media (foundation-structure-soil) are the three primary factors that may affect the surface ground motion amplitudes near the structure.
NASA Astrophysics Data System (ADS)
Feng, Fanrong; Wu, Jianhong; Gao, Fei
2015-11-01
The analysis of initial phase of diffraction wave of grating mask is based on rigorous coupled-wave analysis method. In this paper, the general diffraction analysis numerical code based on the rigorous coupled-wave analysis (RCWA) is written by MATLAB software to calculate the 0th refraction wave of grating mask. Since large measurement errors will occur while measuring the grove shape by AFM, the method of measuring the initial phase of diffraction wave was proposed and the feasibility of this method has also been verified.
Matter-wave diffraction at the natural limit
NASA Astrophysics Data System (ADS)
Brand, Christian; Sclafani, Michele; Knobloch, Christian; Lilach, Yigal; Juffmann, Thomas; Kotakoski, Jani; Mangler, Clemens; Winter, Andreas; Turchanin, Andrey; Meyer, Jannik; Cheshnovsky, Ori; Arndt, Markus
2016-05-01
The high sensitivity of matter-wave interferometry experiments to forces and perturbations makes them an essential tool for precision measurements and tests of quantum physics. While mostly grating made of laser-light are used, material gratings have the advantage that they are independent of the particle's internal properties. This makes them universally applicable. However, the molecules will experience substantial van der Waals shifts while passing the grating slits, which suggests limiting this perturbation by reducing the material thickness. In a comprehensive study we compared the van der Waals interactions for free-standing gratings made from single and double layer graphene to masks commonly used in atom interferometry. From the population of high fringe orders we deduce a surprisingly strong electrical interaction between the polarizable molecules and the nanomasks. As even for these thinnest diffraction elements which-path information is not shared with the environment, we interpret this as an experimental affirmation of Bohr's arguments in his famous debate with Einstein.
Verification of the Uncertainty Principle by Using Diffraction of Light Waves
ERIC Educational Resources Information Center
Nikolic, D.; Nesic, Lj
2011-01-01
We described a simple idea for experimental verification of the uncertainty principle for light waves. We used a single-slit diffraction of a laser beam for measuring the angular width of zero-order diffraction maximum and obtained the corresponding wave number uncertainty. We will assume that the uncertainty in position is the slit width. For the…
NASA Astrophysics Data System (ADS)
Sano, Yukio
1989-05-01
A qualitative analysis of the mechanical response of rate-dependent media caused by a one-dimensional plane smooth wave front and by a continuous wave front attenuating in the media is performed by an underdetermined system of nonlinear partial differential equations. The analysis reveals that smooth strain, particle velocity, and stress profiles, which the smooth wave front has, are not similar and that the wave front is composed of some partial waves having different properties. The property is represented by a set of strain rate, acceleration, and stress rate. The wave front derived here from the analysis is composed of four different partial waves. The front of the wave front is necessarily a contraction wave in which strain, particle velocity, and stress increase with time, while the rear is a rarefaction wave where they all decrease with time. Between these two wave fronts there are two remaining wave fronts. We call these wave fronts mesocontraction waves I and II. Wave front I is a wave in which stress decreases notwithstanding the increase in strain and particle velocity with time, which is followed by the other, i.e., wave front II, where with time, particle velocity, and stress decrease in spite of the increase in strain. The continuous wave front having continuous and nonsmooth profiles of strain, particle velocity, and stress can also be composed of four waves. These waves possess the same property as the corresponding waves in the smooth wave front mentioned above. The velocities at three boundaries that the waves have are discontinuous. Therefore, these four wave fronts are independent waves, just as a shock wave and a rarefraction wave. Specifically, the front wave, i.e., a contraction wave front is being outrun by a second wave front, the second one is being outrun by a third wave front, and the third is being outrun by a fourth wave front, i.e., a rarefaction wave. We call the second wave front degenerate contraction wave I. We also call the third
Reduction of Bubble Cavitation by Modifying the Diffraction Wave from a Lithotripter Aperture
2012-01-01
Abstract Purpose A new method was devised to suppress the bubble cavitation in the lithotripter focal zone to reduce the propensity of shockwave-induced renal injury. Materials and Methods An edge extender was designed and fabricated to fit on the outside of the ellipsoidal reflector of an electrohydraulic lithotripter to disturb the generation of diffraction wave at the aperture, but with little effect on the acoustic field inside the reflector. Results Although the peak negative pressures at the lithotripter focus using the edge extender at 20 kV were similar to that of the original configuration (-11.1±0.9 vs −10.6±0.7 MPa), the duration of the tensile wave was shortened significantly (3.2±0.54 vs 5.83±0.56 μs, P<0.01). There is no difference, however, in both the amplitude and duration of the compressive shockwaves between these two configurations as well as the −6 dB beam width in the focal plane. The significant suppression effect of bubble cavitation was confirmed by the measured bubble collapse time using passive cavitation detection. At the lithotripter focus, while only about 30 shocks were needed to rupture a blood vessel phantom using the original HM-3 reflector at 20 kV, no damage could be produced after 300 shocks using the edge extender. Meanwhile, the original HM-3 lithotripter at 20 kV can achieve a stone comminution efficiency of 50.4±2.0% on plaster-of-Paris stone phantom after 200 shocks, which is comparable to that of using the edge extender (46.8±4.1%, P=0.005). Conclusions Modifying the diffraction wave at the lithotripter aperture can suppress the shockwave-induced bubble cavitation with significant reduced damage potential on the vessel phantom but satisfactory stone comminution ability. PMID:22332839
Kulak, G.V.
1995-09-01
Features of Bragg diffraction of light by two-partial surface ultrasonic waves in planar gyrotropic optical waveguides placed in an external electric field are considered. General expressions for complex vector amplitudes of diffracted fields are presented. It is shown that the diffracted waves have elliptic polarization, the ellipticity being determined by the linear anisotropy of the waveguide structure, the anisotropy induced by an external electric field, the anisotropy of photoelasticity, and the crystal gyrotropy. 16 refs., 2 figs.
Traveling wave modes of a plane layered anelastic earth
NASA Astrophysics Data System (ADS)
Odom, Robert I.
2016-05-01
Incorporation of attenuation into the normal mode sum representations of seismic signals is commonly effected by applying perturbation theory. This is fine for weak attenuation, but problematic for stronger attenuation. In this work modes of the anelastic medium are represented as complex superpositions of elastic eigenfunctions. For the P-SV system a generalized eigenvalue equation for the complex eigenwavenumbers and complex coefficients used to construct the anelastic eigenfunctions is derived. The generalized eigenvalue problem for the P-SV problem is exactly linear in the eigenwavenumber at the expense of doubling the dimension. The SH problem is exactly linear in the square of the eigenwavenumber. This is in contrast to a similar standing wave problem for the earth free oscillations (Tromp and Dahlen, 1990). Attenuation is commonly incorporated into synthetic seismogram calculations by introduction of complex frequency dependent elastic moduli. The moduli depend nonlinearly on the frequency. The independent variable in the standing wave free oscillation problem is the frequency, which makes the eigenvalue problem nonlinear. The choice of the wavenumber as the independent variable for the traveling wave problem leads to a linear problem. The Earth model may be transversely isotropic. Compressional waves, and both polarizations of shear waves (SV, SH) are treated.
Travelling wave modes of a plane layered anelastic earth
NASA Astrophysics Data System (ADS)
Odom, Robert I.
2016-08-01
Incorporation of attenuation into the normal mode sum representations of seismic signals is commonly effected by applying perturbation theory. This is fine for weak attenuation, but problematic for stronger attenuation. In this work, modes of the anelastic medium are represented as complex superpositions of elastic eigenfunctions. For the P-SV system, a generalized eigenvalue equation for the complex eigenwavenumbers and complex coefficients used to construct the anelastic eigenfunctions is derived. The generalized eigenvalue problem for the P-SV problem is exactly linear in the eigenwavenumber at the expense of doubling the dimension. The SH problem is exactly linear in the square of the eigenwavenumber. This is in contrast to a similar standing wave problem for the earth free oscillations. Attenuation is commonly incorporated into synthetic seismogram calculations by introduction of complex frequency-dependent elastic moduli. The moduli depend nonlinearly on the frequency. The independent variable in the standing wave free oscillation problem is the frequency, which makes the eigenvalue problem nonlinear. The choice of the wavenumber as the independent variable for the travelling wave problem leads to a linear problem. The Earth model may be transversely isotropic. Compressional waves and both polarizations of shear waves (SV, SH) are treated.
The Relativistic Transformation for an Electromagnetic Plane Wave with General Time Dependence
ERIC Educational Resources Information Center
Smith, Glenn S.
2012-01-01
In special relativity, the transformation between inertial frames for an electromagnetic plane wave is usually derived for the time-harmonic case (the field is a sinusoid of infinite duration), even though all practical waves are of finite duration and may not even contain a dominant sinusoid. This paper presents an alternative derivation in which…
The use of the plane wave fluid-structure interaction loading approximation in NASTRAN
NASA Technical Reports Server (NTRS)
Dawson, R. L.
1991-01-01
The Plane Wave Approximation (PWA) is widely used in finite element analysis to implement the loading generated by an underwater shock wave. The method required to implement the PWA in NASTRAN is presented along with example problems. A theoretical background is provided and the limitations of the PWA are discussed.
NASA Technical Reports Server (NTRS)
Dhawan, R.; Gunther, M. F.; Claus, R. O.
1991-01-01
Quantitative measurements of the in-plane particle displacement components of ultrasonic surface acoustic wave fields using extrinsic Fizeau fiber interferometric (EFFI) sensors are reported. Wave propagation in materials and the fiber sensor elements are briefly discussed. Calibrated experimental results obtained for simulated acoustic emission events on homogeneous metal test specimens are reported and compared to previous results obtained using piezoelectric transducers.
An Exact Solution for Geophysical Edge Waves in the {β}-Plane Approximation
NASA Astrophysics Data System (ADS)
Ionescu-Kruse, Delia
2015-12-01
By taking into account the {β}-plane effects, we provide an exact nonlinear solution to the geophysical edge-wave problem within the Lagrangian framework. This solution describes trapped waves propagating eastward or westward along a sloping beach with the shoreline parallel to the Equator.
On the optical theorem and non-plane-wave scattering in quantum mechanics
NASA Astrophysics Data System (ADS)
Gouesbet, G.
2009-11-01
In quantum mechanics, the optical theorem states that the extinction cross section is equal (within a prefactor 4π/k, in which k is a quantum wave number) to the imaginary part of the forward scattering angular function. This theorem is valid for plane wave scattering. We discuss modifications required for non-plane-wave scattering and establish a generalized expression for the extinction cross section in quantum mechanics. Examples are provided for two kinds of quantum shaped beams, namely, Gaussian and Bessel beams.
NASA Astrophysics Data System (ADS)
Gauthier, Robert C.; Alzahrani, Mohammed A.; Jafari, Seyed Hamed
2015-02-01
The plane wave expansion (PWM) technique applied to Maxwell's wave equations provides researchers with a supply of information regarding the optical properties of dielectric structures. The technique is well suited for structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis functions have been employed to cast Maxwell's wave equations into an eigen-matrix formulation from which the resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier- Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical development details will be presented indicating how certain mathematical complications in the process have been overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM, FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z axis component of propagation constant makes the technique applicable to photonic crystal fibers and other waveguide structures. Computational results will be presented for a number of different dielectric geometries including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further enhance the computation process will be reported.
Theoretical calculation of plane wave speeds for alkali metals under pressure.
NASA Technical Reports Server (NTRS)
Eftis, J.; Macdonald, D. E.; Arkilic, G. M.
1971-01-01
Theoretical calculations of the variation with pressure of small amplitude plane wave speeds are performed for sodium and potassium at zero temperature. The results obtained for wave speeds associated with volume dependent second-order elastic coefficients show better agreement with experimental data than for wave speeds associated with shear dependent coefficients. This result is believed to be due to omission of the band structure correction to the strain energy density.
Interaction of a plane shock wave in water with a thin layer of lower density
Bergel`son, V.I.; Nemchinov, I.V.; Orlova, T.I.; Khazins, V.M.
1992-08-01
A numerical analysis is conducted on the interaction of a plane shock wave in water with a thin layer of lower density, which is perpendicular to the wave front. Parameters are defined for the perturbed flow structure and for large-scale precursors, which arise ahead of the shock front. Possibilities are discussed of experimentally investigating this phenomena with a cylindrical shock wave using standard explosives. 4 refs., 4 figs.
Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures.
Chen, A-Li; Yan, Dong-Jia; Wang, Yue-Sheng; Zhang, Chuanzeng
2016-02-01
In this paper, anti-plane transverse wave propagation in nanoscale periodic layered piezoelectric structures is studied. The localization factor is introduced to characterize the wave propagation behavior. The transfer matrix method based on the nonlocal piezoelectricity continuum theory is used to calculate the localization factor. Additionally, the stiffness matrix method is applied to compute the wave transmission spectra. A cut-off frequency is found, beyond which the elastic waves cannot propagate through the periodic structure. The size effect or the influence of the ratio of the internal to external characteristic lengths on the cut-off frequency and the wave propagation behavior are investigated and discussed. PMID:26518526
Feasibility of detecting near-surface feature with Rayleigh-wave diffraction
Xia, J.; Nyquist, J.E.; Xu, Y.; Roth, M.J.S.; Miller, R.D.
2007-01-01
Detection of near-surfaces features such as voids and faults is challenging due to the complexity of near-surface materials and the limited resolution of geophysical methods. Although multichannel, high-frequency, surface-wave techniques can provide reliable shear (S)-wave velocities in different geological settings, they are not suitable for detecting voids directly based on anomalies of the S-wave velocity because of limitations on the resolution of S-wave velocity profiles inverted from surface-wave phase velocities. Therefore, we studied the feasibility of directly detecting near-surfaces features with surface-wave diffractions. Based on the properties of surface waves, we have derived a Rayleigh-wave diffraction traveltime equation. We also have solved the equation for the depth to the top of a void and an average velocity of Rayleigh waves. Using these equations, the depth to the top of a void/fault can be determined based on traveltime data from a diffraction curve. In practice, only two diffraction times are necessary to define the depth to the top of a void/fault and the average Rayleigh-wave velocity that generates the diffraction curve. We used four two-dimensional square voids to demonstrate the feasibility of detecting a void with Rayleigh-wave diffractions: a 2??m by 2??m with a depth to the top of the void of 2??m, 4??m by 4??m with a depth to the top of the void of 7??m, and 6??m by 6??m with depths to the top of the void 12??m and 17??m. We also modeled surface waves due to a vertical fault. Rayleigh-wave diffractions were recognizable for all these models after FK filtering was applied to the synthetic data. The Rayleigh-wave diffraction traveltime equation was verified by the modeled data. Modeling results suggested that FK filtering is critical to enhance diffracted surface waves. A real-world example is presented to show how to utilize the derived equation of surface-wave diffractions. ?? 2006 Elsevier B.V. All rights reserved.
NASA Astrophysics Data System (ADS)
Laven, Philip; Lock, James A.; Adam, John A.
2015-09-01
We calculated scattering of an electromagnetic plane wave by a radially inhomogeneous particle and a radially inhomogeneous bubble when the square of the refractive index profile is parabolic as a function of radius. Such a particle or bubble is called a generalized Luneburg lens. A wide variety of scattering phenomena can occur, depending on the value of the two adjustable parameters of the parabola. These phenomena, including transmission rainbows, the weak caustic for near-critical-angle scattering by a bubble, surface orbiting, the interior orbiting paths of morphology-dependent resonances, and the separation of diffraction are studied here using wave theory and time domain scattering. These phenomena are also compared with their appearance or absence for scattering by a homogeneous sphere.
Well-posedness and generalized plane waves simulations of a 2D mode conversion model
NASA Astrophysics Data System (ADS)
Imbert-Gérard, Lise-Marie
2015-12-01
Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the plasma center. This work focuses on a mathematical model of wave propagation around the mode conversion region, from both theoretical and numerical points of view. It aims at developing, for a well-posed equation, specific basis functions to study a wave mode conversion process. These basis functions, called generalized plane waves, are intrinsically based on variable coefficients. As such, they are particularly adapted to the mode conversion problem. The design of generalized plane waves for the proposed model is described in detail. Their implementation within a discontinuous Galerkin method then provides numerical simulations of the process. These first 2D simulations for this model agree with qualitative aspects studied in previous works.
Wave dislocations in the diffraction pattern of a higher-order optical catastrophe
NASA Astrophysics Data System (ADS)
Nye, J. F.
2010-01-01
The paper explores a partial unfolding of the canonical three-dimensional diffraction field associated with the optical catastrophe X9 with modulus K = -6. A practical realization would be the focal region of a thin lens created by setting a drop of water on a horizontal glass slide and constraining its perimeter to be square. The pattern of caustics formed around the focus is a twisted and ribbed double trumpet with 4-fold symmetry. Like all diffraction catastrophes the essential structure is based on a pattern of line singularities (wave dislocations or optical vortices) on which the amplitude is zero and the phase is indeterminate. The caustic is encircled on the outside, and in the focal plane, by a highly puckered and non-circular ring and a forest of other dislocations. Far from the axis these are organized by the planar group 3m, despite the 4-fold symmetry. On the inside, the dislocation lines form a curved quasi-periodic lattice of small, nearly planar, nearly circular, rings based on the tetragonal space group I4mm. There are similarities to the pattern for the elliptic umbilic catastrophe, and, just as in that case, far from the focus the inner rings in lines close to the ribs of the caustic eventually join together to become the straight inner dislocations of the Pearcey pattern for the cusp. But the way in which this transition is accomplished, which involves four simultaneous reconnections, is quite different for the two catastrophes. Further, in the elliptic (and hyperbolic) umbilic catastrophes diffraction splits the focal spot longitudinally; in X9 with K = -6 it does not.
Source extension of chorus waves in the equatorial plane
NASA Astrophysics Data System (ADS)
Hayosh, M.; Santolik, O.; Parrot, M.
2009-04-01
We use measurements of the Cluster spacecraft and a ray tracing simulation to estimate the location and size of the global source of whistler-mode chorus emissions. In this study we use the data provided simultaneously by the STAFF-SA instruments on the four Cluster spacecraft on 19 August, 2003. To determine the direction of propagation of chorus we calculate Poynting vector whereas a ray-tracing method is used to estimate the chorus source extension. For the first time this analysis has been made along whole particular Cluster orbit in both hemispheres. Our study shows that minimum size of the global chorus source region in the equatorial plane is between 1-3 Earth's radii. The resulting location of the chorus source region is at radial distances between 3 and 8 Earth radii. This result is in agreement with previous analysis of Cluster data by Parrot et al., 2003, 2004 and with the study of Santolik et al., 2005 who analyzed data from the Double Star TC-1 spacecraft.
Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets.
Deringer, Volker L; Tchougréeff, Andrei L; Dronskowski, Richard
2011-06-01
Simple, yet predictive bonding models are essential achievements of chemistry. In the solid state, in particular, they often appear in the form of visual bonding indicators. Because the latter require the crystal orbitals to be constructed from local basis sets, the application of the most popular density-functional theory codes (namely, those based on plane waves and pseudopotentials) appears as being ill-fitted to retrieve the chemical bonding information. In this paper, we describe a way to re-extract Hamilton-weighted populations from plane-wave electronic-structure calculations to develop a tool analogous to the familiar crystal orbital Hamilton population (COHP) method. We derive the new technique, dubbed "projected COHP" (pCOHP), and demonstrate its viability using examples of covalent, ionic, and metallic crystals (diamond, GaAs, CsCl, and Na). For the first time, this chemical bonding information is directly extracted from the results of plane-wave calculations. PMID:21548594
NASA Astrophysics Data System (ADS)
Borzdov, G. N.
2016-06-01
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency. Each standing wave consists of two eigenwaves with different complex amplitudes and opposite directions of propagation. The fundamental solution is obtained in the form of the projection operator defining the subspace of solutions to the Dirac equation. It is illustrated by the analysis of the ground state and the spin precession of the Dirac electron in the field of two counterpropagating plane waves with left and right circular polarizations. Interrelations between the fundamental solution and approximate partial solutions is discussed and a criterion for evaluating the accuracy of approximate solutions is suggested.
Plane-wave decomposition by spherical-convolution microphone array
NASA Astrophysics Data System (ADS)
Rafaely, Boaz; Park, Munhum
2001-05-01
Reverberant sound fields are widely studied, as they have a significant influence on the acoustic performance of enclosures in a variety of applications. For example, the intelligibility of speech in lecture rooms, the quality of music in auditoria, the noise level in offices, and the production of 3D sound in living rooms are all affected by the enclosed sound field. These sound fields are typically studied through frequency response measurements or statistical measures such as reverberation time, which do not provide detailed spatial information. The aim of the work presented in this seminar is the detailed analysis of reverberant sound fields. A measurement and analysis system based on acoustic theory and signal processing, designed around a spherical microphone array, is presented. Detailed analysis is achieved by decomposition of the sound field into waves, using spherical Fourier transform and spherical convolution. The presentation will include theoretical review, simulation studies, and initial experimental results.
Qualitative analysis of response caused by growing plane waves by underdetermined system theory
NASA Astrophysics Data System (ADS)
Sano, Yukio
1991-03-01
A qualitative analysis of the mechanical response of rate-dependent media caused by one-dimensional plane smooth- and continuous-wave fronts with the growing peaks of strain, particle velocity, and stress is performed by an underdetermined system of nonlinear partial differential equations. The response found by the analysis reveals that strain, particle velocity, and stress profiles in the smooth-wave front are not similar and that the front is composed of five partial waves having different properties. The property is represented by the set of strain rate, acceleration, and stress rate as in a previous study. The front of the wave front is necessarily a contraction wave in which strain, particle velocity, and stress increase with time. The second partial wave is another contraction wave. We call the wave a vice-contraction wave. The rear is assumed to be a rarefaction wave where they all decrease with time. Between these two partial waves there are two remaining partial waves. We call these waves mesorarefaction waves I and II. Wave II is a wave in which particle velocity and stress increase, notwithstanding the decrease in strain with time. It is followed by wave I in which the increase in stress with time occurs in spite of the decrease in strain and particle velocity. The continuous-wave front, which has discontinuous-movement velocities at the continuous, but nonsmooth, positions in the profiles of strain, particle velocity, and stress, is composed of five independent waves. These waves are a contraction wave, a vice-contraction wave, evolutional rarefaction waves II and I, and a rarefaction wave which possess the same properties as the corresponding partial waves in the smooth-wave front mentioned above. Both in the smooth-growing-wave front and in the continuous one the peak precedence is in the order of the strain, particle velocity, and stress peaks. The stress-strain path and stress-particle velocity path at a position in a rate-dependent medium which is
An algorithm for the calculation of the partial wave expansion of the Coulomb-distorted plane wave
NASA Astrophysics Data System (ADS)
Hornyak, I.; Kruppa, A. T.
2015-12-01
The partial wave expansion of the Coulomb-distorted plane wave is determined by the help of the complex generalized hypergeometric function 2F2(a , a ; a + l + 1 , a - l ; z) . An algorithm for the calculation of 2F2(a , a ; a + l + 1 , a - l ; z) is created and it is implemented as a FORTRAN-90 code. The code is fast and its accuracy is 14 significant decimal digits.
Cascading processes in the nonlinear diffraction of light by standing acoustic waves
NASA Astrophysics Data System (ADS)
Dadoenkova, Yu. S.; Dadoenkova, N. N.; Bentivegna, F. F. L.; Lyubchanskii, I. L.; Lee, Y. P.
2016-01-01
The contribution of two types of cascading process to the nonlinear optical diffraction of electromagnetic waves from a standing acoustic wave in a GaAs crystal is theoretically studied. The first type of cascading process results from second-harmonic generation followed by linear acousto-optical diffraction, while the second type involves linear acousto-optical diffraction from the standing acoustic wave and subsequent sum-frequency generation. In contrast to the third, direct, nonlinear acousto-optical diffraction process we previously investigated, the photoelastic interaction between electromagnetic and acoustic waves is here linear. We establish the rules governing the cascading processes and show that in most cases the output signal simultaneously results from two or even three of the possible nonlinear diffraction mechanisms. However, we demonstrate that a careful choice of the incidence angles of the incoming electromagnetic waves, of the polarization combinations of the incoming and diffracted waves, and of the type of acoustic wave (longitudinal or transverse) makes it always possible to distinguish between the direct and either of the two cascading processes.
Woods, Daniel C; Bolton, J Stuart; Rhoads, Jeffrey F
2015-10-01
The transmission of airborne sound into high-impedance media is of interest in several applications. For example, sonic booms in the atmosphere may impact marine life when incident on the ocean surface, or affect the integrity of existing structures when incident on the ground. Transmission across high impedance-difference interfaces is generally limited by reflection and refraction at the surface, and by the critical angle criterion. However, spatially decaying incident waves, i.e., inhomogeneous or evanescent plane waves, may transmit energy above the critical angle, unlike homogeneous plane waves. The introduction of a decaying component to the incident trace wavenumber creates a nonzero propagating component of the transmitted normal wavenumber, so energy can be transmitted across the interface. A model of evanescent plane waves and their transmission across fluid-fluid and fluid-solid interfaces is developed here. Results are presented for both air-water and air-solid interfaces. The effects of the incident wave parameters (including the frequency, decay rate, and incidence angle) and the interfacial properties are investigated. Conditions for which there is no reflection at the air-solid interface, due to impedance matching between the incident and transmitted waves, are also considered and are found to yield substantial transmission increases over homogeneous incident waves. PMID:26520290
Nonlinear Breit-Wheeler process in the collision of a photon with two plane waves
NASA Astrophysics Data System (ADS)
Wu, Yuan-Bin; Xue, She-Sheng
2014-07-01
The nonlinear Breit-Wheeler process of electron-positron pair production off a probe photon colliding with a low-frequency and a high-frequency electromagnetic wave that propagate in the same direction is analyzed. We calculate the pair-production probability and the spectra of the created pair in the nonlinear Breit-Wheeler processes of pair production off a probe photon colliding with two plane waves or one of these two plane waves. The differences of these two cases are discussed. We evidently show, in the two-wave case, the possibility of Breit-Wheeler pair production with simultaneous photon emission into the low-frequency wave and the high multiphoton phenomena: (i) Breit-Wheeler pair production by absorption of the probe photon and a large number of photons from the low-frequency wave, in addition to the absorption of one photon from the high-frequency wave; (ii) Breit-Wheeler pair production by absorption of the probe photon and one photon from the high-frequency wave with simultaneous emission of a large number of photons into the low-frequency wave. The phenomenon of photon emission into the wave cannot happen in the one-wave case. Compared with the one-wave case, the contributions from high multiphoton processes are largely enhanced in the two-wave case. The results presented in this article show a possible way to access the observations of the phenomenon of photon emission into the wave and high multiphoton phenomenon in Breit-Wheeler pair production even with the laser-beam intensity of order 1018 W/cm2.
Free energy and phase transition of the matrix model on a plane wave
Hadizadeh, Shirin; Ramadanovic, Bojan; Semenoff, Gordon W.; Young, Donovan
2005-03-15
It has recently been observed that the weakly coupled plane-wave matrix model has a density of states which grows exponentially at high energy. This implies that the model has a phase transition. The transition appears to be of first order. However, its exact nature is sensitive to interactions. In this paper, we analyze the effect of interactions by computing the relevant parts of the effective potential for the Polyakov loop operator in the finite temperature plane-wave matrix model to three-loop order. We show that the phase transition is indeed of first order. We also compute the correction to the Hagedorn temperature to order two loops.
Killing spinors and exact plane-wave solutions of extended supergravity
NASA Astrophysics Data System (ADS)
Hull, C. M.
1984-07-01
Urrutia's ansatz for exact plane-wave solutions of simple supergravity is generalized to N=2 extended supergravity and conditions are given for the solutions to be nontrivial. Conditions are also given for the plane-wave background to be invariant under a local supersymmetry transformation generated by a Killing spinor. It is seen that even though a bosonic background can admit a spin-32 solution when it does not possess a Killing spinor, if it is supersymmetric it admits a more general gravitino solution. Comparison is made with the solutions of Aichelburg and Dereli.
Solid explosive plane-wave lenses pressed-to-shape with dies
Olinger, B.
2007-11-01
Solid-explosive plane-wave lenses 1", 2" and 4¼" in diameter have been mass-produced from components pressed-to-shape with aluminum dies. The method used to calculate the contour between the solid plane-wave lens components pressed-to-shape with the dies is explained. The steps taken to press, machine, and assemble the lenses are described. The method of testing the lenses, the results of those tests, and the corrections to the dies are reviewed. The work on the ½", 8", and 12" diameter lenses is also discussed.
kṡp formula for use with linearized augmented plane waves
NASA Astrophysics Data System (ADS)
Shishidou, Tatsuya; Oguchi, Tamio
2008-12-01
We provide kṡp formalism within the full-potential linearized augmented plane-wave (LAPW) method. Unlike the pure plane waves, the LAPW functions do not behave trivially in moving from k to k+q and their incompleteness as a basis set should be taken into account. Derivatives of the sphere matching coefficients play the key role, for which we find a simple formula. Concrete formula for the kṡp matrix elements is derived and numerically tested. Generalized second-order perturbation theory allowing for a degenerate case is presented and the literally exact electronic band gradients and curvatures are accessible.
Vectorial spherical-harmonics representation of an inhomogeneous elliptically polarized plane wave.
Frezza, F; Mangini, F
2015-07-01
In this paper, a generalization of the vectorial spherical-harmonics expansion of an inhomogeneous elliptically polarized plane wave is presented. The solution has been achieved using the Legendre functions generalized via hypergeometric and gamma functions, shifting the difficulty to the determination of only expansion coefficients. In order to validate the presented method, a Matlab code has been implemented. To compare the results a Mie scattering by a sphere is considered, then a truncation criterion for the numerical evaluation of the series is proposed, and the Mie scattering coefficients by perfectly conducting and dielectric spheres excited by an inhomogeneous elliptically polarized plane wave are shown. PMID:26367169
Efficiency of magnetic plane wave pumping of a ferrofluid through a planar duct
NASA Astrophysics Data System (ADS)
Felderhof, B. U.
2011-09-01
The efficiency of ferrohydrodynamic pumping of a ferrofluid through a planar duct by means of a running magnetic plane wave is studied to second order in the amplitude of the exciting current density. The rate of dissipation in the fluid is calculated from the first order magnetic field and magnetization. It turns out that the efficiency, defined as the ratio of net flow velocity to power input, is comparable in magnitude to that for Stokes peristaltic pumping. The theory for electrohydrodynamic pumping of a polar liquid by means of a running electric plane wave is shown to be nearly identical.
Optical measurements of the mutual reflection of two-plane shock waves
Barbosa, F.J.; Skews, B.W.
1995-12-31
A bifurcated shock tube is used to create two synchronized waves of equal strength. Essentially a single shock wave is split symmetrically in two, the two waves then are later brought back together at a trailing edge of a wedge to interact, the plane of symmetry acting as an ideal rigid wall. The normal method of studying mach reflections is to allow a plane shock wave to impinge on a wedge, however the boundary layer growth on the wedge surface effectively ensures that the flow direction behind the Mach stem does not have to satisfy the boundary condition of being parallel to the surface of the wedge. Thus the transition from regular to Mach reflection occurs at higher angles of incidence than theory allows. The present experiment was initiated to generate data on the ideal cause of reflection off a plane wall. The advantage of the new system is that like classical theory and computational solutions of the inviscid Euler equations, the boundary layer no slip condition is not imposed at the plane of reflection. Optical methods are used to investigate the post-shock flow, as well as to help explain the complex interactions which occur when the two shock waves are not synchronized. These interactions show many very interesting features and clearly indicate the need for higher resolution measurements such as are obtained using holographic interferometry, and also to extend the work to different wedge angles and Mach numbers.
Plane shock waves and Haff's law in a granular gas
NASA Astrophysics Data System (ADS)
Reddy, Lakshminarayana; Alam, Meheboob
2015-11-01
The Riemann problem of planar shock waves is analyzed for a dilute granular gas by solving Euler- and Navier-Stokes-order equations numerically. The density and temperature profiles are found to be asymmetric, with the maxima of both density and temperature occurring within the shock-layer. The density-peak increases with increasing Mach number and inelasticity, and is found to propagate at a steady speed at late times. The granular temperature at the upstream end of the shock decay according to Haff's law [ θ (t) ~t-2 ], but the downstream temperature decays faster than its upstream counterpart. The Haff's law seems to hold inside the shock up-to a certain time for weak shocks, but deviations occur for strong shocks. The time at which the maximum temperature deviates from Haff's law follows a power-law scaling with upstream Mach number and the restitution coefficient. The continual build-up of density inside the shock is discussed, the origin of which seems to be tied to a pressure instability in granular gases. It is shown that the granular energy equation must be `regularized' to arrest the maximum density, and the regularized hydrodynamic equations should be used for shock calculations (Reddy & Alam, 2015, J. Fluid Mech., to be published).
Active control of fan-generated plane wave noise
NASA Technical Reports Server (NTRS)
Gerhold, Carl H.; Nuckolls, William E.; Santamaria, Odillyn L.; Martinson, Scott D.
1993-01-01
Subsonic propulsion systems for future aircraft may incorporate ultra-high bypass ratio ducted fan engines whose dominant noise source is the fan with blade passage frequency less than 1000 Hz. This low frequency combines with the requirement of a short nacelle to diminish the effectiveness of passive duct liners. Active noise control is seen as a viable method to augment the conventional passive treatments. An experiment to control ducted fan noise using a time domain active adaptive system is reported. The control sound source consists of loudspeakers arrayed around the fan duct. The error sensor location is in the fan duct. The purpose of this experiment is to demonstrate that the in-duct error sensor reduces the mode spillover in the far field, thereby increasing the efficiency of the control system. In this first series of tests, the fan is configured so that predominantly zero order circumferential waves are generated. The control system is found to reduce the blade passage frequency tone significantly in the acoustic far field when the mode orders of the noise source and of the control source are the same. The noise reduction is not as great when the mode orders are not the same even though the noise source modes are evanescent, but the control system converges stably and global noise reduction is demonstrated in the far field. Further experimentation is planned in which the performance of the system will be evaluated when higher order radial and spinning modes are generated.
Role of diffractive optical elements in the design of mid-wave infrared zoom lenses
NASA Astrophysics Data System (ADS)
Hudyma, Russell M.
1993-08-01
The advantages of hybrid refractive/diffractive components in medium wave infrared (MWIR) zooms are illustrated through the use of design examples. The examples illustrate that hybrids may be used to simplify the construction of achromatic or athermal zoom groups.
NASA Astrophysics Data System (ADS)
Ko, Seung H.; Ryu, Sang G.; Misra, Nipun; Pan, Heng; Grigoropoulos, Costas P.; Kladias, Nick; Panides, Elias; Domoto, Gerald A.
2008-10-01
Short pulsed laser induced single acoustic wave generation, propagation, interaction with rigid structures, and focusing in water are experimentally and numerically studied. A large area short duration single plane acoustic wave was generated by the thermoelastic interaction of a homogenized nanosecond pulsed laser beam with a liquid-solid interface and propagated at the speed of sound in water. Laser flash schlieren photography was used to visualize the transient interaction of the plane acoustic wave with various submerged rigid structures [(a) a single block, (b) double blocks, (c) 33° tilted single block, and (d) concave cylindrical acoustic lens configurations]. Excellent agreement between the experimental results and numerical simulation is observed. Our simulation results demonstrate that the laser induced planar acoustic wave can be focused down to several tens of micron size and several bars in pressure.
NASA Astrophysics Data System (ADS)
Olson, Erik R.; Knuteson, Robert O.; Revercomb, Hank E.; Li, Jun; Huang, Hung-Lung A.
2004-10-01
The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) and the Hyperspectral Environmental Suite (HES) instruments are geostationary infrared spectrometers. Geostationary orbit provides observations with very good time resolution, but also increases the effect of diffraction. There can be significant differences in emitted radiances due to clouds and changes in surface characteristics. High, thick clouds in particular are much cooler than clear areas. Diffraction causes radiation that originates from cloudy areas outside of the detector field of view to contaminate the clear pixels. GIFTS will also have two detector arrays on different focal planes, which may not be perfectly aligned. This can cause spatial misalignment between the data for the two spectral regions. High spatial resolution numerical models run at the University of Wisconsin - Cooperative Institute for Meteorological Satellite Studies (UW-CIMSS) provide data for examining the diffraction and misalignment effects. The model data represents a variable cloud case during the IHOP field experiment at 1.3-km resolution. This paper outlines the production of high spatial resolution simulated data, characterization of the far field diffraction effects on radiances, and analysis of misalignment effects on temperature and moisture profile retrievals.
From plane waves to local Gaussians for the simulation of correlated periodic systems.
Booth, George H; Tsatsoulis, Theodoros; Chan, Garnet Kin-Lic; Grüneis, Andreas
2016-08-28
We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller-Plesset perturbation theory. PMID:27586908
Mid-Wave and Long-Wave Infrared Dualband Megapixel QWIP Focal Plane Array
NASA Technical Reports Server (NTRS)
Gunapala, S. D.; Bandara, S. V.; Liu, J. K.; Mumolo, J. M.; Hill, C. J.; Ting, D. Z.; Kurth, E.; Woolaway, J.; LeVan, P. D.; Tidrow, M. Z.
2008-01-01
Mid-wavelength infrared (MWIR) and long-wavelength infrared (LWIR) 1024x1024 pixel InGaAs/GaAs/AlGaAs based quantum well infrared photodetector (QWIP) focal planes and a 320x256 pixel dual-band pixel co-registered simultaneous QWIP focal plane array have been demonstrated as pathfinders. In this paper, we discuss the development of 1024x1024 MWIR/LWIR dual-band pixel co-registered simultaneous QWIP focal plane array.
Three-wave diffraction in damaged epitaxial layers with a wurtzite structure
NASA Astrophysics Data System (ADS)
Kyutt, R. N.
2011-05-01
Three-wave diffraction of X-rays is measured using the Renninger scheme for a series of GaN epitaxial layers of various thicknesses and degrees of structural perfection. In each 30°-angular interval of azimuthal rotation, all ten three-wave peaks determined by the geometry of diffraction with the 0001 first forbidden reflection and Cu K α radiation are observed. The φ- and θ-scanned diffraction curves are measured for each three-wave combination. The angular FWHM of the diffraction peaks formed in experiments and its relation with the parameters of the two-wave diffraction pattern and the dislocation structure of the layers are analyzed. It is shown that the φ-scan peaks are less sensitive to the degree of structural perfection than the γ-mode peaks. The strongest dependence on the dislocation density for the latter peaks is observed for the (1bar 100)/(bar 1101) and (3bar 2bar 10)/(bar 3211) three-wave combinations with a pure Laue component of secondary radiation, while the (01bar 13)/(0bar 11bar 2) combination with a large Bragg component exhibits the weakest dependence. Splitting of three-wave Renninger peaks associated with the coarse-block structure of some of the layers with rotations of the blocks about the normal to the surface is detected. The total integrated intensity of all three-wave combinations is determined and their ratios are in qualitative agreement with the theory.
Guided torsional wave generation of a linear in-plane shear piezoelectric array in metallic pipes.
Zhou, Wensong; Yuan, Fuh-Gwo; Shi, Tonglu
2016-02-01
Cylindrical guided waves based techniques are effective and promising tools for damage detection in long pipes. The essential operations are generation and reception of guided waves in the structures utilizing transducers. A novel in-plane shear (d36 type) PMNT wafer is proposed to generate and receive the guided wave, especially the torsional waves, in metallic pipes. In contrast to the traditional wafer, this wafer will directly introduce in-plane shear deformation when electrical field is conveniently applied through its thickness direction. A single square d36 PMNT wafer is bonded on the surface of the pipe positioned collinearly with its axis, when actuated can predominantly generate torsional (T) waves along the axial direction, circumferential shear horizontal (C-SH) waves along circumferential direction, and other complex cylindrical Lamb-like wave modes along other helical directions simultaneously. While a linear array of finite square size d36 PMNT wafers was equally spaced circumferentially, when actuated simultaneously can nearly uniform axisymmetric torsional waves generate in pipes and non-symmetric wave modes can be suppressed greatly if the number of the d36 PMNT wafer is sufficiently large. This paper first presents the working mechanism of the linear d36 PMNT array from finite element analysis (FEA) by examining the constructive and destructive displacement wavefield phenomena in metallic pipes. Furthermore, since the amplitude of the received fundamental torsional wave signal strongly depends on frequency, a series of experiments are conducted to determine the frequency tuning curve for the torsional wave mode. All results indicate the linear d36 PMNT array has potential for efficiently generating uniform torsional wavefield of the fundamental torsional wave mode, which is more effective in monitoring structural health in metallic pipes. PMID:26548525
A beamforming method for plane wave Doppler imaging of high flow velocities
NASA Astrophysics Data System (ADS)
Mansour, Omar; Poepping, Tamie L.; Lacefield, James C.
2016-04-01
Plane wave imaging is desirable for its ability to achieve high frame rates, allowing the capture of fast dynamic events, and continuous Doppler data. In most implementations of plane-wave imaging, multiple low resolution image (LRI) frames from different plane wave tilt angles are compounded to form a single high resolution image (HRI) frame, thereby reducing the frame rate. Compounding is a low-pass mean filter that causes attenuation and aliasing to signals with high Doppler shifts. On the other hand, the lateral beam profile and hence the quality of the HRI frames is improved by increasing the number of compounded frames. Therefore, a tradeoff exists between the Doppler limits and beam profile. In this paper, we present a method that eliminates this tradeoff and produces high resolution images without the use of compounding. The method suppresses the off-focus (clutter) signal by spreading its spectrum, while keeping the spectrum of the in-focus signal intact. The spreading is achieved by using a random sequence of tilt angles, as opposed to a linear sweep. Experiments performed using a carotid vessel phantom with constant flow demonstrate that the spread-spectrum method more accurately measures the parabolic flow profile of the vessel and in particular outperforms conventional plane-wave Doppler at higher flow velocities. The spread-spectrum method is expected to be valuable for Doppler applications that require measurement of high velocities at high frame rates.
Determination of the plane specific elastic constants of Waspaloy using neutron diffraction
Stone, H.J.; Reed, R.C.; Holden, T.M.
1999-01-08
In the present paper, the plane specific elastic constants for Waspaloy, a high strength nickel-base superalloy, have been determined with a considerable degree of precision. For this purpose, in-situ tensile tests have been carried out in a neutron diffractometer. The data which are reported are of considerable significance, since they allow an accurate determination of the residual stress slate from an estimate of the local d-spacing from the hkl lattice reflection. Thus, the data should be of interest to those interested in the determination of the residual stress state in components which are fabricated from Waspaloy, and nickel-base superalloys in general.
Zamboni-Rached, Michel; de Assis, Mariana Carolina; Ambrosio, Leonardo A
2015-07-01
In this work, we propose the generation of diffraction-resistant beams by using a parabolic reflector and a source of spherical waves positioned at a point slightly displaced from its focus (away from the reflector). In our analysis, considering the reflector dimensions much greater than the wavelength, we describe the main characteristics of the resulting beams, showing their properties of resistance to the diffraction effects. Due to its simplicity, this method may be an interesting alternative for the generation of long-range diffraction-resistant waves. PMID:26193137
Computational Electromagnetic Dosimetry of a Human Body in a Vehicle for Plane-wave Exposure
NASA Astrophysics Data System (ADS)
Hirata, Akimasa
The present study investigated whole-body specific absorption rate of a human body in a vehicle cabin for plane-wave exposure. The rationale for this investigation is that fields in the vehicle without human have been enhanced in particular frequency region due to standing waves, and thus power absorption in the human body is of interest. For our computational results, the whole-body average specific absorption rate of the human in the vehicle was found to be 60% smaller than that in free space. The reason for this upset is that the standing wave over the vehicle cabin was suppressed due to power absorption by the human.
Formation of Roll-Waves on Thin Laminar Flow down an Inclined Plane Wall
NASA Astrophysics Data System (ADS)
Tougou, Hirohumi
1980-02-01
The linear stability of periodic permanent roll-wave trains on thin laminar flow of a viscous fluid down an inclined plane wall has been investigated analytically on the basis of a hydraulic model. The analytical result is here confirmed by following numerically the time development of a periodic initial disturbance superimposed upon a basic steady parallel flow into a stable or unstable permanent roll-wave train. Furthermore, it is shown that roll-waves can be generated successively from a localized initial disturbance.
ERIC Educational Resources Information Center
Maurines, Laurence
2010-01-01
This particular study is part of a research programme on the difficulties encountered by students when learning about wave phenomena in a three-dimensional medium in the absence or presence of obstacles. It focuses on how students reason in situations in which wave optics need to be used: diffraction of light by an aperture, imaging in the…
Interference Phenomena of Diffraction Waves Originating on the Boundary of a Small Obstacle
NASA Astrophysics Data System (ADS)
Itô, Hiroshi; Kanai, Norikane
1988-03-01
Existence of boundary diffraction waves originating at every point of the outline of an obstacle illuminated by coherent light is studied experimentally. Optical fringes appearing in the shadow region of the obstacle are recognized to be made by interference of this kind of wave.
Reflection of electromagnetic waves from mixtures of plane gravitational and scalar waves
Gurtug, O.; Halilsoy, M.; Unver, O.
2006-08-15
We consider colliding wave packets consisting of hybrid mixtures of electromagnetic, gravitational, and scalar waves. Irrespective of the scalar field, the electromagnetic wave still reflects from the gravitational wave. Some reflection processes are given for different choice of packets in which the Coulomb-like component {psi}{sub 2} vanishes. Exact solution for multiple reflection of an electromagnetic wave from successive impulsive gravitational waves is obtained in a closed form. It is shown that a successive sign flip in the Maxwell spinor arises as a result of encountering with an impulsive train (i.e. the Dirac's comb curvature) of gravitational waves. Such an observable effect may be helpful in the detection of gravitational wave bursts.
Schwab, Hans-Martin; Beckmann, Martin F.; Schmitz, Georg
2016-01-01
Photoacoustic imaging aims to visualize light absorption properties of biological tissue by receiving a sound wave that is generated inside the observed object as a result of the photoacoustic effect. In clinical applications, the strong light absorption in human skin is a major problem. When high amplitude photoacoustic waves that originate from skin absorption propagate into the tissue, they are reflected back by acoustical scatterers and the reflections contribute to the received signal. The artifacts associated with these reflected waves are referred to as clutter or skin echo and limit the applicability of photoacoustic imaging for medical applications severely. This study seeks to exploit the acoustic tissue information gained by plane wave ultrasound measurements with a linear array in order to correct for reflections in the photoacoustic image. By deriving a theory for clutter waves in k-space and a matching inversion approach, photoacoustic measurements compensated for clutter are shown to be recovered. PMID:27446669
Schwab, Hans-Martin; Beckmann, Martin F; Schmitz, Georg
2016-04-01
Photoacoustic imaging aims to visualize light absorption properties of biological tissue by receiving a sound wave that is generated inside the observed object as a result of the photoacoustic effect. In clinical applications, the strong light absorption in human skin is a major problem. When high amplitude photoacoustic waves that originate from skin absorption propagate into the tissue, they are reflected back by acoustical scatterers and the reflections contribute to the received signal. The artifacts associated with these reflected waves are referred to as clutter or skin echo and limit the applicability of photoacoustic imaging for medical applications severely. This study seeks to exploit the acoustic tissue information gained by plane wave ultrasound measurements with a linear array in order to correct for reflections in the photoacoustic image. By deriving a theory for clutter waves in k-space and a matching inversion approach, photoacoustic measurements compensated for clutter are shown to be recovered. PMID:27446669
Theory of steady-state plane tunneling-assisted impact ionization waves
Kyuregyan, A. S.
2013-07-15
The effect of band-to-band and trap-assisted tunneling on the properties of steady-state plane ionization waves in p{sup +}-n-n{sup +} structures is theoretically analyzed. It is shown that such tunneling-assisted impact ionization waves do not differ in a qualitative sense from ordinary impact ionization waves propagating due to the avalanche multiplication of uniformly distributed seed electrons and holes. The quantitative differences of tunneling-assisted impact ionization waves from impact ionization waves are reduced to a slightly different relation between the wave velocity u and the maximum field strength E{sub M} at the front. It is shown that disregarding impact ionization does not exclude the possibility of the existence of tunneling-assisted ionization waves; however, their structure radically changes, and their velocity strongly decreases for the same E{sub M}. A comparison of the dependences u(E{sub M}) for various ionization-wave types makes it possible to determine the conditions under which one of them is dominant. In conclusion, unresolved problems concerning the theory of tunneling-assisted impact ionization waves are discussed and the directions of further studies are outlined.
NASA Astrophysics Data System (ADS)
Bijarnia, R.; Singh, B.
2016-05-01
The paper is concerned with the propagation of plane waves in a transversely isotropic two temperature generalized thermoelastic solid half-space with voids and rotation. The governing equations are modified in the context of Lord and Shulman theory of generalized thermoelasticity and solved to show the existence of four plane waves in the x - z plane. Reflection of these plane waves from thermally insulated stress free surface is also studied to obtain a system of four non-homogeneous equations. For numerical computations of speed and reflection coefficients, a particular material is modelled as transversely isotropic generalized thermoelastic solid half-space. The speeds of plane waves are computed against the angle of propagation to observe the effects of two temperature and rotation. Reflection coefficients of various reflected waves are also computed against the angle of incidence to observe the effects of various parameters.
NASA Astrophysics Data System (ADS)
Marston, Philip L.
2003-04-01
The coupling of sound to buried targets can be associated with acoustic evanescent waves when the sea bottom is smooth. To understand the excitation of guided waves on buried fluid cylinders and shells by acoustic evanescent waves and the associated target resonances, the two-dimensional partial wave series for the scattering is found for normal incidence in an unbounded medium. The shell formulation uses the simplifications of thin-shell dynamics. The expansion of the incident wave becomes a double summation with products of modified and ordinary Bessel functions [P. L. Marston, J. Acoust. Soc. Am. 111, 2378 (2002)]. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on depth. Some consequences of this imbalance of partial-wave amplitudes are given by modifying previous ray theory for the scattering [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 97, 777-783 (1995)]. The exponential dependence of the scattering on the location of a scatterer was previously demonstrated in air [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].
Plane wave transport method for low symmetry lattices and its application
Srivastava, Manoj K; Wang, Yan; Zhang, Xiaoguang; Nicholson, Don M; Cheng, Hai-Ping
2012-01-01
The existing first-principles plane wave transport method implementation \\cite{,choi-1,qe} has the limitation that it only allows transport directions along lattice vectors perpendicular to the basal plane formed by two other lattice vectors. We generalize the algorithm to low symmetry, nonorthogonal lattices thus allowing solution to problems in which the transport direction is not along any lattice vectors. As an application, we calculate the transmission and reflection coefficients, and determine interface resistance of various grain boundaries in crystalline copper.
Ring-plane traveling-wave tube slow-wave circuit design simulations at V-Band frequencies
Kory, C.L.; Wilson, J.D.
1995-06-01
The V-Band frequency range of 59-64 GHz is a region of the millimeter-wave spectrum that has been designated for intersatellite communications. As a first effort to develop a high-efficiency V-band TWT, variations on a ring-plane slow-wave circuit were computationally investigated to develop an alternative to the more conventional ferruled coupled-cavity circuit. The ring-plane circuit was chosen because of its high interaction impedance, large beam aperture, and excellent thermal dissipation properties. Despite the high-power capabilities of the ring-plane TWT, disadvantages of low bandwidth and high voltage requirements have until now prevented its acceptance outside the laboratory. In this paper, the authors use the three-dimensional electromagnetic simulation code MAFIA to investigate methods of increasing the bandwidth and lowering the operating voltage. Dispersion, impedance, and attenuation calculations for various geometric variations and loading distributions were performed. Based on the results of the variations, a circuit termed the finned-ladder TWT slowwave circuit was designed and is compared here to the scaled ring-plane prototype and the conventional ferruled coupled-cavity TWT circuit over the V-band frequency range.
Ring-plane traveling-wave tube slow-wave circuit design simulations at V-Band frequencies
NASA Technical Reports Server (NTRS)
Kory, Carol L.; Wilson, Jeffrey D.
1995-01-01
The V-Band frequency range of 59-64 GHz is a region of the millimeter-wave spectrum that has been designated for intersatellite communications. As a first effort to develop a high-efficiency V-band TWT, variations on a ring-plane slow-wave circuit were computationally investigated to develop an alternative to the more conventional ferruled coupled-cavity circuit. The ring-plane circuit was chosen because of its high interaction impedance, large beam aperture, and excellent thermal dissipation properties. Despite the high-power capabilities of the ring-plane TWT, disadvantages of low bandwidth and high voltage requirements have until now prevented its acceptance outside the laboratory. In this paper, we use the three-dimensional electromagnetic simulation code MAFIA to investigate methods of increasing the bandwidth and lowering the operating voltage. Dispersion, impedance, and attenuation calculations for various geometric variations and loading distributions were performed. Based on the results of the variations, a circuit termed the finned-ladder TWT slowwave circuit was designed and is compared here to the scaled ring-plane prototype and the conventional ferruled coupled-cavity TWT circuit over the V-band frequency range.
Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
NASA Astrophysics Data System (ADS)
Rawat, Subhandu; Cossu, Carlo; Rincon, François
2016-06-01
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite-period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi-streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size Lz of the domain in which they are computed is increased. On the contrary, the upper branch of travelling-wave solutions develops multiple streaks when Lz is increased. Upper-branch travelling-wave solutions can be continued into coherent solutions to the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.
The instability of finite amplitude Rossby waves on the infinite beta-plane
NASA Astrophysics Data System (ADS)
Anderson, Jeffrey L.
The normal mode instability problem for a stationary Rossby wave of finite amplitude and arbitrary orientation is examined on the infinite beta-plane using a Floquet technique. A survey of the instability problem as a function of the basic state wave amplitude and wave orientation is presented. In the large amplitude case, two modes of instability are found, while in the small amplitude case, a family of resonant interactions can completely describe the Floquet results. For intermediate values of amplitude, a combination of the large and small amplitude limits can explain the instabilities. For the range of greatest geophysical interest, two physically distinct unstable modes of approximately equal growth rate are available for certain values of the basic state wave orientation. Relevance to geophysical flows and the instability problem on the sphere are discussed briefly.
Cavity-based linear polarizer immune to the polarization direction of an incident plane wave.
Wang, Jiang; Shen, Zhongxiang; Gao, Xiang; Wu, Wen
2016-01-15
We herein report a linear polarizer based on a 2D array of substrate integrated waveguide cavities, which can convert an arbitrary linearly polarized (LP) incident wave into an outgoing LP wave in a specified polarization direction with constant transmittance. Two orthogonal slots etched on the front surface of the cavity are utilized to couple a wave of arbitrary polarization into the cavity, while another slot on the back side helps to couple the field out along a desired polarization direction. Microwave experiments are performed as a proof of concept. The proposed polarizer exhibits very good performance with stable transmittance as 50% and a polarization extinction ratio over 45 dB. The new polarizer is potentially useful in novel polarization-selective devices that are immune to the polarization direction of an incident plane wave. PMID:26766730
Diffraction of spin waves from a submicrometer-size defect in a microwaveguide
NASA Astrophysics Data System (ADS)
Birt, Daniel R.; O'Gorman, Brian; Tsoi, Maxim; Li, Xiaoqin; Demidov, Vladislav E.; Demokritov, Sergej O.
2009-09-01
We have experimentally studied the diffraction of spin waves propagating in a Permalloy-film microwaveguide from a submicrometer-sized circular defect. For microwave excitation above the cutoff frequency of the fundamental transverse mode, the defect leads to a frequency dependent reflection of the spin wave. The efficiency of the reflection appears to be dependent on the wavelength of the incident spin wave in a nonmonotonous way. The observed two-dimensional spin wave distribution pattern after the defect can be understood based on the interference of several copropagating modes, suggesting that the defect couples the fundamental mode with higher order modes.
Quantum mechanics of lattice gas automata: One-particle plane waves and potentials
Meyer, D.A.
1997-05-01
Classical lattice gas automata effectively simulate physical processes, such as diffusion and fluid flow (in certain parameter regimes), despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined {ital quantum} lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can effectively simulate. Studying the single particle sector of a one-dimensional quantum lattice gas we find discrete analogs of plane waves and wave packets, and then investigate their behavior in the presence of inhomogeneous potentials. {copyright} {ital 1997} {ital The American Physical Society}
Relativistic Two-Boson System in Presence of Electromagnetic Plane Wave
NASA Astrophysics Data System (ADS)
Droz-Vincent, Ph.
2016-09-01
The relativistic two-body problem is considered for spinless particles subject to an external electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided the mutual interaction between particles is known), it is possible to write down explicitly a pair of coupled wave equations (corresponding to a pair of mass-shell constraints) which takes into account also the field contribution. These equations are manifestly covariant; constants of the motion are exhibited, so one ends up with a reduced problem involving five degrees of freedom.
Mid-wave infrared metasurface microlensed focal plane array for optical crosstalk suppression.
Akın, Onur; Demir, Hilmi Volkan
2015-10-19
Spatial crosstalk is one of the fundamental drawbacks of diminishing pixel size in mid-wave infrared focal plane arrays (IR-FPAs). We proposed an IR-FPA using the concept of optical phase discontinuities for substantial optical crosstalk suppression. This IR-FPA consists of asymmetrically tailored V-shaped optical antennas. Full-wave simulations confirmed major improvements in narrowing the intensity distribution of incident light beam by over 30-folds and concentrating these distributions in the central pixel of IR-FPA by achieving optical crosstalks of <1%. PMID:26480363
Acoustic plane waves incident on an oblique clamped panel in a rectangular duct
NASA Technical Reports Server (NTRS)
Unz, H.; Roskam, J.
1980-01-01
The theory of acoustic plane waves incident on an oblique clamped panel in a rectangular duct was developed from basic theoretical concepts. The coupling theory between the elastic vibrations of the panel (plate) and the oblique incident acoustic plane wave in infinite space was considered in detail, and was used for the oblique clamped panel in the rectangular duct. The partial differential equation which governs the vibrations of the clamped panel (plate) was modified by adding to it stiffness (spring) forces and damping forces. The Transmission Loss coefficient and the Noise Reduction coefficient for oblique incidence were defined and derived in detail. The resonance frequencies excited by the free vibrations of the oblique finite clamped panel (plate) were derived and calculated in detail for the present case.
A standing wave linear ultrasonic motor operating in in-plane expanding and bending modes.
Chen, Zhijiang; Li, Xiaotian; Ci, Penghong; Liu, Guoxi; Dong, Shuxiang
2015-03-01
A novel standing wave linear ultrasonic motor operating in in-plane expanding and bending modes was proposed in this study. The stator (or actuator) of the linear motor was made of a simple single Lead Zirconate Titanate (PZT) ceramic square plate (15 × 15 × 2 mm(3)) with a circular hole (D = 6.7 mm) in the center. The geometric parameters of the stator were computed with the finite element analysis to produce in-plane bi-mode standing wave vibration. The calculated results predicted that a driving tip attached at midpoint of one edge of the stator can produce two orthogonal, approximate straight-line trajectories, which can be used to move a slider in linear motion via frictional forces in forward or reverse direction. The investigations showed that the proposed linear motor can produce a six times higher power density than that of a previously reported square plate motor. PMID:25832267
NASA Astrophysics Data System (ADS)
Sei, Norihiro; Sakai, Takeshi; Hayakawa, Ken; Tanaka, Toshinari; Hayakawa, Yasushi; Nakao, Keisuke; Nogami, Kyoko; Inagaki, Manabu
2015-10-01
We propose a high-peak-power terahertz-wave source based on an electron accelerator. By passing an electron beam through a hollow conical dielectric with apex facing the incident electron beam, the wave front of coherent Cherenkov radiation generated on the inner surface of the hollow conical dielectric matches the basal plane. Using the electron beam generated at the Laboratory for Electron Beam Research and Application at Nihon University, the calculated power of coherent Cherenkov radiation that matched the circular plane (CCR-MCP) was above 1 MW per micropulse with a short interval of 350 ps, for wavelengths ranging from 0.5 to 5 mm. The electron beam is not lost for generating the CCR-MCP beam by using the hollow conical dielectric. It is possible to combine the CCR-MCP beams with other light sources based on an accelerator.
Dmitrenko, A.G.; Mukomolov, A.I.
1995-12-01
A numerical method of solving the problem of the diffraction of electromagnetic waves by a three-dimensional magnetodielectric body of arbitrary shape in the resonance frequency region is proposed. The method is applied in the form of a FORTRAN software package for calculating the components of the diffraction field of bodies with different electrodynamic and geometrical parameters. The directivity parameters of some bodies of complex shape are given.
A nonperturbative definition of N = 4 Super Yang-Mills by the plane wave matrix model
Shimasaki, Shinji
2008-11-23
We propose a nonperturbative definition of N = 4 Super Yang-Mills(SYM). We realize N = 4 SYM on RxS{sup 3} as the theory around a vacuum of the plane wave matrix model. Our regularization preserves 16 supersymmetries and the gauge symmetry. We perform the one-loop calculation to give evidence that in the continuum limit the superconformal symmetry is restored.
Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C
2011-06-01
The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well. PMID:21643384
NASA Astrophysics Data System (ADS)
Pickard, Chris J.; Winkler, Björn; Chen, Roger K.; Payne, M. C.; Lee, M. H.; Lin, J. S.; White, J. A.; Milman, V.; Vanderbilt, David
2000-12-01
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, UO3, U3O8, UC2, α-CeC2, CeB6, CeSe, CeO2, NdB6, TmOI, LaBi, LaTiO3, YbO, and elemental Lu.
Pickard; Winkler; Chen; Payne; Lee; Lin; White; Milman; Vanderbilt
2000-12-11
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, UO3, U3O8, UC2, alpha-CeC2, CeB6, CeSe, CeO2, NdB6, TmOI, LaBi, LaTiO3, YbO, and elemental Lu. PMID:11102201
Simulations and cold-test results of a prototype plane wave transformer linac structure
NASA Astrophysics Data System (ADS)
Kumar, Arvind; Pant, K. K.; Krishnagopal, S.
2002-03-01
We have built a 4-cell prototype plane wave transformer (PWT) linac structure. We discuss here details of the design and fabrication of the PWT linac structure. We present results from superfish and gdfidl simulations as well as cold tests, which are in good agreement with each other. We also present detailed tolerance maps for the PWT structure. We discuss beam dynamics simulation studies performed using parmela.
Status of very long infrared-wave focal plane array development at DEFIR
NASA Astrophysics Data System (ADS)
Gravrand, O.; Chorier, Ph.
2009-05-01
The very long infrared wavelength (>14μm) is a very challenging range for the design of large HgCdTe focal plane arrays. As the wavelength gets longer (ie the semiconductor gap gets smaller), the physic of photodiodes asks for numerous technological improvements to keep a high level of detection performance. DEFIR (LETI-Sofradir common research team) has been highly active in this field during the last few years. The need (mainly expressed by the space industry ESA and CNES) of very long wave focal plane arrays appears very demanding in terms of dark current, defect density and of course quantum efficiency. This paper aims at presenting a status of long and very long wave focal plane array development at DEFIR for three different ion implanted technologies: n on p mercury vacancies doped technology, n on p extrinsic doped technology, and p on n arsenic on indium technology. Special focus is done to 15μm cut off n/p focal plane array fabricated in our laboratory demonstrating high uniformity, diffusion and shot noise limited photodiodes at 50K.
Finite Frequency Measurements of Conventional and Core-diffracted P-waves (P and Pdiff)
NASA Astrophysics Data System (ADS)
Hosseini, K.; Sigloch, K.; Stähler, S. C.
2014-12-01
Core-diffracted waves are body waves that dive deep enough to sense the core, and by interaction with this wave guide become dispersive. They sample the core-mantle boundary and the lower third of the mantle extensively. In ray theoretical modeling, the deepest part of the ray starts to graze the core at around 97 degrees distance, but ray theory is a very poor approximation to propagation of core-diffracted waves. In reality, finite-frequency waves with their spatially extend sensitivity regions start to sense the core at significantly smaller distances already. The actual, non-ray-like sensitivities have been difficult to model, as have been the associated synthetic seismograms. Core-diffracted waves have therefore not been used in tomography, despite abundant observations of these phases on modern broadband seismograms. Hence current global body-wave tomographies illuminate the lower third of the mantle much less well than the upper and especially the middle third. This study aims for broadband, global waveform tomography that seamlessly incorporates core-diffracted phases alongside conventional, teleseismic waves as well as regional body-waves. Here, we investigate the properties of P-diffracted waves in terms of waveform characteristics and travel-time measurements as compared to teleseismic P-wave measured by the same methods. Travel time anomalies, the primary data for tomography, are measured by waveform cross-correlation of data with synthetics, where the synthetics are calculated from fully numerical wave propagation in a spherically symmetric background model. These same numerical tools will be used to calculate the associated sensitivity kernels for tomography (figure, top). Demonstrating the extent to which waveform modeling can fit real data, we assemble and discuss a global data set of 851,905 Pdiff and 2,368,452 P-wave multi-frequency cross-correlation travel times. Findings are summarized in the Pdiff travel time map (figure, bottom) in which most
NASA Astrophysics Data System (ADS)
Caleb Dhanasekaran, P.; Poddar, M.
A FORTRAN program utilizing an integral equation calculates 10 field quantities relating to the electromagnetic (EM) scattering of plane wave by a perfectly conducting half-plane buried in a finitely conducting layered half-space. The computing algorithm is executable on a computer of small storage capacity such as PDP 11/40 and as such is useful to many exploration scientists without the facility of a mainframe computer, for computing model curves to interpret field data.
Diffraction using laser-driven broadband electron wave packets
NASA Astrophysics Data System (ADS)
Xu, Junliang; Blaga, Cosmin I.; Zhang, Kaikai; Lai, Yu Hang; Lin, C. D.; Miller, Terry A.; Agostini, Pierre; Dimauro, Louis F.
2014-08-01
Directly monitoring atomic motion during a molecular transformation with atomic-scale spatio-temporal resolution is a frontier of ultrafast optical science and physical chemistry. Here we provide the foundation for a new imaging method, fixed-angle broadband laser-induced electron scattering, based on structural retrieval by direct one-dimensional Fourier transform of a photoelectron energy distribution observed along the polarization direction of an intense ultrafast light pulse. The approach exploits the scattering of a broadband wave packet created by strong-field tunnel ionization to self-interrogate the molecular structure with picometre spatial resolution and bond specificity. With its inherent femtosecond resolution, combining our technique with molecular alignment can, in principle, provide the basis for time-resolved tomography for multi-dimensional transient structural determination.
Diffraction using laser-driven broadband electron wave packets
NASA Astrophysics Data System (ADS)
Xu, Junliang; Blaga, Cosmin I.; Zhang, Kaikai; Lai, Yu Hang; Lin, C. D.; Miller, Terry A.; Agostini, Pierre; Dimauro, Louis F.
2015-05-01
Directly monitoring atomic motion during a molecular transformation with atomic-scale spatio-temporal resolution is a frontier of ultrafast optical science and physical chemistry. Here we provide the foundation for a new imaging method, fixed-angle broadband laser-induced electron scattering, based on structural retrieval by direct one-dimensional Fourier transform of a photoelectron energy distribution observed along the polarization direction of an intense ultrafast light pulse. The approach exploits the scattering of a broadband wave packet created by strong-field tunnel ionization to self-interrogate the molecular structure with picometer spatial resolution and bond specificity. With its inherent femtosecond resolution, combining our technique with molecular alignment can, in principle, provide the basis for time-resolved tomography for multi-dimensional transient structural determination.
NASA Astrophysics Data System (ADS)
Xiao, Mufei
2000-03-01
We have found the rigorous solution of transient propagation of electronmagnetic waves through a medium. The rogorousness enables the solution to exhibit its apparent consistency with the Einstein causality. Thus, we confirm that faster-than-light or superluminal propagation of electromagnetic waves is not possible. Evanescent transmission gives rise to the diffraction in time, which is the actual reason for deformation of group propagation. Based on the principle of diffraction in time, superluminal group propagation can be understood. The findings are also instructive for understanding the time problem for particle tunneling.
3D resolution tests of two-plane wave approach using synthetic seismograms
NASA Astrophysics Data System (ADS)
Ceylan, S.; Larmat, C. S.; Sandvol, E. A.
2012-12-01
Two-plane wave tomography (TPWT) is becoming a standard approach to obtain fundamental mode Rayleigh wave phase velocities for a variety of tectonic settings. A recent study by Ceylan et al. (2012) has applied this method to eastern Tibet, using data from INDEPTH-IV and Namche-Barwa seismic experiments. The TPWT assumes that distortion of wavefronts at each station can be expressed as the sum of two plane waves. However, there is currently no robust or complete resolution test for TPWT, to address its limitations such as wavefront healing. In this study, we test the capabilities of TPWT and resolution of INDEPTH-IV seismic experiment, by performing 3D resolution tests using synthetic seismograms. Utilizing SPECFEM3D software, we compute synthetic data sets resolving periods down to ~30 s. We implement a checkerboard upper mantle (for depths between 50 and 650 km) with variable cell sizes, superimposed to PREM as the background model. We then calculate fundamental mode surface wave phase velocities using TPWT for periods between 33-143 seconds, using synthetic seismograms computed from our three dimensional hypothetical model. Assuming a constant Poisson's ratio, we use partial derivatives from Saito (1988) to invert for shear wave velocities. We show that the combination of TPWT and Saito (1988) methods is capable of retrieving anomalies down to depths of ~200 km for Rayleigh waves. Below these depths, we observe evidence of both lateral and vertical smearing. We also find that the traditional method for estimating the resolution of TPWT consistently overestimates phase velocity resolutions. Love waves exhibit adequate resolution down to depths of ~100 km. At depths greater than 100 km, smearing is more evident in SH wave results than those of SV waves. Increased smearing of SH waves is most probably due to propagation characteristics and shallower sensitivity of Love waves. Our results imply that TPWT can be applied to Love waves, making future investigations of
NASA Astrophysics Data System (ADS)
Sahu, Sanjeev A.; Paswan, Brijendra; Chattopadhyay, Amares
2016-01-01
A problem of reflection and transmission of plane wave is presented. The considered geometry consists of an isotropic layer bonded between two highly anisotropic media (Triclinic crystalline). We set to find a relation between direction of motion and direction of propagation of waves as they are not same in anisotropic medium. The incident plane wave reflects three waves (?, and ?) at the interface of isotropic layer and lower half-space. A closed form expression for velocity profile is obtained. We have found the reflection/transmission coefficients and energy ratios of different reflected and transmitted waves. Variations in obtained amplitude ratios and energy ratios with respect to incident angle have been shown graphically.
NASA Astrophysics Data System (ADS)
Bogdanov, O. V.; Kazinski, P. O.
2015-02-01
The problem of scattering of ultrarelativistic electrons by a strong plane electromagnetic wave of a low (optical) frequency and linear polarization is solved in the semiclassical approximation, when the electron wave packet size is much smaller than the wavelength of electromagnetic wave. The exit momenta of ultrarelativistic electrons scattered are found using the exact solutions to the equations of motion with radiation reaction included (the Landau-Lifshitz equation). It is found that the momentum components of electrons traversed the electromagnetic wave depend weakly on the initial values of momenta. These electrons are mostly scattered at small angles to the propagation direction of the electromagnetic wave. The maximum Lorentz factor of electrons crossed the electromagnetic wave is proportional to the work done by the electromagnetic field and is independent of the initial momentum. The momentum component parallel to the electric field vector of the electromagnetic wave is determined solely by the laser beam diameter measured in the units of the classical electron radius. As for the reflected electrons, they for the most part lose the energy, but remain relativistic. A reflection law that relates the incident and reflection angles and is independent of any parameters is found.
Mitri, F G
2016-03-01
This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves. The major (or minor) semi-axis of the ellipse coincides with the direction of the incident waves. The scattering coefficients for the rigid elliptical cylinder are determined by imposing the Neumann boundary condition for an immovable surface and solving a resulting system of linear equations by matrix inversion. The present method, which utilizes standard cylindrical (Bessel and Hankel) wave functions, presents an advantage over the solution for the scattering that is ordinarily expressed in a basis of elliptical Mathieu functions (which are generally non-orthogonal). Furthermore, an integral equation showing the direct connection of the radiation force function with the square of the scattering form function in the far-field from the scatterer (applicable for plane waves only), is noted and discussed. An important application of this integral equation is the adequate evaluation of the radiation force function from a bistatic measurement (i.e., in the polar plane) of the far-field scattering from any 2D object of arbitrary shape. Numerical predictions are evaluated for the acoustic backscattering form function and the radiation force function, which is the radiation force per unit length, per characteristic energy density, and per unit cross-sectional surface of the ellipse, with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes, as well as the dimensionless size parameter kb, without the restriction to a particular range of frequencies. The results are particularly relevant in acoustic levitation, acousto-fluidics and particle dynamics applications. PMID:26726146
Discontinuity-free edge-diffraction model for characterization of focused wave fields.
Sedukhin, Andrey G
2010-03-01
A model of discontinuity-free edge diffraction is proposed that is valid in the framework of the scalar Debye approximation and describes the formation process and approximate structure of the stationary diffracted field of a monochromatic converging spherical wave of limited angular opening throughout the whole space about the focus. The field is represented semianalytically in terms of the sum of a direct quasi-spherical wave and two edge quasi-conical waves of the zeroth and first order. The angular spectrum amplitudes of all these waves have smooth continuous variations of the real and imaginary parts in polar angle and radius, the separable nonanalytic functions defining the polar-angle variations of the amplitudes being found by optimization techniques. PMID:20208956
Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices
NASA Astrophysics Data System (ADS)
Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; Ma, Yi-Ping
2016-01-01
Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. For weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. The transition between these two types of propagation is explored.
Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices
Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; Ma, Yi-Ping
2016-01-25
We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. Formore » weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.« less
NASA Astrophysics Data System (ADS)
Yoshida, Shuhei; Mori, Jun; Yamamoto, Manabu
2015-05-01
Many kinds of recording techniques have been proposed for holographic data storages (HDS). Multiplexing recording technique is a primary contributor to determining the recording density in HDS. The method that utilizes spherical reference waves is characterized by the ability to enable multiplexing recording only by displacing (shifting or rotating) the recording medium. In this study, we propose a theoretical diffraction model of peristrophic multiplexing with spherical reference wave for HDS.
Ultrafast Kikuchi diffraction: nanoscale stress-strain dynamics of wave-guiding structures.
Yurtsever, Aycan; Schaefer, Sascha; Zewail, Ahmed H
2012-07-11
Complex structural dynamics at the nanoscale requires sufficiently small probes to be visualized. In conventional imaging using electron microscopy, the dimension of the probe is large enough to cause averaging over the structures present. However, by converging ultrafast electron bunches, it is possible to select a single nanoscale structure and study the dynamics, either in the image or using electron diffraction. Moreover, the span of incident wave vectors in a convergent beam enables sensitivity levels and information contents beyond those of parallel-beam illumination with a single wave vector Bragg diffraction. Here, we report the observation of propagating strain waves using ultrafast Kikuchi diffraction from nanoscale volumes within a wedge-shaped silicon single crystal. It is found that the heterogeneity of the strain in the lateral direction is only 100 nm. The transient elastic wave gives rise to a coherent oscillation with a period of 30 ps and with an envelope that has a width of 140 ps. The origin of this elastic deformation is theoretically examined using finite element analysis; it is identified as propagating shear waves. The wedge-shaped structure, unlike parallel-plate structure, is the key behind the traveling nature of the waves as its angle permits "transverse" propagation; the parallel-plate structure only exhibits the "longitudinal" motion. The studies reported suggest extension to a range of applications for nanostructures of different shapes and for exploring their ultrafast eigen-modes of stress-strain profiles. PMID:22667321
Monochromatic plane-fronted waves in conformal gravity are pure gauge
NASA Astrophysics Data System (ADS)
Fabbri, Luca; Paranjape, M. B.
2011-05-01
We consider plane-fronted, monochromatic gravitational waves on a Minkowski background, in a conformally invariant theory of general relativity. By this we mean waves of the form: gμν=ημν+γμνF(k·x), where γμν is a constant polarization tensor, and kμ is a lightlike vector. We also assume the coordinate gauge condition |g|-1/4∂τ(|g|1/4gστ)=0 which is the conformal analog of the harmonic gauge condition gμνΓμνσ=-|g|-1/2∂τ(|g|1/2gστ)=0, where det[gμν]≡g. Requiring additionally the conformal gauge condition g=-1 surprisingly implies that the waves are both transverse and traceless. Although the ansatz for the metric is eminently reasonable when considering perturbative gravitational waves, we show that the metric is reducible to the metric of Minkowski space-time via a sequence of coordinate transformations which respect the gauge conditions, without any perturbative approximation that γμν be small. This implies that we have, in fact, exact plane-wave solutions; however, they are simply coordinate/conformal artifacts. As a consequence, they carry no energy. Our result does not imply that conformal gravity does not have gravitational wave phenomena. A different, more generalized ansatz for the deviation, taking into account the fourth-order nature of the field equation, which has the form gμν=ημν+Bμν(n·x)G(k·x), indeed yields waves which carry energy and momentum [P. D. Mannheim, Gen. Relativ. Gravit.GRGVA80001-7701 43, 703 (2010)10.1007/s10714-010-1088-z]. It is just surprising that transverse, traceless, plane-fronted gravitational waves, those that would be used in any standard, perturbative, quantum analysis of the theory, simply do not exist.
Acoustic multipath arrivals in the horizontal plane due to approaching nonlinear internal waves.
Badiey, Mohsen; Katsnelson, Boris G; Lin, Ying-Tsong; Lynch, James F
2011-04-01
Simultaneous measurements of acoustic wave transmissions and a nonlinear internal wave packet approaching an along-shelf acoustic path during the Shallow Water 2006 experiment are reported. The incoming internal wave packet acts as a moving frontal layer reflecting (or refracting) sound in the horizontal plane. Received acoustic signals are filtered into acoustic normal mode arrivals. It is shown that a horizontal multipath interference is produced. This has previously been called a horizontal Lloyd's mirror. The interference between the direct path and the refracted path depends on the mode number and frequency of the acoustic signal. A mechanism for the multipath interference is shown. Preliminary modeling results of this dynamic interaction using vertical modes and horizontal parabolic equation models are in good agreement with the observed data. PMID:21476621
Plane-wave Sf S reconstruction of water surface characteristics from Lambertian reflectance data
NASA Astrophysics Data System (ADS)
Huang, Jian; O'Sullivan, Finbarr; Jike, Linhao
2012-06-01
The classical shape from shading (SfS) problem of computer vision is concerned with the reconstruction of a 3D object surface from its photographic image. Essential non-uniqueness and intrinsic nonlinearity make the problem challenging. This work considers the case where the object is a water surface so that the statistical approximation by superposition of plane waves is natural. An efficient greedy algorithm involving recursive refinement of wave fronts, subject to a wave-front frequency constraint is developed. The approach is evaluated using simulated reflectance data based on a set of wind-generated wave-field images obtained from detailed wave-tank measurements. The traditional setup for the SfS problem (orthographic cameras, light sources at infinity and the Lambertian surfaces) is used. Generalization to include a specular (Phong) reflectance component is also discussed. Results indicate that key statistical characteristics of the wave field related to its stage of development (evolution) are properly recovered by the approach. Thus there may be future potential for novel photographic-based remote sensing of physical drivers (e.g. wind velocity) of local water surface patterns.
Rossby wave radiation by an eddy on a beta-plane: Experiments with laboratory altimetry
Zhang, Y.; Afanasyev, Y. D.
2015-07-15
Results from the laboratory experiments on the evolution of vortices (eddies) generated in a rotating tank with topographic β-effect are presented. The focus of the experiments is on the far-field flow which contains Rossby waves emitted by travelling vortices. The surface elevation and velocity fields are measured by the altimetric imaging velocimetry. The experiments are supplemented by shallow water numerical simulations as well as a linear theory which describes the Rossby wave radiation by travelling vortices. The cyclonic vortices observed in the experiments travel to the northwest and continuously radiate Rossby waves. Measurements show that initially axisymmetric vortices develop a dipolar component which enables them to perform translational motion. A pattern of alternating zonal jets to the west of the vortex is created by Rossby waves with approximately zonal crests. Energy spectra of the flows in the wavenumber space indicate that a wavenumber similar to that introduced by Rhines for turbulent flows on the β-plane can be introduced here. The wavenumber is based on the translational speed of a vortex rather than on the root-mean-square velocity of a turbulent flow. The comparison between the experiments and numerical simulations demonstrates that evolving vortices also emit inertial waves. While these essentially three-dimensional non-hydrostatic waves can be observed in the altimetric data, they are not accounted for in the shallow water simulations.
Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector.
Tsai, Yi-Te; Zhu, Jinying; Haberman, Michael R
2013-04-01
A time domain analytical solution is presented to calculate the pressure response along the axis of a paraboloidal reflector for a normally incident plane wave. This work is inspired by Hamilton's axial solution for an ellipsoidal mirror and the same methodology is employed in this paper. Behavior of the reflected waves along reflector axis is studied, and special interest is placed on focusing gain obtained at the focal point. This analytical solution indicates that the focusing gain is affected by reflector geometry and the time derivative of the input signal. In addition, focused pressure response in the focal zone given by various reflector geometries and input frequencies are also investigated. This information is useful for selecting appropriate reflector geometry in a specific working environment to achieve the best signal enhancement. Numerical simulation employing the finite element method is used to validate the analytical solution, and visualize the wave field to provide a better understanding of the propagation of reflected waves. This analytical solution can be modified to apply to non-planar incident waves with axisymmetric wavefront and non-uniform pressure distribution. An example of incident waves with conical-shaped wavefront is presented. PMID:23556573
NASA Astrophysics Data System (ADS)
Boivin, Guillaume; Viens, Martin; Belanger, Pierre
2016-02-01
The shear horizontal guided wave fundamental mode (SH0) has the particularity of being the only non-dispersive plate guided wave mode. This characteristic makes this ultrasonic guided wave mode very attractive in non-destructive testing, facilitating signal processing for long range inspections. It is, however, difficult to generate only a single guided wave mode when using piezoelectric transduction. This work aims to develop a piezoelectric transducer capable of generating a virtually pure plane zeroth order shear horizontal wave. The chosen material was the PZT-5H for its dominant d15 piezoelectric constant, which makes it a perfect candidate for SH-wave generation. The transducer dimensions were optimised using an analytical model based on the Huygens' principle of superposition and the dipole pattern of a shear point source. A 3D multiphysics finite element model was then used to validate the analytical model results. Experimental validation was finally conducted with a laser Doppler vibrometer (LDV) system. Excellent agreement between the analytical model, finite element model and experimental validation was seen.
Shock wave diffraction in the presence of a supersonic co-flow jet
NASA Astrophysics Data System (ADS)
Gnani, F.; Lo, K. H.; Zare-Behtash, H.; Kontis, K.
2016-03-01
The interaction between a diffracting shock wave and a uniform jet is a case that so far has only been partially investigated. This interaction is extremely important for the control of noise generation and improvement of combustor performance. To fill this knowledge gap, three geometries of the diffracting corner, namely a straight ramp, a serrated ramp, and a rounded corner, have been tested experimentally to study the interaction of shock diffraction with a supersonic co-flow jet at incident Mach numbers of 1.31 and 1.59, with Reynolds numbers of 1.08× 106 and 1.68× 106 , respectively. Schlieren photography was employed to analyse the evolution of the flow phenomena. The aim is to provide a qualitative understanding of the interaction between the diffracting shock wave and the uniform jet relevant to future high-speed transport. The results show that the flow field evolves more rapidly and develops stronger structures for a higher shock Mach number. The diffraction around a rounded splitter develops a periodical vortical structure which continues after the disturbance introduced by the passage of the shock wave is removed.
Rohde, A H; Veidt, M; Rose, L R F; Homer, J
2008-03-01
This paper investigates the feasibility of plate-wave diffraction tomography for the reconstruction of flexural inhomogeneities in plates using the results of computer simulation studies. The numerical implementation of the fundamental reconstruction algorithm, which has recently been developed by Wang and Rose [C.H. Wang, L.R.F. Rose, Plate-wave diffraction tomography for structural health monitoring, Rev. Quant. Nondestr. Eval. 22 (2003) 1615-1622] is investigated addressing the essential effects of applying the discrete form of the Fourier diffraction theorem for solving the inverse problem as discussed by Kak and Slaney [A.C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging, IEEE Press, New York, 1988] for the acoustic case, viz. diffraction limited sensitivity, influence of weak scatterer assumption, damage location and scatter field data processing in time and Fourier space as well as experimental limitations such as finite receiver length and limited views. The feasibility of the imaging technique is investigated for cylindrical inhomogeneities of various severities and relative position within the interrogation space and a normal incident interrogation configuration. The results show that plate-wave diffraction tomography enables the quantitative reconstruction of location, size and severity of plate damage with excellent sensitivity and offers the potential for detecting corrosion thinning, disbonds and delamination damage in structural integrity management applications. PMID:18022207
Shock wave diffraction in the presence of a supersonic co-flow jet
NASA Astrophysics Data System (ADS)
Gnani, F.; Lo, K. H.; Zare-Behtash, H.; Kontis, K.
2016-05-01
The interaction between a diffracting shock wave and a uniform jet is a case that so far has only been partially investigated. This interaction is extremely important for the control of noise generation and improvement of combustor performance. To fill this knowledge gap, three geometries of the diffracting corner, namely a straight ramp, a serrated ramp, and a rounded corner, have been tested experimentally to study the interaction of shock diffraction with a supersonic co-flow jet at incident Mach numbers of 1.31 and 1.59, with Reynolds numbers of 1.08× 106 and 1.68× 106, respectively. Schlieren photography was employed to analyse the evolution of the flow phenomena. The aim is to provide a qualitative understanding of the interaction between the diffracting shock wave and the uniform jet relevant to future high-speed transport. The results show that the flow field evolves more rapidly and develops stronger structures for a higher shock Mach number. The diffraction around a rounded splitter develops a periodical vortical structure which continues after the disturbance introduced by the passage of the shock wave is removed.
On plane-wave relativistic electrodynamics in plasmas and in vacuum
NASA Astrophysics Data System (ADS)
Fiore, Gaetano
2014-06-01
We revisit the exact microscopic equations (in differential, and equivalent integral form) ruling a relativistic cold plasma after the plane-wave Ansatz, without customary approximations. We show that in the Eulerian description the motion of a very diluted plasma initially at rest and excited by an arbitrary transverse plane electromagnetic travelling-wave has a very simple and explicit dependence on the transverse electromagnetic potential; for a non-zero density plasma the above motion is a good approximation of the real one as long as the back-reaction of the charges on the electromagnetic field can be neglected, i.e. for a time lapse decreasing with the plasma density, and can be used as initial step in an iterative resolution scheme. As one of many possible applications, we use these results to describe how the ponderomotive force of a very intense and short plane laser pulse hitting normally the surface of a plasma boosts the surface electrons into the ion background. In response to this penetration, the electrons are pulled back by the electric force exerted by the ions and the other displaced electrons and may leave the plasma with high energy in the direction opposite to that of propagation of the pulse ‘slingshot effect’ (Fiore G et al 2013 arXiv:1309.1400).
Refinement of a discontinuity-free edge-diffraction model describing focused wave fields.
Sedukhin, Andrey G
2010-03-01
Two equivalent forms of a refined discontinuity-free edge-diffraction model describing the structure of a stationary focused wave field are presented that are valid in the framework of the scalar Debye integral representation for a diffracted rotationally symmetric converging spherical wave of a limited yet not-too-low angular opening. The first form describes the field as the sum of a direct quasi-spherical wave and a plurality of edge quasi-conical waves of different orders, the optimum discontinuity-free angular spectrum functions of all the waves being dependent on the polar angle only. According to the second form, the focused field is fully characterized by only three components--the same quasi-spherical wave and two edge quasi-conical waves of the zero and first order, of which the optimum discontinuity-free angular spectrum functions are dependent on both the polar angle and the polar radius counted from the geometrical focus. PMID:20208957
On the convergence of the coupled-wave approach for lamellar diffraction gratings
NASA Technical Reports Server (NTRS)
Li, Lifeng; Haggans, Charles W.
1992-01-01
Among the many existing rigorous methods for analyzing diffraction of electromagnetic waves by diffraction gratings, the coupled-wave approach stands out because of its versatility and simplicity. It can be applied to volume gratings and surface relief gratings, and its numerical implementation is much simpler than others. In addition, its predictions were experimentally validated in several cases. These facts explain the popularity of the coupled-wave approach among many optical engineers in the field of diffractive optics. However, a comprehensive analysis of the convergence of the model predictions has never been presented, although several authors have recently reported convergence difficulties with the model when it is used for metallic gratings in TM polarization. Herein, three points are made: (1) in the TM case, the coupled-wave approach converges much slower than the modal approach of Botten et al; (2) the slow convergence is caused by the use of Fourier expansions for the permittivity and the fields in the grating region; and (3) is manifested by the slow convergence of the eigenvalues and the associated modal fields. The reader is assumed to be familiar with the mathematical formulations of the coupled-wave approach and the modal approach.
Radiation of de-excited electrons at large times in a strong electromagnetic plane wave
NASA Astrophysics Data System (ADS)
Kazinski, P. O.
2013-12-01
The late time asymptotics of the physical solutions to the Lorentz-Dirac equation in the electromagnetic external fields of simple configurations-the constant homogeneous field, the linearly polarized plane wave (in particular, the constant uniform crossed field), and the circularly polarized plane wave-are found. The solutions to the Landau-Lifshitz equation for the external electromagnetic fields admitting a two-parametric symmetry group, which include as a particular case the above mentioned field configurations, are obtained. Some general properties of the total radiation power of a charged particle are established. In particular, for a circularly polarized wave and constant uniform crossed fields, the total radiation power in the asymptotic regime is independent of the charge and the external field strength, when expressed in terms of the proper-time, and equals a half the rest energy of a charged particle divided by its proper-time. The spectral densities of the radiation power formed on the late time asymptotics are derived for a charged particle moving in the external electromagnetic fields of the simple configurations pointed above. This provides a simple method to verify experimentally that the charged particle has reached the asymptotic regime.
The radiation of sound by the instability waves of a compressible plane turbulent shear layer
NASA Technical Reports Server (NTRS)
Tam, C. K. W.; Morris, P. J.
1980-01-01
The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near- and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.