Showing papers on "Plane wave published in 1996"
TL;DR: The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set and is separable and has optimal decay properties in both real and Fourier space.
Abstract: We present pseudopotential coefficients for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, seven coefficients are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive atomic and molecular test calculations. \textcopyright{} 1996 The American Physical Society.
5,009 citations
TL;DR: In this paper, an inversion scheme for two-dimensional inverse scattering problems in the resonance region is proposed, which does not use nonlinear optimization methods and is relatively independent of the geometry and physical properties of the scatterer, assuming that the far field pattern corresponding to observation angle and plane waves incident at angle is known for all.
Abstract: This paper is concerned with the development of an inversion scheme for two-dimensional inverse scattering problems in the resonance region which does not use nonlinear optimization methods and is relatively independent of the geometry and physical properties of the scatterer It is assumed that the far field pattern corresponding to observation angle and plane waves incident at angle is known for all From this information, the support of the scattering obstacle is obtained by solving the integral equation where k is the wavenumber and is on a rectangular grid containing the scatterer The support is found by noting that is unbounded as approaches the boundary of the scattering object from inside the scatterer Numerical examples are given showing the practicality of this method
750 citations
TL;DR: A complete analytical 4 34 matrix algorithm is obtained using Berreman’s 4 34 differential matrices and can be used immediately, for example, to analyze ellipsometric investigations.
Abstract: We present a unified theoretical approach to electromagnetic plane waves reflected or transmitted at arbitrarily anisotropic and homogeneous layered systems. Analytic expressions for the eigenvalues for the four-wave components inside a randomly oriented anisotropic medium are reported explicitly. As well, the partial transfer matrix for a slab of a continuously twisted biaxial material at normal incidence is described. Transition matrices for the incident and exit media are presented. Hence, a complete analytical 4\ifmmode\times\else\texttimes\fi{}4 matrix algorithm is obtained using Berreman's 4\ifmmode\times\else\texttimes\fi{}4 differential matrices [D. W. Berreman, J. Opt. Soc. Am. 62, 502 (1972)]. The algorithm has a general approach for materials with linear optical response behavior and can be used immediately, for example, to analyze ellipsometric investigations. \textcopyright{} 1996 The American Physical Society.
374 citations
TL;DR: In this article, a scheme for projection of plane wave states onto a localised basis set is proposed, which is used to calculate atomic charges and bond populations, and is illustrated by application to a selection of small molecules.
Abstract: Plane wave basis sets are widely used in ab initio electronic structure calculations even though such an expansion in terms of extended states does not provide a natural way of quantifying local atomic properties. To overcome this deficiency we have implemented a scheme for projection of plane wave states onto a localised basis set. This approach is used to calculate atomic charges and bond populations, and is illustrated by application to a selection of small molecules. Finally, we calculate the changes in these quantities induced by adsorption of a molecule onto a zeolite substrate. Thus, using the procedure described in this paper, plane wave calculations can yield the same information as traditional quantum chemical methods.
286 citations
TL;DR: In this paper, a theoretical investigation of resonant scattering from two-dimensional gratings is presented, which is explained in terms of the coupling between the incident plane wave and guided modes that can be supported by the twodimensional grating waveguide structure.
Abstract: A theoretical investigation of resonant scattering from two-dimensional gratings is presented. Abrupt changes of diffraction efficiency over a small parameter range have been observed by rigorous coupled-wave analysis. The peak reflection or transmission efficiencies can approach unity. This phenomenon is explained in terms of the coupling between the incident plane wave and guided modes that can be supported by the two-dimensional-grating waveguide structure. Because of the double periodicity, the incident field can be coupled into any direction in the grating plane. The guided modes supported by two-dimensional gratings are found by rigorous solution of the homogeneous problem associated with the scattering (inhomogeneous) problem. The complex propagation constants for the guided modes provide estimates of both the resonance angle and width. In addition, to illustrate the implication of the radical change in the phase and amplitude of the propagating waves, we report a study of finite-beam diffraction in the resonant scattering region. Applications for the structures include polarization-independent narrow-band filters and bandwidth-tunable filters. It is shown that, because of the double resonance, the polarization-independent narrow-band filters have a large angular tolerance.
251 citations
TL;DR: In this article, the authors developed the full second-order wavemaker theory (including superharmonics as well as subharmonics) valid for rotational and translatory wave board motion.
242 citations
TL;DR: Huang et al. as discussed by the authors used a Hilbert transform to produce the phase-amplitude diagram and the Hilbert Spectrum, and found that the wave fusion event could occur in finite band widths and wind wave fields as well; and it is indeed the mechanism responsible for the frequency downshift in nonlinear wave evolution in general.
Abstract: It has long been recognized that the frequency downshift in the wave field evolution is a consequence of nonlinear wave-wave interactions and that the frequency downshift is also necessary for the wind wave field to grow. Yet the detailed mechanism for the frequency change is still unknown: Is the process continuous and gradual? Or, is the frequency of a wave train varying gradually and continuously? Recently, Huang et al. (1995) found that the frequency downshift for a narrow band wave train is through wave fusion, an event described as two waves merging to form one wave, or n waves merging to form n—1 waves. The process was seen tobe local, abrupt, and discrete. Such an event cannot be studied by the traditional Fourier analysis. Using a Hilbert transform to produce the phase-amplitude diagram and the Hilbert Spectrum, we found that in addition to the narrow band waves, the wave fusion event could occur in finite band widths and wind wave fields as well; and it is indeed the mechanism responsible for the frequency downshift in nonlinear wave evolution in general. Specifically, the frequency downshift is an accumulation of wave fusion events, which is also the same phenomena of the “lost crest” observed by Lake and Yuen (1978), and the “crest pairing” observed by Ramamonjiarisoa and Mollo-Christensen (1979). We have made quantitative measure of this fusion through Hilbert analysis techniques. Other than the fusion process, the local frequency can have small variations due to the amplitude modulations. Because of the abrupt and discrete localized variations of wave frequency, a new paradigm is needed to describe the nonlinear wave evolution processes.
240 citations
TL;DR: In this paper, an easily reproduced experiment that allows the student to investigate the intensity and phase structure of transverse laser modes is presented. But the results are limited to the Laguerre-Gaussian modes.
Abstract: We outline an easily reproduced experiment that allows the student to investigate the intensity and phase structure of transverse laser modes. In addition to discussing the usual Hermite–Gaussian laser modes we detail how Laguerre–Gaussian laser modes can be obtained by the direct conversion of the Hermite–Gaussian output. A Mach–Zehnder interferometer allows the phase structure of the Laguerre–Gaussian modes to be compared with the phase structure of a plane wave with the same frequency. The resulting interference patterns clearly illustrate the azimuthal phase dependence of the Laguerre–Gaussian modes, which is the origin of the orbital angular momentum associated with each of them.
236 citations
TL;DR: In this paper, a normal mode method for propagation modeling in acousto-elastic ocean waveguides is described, where the downward and upward looking plane wave reflection coefficients R1 and R2 at a reference depth in the fluid and searching the complex k plane for points where the product R1R2=1.
Abstract: A normal mode method for propagation modeling in acousto‐elastic ocean waveguides is described. The compressional (p‐) and shear (s‐) wave propagation speeds in the multilayer environment may be constant or have a gradient (1/c2 linear) in each layer. Mode eigenvalues are found by analytically computing the downward‐ and upward‐looking plane wave reflection coefficients R1 and R2 at a reference depth in the fluid and searching the complex k plane for points where the product R1R2=1. The complex k‐plane search is greatly simplified by following the path along which |R1R2|=1. Modes are found as points on the path where the phase of R1R2 is a multiple of 2π. The direction of the path is found by computing the derivatives d(R1R2)/dk analytically. Leaky modes are found, allowing the mode solution to be accurate at short ranges. Seismic interface modes such as the Scholte and Stonely modes are also found. Multiple ducts in the sound speed profile are handled by employing multiple reference depths. Use of Airy function solutions to the wave equation in each layer when computing R1 and R2 results in computation times that increase only linearly with frequency.
227 citations
TL;DR: A first-principles calculation of two second-order optical response functions as well as the dielectric function for GaAs and GaP based on a series of self-consistent LDA calculations using the full-potential linearized augmented plane wave method.
Abstract: We present a first-principles calculation of two second-order optical response functions as well as the dielectric function for GaAs and GaP. Specifically, we evaluate the dielectric function \ensuremath{\epsilon}(\ensuremath{\omega}) and the second-harmonic generation response coefficient ${\mathrm{\ensuremath{\chi}}}^{(2)}$(-2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega}) over a large frequency range. The electronic linear electro-optic susceptibility ${\mathrm{\ensuremath{\chi}}}^{(2)}$(-\ensuremath{\omega};\ensuremath{\omega},0) is also evaluated below the band gap. These results are based on a series of self-consistent LDA calculations using the full-potential linearized augmented plane wave method. Self-energy corrections are included at the level of the ``scissors'' approximation, which corrects for the underestimation of the local density approximation band gap and produces a change in the velocity matrix elements. The analytic expressions for the second-order response functions are free of the unphysically divergent terms at zero frequency that have previously plagued such calculations. Results for ${\mathrm{\ensuremath{\chi}}}^{(2)}$(-\ensuremath{\omega};\ensuremath{\omega},0) are in good agreement with experiment below the band gap and those for ${\mathrm{\ensuremath{\chi}}}^{(2)}$(-2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega}) are compared with experimental data where available. We note that despite the equivalence of both of these second-order response functions at zero frequency, there seems to be some discrepancy between the experimental results for these functions in this regime. \textcopyright{} 1996 The American Physical Society.
217 citations
TL;DR: In this paper, the poroelastic equations are based on a transversely isotropic extension of Biot's theory, and the problem is of plane strain type, describing qP−qS propagation.
Abstract: Porous media are anisotropic due to bedding, compaction, and the presence of aligned microcracks and fractures. Here, it is assumed that the skeleton (and not the solid itself) is anisotropic. The rheological model also includes anisotropic tortuosity and permeability. The poroelastic equations are based on a transversely isotropic extension of Biot’s theory, and the problem is of plane strain type, i.e., two dimensional, describing qP−qS propagation. In the high‐frequency case, the (two) viscodynamic operators are approximated by Zener relaxation functions that allow a closed differential formulation of Biot’s equation of motion. A plane‐wave analysis derives expressions for the slowness, attenuation, and energy velocity vectors, and quality factor for homogeneous viscoelastic waves. The slow wave shows an anomalous polarization behavior. In particular, when the medium is strongly anisotropic the polarization is quasishear and the wave presents cuspidal triangles. Anisotropic tortuosity affects mainly th...
TL;DR: In this paper, a spectral-domain dyadic Green's function for electromagnetic fields in cylindrically multilayered media with circular cross section is derived in terms of matrices of the cylindrical vector wave functions.
Abstract: A spectral-domain dyadic Green's function for electromagnetic fields in cylindrically multilayered media with circular cross section is derived in terms of matrices of the cylindrical vector wave functions. Some useful concepts, such as the effective plane wave reflection and transmission coefficients, are extended in the present spectral domain eigenfunction expansion. The coupling coefficient matrices of the scattering dyadic Green's functions are given by applying the principle of scattering superposition. The general solution has been applied to the case of axial symmetry (n=0, n is eigenvalue parameter in /spl phi/ direction) where the scattering coefficients are decoupled between TM and TE waves. Two specific geometries, i.e., two- and three-layered media that are frequently employed to model the practical problems are considered in detail, and the coupling coefficient matrices of their dyadic Green's functions are given, respectively.
TL;DR: In this paper, the authors extended the linearized augmented plane wave code WIEN by the evaluation of forces, and demonstrated the high accuracy of the force calculation, and use them for an efficient geometry optimization of poly-atomic systems.
TL;DR: In this paper, the response of an infinite two-dimensional periodic structure to point harmonic loading is analyzed and the response amplitude has a relatively smooth spatial distribution; if a caustic is present then the response has a complex spatial pattern and a "dead region" of very low response occurs.
TL;DR: In this paper, a plane-wave decomposition in the exit pupil is used to explore three-dimensional image distributions formed by high numerical aperture (NA > 0.6) lenses in homogeneous, isotropic, linear, and source-free thin films.
Abstract: A description is given of a modeling technique that is used to explore three-dimensional image distributions formed by high numerical aperture (NA > 0.6) lenses in homogeneous, isotropic, linear, and source-free thin films. The approach is based on a plane-wave decomposition in the exit pupil. Factors that are due to polarization, aberration, object transmittance, propagation, and phase terms are associated with each plane-wave component. These are combined with a modified thin-film matrix technique in a derivation of the total field amplitude at each point in the film by a coherent vector sum over all plane waves. One then calculates the image distribution by squaring the electric-field amplitude. The model is used to show how asymmetries present in the polarized image change with the influence of a thin film. Extensions of the model to magneto-optic thin films are discussed.
TL;DR: In this paper, a new method for the analysis of the diffraction of a plane wave impinging on a perfectly conducting circular cylinder in front of a generally reflecting surface is presented, characterized by its complex reflection coefficient, enabling us to treat a wide class of reflecting surfaces.
Abstract: A new method for the analysis of the diffraction of a plane wave impinging on a perfectly conducting circular cylinder in front of a generally reflecting surface is presented. The surface is characterized by its complex reflection coefficient, enabling us to treat a wide class of reflecting surfaces. The presence of the surface is taken into account by means of a suitable expansion of the reflected field in terms of cylindrical functions. The method gives the solution of the scattering problem in both the near and the far field regardless of the polarization state of the incident field. Numerical examples for dielectric interfaces are presented, and comparisons are made with results presented in the literature.
TL;DR: It is shown under very general assumptions that it is not possible to distinguish experimentally neutrinos produced in some region of space as wave packets from those produced in the same region ofspace as plane waves with the same energy distribution.
Abstract: We study the effect of coherent and incoherent broadening on neutrino oscillations both in vacuum and in the presence of matter (the MSW effect). We show under very general assumptions that it is not possible to distinguish experimentally neutrinos produced in some region of space as wave packets from those produced in the same region of space as plane waves with the same energy distribution. {copyright} {ital 1995 The American Physical Society.}
TL;DR: In this paper, the authors derived mathematical expressions for the far-field backscattering amplitude spectrum resulting from oblique insonification of an infinite, transversely isotropic elastic cylinder by a plane acoustic wave.
Abstract: Mathematical expressions are derived for the far‐field backscattering amplitude spectrum resulting from oblique insonification of an infinite, transversely isotropic elastic cylinder by a plane acoustic wave. The normal‐mode solution is based on decoupling of the scalar potential representing the horizontally polarized shear wave from those of the compressional and vertically polarized waves. The solution degenerates to the well‐known simple model for isotropic cylinders in the case of very weak anisotropy. The solution is used to study the influence of each element of the stiffness matrix on the various resonant modes of vibration. Perturbations of the elements c33 and c44, which characterize the cylinder along the axis, significantly affect resonant frequencies corresponding to axially guided waves. Perturbations of c11 and c12, which characterize the material on the transverse plane, predominantly affect the Rayleigh and Whispering Gallery resonance frequencies. Perturbations of c13 affect all three ty...
TL;DR: In this paper, a generalized minimum variance technique was developed to obtain a high wave vector resolution, even though the spatial grid is restricted to only a few sampling positions, using the amplitude and phase information of the magnetic field from the four satellite positions and determining the optimum wave field corresponding to the measured data.
Abstract: The main goal of the Cluster mission, consisting of four identical spacecraft, is the spatial resolution of plasma structures. For the determination of the wave vectors of a wave field from four positions, classical Fourier analysis is inappropriate. We develop a generalized minimum variance technique which gives a high wave vector resolution though the spatial grid is restricted to only a few sampling positions. This technique uses the amplitude and phase information of the magnetic field from the four satellite positions and determines the optimum wave field corresponding to the measured data. The components of the magnetic field are assumed to be normally distributed. The divergence-free nature of the magnetic field is used as a constraint. Using the magnetic data measured at four positions allows up to seven different wave vectors at one frequency to be uniquely resolved.
22 Sep 1996
TL;DR: A space-alternating generalized expectation-maximization (SAGE) algorithm is proposed to replace the high-dimensional optimization procedure necessary to compute the joint maximum-likelihood estimate of the waves parameters by several separate maximization processes which can be performed sequentially.
Abstract: In the last few years, issues concerning the spatial resolution of the received electromagnetic field have attracted a lot of attention in mobile communications. A new method for the high resolution of the electromagnetic field with respect to both the incidence direction and delay is presented. The underlying discrete propagation model relies on the assumption that a finite known number of transverse electromagnetic plane waves characterized by their complex amplitude, propagation delay, and azimuthal incidence direction are impinging in a neighborhood of the receiver position. A space-alternating generalized expectation-maximization (SAGE) algorithm is proposed to replace the high-dimensional optimization procedure necessary to compute the joint maximum-likelihood estimate of the waves parameters by several separate maximization processes which can be performed sequentially. The resolution and the mean convergence rate of the scheme are evaluated by means of Monte-Carlo simulations considering discrete synthetic propagation environments. Finally, the applicability of the SAGE algorithm to real propagation environments is demonstrated.
Abstract: Subsurface georadar is a high-resolution technique based on the propagation of high-frequency radio waves. Modeling radio waves in a realistic medium requires the simulation of the complete wavefield and the correct description of the petrophysical properties, such as conductivity and dielectric relaxation. Here, the theory is developed for 2-D transverse magnetic (TM) waves, with a different relaxation function associated to each principal permittivity and conductivity component. In this way, the wave characteristics (e.g., wavefront and attenuation) are anisotropic and have a general frequency dependence. These characteristics are investigated through a plane-wave analysis that gives the expressions of measurable quantities such as the quality factor and the energy velocity. The numerical solution for arbitrary heterogeneous media is obtained by a grid method that uses a time-splitting algorithm to circumvent the stiffness of the differential equations. The modeling correctly reproduces the amplitude and the wavefront shape predicted by the plane-wave analysis for homogeneous media, confirming, in this way, both the theoretical analysis and the numerical algorithm. Finally, the modeling is applied to the evaluation of the electromagnetic response of contaminant pools in a sand aquifer. The results indicate the degree of resolution (radar frequency) necessary to identify the pools and the differences between the anisotropic and isotropic radargrams versus the source-receiver distance.
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01 Sep 1996
TL;DR: Electromagnetic plane waves digital imaging and processing electronic and optical tunnel effect optical microscopy and nanoscopy scanning probe Optical microscopy optical converters and probes as discussed by the authors. But this is not the case for all of them.
Abstract: Electromagnetic plane waves digital imaging and processing electronic and optical tunnel effect optical microscopy and nanoscopy scanning probe optical microscopy optical converters and probes.
TL;DR: A complete set of cavity modes in planar dielectric microcavities is presented which naturally includes guided modes and shows that most of these orthonormal fields can be derived from a coherent superposition of plane waves incoming on the stack from the air and from the substrate.
Abstract: A complete set of cavity modes in planar dielectric microcavities is presented which naturally includes guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incoming on the stack from the air and from the substrate. Spontaneous emission of a dipole located inside the microcavity is analyzed, in terms of cavity modes. Derivation of the radiation pattern in the air and in the substrate is presented. The power emitted into the guided modes is also determined. Finally, a numerical analysis of the radiative properties of an erbium atom located in a Fabry-P\'erot multilayer dielectric microcavity is investigated. We show that a large amount of light is emitted into the guided modes of the structure, in spite of the Fabry-P\'erot resonance, which increases the spontaneous emission rate in a normal direction. \textcopyright{} 1996 The American Physical Society.
01 Jan 1996
TL;DR: In this paper, an infinite cylindrical sandwich shell is studied in the context of the transmission of airborne sound into aircraft interiors and an explicit expression of transmission loss is derived in terms of modal impedance of the fluids and the shell.
Abstract: Sound transmission through an infinite cylindrical sandwich shell is studied in the context of the transmission of airborne sound into aircraft interiors. The cylindrical shell is immersed in fluid media and excited by an oblique incident plane sound wave. The internal and external fluids are different and there is uniform airflow in the external fluid medium. An explicit expression of transmission loss is derived in terms of modal impedance of the fluids and the shell. The results show the effects of (a) the incident angles of the plane wave; (b) the flight conditions of Mach number and altitude of the aircraft; (c) the ratios between the core thickness and the total thickness of the shell; and (d) the structural loss factors on the transmission loss. Comparisons of the transmission loss are made among different shell constructions and different shell theories.
TL;DR: In this paper, a Newton method is presented for the approximate solution of the inverse problem to determine the shape of a two-dimensional crack from a knowledge of the far field pattern for the scattering of time-harmonic elastic plane waves.
Abstract: A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a two-dimensional crack from a knowledge of the far field pattern for the scattering of time-harmonic elastic plane waves. Frechet differentiability with respect to the boundary is shown for the far field operator, which for a fixed incident wave maps the crack onto the far field pattern of the scattered wave. Some numerical reconstructions illustrate the feasibility of the method.
06 May 1996
TL;DR: In this paper, a Perfectly Absorbing Technique (PAT) is proposed for numerical solutions of the Euler equations, which is capable of absorbing the out-going acoustic, vorticity and entropy waves at numerical boundaries without reflection (theoretically) for any angle of incidence and frequency of the wave.
Abstract: A Perfectly Absorbing Technique (PAT) is proposed for numerical solutions of the Euler equations. This technique follows the recent studies of Perfectly Matched Layer (PML) as absorbing boundary conditions. In the present paper, we construct the Perfectly Matched Layer equations for linear as well as non-linear Euler equations as an absorbing boundary condition. Plane wave solutions and propagation properties are analyzed for a uniform flow in an arbitrary direction. It is shown that the proposed PML equations are capable of absorbing the out-going acoustic, vorticity and entropy waves at numerical boundaries without reflection (theoretically) for any angle of incidence and frequency of the wave. The absorption rate is also independent of the wave frequency/wavelength. The PML equations are then extended to non-uniform mean flows. Moreover, by introducing a "pseudo mean flow", PML equations for nonlinear Euler equations are constructed. The pseudo mean flow needs not to be an accurate prediction of the actual mean steady flow. Consequently, it becomes possible to apply the PML equations without the exact mean flow being available. Numerical examples that demonstrate the validity of the proposed absorbing boundary conditions are presented.
TL;DR: In this article, the authors adapted the well-known "zigzag" ray model for use with a periodic waveguide (i.e., replacing the plane wave rays with Bloch wave rays), and showed that thin films of high refractive index, supported by a low index substrate and fully etched through with periodic pattern, can support guided modes.
Abstract: By adapting the well-known 'zigzag' ray model for use with a periodic waveguide (i.e. replacing the plane wave rays with Bloch wave rays), we show that thin films of high refractive index, supported by a low index substrate and fully etched through with a periodic pattern, can support guided modes. From the dispersion relation of these guided Bloch modes, it is shown that the in-plane modal group velocity can be zero, suggesting applications in enhanced dipole-field interactions and control of spontaneous emission in waveguide lasers.
TL;DR: In this article, the authors characterized the cross sections of arbitrary-shaped non-paraxial light beams by the zero, first and second order moments of the energy flux spatial distribution.
TL;DR: In this paper, exact travelling-wave solutions of the (2 + 1)-dimensional sine -Gordon equation possessing a velocity smaller than the velocity of the linear waves in the correspondent model system are obtained.
Abstract: Exact travelling-wave solutions of the (2 + 1)-dimensional sine - Gordon equation possessing a velocity smaller than the velocity of the linear waves in the correspondent model system are obtained. The dependence of their dispersion relations and allowed areas for the wave parameters on the wave amplitude are discussed. The obtained waves contain as particular cases static structures consisting of elementary cells with zero topological charge. The self-consistent parameters of one static structure are calculated. The obtained structures require minima spatial system sizes for their existence. As an illustration the obtained results are applied for a description of structures in spin systems with an anisotropy created by a magnetic field or by a crystal anisotropy field.