Showing papers on "Plane wave published in 2003"

Reflection phase characterizations of the EBG ground plane for low profile wire antenna applications

Abstract: Mushroom-like electromagnetic band-gap (EBG) structures exhibit unique electromagnetic properties that have led to a wide range of electromagnetic device applications. This paper focuses on the reflection phase feature of EBG surfaces: when plane waves normally illuminate an EBG structure, the phase of the reflected field changes continuously from 180/spl deg/ to -180/spl deg/ versus frequency. One important application of this feature is that one can replace a conventional perfect electric conductor (PEC) ground plane with an EBG ground plane for a low profile wire antenna design. For this design, the operational frequency band of an EBG structure is defined as the frequency region within which a low profile wire antenna radiates efficiently, namely, having a good return loss and radiation patterns. The operational frequency band is the overlap of the input-match frequency band and the surface-wave frequency bandgap. It is revealed that the reflection phase curve can be used to identify the input-match frequency band inside of which a low profile wire antenna exhibits a good return loss. The surface-wave frequency bandgap of the EBG surface that helps improve radiation patterns is very close to its input-match frequency band, resulting in an effective operational frequency band. In contrast, a thin grounded slab cannot work efficiently as a ground plane for low profile wire antennas because its surface-wave frequency bandgap and input-match frequency band do not overlap. Parametric studies have been performed to obtain design guidelines for EBG ground planes. Two novel EBG ground planes with interesting electromagnetic features are also presented. The rectangular patch EBG ground plane has a polarization dependent reflection phase and the slotted patch EBG ground plane shows a compact size.

Singular value decomposition methods for wave propagation analysis

Abstract: [1] We describe several newly developed methods for propagation analysis of electromagnetic plasma waves. We make use of singular value decomposition (SVD) technique and we determine the wave vector direction, ellipticity and directions of axes of the polarization ellipse, wave refractive index, transfer function of electric antennas, estimators of the planarity of polarization, and electromagnetic planarity. Simulations of Z-mode waves, which simultaneously propagate with different wave vectors, indicate that the SVD methods give reasonable results even if the assumption on the presence of a single plane wave is invalid. Simulations of whistler mode waves show that these methods can be used to recognize cases when the waves simultaneously propagate with wave vectors in two opposite hemispheres. Finally, we show an example of analysis of natural whistler mode and Z-mode emissions measured in the high-altitude auroral region by the MEMO experiment onboard the INTERBALL spacecraft.

Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves

Abstract: A novel method for simulating field propagation is presented. The method, based on the angular spectrum of plane waves and coordinate rotation in the Fourier domain, removes geometric limitations posed by conventional propagation calculation and enables us to calculate complex amplitudes of diffracted waves on a plane not parallel to the aperture. This method can be implemented by using the fast Fourier transformation twice and a spectrum interpolation. It features computation time that is comparable with that of standard calculation methods for diffraction or propagation between parallel planes. To demonstrate the method, numerical results as well as a general formulation are reported for a single-axis rotation.

Photonic band structures solved by a plane-wave-based transfer-matrix method.

Abstract: Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method.

Superfluidity of Bose–Einstein condensate in an optical lattice: Landau–Zener tunnelling and dynamical instability

Abstract: Superflow of a Bose–Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results of the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau–Zener tunnelling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making a transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.

Excited state nuclear forces from the Tamm–Dancoff approximation to time-dependent density functional theory within the plane wave basis set framework

Abstract: An efficient formulation of time-dependent linear response density functional theory for the use within the plane wave basis set framework is presented. The method avoids the transformation of the Kohn–Sham matrix into the canonical basis and references virtual orbitals only through a projection operator. Using a Lagrangian formulation nuclear derivatives of excited state energies within the Tamm–Dancoff approximation are derived. The algorithms were implemented into a pseudo potential/plane wave code and applied to the calculation of adiabatic excitation energies, optimized geometries and vibrational frequencies of three low lying states of formaldehyde. An overall good agreement with other time-dependent density functional calculations, multireference configuration interaction calculations and experimental data was found.

Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability

Abstract: Superflow of Bose-Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results on the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau-Zener tunneling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.

Tsunamis generated by subaerial mass flows

Abstract: [1] Tsunamis generated in lakes and reservoirs by subaerial mass flows pose distinctive problems for hazards assessment because the domain of interest is commonly the “near field,” beyond the zone of complex splashing but close enough to the source that wave propagation effects are not predominant. Scaling analysis of the equations governing water wave propagation shows that near-field wave amplitude and wavelength should depend on certain measures of mass flow dynamics and volume. The scaling analysis motivates a successful collapse (in dimensionless space) of data from two distinct sets of experiments with solid block “wave makers.” To first order, wave amplitude/water depth is a simple function of the ratio of dimensionless wave maker travel time to dimensionless wave maker volume per unit width. Wave amplitude data from previous laboratory investigations with both rigid and deformable wave makers follow the same trend in dimensionless parameter space as our own data. The characteristic wavelength/water depth for all our experiments is simply proportional to dimensionless wave maker travel time, which is itself given approximately by a simple function of wave maker length/water depth. Wave maker shape and rigidity do not otherwise influence wave features. Application of the amplitude scaling relation to several historical events yields “predicted” near-field wave amplitudes in reasonable agreement with measurements and observations. Together, the scaling relations for near-field amplitude, wavelength, and submerged travel time provide key inputs necessary for computational wave propagation and hazards assessment.

Transverse Fivebranes in Matrix Theory

Abstract: M-theory on the maximally supersymmetric plane wave background of eleven-dimensional supergravity admits spherical BPS transverse M5-branes with zero light-cone energy. We give direct evidence that the single M5-brane state corresponds to the trivial (X = 0) classical vacuum in the large N limit of the plane wave matrix theory. In particular, we show that the linear fluctuation spectrum of the spherical fivebrane matches exactly with the set of exactly protected excited states about the X = 0 vacuum in the matrix model. These states include geometrical fluctuations of the sphere, excitations of the worldvolume two-form field, and fermion excitations. In addition, we propose a description of multiple fivebrane states in terms of matrix model vacua. Finally, we discuss how to obtain the continuum D2/M2 and NS5/M5 theories on spheres from the matrix model. The matrix model can be viewed as a regularization for these theories.

Nonlinear interaction of plane ultrasonic waves with an interface between rough surfaces in contact.

Abstract: A theoretical investigation of the nonlinear interaction between an acoustic plane wave and an interface formed by two rough, nonconforming surfaces in partial contact is presented. The macroscopic elastic properties of such a nonlinear interface are derived from micromechanical models accounting for the elastic interaction that is characteristic of spherical bodies in contact. These results are used to formulate set of boundary conditions for the acoustic field, which are to be enforced at the imperfect interface. The scattering problem is solved for plane wave incidence by using a simple perturbation approach and the harmonic balance method. Sample results are presented for arbitrary wave polarization and angle of incidence. The relative magnitude of the nonlinear signals and their potential use toward the nondestructive evaluation of imperfect interfaces are assessed. In particular, attention is drawn to the enhanced nonlinear response of an interface insonified by a shear vertical wave in the neighborhood of the longitudinal critical angle. The motivation for this investigation is provided by the need to develop nondestructive methods to detect and localize small, partially closed cracks in metals with coarse microstructures.

Dynamic model of artificial reactive impedance surfaces

Abstract: New artificial reactive impedance surfaces have been recently suggested by Sievenpiper et al. for antenna and waveguide applications. In particular, high impedance values corresponding to a magnetic wall can be realized in dense arrays of conducting patches over a conducting plane. In this paper, a dynamic model for the electromagnetic properties of such structures is developed. The analytical model takes into account electromagnetic interactions between all patches in infinite arrays excited by normally incident plane waves, as well as higher-order Floquet modes between the array and the ground plane. The results are compared with the known experiments.

Tunable face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals

Abstract: We report on the fabrication and electro-optic measurements of face-centered-cubic (fcc) lattices in holographic polymer dispersed liquid-crystal materials. Four linearly polarized coherent plane waves were interfered to generate a fcc optical lattice that was subsequently and indefinitely recorded as an arrayed pattern of nanometer-sized liquid-crystal droplets ∼50 nm at lattice nodes within a polymer matrix. Observed transmission spectra and Kossel diffraction curves are consistent with fcc crystal structure. A completely reversible 2% wavelength shift of the ±1 1 1 stop band was observed on application of an electric field.

D-brane interactions in type IIB plane wave background

Abstract: The cylinder diagrams that determine the static interactions between pairs of Dp-branes in the type IIB plane wave background are evaluated. The resulting expressions are elegant generalizations of the flat-space formulae that depend on the value of the Ramond-Ramond flux of the background in a non-trivial manner. If each of the interacting D-branes separately preserves half the supersymmetries, the closed-string and open-string descriptions consistently transform into each other under a modular transformation. These results are derived for configurations of euclidean signature D(p+1)-instantons but also generalize to lorentzian signature Dp-branes.

LISA response function

Abstract: The orbital motion of the Laser Interferometer Space Antenna (LISA) introduces modulations into the observed gravitational wave signal. These modulations can be used to determine the location and orientation of a gravitational wave source. The complete LISA response to an arbitrary gravitational wave is derived using a coordinate free approach in the transverse-traceless gauge. The general response function reduces to that found by Cutler for low frequency, monochromatic plane waves. Estimates of the noise in the detector are found to be complicated by the time variation of the interferometer arm lengths.

Multipole Expansion of Strongly Focussed Laser Beams

Abstract: Multipole expansion of an incident radiation field-that is, representation of the fields as sums of vector spherical wavefunctions-is essential for theoretical light scattering methods such as the T-matrix method and generalised Lorenz-Mie theory (GLMT). In general, it is theoretically straightforward to find a vector spherical wavefunction representation of an arbitrary radiation field. For example, a simple formula results in the useful case of an incident plane wave. Laser beams present some difficulties. These problems are not a result of any deficiency in the basic process of spherical wavefunction expansion, but are due to the fact that laser beams, in their standard representations, are not radiation fields, but only approximations of radiation fields. This results from the standard laser beam representations being solutions to the paraxial scalar wave equation. We present an efficient method for determining the multipole representation of an arbitrary focussed beam. (C) 2003 Elsevier Science Ltd. All rights reserved.

Multipole expansion of strongly focussed laser beams

Abstract: Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised Lorenz-Mie theory (GLMT). In general, it is theoretically straightforward to find a vector spherical wavefunction representation of an arbitrary radiation field. For example, a simple formula results in the useful case of an incident plane wave. Laser beams present some difficulties. These problems are not a result of any deficiency in the basic process of spherical wavefunction expansion, but are due to the fact that laser beams, in their standard representations, are not radiation fields, but only approximations of radiation fields. This results from the standard laser beam representations being solutions to the paraxial scalar wave equation. We present an efficient method for determining the multipole representation of an arbitrary focussed beam.

The self-imaging phenomenon and its applications

Abstract: The self-imaging effect can be obtained as the result of the diffraction of a plane wave by the periodic structure. It is known as the Talbot effect. The self-imaging phenomenon is discussed here also from the new viewpoint as a class of the propagation-invariant wavefields. The repetition of an object can be achieved by the superposition of nondiffracting beams.

Air-coupled acoustic imaging with zero-group-velocity Lamb modes

Abstract: A Lamb wave resonance has been found that allows unusually efficient transmission of airborne sound waves through plates. This occurs at the zero-group-velocity point at the frequency minimum of the first-order symmetric (S1) Lamb mode. At this frequency, plane waves with a range of incident angles can couple between the air and the Lamb mode in the solid plate, dominating the spectrum of transmitted focused sound beams by 10 dB or more. We use this frequency for C-scan imaging, and demonstrate the detection of both a 3.2-mm-diameter buried flaw and a subwavelength thickness changes of .005λ (1%).

Computer-generated holograms of three-dimensional objects synthesized from their multiple angular viewpoints

Abstract: Synthesizing computer-generated holograms (CGHs) of a general three-dimensional (3D) object is usually a heavy computational task. We propose and demonstrate a new algorithm for computing CGHs of 3D objects. In our scheme, many different angular projections of computer-designed 3D objects are numerically processed to yield a single two-dimensional complex matrix. This matrix is equivalent to the complex amplitude of a wave front on the rear focal plane of a spherical lens when the object is located near the front focal point and illuminated by a plane wave. Therefore the computed matrix can be used as a CGH after it is encoded to a real positive-valued transparency. When such CGH is illuminated by a plane wave, a 3D real image of the objects is constructed. The number of computer operations are equivalent to those of a two-dimensional Fourier CGH. Computer and optical constructions of 3D objects, both of which show the feasibility of the proposed approach, are described.

2D dynamic response of unlined and lined tunnels in poroelastic soil to harmonic body waves

Abstract: The problem of harmonic wave diffraction by tunnels in an infinite poroelastic saturated soil obeying Biot's theory is studied numerically under conditions of plane strain and the effect of poroelasticity on the response is assessed through some parametric studies. The method is based on the theory of Mei and Foda, which considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer at the free boundaries. Both problems are solved numerically by the boundary element method in the frequency domain. Results dealing with the response of a circular tunnel with and without an elastic concrete liner in an infinite poroelastic medium to incident harmonic P and SV plane waves are provided and compared against analytical ones as well as to those corresponding to linear elastic soil behaviour. Copyright © 2002 John Wiley & Sons, Ltd.

In-phase reflection and EM wave suppression characteristics of electromagnetic band gap ground planes

Abstract: The reflection phases of incident plane waves on EBG surfaces are found and compared for mushroom-like EBG and UC-EBG structures. It is noticed that the in-phase reflection phase occurs at a lower frequency for mushroom-like than the UC-EBG for the same cell size. A suspended stripline over an EBG ground plane is used to model the EM wave suppression characteristics of EBG structures. The drop in S21 shows a clear band gap for EM wave suppression; however this region does not match with the resonant frequency of the normal incident for the mushroom like structure because of the dependence of resonant frequency on polarization and angle of the incident wave. It is found that the resonant frequency of an obliquely incident TM matches well with the band gap result of the suspended strip.

Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body

Abstract: The method of moments technique for analyzing electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body is presented based on the combined field integral equations. The body is assumed to be illuminated by a plane wave. The surface equivalence principle is used to replace the body by equivalent electric and magnetic surface currents. These currents radiating in unbounded free space produce the correct scattered field outside. The negatives of these currents produce the correct total internal field, when radiating in an unbounded chiral medium. By enforcing the continuity of the tangential components of the total electric and magnetic fields on the surface of the body, a set of coupled integral equations is obtained for the equivalent surface currents. The surface of the body is modeled using triangular patches. The triangular rooftop vector expansion functions are used for both equivalent surface currents. The coefficients of these expansion functions are obtained using the method of moments. The mixed potential formulation for a chiral medium is developed and used to obtain explicit expressions for the electric and magnetic fields produced by surface currents. Numerical results for bistatic radar cross sections are presented for three chiral scatterers - a sphere, a finite circular cylinder, and a cube.

Weak solutions to a nonlinear variational wave equation

Abstract: We establish the global existence of weak solutions to the Cauchy problem for a nonlinear variational wave equation, where the wave speed is a given monotone function of the wave amplitude. The equation arises in modeling wave motions of nematic liquid crystals, long waves on a dipole chain, and a few other fields. We use the Young-measure method in the setting of Lp spaces. We overcome the difficulty that oscillations get amplified by the growth terms of the equation.

Black strings in asymptotically plane wave geometries

Abstract: We present a class of black string spacetimes which asymptote to maximally symmetric plane wave geometries. Our construction will rely on a solution generating technique, the null Melvin twist, which deforms an asymptotically flat black string spacetime to an asymptotically plane wave black string spacetime while preserving the event horizon.

Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides

Abstract: The plane-wave-based transfer-matrix method (TMM) exhibits a peculiar advantage of being capable of solving eigenmodes involved in an infinite photonic crystal and electromagnetic (EM) wave propagation in finite photonic crystal slabs or even semi-infinite photonic crystal structures within the same theoretical framework. In addition, this theoretical approach can achieve much improved numerical convergency in solution of photonic band structures than the conventional plane-wave expansion method. In this paper we employ this TMM in combination with a supercell technique to handle two important kinds of three-dimensional (3D) photonic crystal waveguide structures. The first one is waveguides created in a 3D layer-by-layer photonic crystal that possesses a complete band gap, the other more popular one is waveguides built in a two-dimensional photonic crystal slab. These waveguides usually have mirror-reflection symmetries in one or two directions perpendicular to their axis. We have taken advantage of these structural symmetries to reduce the numerical burden of the TMM solution of the guided modes. The solution to the EM problems under these mirror-reflection symmetries in both the real space and the plane-wave space is discussed in a systematic way and in great detail. Both the periodic boundary condition and the absorbing boundary condition are employed to investigate structures with or without complete 3D optical confinement. The fact that the EM field components investigated in the TMM are collinear with the symmetric axes of the waveguide brings great convenience and clarity in exploring the eigenmode symmetry in both the real space and the plane-wave space. The classification of symmetry involved in the guided modes can help people to better understand the coupling of the photonic crystal waveguides with external channels such as dielectric slab or wire waveguides.

Equation of state and phonon frequency calculations of diamond at high pressures

Abstract: The pressure-volume relationship and the zone-center optical-phonon frequency of cubic diamond at pressures up to 600 GPa have been calculated based on density-functional theory within the local-density approximation and the generalized gradient approximation. Three different approaches, viz. a pseudopotential method applied in the basis of plane waves, an all-electron method relying on augmented plane waves plus local orbitals, and an intermediate approach implemented in the basis of projector augmented waves have been used. All these methods and approximations yield consistent results for the pressure derivative of the bulk modulus and the volume dependence of the mode Gr\"uneisen parameter of diamond. The results are at variance with recent precise measurements up to 140 GPa. Possible implications for the experimental pressure determination based on the ruby luminescence method are discussed.