Showing papers on "Dispersion relation published in 2003"

Ultraviolet modifications of dispersion relations in effective field theory

Abstract: The existence of a fundamental ultraviolet scale, such as the Planck scale, may lead to modifications of the dispersion relations for particles at high energies in some scenarios of quantum gravity. We apply effective field theory to this problem and identify dimension-5 operators that do not mix with dimensions 3 and 4 and lead to cubic modifications of dispersion relations for scalars, fermions, and vector particles. Further we show that, for electrons, photons and light quarks, clock comparison experiments bound these operators at ${10}^{\ensuremath{-}5}/{M}_{\mathrm{P}\mathrm{l}}$.

Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions.

Abstract: The focus of the present work is to provide an analysis for the acoustic and thermal properties of the energy-conserving lattice Boltzmann models, and a solution to the numerical defects and instability associated with these models in two and three dimensions. We discover that a spurious algebraic coupling between the shear and energy modes of the linearized evolution operator is a defect universal to the energy-conserving Boltzmann models in two and three dimensions. This spurious mode coupling is highly anisotropic and may occur at small values of wave number k along certain directions, and it is a direct consequence of the following key features of the lattice Boltzmann equation: (1) its simple spatial-temporal dynamics, (2) the linearity of the relaxation modeling for collision operator, and (3) the energy-conservation constraint. To eliminate the spurious mode coupling, we propose a hybrid thermal lattice Boltzmann equation (HTLBE) in which the mass and momentum conservation equations are solved by using the multiple-relaxation-time model due to d'Humieres, whereas the diffusion-advection equation for the temperature is solved separately by using finite-difference technique (or other means). Through the Chapman-Enskog analysis we show that the hydrodynamic equations derived from the proposed HTLBE model include the equivalent effect of gamma=C(P)/C(V) in both the speed and attenuation of sound. Appropriate coupling between the energy and velocity field is introduced to attain correct acoustics in the model. The numerical stability of the HTLBE scheme is analyzed by solving the dispersion equation of the linearized collision operator. We find that the numerical stability of the lattice Boltzmann scheme improves drastically once the spurious mode coupling is removed. It is shown that the HTLBE scheme is far superior to the existing thermal LBE schemes in terms of numerical stability, flexibility, and possible generalization for complex fluids. We also present the simulation results of the convective flow in a rectangular cavity with different temperatures on two opposite vertical walls and under the influence of gravity. Our numerical results agree well with the pseudospectral result.

Optical pulse propagation in metal nanoparticle chain waveguides

Abstract: Finite-difference time-domain simulations show direct evidence of optical pulse propagation below the diffraction limit of light along linear arrays of spherical noble metal nanoparticles with group velocities up to 0.06c. The calculated dispersion relation and group velocities correlate remarkably well with predictions from a simple point-dipole model. A change in particle shape to spheroidal particles shows up to a threefold increase in group velocity. Pulses with transverse polarization are shown to propagate with negative phase velocities antiparallel to the energy flow.

Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations

Abstract: The lattice thermal conductivity of crystalline Si nanowires is calculated. The calculation uses complete phonon dispersions, and does not require any externally imposed frequency cutoffs. No adjustment to nanowire thermal conductivity measurements is required. Good agreement with experimental results for nanowires wider than 35 nm is obtained. A formulation in terms of the transmission function is given. Also, the use of a simpler, nondispersive ``Callaway formula,'' is discussed from the complete dispersions perspective.

Methods for the determination of the optical constants of thin films from single transmission measurements: a critical review

Abstract: Optical transmission measurements are commonly used for the routine determination of thin film optical constants. This paper presents an overview of the different methods of evaluating these transmission data, leading to values for the complex refractive index. Three different groups of methods are distinguished using: (1) at least two different optical measurements; (2) dispersion relations or general physical constraints to approximate the behaviour of the wavelength-dependent refractive index; and (3) a `virtual' measurement as a second variable. The methods from groups (2) and (3) (requiring only a single transmission measurement) are treated in more detail and are evaluated in terms of their accuracy.

Improved dispersion relations for GaAs and applications to nonlinear optics

Abstract: The refractive index of GaAs has been measured in the wavelength range from 0.97 to 17 μm, which covers nearly the entire transmission range of the material. Linear and quadratic temperature coefficients of the refractive index have been fitted to data measured between room temperature and 95 °C. In the midinfrared, the refractive index and temperature dependence are obtained from analysis of etalon fringes measured by Fourier-transform spectroscopy in undoped GaAs wafers. In the near infrared, the refractive index is deduced from the quasiphasematching (QPM) wavelengths of second-harmonic generation in orientation-patterned GaAs crystals. Two alternative empirical expressions are fitted to the data to give the refractive index as a function of wavelength and temperature. These dispersion relations agree with observed QPM conditions for midinfrared difference-frequency generation and second-harmonic generation. Predictions for various nonlinear optical interactions are presented, including tuning curves f...

Accurate density functional calculations for the phonon dispersion relations of graphite layer and carbon nanotubes

Abstract: Accurate calculations for the phonon dispersion relations of single-wall armchair and zigzag nanotubes are presented. The calculations are performed using a plane-wave basis set and density functional theory. To ensure the accuracy of the presented calculations, the phonon dispersion relation of an isolated graphite layer is calculated and the results are compared to experiment. Errors are small, but some notable discrepancies between experiment and theory are observed and discussed. For armchair and zigzag nanotubes the dependence of Raman-active and infrared-active modes on the radius is investigated in detail concentrating on the modes in the G band. The results are compared to those predicted by the zone-folding method using the calculated force constants for graphite. We find a general softening of most high-frequency modes and a substantial lowering of one particular longitudinal ${A}_{1}$ mode in metallic tubes. We associate this mode with the Breit-Wigner-Fano lines observed usually in metallic tubes. The precise electronic mechanism leading to the softening of the longitudinal ${A}_{1}$ mode is discussed in detail.

Plasmon dispersion relation of Au and Ag nanowires

Abstract: We have studied surface plasmon modes on silver and gold nanowires of a fixed cross section and different lengths, produced by electron beam lithography. The optically excited modes are determined by extinction spectroscopy and can be interpreted in terms of standing plasmon polariton waves. The eigenfrequencies are found to follow a dispersion relation similar to that for a planar metal/dielectric interface.

Transmission and dispersion relations of perfect and defect-containing waveguide structures in phononic band gap materials

Abstract: By using a combination of finite difference time domain (FDTD) and plane wave expansion (PWE) methods, we study the propagation of acoustic waves through waveguide structures in phononic band gap crystals composed of solid constituents. We investigate transmission through perfect linear waveguides, waveguides containing a resonant cavity, or waveguides coupled with a side branch resonator such as a cavity or a stub. A linear guide can support one or several modes falling in the absolute band gap of the phononic crystal. It can be made monomode over a large frequency range of the band gap by varying the width of the guide. The transmission through a guide containing a cavity can be made very selective and reduced to narrow peaks associated with some of the eigenmodes of the cavity. The effect of a side branch resonator is to induce zeros of transmission in the spectrum of the perfect guide that appear as narrow dips with frequencies depending upon the shape of the resonator and its coupling with the guide. We find perfect correspondences between the peaks in the transmission spectrum of a waveguide containing a cavity and the dips in the transmission of a cavity side coupled waveguide. Finally, when a gap exists in the spectrum of the perfect guide, a stub can also permit selective transmission of frequency in this gap. The results are discussed in relation with the symmetry of the modes associated with a linear guide or with a cavity.

Long-surface-wave instability in dense granular flows

Abstract: In this paper we present an experimental study of the long-surface-wave instability that can develop when a granular material flows down a rough inclined plane. The threshold and the dispersion relation of the instability are precisely measured by imposing a controlled perturbation at the entrance of the flow and measuring its evolution down the slope. The results are compared with the prediction of a linear stability analysis conducted in the framework of the depth-averaged or Saint-Venant equations. We show that when the friction law proposed in Pouliquen (1999a) is introduced in the Saint-Venant equations, the theory is able to predict quantitatively the stability threshold and the phase velocity of the waves but fails in predicting the observed cutoff frequency. The instability is shown to be of the same nature as the long-wave instability observed in classical fluids but with characteristics that can dramatically differ due to the specificity of the granular rheology.

Anisotropic transport in a two-dimensional electron gas in the presence of spin-orbit coupling

Abstract: In a two-dimensional electron gas as realized by a semiconductor quantum well, the presence of spin-orbit coupling of both the Rashba and Dresselhaus type leads to anisotropic dispersion relations and Fermi contours. We study the effect of this anisotropy on the electrical conductivity in the presence of fixed impurity scatterers. The conductivity also shows in general an anisotropy which can be tuned by varying the Rashba coefficient. This effect provides a method of detecting and investigating spin-orbit coupling by measuring spin-unpolarized electrical currents in the diffusive regime. Our approach is based on an exact solution of the two-dimensional Boltzmann equation and provides also a natural framework for investigating other transport effects including the anomalous Hall effect.

An acoustic wave equation for orthorhombic anisotropy

Abstract: Using a dispersion relation derived under the acoustic medium assumption, I obtain an acoustic wave equation for orthorhombic media. Although an acoustic wave equation does not strictly describe a wave in anisotropic media, it accurately describes the kinematics of P-waves. The orthorhombic acoustic wave equation, unlike the transversely isotropic one, is a sixth-order equation with three sets of complex conjugate solutions. Only one set of these solutions are perturbations of the familiar acoustic wavefield solution for isotropic media for incoming and outgoing P-waves and, thus, are of interest here. The other two sets of solutions are simply the result of this artificially derived sixth-order equation.

Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis

Abstract: Veselago medium (also called double negative material, backward medium, left-handed medium) is a medium with both negative isotropic dielectric permittivity and permeability. It has the effect of backward waves with negative (anomalous) refraction, in contrast to the usual forward waves with normal refraction in normal isotropic dielectrics and/or magnetics. In this paper, examples of the existence of backward waves (with respect to the interface) without negative refraction, and negative refraction without backward waves in uniaxial dielectrics with negative permittivity along the anisotropy axis, are presented. Considering these examples increases the possibility of designing backward wave materials and negative refraction materials without using magnetic media. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 259–263, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10887

Analysis of mode structure in hollow dielectric waveguide fibers

Abstract: In this paper, we analyze the electromagnetic mode structure of an OmniGuide fiber\char22{}a hollow dielectric waveguide in which light is confined by a large index-contrast omnidirectional dielectric mirror. In particular, we find that the modes in an OmniGuide fiber are similar to those in a hollow metallic waveguide in their symmetries, cutoff frequencies, and dispersion relations. We show that the differences can be predicted by a model based on a single parameter\char22{}the phase shift upon reflection from the dielectric mirror. The analogy to the metal waveguide extends to the transmission properties, resulting in the identification of the ${\mathrm{TE}}_{01}$ mode as the lowest-loss mode of the OmniGuide fiber.

Guided waves propagating in sandwich structures made of anisotropic, viscoelastic, composite materials.

Abstract: The propagation of Lamb-like waves in sandwich plates made of anisotropic and viscoelastic material layers is studied. A semi-analytical model is described and used for predicting the dispersion curves (phase velocity, energy velocity, and complex wave-number) and the through-thickness distribution fields (displacement, stress, and energy flow). Guided modes propagating along a test-sandwich plate are shown to be quite different than classical Lamb modes, because this structure does not have the mirror symmetry, contrary to most of composite material plates. Moreover, the viscoelastic material properties imply complex roots of the dispersion equation to be found that lead to connections between some of the dispersion curves, meaning that some of the modes get coupled together. Gradual variation from zero to nominal values of the imaginary parts of the viscoelastic moduli shows that the mode coupling depends on the level of material viscoelasticity, except for one particular case where this phenomenon exists whether the medium is viscoelastic or not. The model is used to quantify the sensitivity of both the dispersion curves and the through-thickness mode shapes to the level of material viscoelasticity, and to physically explain the mode-coupling phenomenon. Finite element software is also used to confirm results obtained for the purely elastic structure. Finally, experiments are made using ultrasonic, air-coupled transducers for generating and detecting guided modes in the test-sandwich structure. The mode-coupling phenomenon is then confirmed, and the potential of the air-coupled system for developing single-sided, contactless, NDT applications of such structures is discussed.

Dispersion management for atomic matter waves.

Abstract: We demonstrate the control of the dispersion of matter wave packets utilizing periodic potentials. This is analogous to the technique of dispersion management known in photon optics. Matter wave packets are realized by Bose-Einstein condensates of $^{87}\mathrm{R}\mathrm{b}$ in an optical dipole potential acting as a one-dimensional waveguide. A weak optical lattice is used to control the dispersion relation of the matter waves during the propagation of the wave packets. The dynamics are observed in position space and interpreted using the concept of effective mass. By switching from positive to negative effective mass, the dynamics can be reversed. The breakdown of the approximation of constant, as well as experimental signatures of an infinite effective mass are studied.

Interface optical-phonon modes and electron–interface-phonon interactions in wurtzite GaN/AlN quantum wells

Abstract: Based on the dielectric-continuum model and Loudon's uniaxial crystal model, the equation of motion for the p-polarization field in an arbitrary wurtzite multilayer heterostructure is solved exactly for the interface optical-phonon modes The polarization eigenvector, the dispersion relation, and the electron\char21{}interface-phonon interaction Fr\"ohlich-like Hamiltonian are derived using the transfer-matrix method The analytical formulas can be directly applied to single heterojunctions, single and multiple quantum wells (QW's), and superlattices Considering the strains of QW structures and the anisotropy effects of wurtzite crystals, the dispersion relations of the interface phonons and the electron\char21{}interface-phonon coupling strengths are investigated for GaN/AlN single and coupled QW's We find that there are four (eight) interface optical-phonon branches with definite symmetry with respect to the symmetric center of a single (coupled) QW Typical features in the dispersion curves are evidenced which are due to the anisotropy effects of wurtzite crystals The lower-frequency modes are much more important for the electron\char21{}interface-phonon interactions than the higher-frequency modes For the lower-frequency interface phonons, the intensity of the electron-phonon interactions is reduced due to the strain effects of the QW structures For the higher-frequency interface modes, the influence of the strains on the electron-phonon interactions can be ignored

Comparison of the dispersion properties of several low-dispersion finite-difference time-domain algorithms

Abstract: A comparison of the accuracy of several low-dispersion finite-difference time-domain (FDTD) schemes in two dimensions is presented. Each algorithm is reviewed and its FDTD update equations presented. The dispersion relation of each FDTD algorithm is also given. The accuracy of each FDTD scheme is compared via direct evaluation of the dispersion relation. Results are presented showing the dispersion errors of each algorithm as a function of propagation angle and cell size. Tables are shown that present for each algorithm the optimal Courant number at a specified discretization as well as the number of floating point operations needed to update each cell (three fields) at each time step. The advantages and disadvantages of each algorithm are briefly discussed. While some schemes are more wideband than others, almost all provide substantial improvement in the dispersion errors compared with the classical Yee (1966) FDTD algorithm.

Backward wave region and negative material parameters of a structure formed by lattices of wires and split-ring resonators

Abstract: A structure formed by combined lattices of infinitely long wires and split-ring resonators is studied. A dispersion equation is derived and then used to calculate the effective permittivity and permeability in the frequency band where the lattice can be homogenized. The backward wave region in which both the effective permittivity and permeability are negative is analyzed. Some open and controversial questions are discussed. It is shown that previous experimental results confirming the existence of backward waves in such a structure can be in deed explained in terms of negative material parameters. However, these parameters are not quasi-static and thus the known analytical formulas for the effective material parameters of this structure, which have been widely used and discussed in the literature, were not correct, and it was the reason of some objections to the authors of that experiment.

Band structure for a one-dimensional photonic crystal containing left-handed materials

Abstract: The explicit dispersion equation for a one-dimensional periodic structure with alternative layers of left-handed material (LHM) and right-handed material (RHM) is given and analyzed. Some unusual phenomena such as spurious modes with complex frequencies, discrete modes and photon tunneling modes are observed in the band structure. The existence of spurious modes with complex frequencies is a common problem in the calculation of the band structure for such a photonic crystal. Discrete modes may exist regardless whether the optical length of the LHM layer cancels the optical length of the RHM layer or not. Physical explanation and significance are given for the discrete modes (with real values of wave number) and photon tunneling propagation modes (with imaginary wave numbers in a limited region).

Photonic surface-wave excitation: photonic crystal–metal interface

Abstract: We demonstrate the existence of electromagnetic surface modes and surface plasma waves in the interface of a one-dimensional photonic crystal and a metal. These modes can exist in the region in which bandgaps of the photonic crystal overlap and in the region below the plasma frequency of a metal in the frequency wave-vector space. An analytic dispersion relation to determine the existence of these electromagnetic surface modes is obtained, and it is shown that these modes can be excited and observed without prism or grating configurations even under normal incidence from vacuum.

Instability mechanisms in swirling flows

Abstract: We investigate the stability of the screened Rankine vortex with added plug flow where the azimuthal velocity decreases abruptly outside the core of the vortex. The jump in circulation is known to induce centrifugal and azimuthal Kelvin–Helmholtz instabilities. Their effect on the stability of the different azimuthal wave number m is discussed using physical considerations associated with asymptotic expansions and numerical computations of the dispersion relation. It is shown that the axial shear and centrifugal instability are active for all m, and that modes with |m|⩾2 are also destabilized by azimuthal shear. In contrast, the bending modes m=±1 are stabilized by a coupling with Kelvin waves in the core. Effects of rotation on the absolute/convective transition are also discussed. The absolute instability of positive helical modes is seen to be promoted by centrifugal instability and azimuthal shear.

Compressional waves in complex (dusty) plasmas under microgravity conditions

Abstract: Complex plasmas consist of electrons, ions and charged microparticles, with typical charge-to-mass ratios 1:10−5:10−13. The interest in these systems has grown explosively, because they can be investigated at the kinetic level (the microparticles). However, on Earth the supporting forces (against gravity) are of the same order as the electrostatic interparticle forces—and hence only strongly compressed systems can be investigated. Under microgravity conditions these “body forces” are a factor 102 smaller which allows the experimental investigation of weakly compressed three-dimensional complex plasmas. One way to study these systems is by the controlled excitation of low-frequency compressional waves. The first such experiments, conducted with the PKE-Nefedov laboratory on the International Space Station is reported. The waves were excited by modulating the voltage on the rf electrodes. By varying the modulation frequency the dispersion relation was measured. The results are compared with existing theoret...

Highly sensitive plasma absorption probe for measuring low-density high-pressure plasmas

Abstract: This article reports a new type of sensitive plasma absorption probe (PAP), which is characterized with a thin wire antenna directly exposed to plasma. In the sensitive PAP, the power reflection coefficient resonantly decreases at a certain frequency due to absorption of a surface wave, which is excited along a sheath formed around the antenna. The electron density is derived from the measured absorption frequency in comparison to a wave dispersion relation: the dispersion is calculated under assumptions that the sheath width is twice the Debye length and that wavelength is twice the antenna length. This sensitive PAP also enables measurements of very low electron densities (∼108 cm−3) and very high pressures (∼10 Torr), in comparison to a conventional standard PAP. In addition, both electron temperature and electron density can be measured using a pair of sensitive PAPs of different antenna radii.

Differential forms of the Kramers-Kronig dispersion relations

Abstract: Differential forms of the Kramers-Kronig dispersion relations provide an alternative to the integral Kramers-Kronig dispersion relations for comparison with finite-bandwidth experimental data. The differential forms of the Kramers-Kronig relations are developed in the context of tempered distributions. Results are illustrated for media with attenuation obeying an arbitrary frequency power law (/spl alpha/(/spl omega/) = /spl alpha//sub 0/ + /spl alpha//sub 1/ |/spl omega/|/sup y/). Dispersion predictions using the differential dispersion relations are compared to the measured dispersion for a series of specimens (two polymers, an egg yolk, and two liquids) exhibiting attenuation obeying a frequency power law (1.00 /spl les/ y /spl les/ 1.99), with very good agreement found. For this form of ultrasonic attenuation, the differential Kramers-Kronig dispersion prediction is found to be identical to the (integral) Kramers-Kronig dispersion prediction.

Anomalous diffusion of vibrational energy in proteins

Abstract: The evolution of vibrational wave packets built from the normal modes of cytochrome c, myoglobin and green fluorescent protein is investigated. Vibrational energy flow in these proteins is found to exhibit anomalous subdiffusion, a consequence of trapping of energy by spatially localized normal modes contained in the wave packet. Anomalous subdiffusion is characterized by an exponent, ν, that is related to the spectral dimension, d, and fractal dimension, D, of the protein. The dispersion relation describing variation of the protein’s normal mode frequencies with wave number is also characterized by an exponent, a, that is related to d and D. Values of the exponent, a, computed for the three proteins are consistent with the computed values for ν. The values of D obtained from ν, a, and d for each protein are the same within computational error, and close to the mass fractal dimension computed for each protein, all values falling in the range D=2.3±0.2. We find also that relaxation of the center of ener...

Is there an imprint of Planck-scale physics on inflationary cosmology?

Abstract: We study the effects of the trans-Planckian dispersion relation on the spectrum of the primordial density perturbations during inflation. In contrast to the earlier analyses, we do not assume any specific form of the dispersion relation and allow the initial state of the field to be arbitrary. We obtain the spectrum of vacuum fluctuations of the quantum field by considering a scalar field satisfying the linear wave equation with higher spatial derivative terms propagating in the de Sitter spacetime. We show that the power spectrum does not strongly depend on the dispersion relation and that the form of the dispersion relation does not play a significant role in obtaining the corrections to the scale invariant spectrum. We also show that the signatures of the deviations from the flat scale-invariant spectrum from the CMBR observations due to quantum gravitational effects cannot be differentiated from the standard inflationary scenario with an arbitrary initial state.