Showing papers on "Dispersion relation published in 1997"

Optical constants of epitaxial AlGaN films and their temperature dependence

Abstract: We have studied the dependence of the absorption edge and the refractive index of wurtzite AlxGa1−xN films on temperature and composition using transmission and photothermal deflection spectroscopy. The Al molar fraction of the AlxGa1−xN films grown by plasma induced molecular beam epitaxy was varied through the entire range of composition (0⩽x⩽1). We determined the absorption edges of AlxGa1−xN films and a bowing parameter of 1.3±0.2 eV. The refractive index in the photon energy range between 1 and 5.5 eV and temperatures between 7 and 295 K was deduced from the interference fringes. The static refractive index n(0) changed from 2.29 for GaN to 1.96 for AlN at room temperature. A variation of temperature from 295 to 7 K resulted in a decrease of refractive index (at photon energies close to the band gap) by 0.05±0.01 and in an energy shift of the absorption edge of about 64±5 meV independent of the Al content of the films. Using the Kramers–Kronig dispersion relation and an approximation for the dispersion coefficient for photon energies near the band gap, the refractive index could be described as a function of photon energy, Al content, and temperature.

Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion

Abstract: The authors have discovered from numerical modelling that there are stable nonlinear transmission pulses for periodically dispersion managed systems where the path average dispersion may be either anomalous, zero, or even normal.

Determination of the dust screening length by laser-excited lattice waves

Abstract: The screening of dust particles immersed in the sheath of a parallel plate rf discharge in helium is studied by excitation of waves in a linear chain arrangement. The waves are excited by the radiation pressure of a modulated laser beam. The measured dispersion relation is compared with a one-dimensional dust lattice wave to obtain the shielding length. Dust acoustic waves are not compatible with the measured dispersion relation. {copyright} {ital 1997} {ital The American Physical Society}

Experimental and theoretical study of reflection and coherent thermal emissionby a SiC grating supporting a surface-phonon polariton

Abstract: Polarized directional reflectivity and emissivity of a SiC one-dimensional grating are studied. Measurements and calculations are performed between 10 and 11.5 \ensuremath{\mu}m where the real part of the permittivity of SiC is negative. Pronounced dips due to surface-phonon polariton excitations are observed in the reflectivity spectra in p polarization. Thermal emission displays peaks in the same directions and at the same particular frequencies. A comparison between theory and experiments shows a good agreement for both cases. The dispersion relation is obtained theoretically and experimentally. Finally, we discuss the spatial coherence of the monochromatic thermal emission. Indeed, it is shown that the existence of peaks of the emitted-monochromatic radiation, in particular angular directions, implies that, due to surface waves, the thermally excited field is partially spatially coherent along the interface.

The usage of standard finite element codes for computation of dispersion relations in materials with periodic microstructure

Abstract: A method with which standard finite element programs can be used to compute dispersion relations in periodic composites is proposed. The method is applied to two composite microstructures: a two-phase laminate and a fiber composite. The dispersion relations computed for the laminate are compared with a known analytical solution and the agreement is very good. The dispersion relations computed for the fibrous composite are compared with an existing approximate model and experimental results from the literature. The agreement between the approximate model, the experiments, and the computations is very good in the wave guide case and satisfactory for the wave reflect case.

Generalized theory of helicon waves. I. Normal modes

Abstract: The theory of helicon waves is extended to include finite electron mass. This introduces an additional branch to the dispersion relation that is essentially an electron cyclotron or Trivelpiece–Gould (TG) wave with a short radial wavelength. The effect of the TG wave is expected to be important only for low dc magnetic fields and long parallel wavelengths. The normal modes at low fields are mixtures of the TG wave and the usual helicon wave and depend on the nature of the boundaries. Computations show, however, that since the TG waves are damped near the surface of the plasma, the helicon wave at high fields is almost exactly the same as is found when the electron mass is neglected.

Evidence for quasiparticle decay in photoemission from underdoped cuprates

Abstract: I argue that the {open_quotes}gap{close_quotes} recently observed at the Brillouin zone face of cuprate superconductors in photoemission by Marshall {ital et al.}[Phys.Rev.Lett.{bold 76}, 4841 (1996)] and Ding {ital et al.}[Nature {bold 382}, 54 (1996)] is evidence for the decay of the injected hole into a spinon-holon pair. {copyright} {ital 1997} {ital The American Physical Society}

Surface phonon dispersion in graphite and in a lanthanum graphite intercalation compound

Abstract: Using high-resolution electron energy-loss spectroscopy the surface-phonon dispersion of graphite has been determined in the \ensuremath{\Gamma}K direction over the whole energy range and the whole Brillouin zone. Born\char21{}von Karman model calculations are used to describe the dispersion relations. An unexpected result is the splitting of the ZA and ZO mode at the K point. Following a previously introduced procedure to form in situ rare-earth graphite intercalation compounds (GIC), which for lanthanum results in an intermediate carbide phase, we prepared this carbidic phase and the final GIC-like phase. The carbide shows five dispersionless features that may be attributed to Einstein modes of graphite islands. The phonon dispersion of the final phase shows the same modes as graphite shifted in energy: softening of the optical and stiffening of the acoustical phonons occurs. This is described within a Born\char21{}von Karman model by weakening the nearest-neighbor interaction and strengthening the second-nearest-neighbor interaction. The evolution of the phonon dispersion gives a first hint that the GIC-like phase may develop in two stages: first a monolayer graphene on top of the carbide and then the very thin GIC layer.

Acoustic phonon modes of rectangular quantum wires

Abstract: Acoustic phonon modes of a free-standing rectangular quantum wire composed of cubic crystals are theoretically investigated using an algorithm developed to analyse data from resonant ultrasound spectroscopy The normal phonon modes are classified according to their spatial symmetries into a compressional mode termed the dilatational mode and non-compressional modes referred to as the flexural, torsional, and shear modes The formalism that we present is quite general and can be applied to wires of any cubic material As an example, the dispersion relations are obtained for square and rectangular wires of GaAs, taking into account the anisotropic elasticity of the material The dispersion curves for a rectangular wire are compared with those of the approximate hybrid modes referred to as the thickness and width modes, and the validity of the modes is discussed The existence of edge modes is confirmed by examining the spatial distribution of displacement vectors

Statistical sand wave dynamics in one-directional water flows

Abstract: Moving sand waves and the overlying tubulent flow were measured on the Wilga River in Poland, and the Tirnava Mica and Buzau Rivers in Romania. Bottom elevations and flow velocities were measured at six points simultaneously by multi-channel measuring systems. From these data, the linear and two-dimensional sections of the three-dimensional correlation and structure functions and various projections of sand wave three-dimensional spectra were investigated.It was found that the longitudinal wavenumber spectra of the sand waves in the region of large wavenumbers followed Hino's −3 law (S(Kx) ∝K−3x) quite satisfactorily, confirming the theoretical predictions of Hino (1968) and Jain & Kennedy (1974). However, in contrast to Hino (1968), the sand wave frequency spectrum in the high-frequency region was approximated by a power function with the exponent −2, while in the lower-frequency region this exponent is close to −3.A dispersion relation for sand waves has been investigated from analysis of structure functions, frequency spectra and the cross-correlation functions method. For wavelengths less than 0.15–0.25 of the flow depth, their propagation velocity C is inversely proportional to the wavelength λ. When the wavelengths of spectral components are as large as 3–4 times the flow depth, no dispersion occurs. These results proved to be in good qualitative agreement with the theoretical dispersion relation derived from the potential-flow-based analytical models (Kennedy 1969; Jain & Kennedy 1974). We also present another, physically-based, explanation of this phenomenon, introducing two types of sand movement in the form of sand waves. The first type (I) is for the region of large wavenumbers (small wavelengths) and the second one (II) is for the region of small wavenumbers (large wavelengths). The small sand waves move due to the motion of individual sand particles (type I, C∝λ−1) while larger sand waves propagate as a result of the motion of smaller waves on their upstream slopes (type II, C∝λ0). Like the sand particles in the first type, these smaller waves redistribute sand from upstream slopes to downstream ones. Both types result in sand wave movement downstream but with a different propagation velocity.The main characteristics of turbulence, as well as the quantitative values characterizing the modulation of turbulence by sand waves, are also presented.

Ion-acoustic waves in a multicomponent plasma with negative ions

Abstract: Propagation of ion-acoustic waves has been investigated experimentally in an argon plasma mixed with sulfur hexafluoride using a multidipole double-plasma device. The device is separated into a driver and a target section with a magnetic filter. Waves are transmitted by a circular mesh grid placed in the target. Both the fast and the slow modes were observed to propagate downstream in the wide range of the density ratio of negative ions to positive ions. The measured phase velocities are in agreement with theoretical ones calculated from a plasma dispersion relation taking the drift of the plasma into consideration. The out-of-phase oscillation between positive ions and electrons, which is predicted by a fluid model of the multicomponent plasma, has been observed.

Finite Frequency Range Kramers-Kronig Relations: Bounds on the Dispersion

Abstract: Dispersion inequalities are presented to check for the self-consistency of experimentally obtained complex moduli, such as the complex dielectric constant, magnetic permeability, and complex bulk and shear moduli of viscoelastic materials. Unlike the Kramers-Kronig dispersion relations, they only require measurements over a finite frequency range. They can provide highly accurate interpolation formulas for the real part, given its value at a few selected frequencies and given the imaginary part over a range of frequencies.

Enrichment of 3He and Heavy Ions in Impulsive Solar Flares

Abstract: The acceleration of 3He and heavy ions by electromagnetic hydrogen cyclotron waves in a direct single-stage process in impulsive solar flares is investigated analytically and with the help of test particle simulations. We illustrate in detail the mechanism by which a single monochromatic wave can accelerate such ions to MeV and even GeV energies. While somewhat idealized, a monochromatic wave well illustrates the importance of the background magnetic field gradient in the acceleration process. An interesting result of our analysis shows that the acceleration rate is proportional to the magnitude of the magnetic field gradient and is independent of the wave amplitude, while the maximum energy gained increases with decreasing magnetic field gradient and increasing wave amplitude. Heavy ions can also be accelerated by these electromagnetic hydrogen cyclotron waves in a single-stage process by the second or higher harmonic resonance. The acceleration of heavier ions by the same mechanism raises the question of their low enrichment in comparison to much higher enrichment of 3He. The solution is related to the initial small acceleration of the thermal heavy ions at the higher harmonic resonances. The enrichment of the heavy ions increases with the amplitude of the electromagnetic waves and decreases with the plasma density due to Coulomb collisions and absorption of wave energy. Comparison between the rate of cooling of thermal heavy ions due to collisions and heating by waves gives wave intensity and heavy ion ratios which are consistent with observations. The relation between the accelerated heavy ion abundances and their gyrofrequencies in the corona is used to estimate the temperature in the acceleration region. The existence of electromagnetic hydrogen cyclotron waves in flare plasmas is supported by observations in auroral plasmas and by solution of the dispersion relation, which shows that such waves can propagate over long distances along coronal magnetic fields.

Slab plasmon polaritons and waveguide modes in four-layer resonant semiconductor waveguides

Abstract: This paper presents a detailed study of the waveguide and plasmon polariton properties of four-layer systems involving highly doped semiconductor material. The dispersion relations of waveguide and plasmon polariton modes are calculated for different geometrical parameters and material properties. Special attention is paid to the transition region between the latter modes, which exhibits a complex behavior. Slab plasmon polaritons at wavelengths slightly larger than the plasma wavelength, yielding a positive real part of the permittivity, have been found. Finally, applications at wavelengths near the transition region and near the plasma wavelength are proposed and discussed.

Surface Wave Eigenmodes in a Finite-Area Plane Microwave Plasma

Abstract: The resonance frequencies of electromagnetic surface modes propagating along a plane dielectric-plasma interface are computed, taking into account the finite area of the latter. The analysis results in simple analytical formulae for estimating the plasma density at which a given mode can be expected to occur for given geometry and wave frequency. Comparison with measurements in large-area circular plasmas is made.

Resonantly excited nonlinear ion waves

Abstract: One- and two-dimensional simulations and supporting analysis of nonlinear ion acoustic waves as might be associated with the saturation of stimulated Brillouin backscattering (SBBS) are presented. To simulate ion wave phenomena efficiently, while retaining a fully kinetic representation of the ions, a Boltzmann fluid model is used for the electrons, and a particle-in-cell representation is used for the ions. Poisson’s equation is solved in order to retain space-charge effects. We derive a new dispersion relation describing the parametric instability of ion waves, evidence for which is observed in our simulations. One- and two-dimensional simulations of plasma with either initially cold or warm ions (and multi-species ions) exhibit a complex interplay of phenomena that influence the time evolution and relaxation of the amplitude of the excited ion wave: ion trapping, wave steepening, acceleration, heating and tail formation in the ion velocity distribution, parametric decay into longer wavelength ion waves...

Atom-atom interaction in strongly modified reservoirs

Abstract: We extend recent work on two closely spaced atoms interacting through the narrow band of strongly coupled modes at the edge of a photonic band gap. The resonant dipole-dipole interaction (RDDI) is strongly modified for atomic transition frequencies in the vicinity of the band-gap edge, but we show that an analytical approximation to the RDDI agrees very well with the exact RDDI obtained by numerical integration using the exact dispersion relation. Having established the value of the RDDI, we can derive the amplitudes for the two atoms without resorting to the pole approximation which is necessary due to the strongly modified mode structure in the dielectric host. For a wide range of parameters we find beating and population trapping in the long time limit. The distribution of population in the photonic continuum is investigated in the long time limit in the case of one and two atoms. It is found to be strongly asymmetric and to exhibit a strong signature of the unusual mode structure in the material at the band-gap edge.

Dispersion theory of proton Compton scattering in the first and second resonance regions

Abstract: Dispersion theory of proton Compton scattering is extended to energies up to {approximately}1 GeV where excitations of higher resonances and nonresonance double-pion photoproduction become important photoabsorption mechanisms. To saturate s-channel dispersion relations, the VPI partial-wave analysis of single-pion photoproduction and resonance photocouplings is used. Models for double-pion photoproduction and dispersion asymptotic contributions are constructed. The latter are mainly given by {pi}{sup 0} and {sigma}(600) exchanges. Being used in dispersion calculations, they result in a reasonable agreement with all available data on both differential cross sections and polarization observables in Compton scattering. Some unsolved problems are outlined. {copyright} {ital 1997} {ital The American Physical Society}

Electromagnetic surface modes of a dielectric superlattice: the supercell method

Abstract: We present a study of the reliability of the supercell method in calculations of surface electromagnetic modes. For a truncated superlattice constituted of nonabsorbing dielectric layers, we demonstrate that the numerical solutions obtained by this method for transverse-electric waves agree with those based on the Bloch theory for the semi-infinite superlattice. A slab of superlattice with at least nine unit cells yields satisfactory convergence to an analytic dispersion relation for the surface modes. In addition, we apply the supercell method to study in detail the dependence of transverse-electric and transverse-magnetic surface waves on the cut-off position in the cell next to the surface. As a specific case, we choose a TiO2/SiO2 superlattice—layers with relatively high dielectric contrast in the visible spectrum. We find the surface modes strongly dependent on the position of the surface. In fact, they appear only for certain terminations. By plotting the field amplitudes, we show that there exist different possibilities for the guidance of surface waves. The variation of the penetration depth of these modes is also discussed.

Wave damping by a thin layer of viscous fluid

Abstract: The rate of damping of surface gravity–capillary waves is investigated, in a system which consists of a thin layer of a Newtonian viscous fluid of thickness d floating on a Newtonian fluid of infinite depth. The surface and interfacial tensions, elasticities and viscosities are taken into account. In particular, an approximate dispersion relation is derived for the case where kd and (ω/ν+)1/2d are both small, where k is the wavenumber, ω is the angular frequency and ν+ is the kinematic viscosity of the upper fluid. If d→0 while ν+d remains finite, published dispersion relations for viscoelastic surface films of extremely small (e.g., monomolecular) thickness are reproduced, if we add the surface and interfacial tensions, elasticities and viscosities together, and then add an additional 4ρ+ν+d to the surface viscosity, where ρ+ is the density of the upper fluid. A simple approximation is derived for the damping rate and associated frequency shift when their magnitudes are both small. An example is given of...

Transfer matrix method for interface optical-phonon modes in multiple-interface heterostructure systems

Abstract: Interactions of carriers with interface optical phonons dominate over other carrier–phonon scatterings in narrow quantum-well structures. Herein, a transfer matrix method is used to establish a formalism for determining the dispersion relations, electrostatic potentials, and Frohlich interaction Hamiltonians of the interface optical phonons for multiple-interface heterostructure systems within the framework of the macroscopic dielectric continuum model. This method facilitates systematic calculations for complex structures where the conventional method is very difficult to implement. Several specific cases are treated to illustrate the advantages of the general formalism.

Ion cyclotron waves in the Io torus during the Galileo encounter: Warm plasma dispersion analysis

Abstract: During the Galileo-Io flyby, nearly field-aligned, left-hand circularly polarized ion cyclotron waves were observed in a band near the sulfur-dioxide ion gyrofrequency. We have performed a warm plasma dispersion analysis using nominal Io torus composition ratios, pickup ion “ring”-type velocity-space distributions, and a thermal background plasma of typical torus temperature. Analysis shows that the SO2+ wave is dominant, particularly as the ring begins to broaden. The observed spectral peak indicates that the ring distribution of pickup SO2+ is highly unstable and generates waves, but there is unlikely to be sufficient time for ions to fully thermalize before dissociation occurs. Assuming wave-particle scattering of ions towards a “bispherical” shell-type distribution, a free energy analysis and comparison with observed wave amplitudes suggests that the ions are not scattered far from the ring and/or that the SO2+ composition ratio in the Io torus falls off considerably from Io wake values.

A comparison of theory and laboratory measurements of wave propagation and attenuation in grease ice

Abstract: In an experimental study using a wave tank in a laboratory cold room we determine the dispersion relation and amplitude attenuation for surface waves propagating through different thicknesses of grease ice. We compare our results to two ice rheology models: the mass-loading model, which predicts a wavelength decrease relative to open water, and an infinite depth viscous fluid model, which predicts an increasing wavelength as the wave Reynolds number decreases. For a thick grease ice layer in which the waves are strongly damped we observe that the wavelength increases by up to 30% over its open water value in the frequency range of 1.0 Hz<ƒ<1.6 Hz. This trend agrees with the viscous model, and the agreement improves as the ice thickness increases and at higher wave frequencies where conditions approach those of the infinite depth approximation. The Reynolds number decreases approximately exponentially with frequency and is in the range 1

Standing wave patterns in shallow beds of vibrated granular material

Abstract: Conventional and high-speed video imaging was used to observe surface waves in vertically oscillated, thin layers of dry, noncohesive granular material. The onset of wave formation is pressure dependent and sensitive to the preparation of the particle surface. The dispersion relation of these waves is different at high and low frequencies, and the transition can be explained within the context of a hydrodynamical model by the introduction of a frequency dependent viscous cut-off that dominates at high frequency. High-speed imaging also reveals a qualitative change in individual particle movement at high and low frequencies, and the compressibility of the granular layer.

Magnetic field effect on the complex permeability spectra in a Ni-Zn ferrite

Abstract: Complex permeability spectra μ*(=μ′−iμ′′) in a Ni–Zn ferrite was studied in the frequency range from 10 kHz to 3 GHz under dc magnetic field up to 1000 Oe. In the absence of a dc magnetic field, the μ′ spectrum has a frequency dispersion above 1 MHz; the μ′′ spectrum has a maximum at about 2 MHz. This feature can be described by the superposition of the two types of magnetic resonance, domain wall motion with a resonance frequency ωdwr=3.5 MHz and spin rotation with a resonance frequency ωspinr=8.0 MHz. Under dc magnetic field, low frequency permeability μ′ decreases with increasing static field bias. On the other hand, the μ′′ spectrum is broadened and two distinct peaks appear in the external field of 606 Oe. Under about 900 Oe external field, this ferrite becomes to have single-domain structure and the dispersion of domain wall motion in the permeability spectra disappears. In the above 700 Oe external field, high frequency dispersion of μ* shows ferromagnetic resonance characteristics.

Dispersion Theory, Sum Rules, and Their Application to the Analysis of Optical Data

Abstract: The basic optical properties of solids [1, 2], despite their great diversity, are rigorously limited by nature. These limitations take the form of sum rules and dispersion relations that reflect the physical laws governing the dynamics of matter and its interaction with light. Many of these limitations were enumerated in the first half of this century, but in the early 1970s, the discovery of a large number of new sum rules [3-15] deepened our understanding of these constraints and their application. Thus, it is now known that in addition to the celebrated f sum rule for absorption processes, there are companion sum rules for dispersive processes. For example, the real part of the complex refractive index N(ω) = n(ω) + ik(ω) satisfies [3, 4] ∫ 0 ∞ [ n ( ω ) − 1 ] d ω = 0 (1). That is, the refractive index averaged over all frequencies must be unity. Moreover, it may be shown that this restriction arises in part from the inertial property of matter. Related rules—with a similar physical interpretation—have been shown to apply to the complex dielectric function and its inverse.

Bernstein‐Greene‐Kruskal analysis of electrostatic solitary waves observed with Geotail

Abstract: Electrostatic solitary waves (ESW) relevant to the high-frequency component of broadband electrostatic noise spectra observed by Geotail spacecraft in the magnetotail are analyzed. A general description of the ESW, as stationary solutions of Vlasov-Poisson equations, is developed on the basis of the Bernstein-Greene-Kruskal (BGK) technique. It is shown that the structure and relationships among basic parameters of a localized perturbation are primarily determined by resonant and nonresonant plasma screenings of bunched electrons trapped by a potential pulse moving in a plasma. The dependence of the typical width of the pulse on its drift velocity and pulse amplitude is found, which can be treated as a nonlinear dispersion relation for the localized perturbation. The theoretical results are compared with the Geotail data and a particle simulation.