Showing papers on "Dispersion relation published in 2002"
TL;DR: In this article, it is shown that a slab of metamaterial with negative permittivity and permeability can act as a phase compensator/conjugator and, by combining such a slab with another slab made of a conventional dielectric material, one can, in principle, have a 1D cavity resonator whose dispersion relation may not depend on the sum of thicknesses of the interior materials filling this cavity, but instead it depends on the ratio of these thicknesses.
Abstract: We present and analyze theoretically some ideas for thin one-dimensional (1D) cavity resonators in which a combination of a conventional dielectric material and a metamaterial possessing negative permittivity and permeability has been inserted. It is shown that a slab of metamaterial with negative permittivity and permeability can act as a phase compensator/conjugator and, thus, by combining such a slab with another slab made of a conventional dielectric material, one can, in principle, have a 1D cavity resonator whose dispersion relation may not depend on the sum of thicknesses of the interior materials filling this cavity, but instead it depends on the ratio of these thicknesses. In other words, one can, in principle, conceptualize a 1D cavity resonator with the total thickness far less than the conventional /spl lambda//2. Mathematical steps and physical intuitions relevant to this problem are presented.
600 citations
TL;DR: In this article, a theory of the magnetic field driven (semi)metal-insulator phase transition is developed for planar systems with a low density of carriers and a linear (i.e., relativisticlike) dispersion relation for low-energy quasiparticles.
Abstract: A theory of the magnetic field driven (semi)metal-insulator phase transition is developed for planar systems with a low density of carriers and a linear (i.e., relativisticlike) dispersion relation for low-energy quasiparticles. The general structure of the phase diagram of the theory with respect to the coupling constant, the chemical potential, and the temperature is derived in two cases, with and without an external magnetic field. The conductivity and resistivity as functions of temperature and magnetic field are studied in detail. An exact relation for the value of the ``offset'' magnetic field ${B}_{c},$ determining the threshold for the realization of the phase transition at zero temperature, is established. The theory is applied to the description of a recently observed phase transition induced by a magnetic field in highly oriented pyrolytic graphite.
353 citations
TL;DR: In this article, the propagation of magneto-inductive (MI) waves supported by capacitively loaded loops is investigated using a circuit model in which each loop is coupled magnetically to a number of other loops.
Abstract: The propagation of waves supported by capacitively loaded loops is investigated using a circuit model in which each loop is coupled magnetically to a number of other loops. Since the coupling is due to induced voltages the waves are referred to as magnetoinductive (MI) waves. The mathematical formulations are mostly analytical thanks to long standing previous work on the magnetic and electric fields generated by currents flowing in loops. Retardation is neglected, i.e., dimensions of the structure are assumed to be small relative to the free space wavelength. The dispersion relations, derived in the most general case for a tetragonal three-dimensional structure, exhibit both forward and backward waves within a pass band. It is shown that for reproducing the salient features of the waves it is sufficient to take nearest neighbor coupling into account but coupling between loops further away must also be considered if higher accuracy is required. The investigations include that of resonances, conditions for the existence of traveling waves, tolerances, and streamlines of the Poynting vector. Waveguide components, like bends, power dividers and couplers are considered due to the potential applications of the MI waves as magnetic guides. Generality of the results, their possible implications for transverse electromagnetic wave propagation, previous work on similar waves, including the possibility of phase conjugation, are discussed in a separate section.
349 citations
TL;DR: In this paper, the dispersion equation that characterizes the relationship between the natural frequency and the wavenumber can be obtained in a simple form for multilayered rectangular plates, and the present solution includes all previous solutions, such as piezoelectric, piezomagnetic and purely elastic solutions as special cases.
349 citations
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TL;DR: The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schrodinger-Poisson system, and a multistream model representing a statistical mixture of N pure states, each described by a wave function is considered.
Abstract: The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schroedinger-Poisson system. Here, we consider a multistream model representing a statistical mixture of N pure states, each described by a wavefunction. The one-stream and two-stream cases are investigated. We derive the dispersion relation for the two-stream instability and show that a new, purely quantum, branch appears. Numerical simulations of the complete Schroedinger-Poisson system confirm the linear analysis, and provide further results in the strongly nonlinear regime. The stationary states of the Schroedinger-Poisson system are also investigated. These can be viewed as the quantum mechanical counterpart of the classical Bernstein-Greene-Kruskal modes, and are described by a set of coupled nonlinear differential equations for the electrostatic potential and the stream amplitudes.
295 citations
TL;DR: The first treatment of the refraction of physical electromagnetic waves in newly developed negative index media (NIM) is presented, and earlier interpretations of phase refraction as "negative light refraction" and "light focusing by plane slabs" are incorrect.
Abstract: We present the first treatment of the refraction of physical electromagnetic waves in newly developed negative index media (NIM), also known as left-handed media (LHM). The NIM dispersion relation implies that group fronts refract positively even when phase fronts refract negatively. This difference results in rapidly dispersing, very inhomogeneous waves. In fact, causality and finite signal speed always prevent negative wave signal (not phase) refraction. Earlier interpretations of phase refraction as ``negative light refraction'' and ``light focusing by plane slabs'' are therefore incorrect, and published NIM experiments can be explained without invoking negative signal refraction.
293 citations
TL;DR: The existing empirical equations used to estimate the longitudinal dispersion coefficient and the new equations proposed in this study were included in the advective dispersion equation to predict the suspended sediment concentrations at three sites in the Humber Estuary sited along the northeast coast of England.
241 citations
TL;DR: In this article, a generalized plasma dispersion function has been obtained for waves in plasmas with isotropic kappa distributions for arbitrary real kappa, and a Maxwellian distribution perpendicular to it has been used to study the effect of superthermal electrons and ions on ion-acoustic waves propagating at an angle to a magnetic field.
Abstract: A generalized plasma dispersion function has previously been obtained for waves in plasmas with isotropic kappa distributions for arbitrary real kappa [Mace and Hellberg, Phys Plasmas 2, 2098 (1995)] In many instances plasmas are found to have anisotropic power-law distributions, and hence a similar dispersion function for electrostatic waves in plasmas having a one-dimensional kappa distribution along a preferred direction in space, and a Maxwellian distribution perpendicular to it has now been developed It is used to study the effect of superthermal electrons and ions on ion-acoustic waves propagating at an angle to a magnetic field This dispersion function should find application to wave studies both in space plasmas, where the magnetic field defines a preferred direction, and in dusty plasma crystal studies, where the ion flow direction is unique
241 citations
TL;DR: In this paper, an analytical theory of electromagnetic waves in artificial media formed by a rectangular lattice of thin ideally conducting cylinders using the local field approach was developed, and the transcendental dispersion equation was obtained in closed form and solved numerically.
Abstract: An analytical theory of electromagnetic waves in artificial media formed by a rectangular lattice of thin ideally conducting cylinders using the local field approach is developed. As a result, the transcendental dispersion equation is obtained in closed form and solved numerically. Typical dispersion curves are calculated. Using these results, the reflection problem from an interface between a half space of wire medium and free space is solved for plane-wave excitation. In the low-frequency approximation a simple analytical formula for the frequency dependent effective dielectric permittivity is established.
181 citations
TL;DR: The Fourier spectra of longitudinal and transverse waves corresponding to random particle motion were measured in a two-dimensional plasma crystal and the phonons were found to obey a dispersion relation that assumes a Yukawa interparticle potential.
Abstract: The Fourier spectra of longitudinal and transverse waves corresponding to random particle motion were measured in a two-dimensional plasma crystal. The crystal was composed of negatively charged microspheres immersed in a plasma at a low gas pressure. The phonons were found to obey a dispersion relation that assumes a Yukawa interparticle potential. The crystal was in a nonthermal equilibrium, nevertheless phonon energies were almost equally distributed with respect to wave number over the entire first Brillouin zone.
143 citations
TL;DR: In this article, it was shown that a modulated Gaussian beam undergoes negative refraction at the interface between a positive and negative refractive index material, and the interference fronts appear to bend in a manner suggesting positive refraction, such that the true direction of the energy flow associated with the refracted beam is not obvious.
Abstract: We show that a modulated Gaussian beam undergoes negative refraction at the interface between a positive and negative refractive index material. While the refraction of the beam is clearly negative, the modulation interference fronts are not normal to the group velocity, and thus exhibit a sideways motion relative to the beam—an effect due to the inherent frequency dispersion associated with the negative index medium. In particular, the interference fronts appear to bend in a manner suggesting positive refraction, such that for a plane wave, the true direction of the energy flow associated with the refracted beam is not obvious.
TL;DR: In this article, an explicit formula for the temporal growth rate of the elliptical instability in each vortex is obtained as a function of the above global parameters of the system, the Reynolds number Γ 1/v and the non-dimensionalized axial wavenumber kzb of the perturbation.
Abstract: Two parallel Gaussian vortices of circulations Γ1 and Γ2 radii a1 and a2, separated by a distance b may become unstable by the elliptical instability due the elliptic deformation of their cores. The goal of the paper is to analyse this occurrence theoretically in a general framework. An explicit formula for the temporal growth rate of the elliptical instability in each vortex is obtained as a function of the above global parameters of the system, the Reynolds number Γ1/v and the non-dimensionalized axial wavenumber kzb of the perturbation. This formula is based on a known asymptotic expression for the local instability growth rate at an elliptical stagnation point which depends on the local characteristics of the elliptical flow and the inclination angle of the local perturbation wavevector at this point. The elliptical flow characteristics are estimated by considering each Gaussian vortex alone in a weak uniform external strain field whose properties are provided by a point vortex modelling of the vortex pair. The inclination angle is obtained from the dispersion relation for the Gaussian vortex normal modes and the local expression near each vortex centre for the two helical modes of azimuthal wavenumber m = 1 and m = −1 which constitute the elliptical instability global mode. Both the final formula and the hypotheses made for its derivation are tested and validated by direct numerical simulations and large-eddy simulations.
TL;DR: The measured dispersion relations agree reasonably with a recently developed theory, and the comparison yields the shielding parameter and the charge on particles.
Abstract: Dispersion relations of longitudinal and transverse waves in two-dimensional (2D) screened-Coulomb crystals were investigated. The waves were excited in 2D crystals made from complex plasmas, i.e., dusty plasmas, by applying radiation pressure of laser light. The dependencies of the dispersion relation on the shielding parameter, the damping rate, and the wave propagation direction were experimentally measured. The measured dispersion relations agree reasonably with a recently developed theory, and the comparison yields the shielding parameter and the charge on particles.
TL;DR: In this paper, the authors presented a procedure to measure and invert surface wave dispersion and attenuation data simultaneously and, thus, account for the close coupling between the two quantities.
TL;DR: In this paper, the authors identify the effective theory appropriate to the propagation of massless bulk fields in brane-world scenarios, and show that the dominant low-energy effect of asymmetric warping in the bulk is to modify the dispersion relation of the effective 4-dimensional modes.
Abstract: We identify the effective theory appropriate to the propagation of massless bulk fields in brane-world scenarios, to show that the dominant low-energy effect of asymmetric warping in the bulk is to modify the dispersion relation of the effective 4-dimensional modes. We show how such changes to the graviton dispersion relation may be bounded through the effects they imply, through loops, for the propagation of standard model particles. We compute these bounds and show that they provide, in some cases, the strongest constraints on nonstandard gravitational dispersions. The bounds obtained in this way are the strongest for the fewest extra dimensions and when the extra-dimensional Planck mass is the smallest. Although the best bounds come for warped 5-D scenarios, for which M5 is O(TeV), even in 4 dimensions the graviton loop can lead to a bound on the graviton speed which is comparable with other constraints.
TL;DR: In this paper, an analytical model for a rectangular lattice of isotropic scatterers with electric and magnetic resonances is presented, and a self-consistent dispersion equation is derived and then used to calculate correctly the effective permittivity and permeability in the frequency band where the lattice can be homogenized.
Abstract: An analytical model is presented for a rectangular lattice of isotropic scatterers with electric and magnetic resonances. Each isotropic scatterer is formed by putting appropriately 6 $\Omega$-shaped perfectly conducting particles on the faces of a cubic unit cell. A self-consistent dispersion equation is derived and then used to calculate correctly the effective permittivity and permeability in the frequency band where the lattice can be homogenized. The frequency range in which both the effective permittivity and permeability are negative corresponds to the mini-band of backward waves within the resonant band of the individual isotropic scatterer.
TL;DR: In this paper, a lattice Boltzmann model was proposed for 2D advection and anisotropic dispersion equation (AADE) based on the Bhatnagar, Gross and Krook (BGK) model.
TL;DR: In this paper, a new set of 12 force constants of 2D graphite up to the fourth neighbor are determined by a self-consistent fitting procedure, combined with double-resonance Raman theory.
Abstract: Phonon dispersion relations of a two-dimensional (2D) graphite are obtained by fitting dispersive Raman modes that originate from nonzone center phonons near the $\ensuremath{\Gamma}$ or K point in the Brillouin zone (BZ). A new set of 12 force constants of 2D graphite up to the fourth neighbor are determined by a self-consistent fitting procedure, combined with double-resonance Raman theory. Analytical expressions for eigenvalues and eigenvectors at high symmetry points of the BZ are presented.
TL;DR: The frequency-dependent nature of diffraction acts as a kind of dispersion that modifies the pulse front surface, its group velocity, the envelope form, and the carrier frequency, and these changes can be straightforwardly quantified.
Abstract: Basic concepts of three-dimensional wave packets are applied to the description of transverse effects on the propagation of ultrashort (femtosecond) pulses. The frequency-dependent nature of diffraction acts as a kind of dispersion that modifies the pulse front surface, its group velocity, the envelope form, and the carrier frequency. If the diffracted field in the monochromatic case is known, these changes can be straightforwardly quantified. Finding the propagated pulsed beam field reduces to a well-known and simpler problem of one-dimensional pulse propagation with group velocity dispersion. The method is applied to pulsed Gaussian beams and pulsed Bessel beams. Anomalous pulse front behavior, including superluminality in pulsed Gaussian beams is found. The carrier phase at any point of space is calculated.
TL;DR: In this paper, the authors identify the effective theory appropriate to the propagation of massless bulk fields in brane-world scenarios, and show that the dominant low-energy effect of asymmetric warping in the bulk is to modify the dispersion relation of the effective 4-dimensional modes.
Abstract: We identify the effective theory appropriate to the propagation of massless bulk fields in brane-world scenarios, to show that the dominant low-energy effect of asymmetric warping in the bulk is to modify the dispersion relation of the effective 4-dimensional modes. We show how such changes to the graviton dispersion relation may be bounded through the effects they imply, through loops, for the propagation of standard model particles. We compute these bounds and show that they provide, in some cases, the strongest constraints on nonstandard gravitational dispersions. The bounds obtained in this way are the strongest for the fewest extra dimensions and when the extra-dimensional Planck mass is the smallest. Although the best bounds come for warped 5-D scenarios, for which the 5D Planck Mass is O(TeV), even in 4 dimensions the graviton loop can lead to a bound on the graviton speed which is comparable with other constraints.
TL;DR: In this paper, a comprehensive review of nitrogen-induced modifications of the electronic structure of Ga1−yInyNxAs1−x alloys is carried out, and the results are analyzed in terms of the analytical band anti-crossing model as well as the local density approximation calculations and empirical pseudopotential models.
Abstract: In this paper, we carry out a comprehensive review of the nitrogen-induced modifications of the electronic structure of Ga1−yInyNxAs1−x alloys. We study in detail the behaviour of the conduction-band effective mass as a function of Fermi energy, nitrogen content and pressure. From measurements of the plasma frequency for samples with different electron concentrations we have determined the dispersion relation for the lowest conduction band. We have also studied composition, temperature and pressure dependent optical absorption spectra on free-standing layers of Ga1−yInyNxAs1−x (0 ≤ x ≤ 0.025 and 0 ≤ y ≤ 0.09) lattice-matched to GaAs. Spectroscopic ellipsometry measurements performed in a wide photon energy range from 1.5 to 5.5 eV have been used to determine the energy dependence of the dielectric function as well as the energies of E1, E0' and E2 critical point transitions. Experiments have shown that nitrogen has a large effect on the dispersion relations and on the optical spectra for the conduction-band states close to the Γ point. A much smaller effect has been observed for X and L minima as well as for the valence-band states. We have compared our results with other available experimental data. The results are analysed in terms of the analytical band anti-crossing model as well as the local density approximation calculations and empirical pseudopotential models.
TL;DR: In this paper, Korteweg-de Vries equations were derived for the low-frequency and high-frequency modes of the electron cyclotron in a three-component plasma.
Abstract: Waves propagating perpendicular to a magnetic field in a plasma consisting of electrons, positrons, and ions are studied theoretically and numerically. In a three component plasma, there appears a frequency domain in which the magnetosonic waves cannot propagate; thus, we have two separate modes below the electron cyclotron frequency. Their dispersion relations are discussed. Then, Korteweg–de Vries equations are derived for these modes. A solitary wave of the low-frequency mode has a soliton width 1–103 times as large as the electron skin depth and has an electric potential 1–102 times as large as that in an electron–ion plasma; both of them increase with decreasing ion density. A solitary wave of the high-frequency mode has a soliton width of the order of the electron skin depth and has negligibly small electric potential. Three-fluid simulations show that the low-frequency mode solitary pulse can emit high-frequency mode solitons, if the amplitude of the original pulse is large and the ion density is low.
TL;DR: The dispersion relation for the eigenmodes of a cylindrical hollow waveguide is derived and the family of EH(nus) is shown to be a solution of the wave equation up to the first order under the condition k(0)a >>1, where k( 0) is the light wave number and a the capillary tube radius.
Abstract: The properties of the eigenmodes of a capillary tube are examined in the context of ultrashort intense laser pulse guiding. The dispersion relation for the eigenmodes of a cylindrical hollow waveguide is derived and the family of eigenmodes EH(nus) is shown to be a solution of the wave equation up to the first order under the condition k(0)a >>1, where k(0) is the light wave number and a the capillary tube radius. The expressions of the fields for the eigenmodes are given at zero and first order of a small parameter equal to the ratio of the perpendicular to longitudinal wave number and the absorbed intensity at the wall is estimated.
TL;DR: In this article, the many-impurity Anderson model is applied to compound semiconductor alloys in which metallic anion atoms are partially substituted by highly electronegative atoms at low concentrations.
Abstract: The many-impurity Anderson model is applied to compound semiconductor alloys in which metallic anion atoms are partially substituted by highly electronegative atoms at low concentrations. The interaction between the localized states derived from the electronegative atoms and the Bloch states of the semiconductor matrix is treated in a single-site coherent-potential approximation. The solution for the Green's function provides dispersion relations and broadenings for the conduction-band states. The calculations validate the dispersion relations previously obtained from the two-level band anticrossing model. The restructured dispersion relations and optical absorption coefficient are calculated and compared with experimental results of ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ alloys.
TL;DR: Using scaling and universality arguments, the critical behavior of the parameters of pion propagation is determined and it is predicted that, when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of thepion screening mass.
Abstract: We point out that, in analogy with spin waves in antiferromagnets, all parameters describing the real-time propagation of soft pions at temperatures below the QCD chiral phase transition can be expressed in terms of static correlators. This allows, in principle, the determination of the soft pion dispersion relation on the lattice. Using scaling and universality arguments, we determine the critical behavior of the parameters of pion propagation. We predict that, when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of the pion screening mass. This fact is attributed to the decrease of the pion velocity near the phase transition.
TL;DR: In this article, a resonant inelastic x-ray scattering study of the dispersion relations of charge-transfer excitations in insulating La(2)CuO(4) was performed.
Abstract: We report a resonant inelastic x-ray scattering study of the dispersion relations of charge-transfer excitations in insulating La(2)CuO(4).. These data reveal two peaks, both of which show two-dimensional characteristics. The lowest energy excitation has a gap energy of approximately 2.2 eV at the zone enter, and a dispersion of approximately 1 eV. The spectral weight of this mode becomes dramatically smaller around (pi, pi). The second peak shows a smaller dispersion ( approximately 0.5 eV) with a zone-center energy of approximately 3.9 eV. We argue that these are both highly dispersive exciton modes damped by the presence of the electron-hole continuum.
TL;DR: In this article, a unified theory of the mirror instability in space plasmas is developed, which allows the treatment of more general space plasma equilibria such as the Dory-Guest-Harris (DGH) or Kennel-Ashour-Abdalla (KA) loss cone equilibrium, as well as distributions with power law velocity dependence.
Abstract: [1] A unified theory of the mirror instability in space plasmas is developed. In the standard quasi-hydrodynamic approach, the most general mirror-mode dispersion relation is derived and the growth rate of the mirror instability is obtained in terms of arbitrary electron and ion velocity distribution functions. Finite electron temperature effects and arbitrary electron temperature anisotropies are included. The new dispersion relation allows the treatment of more general space plasma equilibria such as the Dory-Guest-Harris (DGH) or Kennel-Ashour-Abdalla (KA) loss cone equilibria, as well as distributions with power law velocity dependence that are modeled by the family of κ-distributions. Under these conditions, we derive the general kinetic mirror instability growth rate including finite electron temperature effects. As for an example of equilibrium particle distribution, we analyze a large class of κ to suprathermal loss cone distributions in view of application to a variety of space plasmas like the solar wind, magnetosheath, ring current plasma, and the magnetospheres of other planets.
TL;DR: In this paper, a theory for normal mode electromagnetic-spin waves propagating in metal-dielectric-ferromagnetic-dieselric-metal film structures is developed for dual electrically or/and magnetically tunable microwave devices.
Abstract: A theory has been developed for normal mode electromagnetic-spin waves propagating in metal–dielectric-ferromagnetic-dielectric-metal film structures. Dipole and exchange interactions are taken into account. An arbitrary direction of the internal bias magnetic field is assumed. A dispersion equation for hybrid waves is derived. Effects of varying the dielectric constants of the dielectric layers and the geometry of the layered structure are analyzed for the dispersion characteristics of hybrid waves. The obtained results are applied to layered structures containing ferromagnetic and ferroelectric layers that could be used as waveguiding structures for dual electrically or/and magnetically tunable microwave devices.
TL;DR: Using the quasiparticle excitation spectrum derived from a Bogoliubov transformation, the Landau critical velocity is found to be anisotropic and can be widely tuned by varying properties of the dressing laser beams.
Abstract: We consider a two-component atomic gas illumined by two intersecting laser beams which induce Raman coupling between the components. This spatially periodic coupling modifies the dispersion relation of the gas. Properties of a Bose-Einstein condensate of such a gas are strongly affected by this modification. Using the quasiparticle excitation spectrum derived from a Bogoliubov transformation, the Landau critical velocity is found to be anisotropic and can be widely tuned by varying properties of the dressing laser beams.
TL;DR: In this paper, the Ritus E p eigenfunction was extended to the case of spin-1 charged particles in a constant electromagnetic field and used to calculate the one-loop neutrino self-energy in the presence of a strong magnetic field.