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Showing papers on "Dispersion relation published in 1994"


Journal ArticleDOI
TL;DR: In this article, the authors describe in detail how to make numerical calculations of the dispersion relations (the band structure) of these complex objects, and how to calculate transmission through, and reflection from them.
Abstract: Building complex materials with structures on a scale comparable to the wavelength of light offers possibilities for radically changing the way light moves around such materials, in the same way that we engineer atomic structure to vary electronic properties of semiconductors. In this paper we describe in detail how to make numerical calculations of the dispersion relations (the band structure) of these complex objects, and how to calculate transmission through, and reflection from them. Finally these methodologies are applied to a colloidal dispersion of metallic particles at 12% volume filling fraction to reproduce the well known characteristics of strong optical absorption.

457 citations


Journal ArticleDOI
TL;DR: In this article, the resonant excitations of high-n magnetohydrodynamic instabilities by the energetic ions/alpha particles in tokamaks are theoretically analyzed and analytical dispersion relations can be derived via the asymptotic matching analysis.
Abstract: The resonant excitations of high‐n magnetohydrodynamic instabilities by the energetic ions/alpha particles in tokamaks are theoretically analyzed. Here, n is the toroidal mode number. The magnetohydrodynamic eigenmodes, typically, consist of two‐scale structures; one corresponds to the singular (‘‘inertial’’) region and the other the regular (ideal) region. Due to the finite‐size orbits, the energetic particle contributions in the singular region are suppressed. Analytical dispersion relations can be derived via the asymptotic matching analysis. The dispersion relations have the generic form of the ‘‘fishbone’’ dispersion relation [Phys. Rev. Lett. 52, 1122 (1984)] and demonstrate, in particular, the existence of two types of modes; that is, the discrete gap mode and the energetic‐particle continuum mode. Specific expressions are given for both the kinetic ballooning modes and the toroidal Alfven modes.

328 citations


Journal ArticleDOI
TL;DR: Experiments on vertically oscillated granular layers reveal, at a critical acceleration, a well-defined transition from a flat surface to standing wave patterns oscillating at half the excitation frequency.
Abstract: Experiments on vertically oscillated granular layers reveal, at a critical acceleration, a well-defined transition from a flat surface to standing wave patterns oscillating at half the excitation frequency. The patterns observed in a cylindrical container are squares or stripes; a continuous transition between these states occurs when the vibration frequency is varied at constant acceleration. The dispersion relation for these parametric granular waves is similar to that for gravity waves in a fluid, but exhibits a well-defined cutoff associated with the particle size.

262 citations


Journal ArticleDOI
TL;DR: A three-dimensional photonic-band-gap structure built by an orderly stacking of dielectric rods offers a viable geometry to extend the photonic band gap to optical regimes and is different from that previously suggested.
Abstract: We have designed, fabricated, and tested a three-dimensional photonic-band-gap structure. The structure is built by an orderly stacking of dielectric rods. A network analyzer is used to measure the transmission and dispersion relations of electromagnetic waves along several crystal directions. The experimental results are in good agreement with the theoretical calculations. The structure is different from that previously suggested, as it is already used to improve the midgap frequency by almost two orders of magnitude, and it offers a viable geometry to extend the photonic band gap to optical regimes.

255 citations


Journal ArticleDOI
TL;DR: The dispersion relation of photons transmitting through a photonic one-dimensional quasicrystal arranged in a Fibonacci sequence was observed by measuring the spectrum of the phase change of the transmitted light using a Michelson-type interferometer.
Abstract: The dispersion relation of photons transmitting through a photonic one-dimensional quasicrystal arranged in a Fibonacci sequence was observed by measuring the spectrum of the phase change of the transmitted light using a Michelson-type interferometer. The phase spectrum obtained clearly showed the self-similar structure characteristic to dispersion curves of Fibonacci lattices.

123 citations


Journal ArticleDOI
TL;DR: In this article, a general dispersion relation has been derived for waves propagating in a homogeneous plasma subject to dissipation by viscosity and thermal conduction, and no assumptions about the strength of the damping have been made.
Abstract: The possible role of waves in the heating of the solar corona has been investigated. A general dispersion relation has been derived for waves propagating in a homogeneous plasma subject to dissipation by viscosity and thermal conduction. The dissipation mechanisms have been incorporated self-consistently into the equations, and no assumptions about the strength of the damping have been made. Solutions of the sixth-order dispersion relation provide information on how the damping of both slow and fast mode waves depends upon the plasma density, temperature, field strength, and angle of propagation relative to the background magnetic field. We provide a detailed comparison to the standard approach, which is to solve for the wave quantities in the absence of dissipation and then to use these quantities in expressions for the heating due to viscosity and thermal conduction.

117 citations


Journal ArticleDOI
TL;DR: In this article, the dispersion curves of electromagnetic waves propagating in a structure consisting of an infinite array of parallel, infinitely long, dielectric rods of arbitrary cross-section, embedded in a medium characterized by a 2D Bravais lattice, were calculated.
Abstract: By the use of the plane wave method we have calculated the dispersion curves (photonic band structure) of electromagnetic waves propagating in a structure consisting of an infinite array of parallel, infinitely long, dielectric rods of arbitrary cross-section, characterized by a dielectric constant ea, embedded in a medium characterized by a dielectric constant eb, when the intersections of the axes of the rods with a perpendicular plane form a two-dimensional Bravais lattice. In contrast with earlier calculations of the photonic band structures of two-dimensional, periodic, dielectric structures, in the present work the electromagnetic waves are assumed to propagate out of the plane perpendicular to the rods. In numerical calculations we study a triangular lattice of air cylinders in a dielectric medium, which has recently been shown to possess a band gap common to waves of both E and H polarization for propagation in the plane perpendicular to the rods. The shifts of the edges of this absolute ...

100 citations


Journal ArticleDOI
TL;DR: Measurements of the zeroth-order transmittance have been performed on gold gratings with periods of 1 and 2 micrometers in the near-infrared region which are in agreement with theoretical results.
Abstract: A resonance phenomenon in the zeroth diffraction order of a gold-wire grating is explained by the excitation of surface polaritons. This effect is connected with a strong enhancement of the electromagnetic fields on the wire surface and consequently with a peak of power losses in the grating material. Measurements of the zeroth-order transmittance have been performed on gold gratings with periods of 1 and 2 micrometers in the near-infrared region which are in agreement with theoretical results. Furthermore, dispersion relations of the first-order coupling mode are presented having large energy gaps in the center of the Brillouin zone. It is shown that this energy gap strongly depends on the wire profile. In this coupling branch, however, practically no dispersion could be observed for optical wavelengths less than the grating period.

90 citations


Journal ArticleDOI
01 Sep 1994-Chaos
TL;DR: A realistic reaction-diffusion model of the CO oxidation on the Pt(110) surface under vacuum conditions is studied, showing a dominance of the global gas-phase coupling over local coupling via surface diffusion and the possibility of wave instabilities under excitable conditions.
Abstract: Among heterogeneously catalyzed chemical reactions, the CO oxidation on the Pt(110) surface under vacuum conditions offers probably the greatest wealth of spontaneous formation of spatial patterns. Spirals, fronts, and solitary pulses were detected at low surface temperatures (T<500 K), in line with the standard phenomenology of bistable, excitable, and oscillatory reaction-diffusion systems. At high temperatures (T greater, similar 540 K), more surprising features like chemical turbulence and standing waves appeared in the experiments. Herein, we study a realistic reaction-diffusion model of this system, with respect to the latter phenomena. In particular, we deal both with the influence of global coupling through the gas phase on the oscillatory reaction and the possibility of wave instabilities under excitable conditions. Gas-phase coupling is shown to either synchronize the oscillations or to yield turbulence and standing structures. The latter findings are closely related to clustering in networks of coupled oscillators and indicate a dominance of the global gas-phase coupling over local coupling via surface diffusion. In the excitable regime wave instabilities in one and two dimensions have been discovered. In one dimension, pulses become unstable due to a vanishing of the refractory zone. In two dimensions, turbulence can also emerge due to spiral breakup, which results from a violation of the dispersion relation.

90 citations


Journal ArticleDOI
TL;DR: In this article, the dispersion curves of surface phonons in insulators, semiconductors and metals have been measured and anomalously soft surface phonon branches below the longitudinal acoustic band were observed.

89 citations


Journal ArticleDOI
TL;DR: In this paper, a 2×2 transfer matrix approach is used to study the elastic response of multilayered systems, and the dispersion relations of the normal modes for both longitudinal and transverse waves are calculated for finite and semi-inifinite structures.
Abstract: A 2×2 transfer matrix approach is used to study the elastic response of multilayered systems. Superlattices with a period of n layers are considered to calculate the dispersion relations of the normal modes for both longitudinal and transverse waves, and the reflectivity of longitudinal modes for finite and semi‐infinite structures. Numerical results of the dispersion relation for a two‐ and three‐layer period superlattice are presented to show the band structure of wave propagation. For transverse waves, it is considered that the single layer may support surface modes and it is found that their interaction with those of the adjacent layers also yield a band structure. The calculated reflectivity of longitudinal elastic waves for the semi‐inifinite superlattices resembles the allowed and forbidden regions of the dispersion relations. The theoretical reflectivity curves of sound waves are compared with the experimental results for the three‐layer systems. A good agreement between theory and experiment is obtained.

Journal ArticleDOI
TL;DR: In this article, the attenuation coefficients of anisotropic wood were measured with the through-transmission technique and some experimental factors that can affect the determination of attenuation coefficient were related to the geometry of the radiation field, and to the scattering and absorption of ultrasonic energy by the solid.

Journal ArticleDOI
TL;DR: In this paper, the authors used linear fitting methods with approximate forms of the dispersion relation to recover density normalized elastic moduli of a transversely isotropic anisotropic medium from data consisting of qP or qSV phase velocities measured in multiple directions.
Abstract: The problem of recovering density-normalized elastic moduli of a transversely isotropic anisotropic medium from data consisting of qP or qSV phase velocities measured in multiple directions is addressed. Previous studies have used linear fitting methods with approximate forms of the dispersion relation. Here, it is shown that with algebraic manipulation, and a prior estimate of the squared shear velocity along the symmetry axis (A55), it is possible to use simple linear methods with an exact alternative form of the anisotropic dispersion relation. The method is demonstrated with an application to data from a walkaway vertical seismic profile (VSP) experiment and then used as a tool to address several questions raised by that experiment. It is shown that given data with realistically achievable accuracy, the prior estimate of A55 cannot be improved by optimizing the fit to qP data. It is shown that a near perfect fit by a transversely isotropic medium with a vertical symmetry axis (TIV) model to qP data collected in a single vertical plane does not rule out azimuthal anisotropy. Finally, it is shown that a variation of the method, combined with an algorithm suggested by Hood and Schoenberg, suggests a practical way to determine from walkaway VSP data, all the parameters of an orthorhombic medium formed by adding vertical fractures to a transversely isotropic medium.

Journal ArticleDOI
TL;DR: The polariton Hamiltonian for a quantum well embedded in a cavity of finite width is derived and the exciton-light interaction is formulated in second quantization and the photon self-interaction term A2 is included.
Abstract: The polariton Hamiltonian for a quantum well embedded in a cavity of finite width is derived. The exciton-light interaction is formulated in second quantization and the photon self-interaction term A2 is included. The importance of the A2 term turns out to be relevant in the case of large values of the cavity width. By solving the equation of motion the dispersion relations for upper and lower polaritons are found. A comparison is made with existing measurements of polariton absorption peaks. The limit of infinite cavity width is carried out and the known results for a quantum well in an infinite medium are recovered.

Journal ArticleDOI
TL;DR: In this paper, the decomposition phenomenon of a nonlinear wave train passing over a submerged shelf without breaking has been investigated by a previously developed numerical model, which is triggered by higher harmonic generation and nonlinear resonant interaction over the shelf.

Journal ArticleDOI
TL;DR: It is argued that the generic nature of the quasiparticle dispersion relation observed in these materials arises from the strong Coulomb interaction and reflects the hole-spin correlations rather than the one-electron interactions which customarily determine the band structure.
Abstract: The momentum dispersion of the peak structure of the single-particle spectral weight A(p,\ensuremath{\omega}) of the two-dimensional Hubbard model is discussed. Using results obtained from Monte Carlo simulations on lattices up to 12\ifmmode\times\else\texttimes\fi{}12 in size, we determine the low-lying quasiparticle dispersion relation. This dispersion relation is anomalously flat near the (\ensuremath{\pi},0) and (0,\ensuremath{\pi}) points of the Brillouin zone, similar to the results of recent angular resolved photoemission measurements of the hole-doped cuprates. We argue that the generic nature of the quasiparticle dispersion relation observed in these materials arises from the strong Coulomb interaction and reflects the hole-spin correlations rather than the one-electron interactions which customarily determine the band structure.

Journal ArticleDOI
TL;DR: The stability of short laser pulses propagating through plasma channels is investigated theoretically and the spatiotemporal growth of a pure dipole perturbation is evaluated in various parameter regimes.
Abstract: The stability of short laser pulses propagating through plasma channels is investigated theoretically. Perturbations to the laser pulse are shown to modify the ponderomotive pressure, which distorts the dielectric properties of the plasma channel. The channel perturbation then further distorts the laser pulse. A set of coupled mode equations is derived, and a matrix dispersion relation is obtained analytically for the special case of a quadratic radial density variation. As an example, the spatiotemporal growth of a pure dipole perturbation is evaluated in various parameter regimes. Mechanisms for suppressing the instability are discussed.

Journal ArticleDOI
TL;DR: In this paper, a modified envelope method, which includes the consideration of the light intensity loss from the back surface of the substrate, was developed and shown to be a simple and convenient tool for obtaining the optical properties and the thickness of the film by using the transmission spectra alone in the medium and weak absorption regions.
Abstract: A modified envelope method, which includes the consideration of the light intensity loss from the back surface of the substrate, was developed and shown to be a simple and convenient tool for obtaining the optical properties and the thickness of the film by using the transmission spectra alone in the medium and weak absorption regions. In the near-optical band gap region, both the transmission and the reflection spectra were used to calculate the optical constants of the films. This technique was applied to the thin films of PZT solid solutions across the entire composition range. The film thickness derived from the envelope method was cross-checked by a computer simulation method and was found to have an accuracy better than 2%. In addition, the refractive indices were fitted to a simple Sellmeier-type equation for determining the dispersion constants for PZT films. The valid wavelength range of these dispersion relations was from 350 to 2000 nm. The refractive index of the PZT films decreased linearly with increasing zirconium content. On the other hand, the optical band gap energy of the PZT films increased with increasing zirconium content.

Journal ArticleDOI
TL;DR: An approach to obtaining efficient single pass mode conversion at high parallel wavenumber from the fast magnetosonic wave to the slow ion Bernstein wave, in a two ion species tokamak plasma, is described and can be adapted to off-axis current drive for current profile control.
Abstract: An approach to obtaining efficient single pass mode conversion at high parallel wavenumber from the fast magnetosonic wave to the slow ion Bernstein wave, in a two ion species tokamak plasma, is described. The intent is to produce localized electron heating or current drive via the mode converted slow wave. In particular, this technique can be adapted to off-axis current drive for current profile control. Modelling for the case of deuterium-tritium plasmas in TFTR is presented.

Journal ArticleDOI
TL;DR: In this paper, the dispersion relations for longitudinal and transverse collective modes from 0.026 to 1 A−1 for a range of temperatures were investigated and the authors showed that the viscoelastic approximation describes the data satisfactorily.
Abstract: Experimental and simulation studies of sound propagation in water have observed, at large wave vectors k (k≳0.25 A−1), a longitudinal sound mode with a velocity of about 3500 m/s, more than twice the hydrodynamic sound velocity. The relation between the hydrodynamic sound mode and the high frequency mode has been the center of contrasting interpretations. In this paper, we report extensive molecular dynamics simulations designed ad hoc to explore the intermediate and low k part of the collective spectrum. We calculate the dispersion relations for longitudinal and transverse collective modes from 0.026 to 1 A−1 for a range of temperatures. At all temperatures studied, the sound velocity increases with k. At the highest studied temperature, the sound velocity changes from values comparable to hydrodynamic sound velocity to ones observed by neutron scattering experiments. We show that the viscoelastic approximation describes the data satisfactorily. We also perform normal mode analysis of quenched liquid configurations to obtain further information about the behavior observed at intermediate frequencies (50–100 cm−1). We find further positive dispersion of the sound branch at these frequencies and indications which suggest the interaction of the sound branch with localized modes as the origin of such dispersion.

Journal ArticleDOI
TL;DR: From a selfconsistent theory for dust charging, the linear dispersion relation for ion acoustic waves was derived in this article, where it was shown that the waves are damped because of energy exchange with the dust-charging process.
Abstract: From a self‐consistent theory for dust‐charging, the linear dispersion relation for ion acoustic waves is derived. It is shown that the waves are damped because of energy exchange with the dust‐charging process.

Journal ArticleDOI
TL;DR: In this paper, a nonlocal semiclassical theory of the optical response of excitons in multiple quantum wells is formulated in a transfer-matrix scheme and applied to a derivation of the dispersion of exciton-polaritons.

Journal ArticleDOI
TL;DR: In this paper, the authors reported the frequency and temperature dependence of the dielectric constant of polycrystalline ErFe 2 O 4-δ with different degrees of oxygen deficiency δ and concluded that the elementary process of the dispersion is related to electron hopping between Fe 2 and Fe 3+ ions.
Abstract: We report the frequency and the temperature dependence of the dielectric constant of polycrystalline ErFe 2 O 4-δ with different degrees of oxygen deficiency δ. A large dielectric relaxation, with the order of magnitude of 10 4 and nearly of the Debye type, is observed in the magnetically ordered states within the temperature and frequency ranges of 150 K to 290 K and 1 kHz to 3 MHz, respectively. The dispersion is larger in the sample with more oxygen deficiency. From the temperature dependence of the characteristic frequency, we conclude that the elementary process of the dispersion is related to electron hopping between Fe 2+ and Fe 3+ ions. A large value of the dielectric constant is consistent with the existence of spontaneous polarization in the magnetic phases of this oxide. We propose that the motion of the polarization domain boundaries is a determining factor of low-frequency dielectric constant.

Journal ArticleDOI
TL;DR: In this paper, the dispersion relation for helicon waves in a cold plasma of radially varying density has been reduced to compact form, and the radial eigenmodes have been computed for different density profiles.
Abstract: The dispersion relation for helicon waves in a cold plasma of radially varying density has been reduced to compact form, and the radial eigenmodes have been computed for different density profiles The results show a marked asymmetry between the left- and right-hand circularly polarized modes: the m=-1 (left) mode has a centrally peaked wave intensity and resonates with a much higher central density than the m=+1 mode Positive feedback is therefore possible, leading to nonlinear channelling of the discharge At a radius where the density falls to a certain value, a singularity arises in the coefficients of the wave equation; care must be taken in integrating through this point This singularity has no physical significance The marked difference between the m=+1 and -1 modes in a non-uniform plasma is caused by a difference in sign of the electron drift along the density gradient Energy deposition is peaked near the radius of the peak in Bz, so that broad, uniform density profiles can be obtained by using the m=+1 mode and narrow, dense columns by using the m=-1 mode These results explain many features observed by various groups over the past two years

Journal ArticleDOI
TL;DR: In this paper, the authors measured the refractive index of binary tellurite glasses with various modifiers in the wavelength range of 0.40-1.71 μm using the minimum deviation method.
Abstract: The refractive index of binary tellurite glasses with various modifiers was measured down to the fifth decimal place in the wavelength range of 0.40-1.71 μm using the minimum-deviation method. An empirical equation based on the single-oscillator Drud-Voigt dispersion equation, n d 2 =A.Nfλ 0 2 +B, is obtained, where n d is the refractive index at 0.5876 μm, N is the number of molecules in a unit volume, f is the average oscillator strength, λ 0 is the average resonance wavelength, and A and B are constants. The refractive index n d of tellurite glasses is substantially determined by the resonance wavelength at the ultraviolet region, which is affected by the main constituent, TeO 2

Journal ArticleDOI
TL;DR: In this paper, the authors used the full electromagnetic dispersion relation derived from linear Vlasov theory in order to examine which of the plasma modes, with observed properties, are unstable in an isotropic Maxwellian plasma in the presence of backstreaming proton beams consistent with Voyager 2 observations at Saturn.
Abstract: Recent studies of low-frequency electromagnetic waves upstream of the Saturn bow shock have shown that these waves, in contrast to those at Earth, are observed not in one, but in at least two, distinct frequency bands. The results of wave mode identification based on the Hall-magnetohydrodynamic (MHD) model of plasma and observed wave polarization suggested that these waves propagate in the high beta intermediate mode. However, the underlying instability was not unambiguously determined. In the present paper we use the full electromagnetic dispersion relation derived from linear Vlasov theory in order to examine which of the plasma modes, with observed properties, are unstable in an isotropic Maxwellian plasma in the presence of backstreaming proton beams consistent with Voyager 2 observations at Saturn. As a result we find that the unstable 'Alfvenic' beam mode, as well as resonant and non-resonant fast magnetosonic modes have properties consistent with the data. Moreover, we find that in contrast to the Earth's upstream waves, at Saturn no 'kinetic' normal mode can account for the observed magnetic polarization.

Journal ArticleDOI
TL;DR: In this paper, the effect of intramonomer electron correlation on the dispersion term of a triangle trimer has been investigated using the diagrammatic many-body perturbation theory.
Abstract: Using the diagrammatic many‐body perturbation theory, various three‐body dispersion terms that appear in the intermolecular Mo/ller–Plesset perturbation theory (MPPT) are identified and classified with regard to the effects of intramonomer electron correlation on the dispersion term. Via the connection with the supermolecular MPPT, it is demonstrated how the leading dispersion nonadditivities arise within supermolecular calculations that employ MPPT or coupled cluster formalisms. The numerical calculations for He3, Ne3, and Ar3 in triangular geometries fully confirm theoretical predictions. The calculated values of dispersion nonadditivity clearly show that the coupled cluster theory with single, double, and noniterative triple excitations provides the proper framework for the efficient inclusion of the intramonomer correlation effects in dispersion nonadditivity. The convergence of the two‐body and three‐body terms is shown to be very similar if we compare the three‐body terms of an order higher than the two‐body terms. This pattern is used to provide the estimates of the total nonadditivities in the three trimers within a few percent accuracy.

Journal ArticleDOI
TL;DR: In this article, the dispersion relations of a two-dimensional TLM mesh and a three-dimensional LTLM mesh with condensed symmetric nodes are calculated using a generalized method which can be applied to any TLM node described by square scattering and propagation matrices of equal dimension.
Abstract: The dispersion relations of a two-dimensional TLM mesh and a three-dimensional TLM mesh with condensed symmetric nodes are calculated. For the calculation of the TLM dispersion relations, we use a generalized method which can be applied to any TLM node described by square scattering and propagation matrices of equal dimension. Introducing the FDTD Hilbert space representation, it is shown that the method is closely related to the method of calculating FDTD dispersion relations. >

Book
01 Aug 1994
TL;DR: In this article, the unification of the optical potential by dispersion relations nuclear charge and matter distributions is discussed, where the nuclear structure of a composite particle is assumed to be independent of its optical potential.
Abstract: The optical potential the spin-orbit potential the energy and radial variations nuclear structure effects the optical potential for composite particles the unification of the optical potential by dispersion relations nuclear charge and matter distributions.

Journal ArticleDOI
TL;DR: The dispersion relation for the overdamped bending modes of a membrane bound to a substrate by an attractive potential is determined and the damping rate γ as a function of the wave vector q behaves, for small q, like γ∼q2 arising from the interplay between the hydrodynamic damping by the surrounding liquid and the restoring force in the binding potential.
Abstract: The dispersion relation for the overdamped bending modes of a membrane bound to a substrate by an attractive potential is determined. The damping rate γ as a function of the wave vector q behaves, for small q, like γ∼q2 arising from the interplay between the hydrodynamic damping by the surrounding liquid and the restoring force in the binding potential. With increasing wave vector q, various crossovers can occur, leading to the possibility of nonmonotonic damping where γ decreases with q as ∼1/q.