Showing papers on "Dispersion relation published in 2006"

Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization

Abstract: We present a numerical analysis of surface plasmon waveguides exhibiting both long-range propagation and spatial confinement of light with lateral dimensions of less than 10% of the free-space wavelength. Attention is given to characterizing the dispersion relations, wavelength-dependent propagation, and energy density decay in two-dimensional Ag/SiO2/Ag structures with waveguide thicknesses ranging from 12 nm to 250 nm. As in conventional planar insulator-metal-insulator (IMI) surface plasmon waveguides, analytic dispersion results indicate a splitting of plasmon modes—corresponding to symmetric and antisymmetric electric field distributions—as SiO2 core thickness is decreased below 100 nm. However, unlike IMI structures, surface plasmon momentum of the symmetric mode does not always exceed photon momentum, with thicker films (d~50 nm) achieving effective indices as low as n=0.15. In addition, antisymmetric mode dispersion exhibits a cutoff for films thinner than d=20 nm, terminating at least 0.25 eV below resonance. From visible to near infrared wavelengths, plasmon propagation exceeds tens of microns with fields confined to within 20 nm of the structure. As the SiO2 core thickness is increased, propagation distances also increase with localization remaining constant. Conventional waveguiding modes of the structure are not observed until the core thickness approaches 100 nm. At such thicknesses, both transverse magnetic and transverse electric modes can be observed. Interestingly, for nonpropagating modes (i.e., modes where propagation does not exceed the micron scale), considerable field enhancement in the waveguide core is observed, rivaling the intensities reported in resonantly excited metallic nanoparticle waveguides.

Dynamical polarization of graphene at finite doping

Abstract: The polarization of graphene is calculated exactly within the random phase approximation for arbitrary frequency, wavevector and doping. At finite doping, the static susceptibility saturates to a constant value for low momenta. At q = 2kF it has a discontinuity only in the second derivative. In the presence of a charged impurity this results in Friedel oscillations which decay with the same power law as the Thomas–Fermi contribution, the latter being always dominant. The spin density oscillations in the presence of a magnetic impurity are also calculated. The dynamical polarization for low q and arbitrary ω is employed to calculate the dispersion relation and the decay rate of plasmons and acoustic phonons as a function of doping. The low screening of graphene, combined with the absence of a gap, leads to a significant stiffening of the longitudinal acoustic lattice vibrations.

Giant Magnons

Abstract: Studies of ${\cal N}=4$ super Yang Mills operators with large R-charge have shown that, in the planar limit, the problem of computing their dimensions can be viewed as a certain spin chain These spin chains have fundamental ``magnon'' excitations which obey a dispersion relation that is periodic in the momentum of the magnons This result for the dispersion relation was also shown to hold at arbitrary 't Hooft coupling Here we identify these magnons on the string theory side and we show how to reconcile a periodic dispersion relation with the continuum worldsheet description The crucial idea is that the momentum is interpreted in the string theory side as a certain geometrical angle We use these results to compute the energy of a spinning string We also show that the symmetries that determine the dispersion relation and that constrain the S-matrix are the same in the gauge theory and the string theory We compute the overall S-matrix at large 't Hooft coupling using the string description and we find that it agrees with an earlier conjecture We also find an infinite number of two magnon bound states at strong coupling, while at weak coupling this number is finite

Refractive indices of human skin tissues at eight wavelengths and estimated dispersion relations between 300 and 1600 nm

Abstract: The refractive index of human skin tissues is an important parameter in characterizing the optical response of the skin. We extended a previously developed method of coherent reflectance curve measurement to determine the in vitro values of the complex refractive indices of epidermal and dermal tissues from fresh human skin samples at eight wavelengths between 325 and 1557 nm. Based on these results, dispersion relations of the real refractive index have been obtained and compared in the same spectral region.

Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines

Abstract: Here we discuss the theory and analyze in detail the guidance properties of linear arrays of metamaterial/plasmonic small particles as nano-scale optical nanotransmission lines, including the effect of material loss. Under the assumption of dipolar approximation for each particle, which is shown to be accurate in the geometry of interest here, we develop closed-form analytical expressions for the eigen-modal dispersion in such arrays. With the material loss included, the conditions for minimal absorption and maximum bandwidth are derived analytically by studying the properties of such dispersion relations. Numerical examples with realistic materials including their ohmic absorption and frequency dispersion are presented. The analytical properties discussed here also provide some further physical insights into the mechanisms underlying the sub-diffraction guidance in such arrays and their fundamental physical limits. Possibility of guiding beams with sub-wavelength lateral confinement and reasonably low decay is discussed offering the possible use of this technique at microwave, infrared and optical frequencies. Interpretation of these results in terms of nanocircuit concepts is presented, and possible extension to 2-D and 3-D nanotrasnsmission line optical metamaterials is also foreseen.

Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains

Abstract: We show that guiding of optical signals in chains of metal nanoparticles is subject to a surprisingly complex dispersion relation. Retardation causes the dispersion relation for transverse modes to split in two anticrossing branches, as is common for polaritons. While huge radiation losses occur above the light line, just below the light line the micron-sized loss lengths are much longer than expected. The anticrossing allows one to create highly localized energy distributions in finite arrays that can be tuned via the illumination wavelength. Our results apply to all linear chains of coupled resonant scatterers.

Spatial dispersion and negative refraction of light

Abstract: Negative refraction occurs at interfaces as a natural consequence of the negative group velocity of waves in one of the interfacing media. The historical origin of this understanding of the phenomenon is briefly discussed. We consider several physical systems that may exhibit normal electromagnetic waves (polaritons) with negative group velocity at optical frequencies. These systems are analyzed in a unified way provided by the spatial dispersion framework. The framework utilizes the notion of the generalized dielectric tensor eij(ω, k) representing the electromagnetic response of the medium to perturbations of frequency ω and wave vector k. Polaritons with negative group velocity can exist in media (whether in natural or in artificial meta-materials) with a sufficiently strong spatial dispersion. Our examples include both gyrotropic and nongyrotropic systems, and bulk and surface polariton waves. We also discuss the relation between the spatial dispersion approach and the more familiar, but more restricted, description involving the dielectric permittivity e(ω) and the magnetic permeability μ(ω) .

Channel plasmon-polaritons: modal shape, dispersion, and losses

Abstract: We theoretically study channel plasmon-polaritons (CPPs) with a geometry similar to that in recent experiments at telecommunication wavelengths [Bozhevolnyi et al., Nature 440, 508 (2006)]. The CPP modal shape, dispersion relation, and losses are simulated by using the multiple multipole method and the finite difference time domain technique. It is shown that, with an increase of the wavelength, the fundamental CPP mode shifts progressively toward the groove opening, ceasing to be guided at the groove bottom and becoming hybridized with wedge plasmon-polaritons running along the groove edges.

Phonon confinement studies in nanocrystalline anatase‐TiO2 thin films by micro Raman spectroscopy

Abstract: Raman studies were performed on titania thin films prepared by polyethylene glycol (PEG) assisted, low-temperature, sol–gel method. The Raman spectra of the films show a systematic blue shift in the peak position and a broadening in the full width at half-maximum (FWHM) when compared with those of the bulk anatase TiO2 powder. Several reports have appeared indicating this kind of peak shift and broadening of FWHM, which were attributed to the confinement of phonons in the anatase nanocrystallites. In this paper, we report an analysis of quantum size effect in the Raman spectra of nanocrystalline TiO2 thin films performed by utilizing the phonon dispersion relation of the anatase phase which has been obtained from a work based on density functional perturbation theory (DFPT). For comparison purposes the quantum size effect calculations have also been done utilizing the dispersion relations of the rutile phase. There is good agreement between the crystallite sizes evaluated from the equally weighted Raman line intensity of the dispersion relations obtained from the DFPT and those determined by X-ray diffraction. Copyright © 2006 John Wiley & Sons, Ltd.

Anomaly of Optical Phonon in Monolayer Graphene

Abstract: The frequency shift and broadening of long-wavelength optical phonons due to interactions with electrons are calculated in a monolayer graphene as a function of the electron density. The broadening disappears and the frequency shift exhibits a logarithmic singularity when the Fermi energy is half of the energy of the optical phonon. The shift increases in proportion to the Fermi energy for sufficiently high electron density.

Phonons in a one-dimensional microfluidic crystal

Abstract: The development of a general theoretical framework for describing the behaviour of a crystal driven far from equilibrium has proved difficult1. Microfluidic crystals, formed by the introduction of droplets of immiscible fluid into a liquid-filled channel, provide a convenient means to explore and develop models to describe non-equilibrium dynamics2,3,4,5,6,7,8,9,10,11. Owing to the fact that these systems operate at low Reynolds number (Re), in which viscous dissipation of energy dominates inertial effects, vibrations are expected to be over-damped and contribute little to their dynamics12,13,14. Against such expectations, we report the emergence of collective normal vibrational modes (equivalent to acoustic ‘phonons’) in a one-dimensional microfluidic crystal of water-in-oil droplets at Re∼10−4. These phonons propagate at an ultra-low sound velocity of ∼100 μm s−1 and frequencies of a few hertz, exhibit unusual dispersion relations markedly different to those of harmonic crystals, and give rise to a variety of crystal instabilities that could have implications for the design of commercial microfluidic systems. First-principles theory shows that these phonons are an outcome of the symmetry-breaking flow field that induces long-range inter-droplet interactions, similar in nature to those observed in many other systems including dusty plasma crystals15,16, vortices in superconductors17,18, active membranes19 and nucleoprotein filaments20.

Collisionality and magnetic geometry effects on tokamak edge turbulent transport. I. A two-region model with application to blobs

Abstract: A two-region model is proposed to study the effect of collisionality and magnetic geometry on electrostatic turbulence and on the propagation of filamentary coherent structures (blobs) in the edge and scrape-off layer. The model invokes coupled vorticity and continuity equations in two different spatial regions along the magnetic field, taking into account the effect of magnetic field fanning and shear, e.g., near magnetic X-points. A linear dispersion relation for unstable modes illustrates the physics of mode disconnection (ballooning) along the magnetic field and its dependence on collisionality and wave number (scale size). Employing an invariant scaling analysis, dimensionless parameters for the nonlinear model are developed and used to describe the regimes of the system. A blob correspondence rule is postulated to relate the linear mode growth rates and regimes to the convective velocity of blobs. Nonlinear numerical simulations of blob convection show good agreement with a blob dispersion relation ...

Collective mode of homogeneous superfluid Fermi gases in the BEC-BCS crossover

Abstract: We perform a detailed study of the collective mode across the whole crossover from the Bose-Einstein condensate (BEC)-to the BCS regime in fermionic gases at zero temperature, covering the whole range of energy beyond the linear regime. This is done on the basis of the dynamical BCS model. We recover first the results of the linear regime in a simple form. Then specific attention is paid to the nonlinear part of the dispersion relation and its interplay with the continuum of single-fermionic excitations. In particular we consider in detail the merging of the collective mode into the continuum of single-fermionic excitations. This occurs not only on the BCS side of the crossover, but also slightly beyond unitarity on the BEC side. Another remarkable feature is the very linear behavior of the dispersion relation in the vicinity of unitarity almost up to merging with the continuum. Finally, while on the BEC side the mode is quite analogous to the Bogoliubov mode, a difference appears at high wave vectors. On the basis of our results we determine the Landau critical velocity in the BEC-BCS crossover which is found to be largest close to unitarity. Our investigation has revealed interesting qualitative features whichmore » deserve experimental exploration as well as further theoretical studies by more sophisticated means.« less

Propagation of surface acoustic waves through sharply bent two-dimensional phononic crystal waveguides using a finite-difference time-domain method

Abstract: In this paper, we adopt the finite-difference time-domain (FDTD) method to analyze surface acoustic waves propagating in two-dimensional phononic waveguides. To implement the FDTD program for dealing with surface acoustic waves, the Bloch theorem and absorbing boundary conditions are employed to deal with the periodic boundary condition and reflection from a numerical boundary. A phononic crystal consisting of circular steel cylinders that form a square lattice in an epoxy matrix is considered as an example to study phononic crystal waveguides. The dispersion relation and displacement fields are calculated to identify the band gaps and eigenmodes. The result shows the existence of a complete band gap of surface waves and thus an acoustic waveguide is created accordingly. Eigenmodes of surface waves inside the waveguide are indicated and pseudo surface acoustic waves propagating inside the straight waveguide are demonstrated. Further, waveguides with a sharp bend are reported and an improved design is suggested to enhance energy transmission.

The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides.

Abstract: We have studied the dispersion of ultrafast pulses in a photonic crystal waveguide as a function of optical frequency, in both experiment and theory. With phase-sensitive and time-resolved near-field microscopy, the light was probed inside the waveguide in a non-invasive manner. The effect of dispersion on the shape of the pulses was determined. As the optical frequency decreased, the group velocity decreased. Simultaneously, the measured pulses were broadened during propagation, due to an increase in group velocity dispersion. On top of that, the pulses exhibited a strong asymmetric distortion as the propagation distance increased. The asymmetry increased as the group velocity decreased. The asymmetry of the pulses is caused by a strong increase of higher-order dispersion. As the group velocity was reduced to 0.116(9)·c, we found group velocity dispersion of -1.1(3)·106 ps2/km and third order dispersion of up to 1.1(4)·105 ps3/km. We have modelled our interferometric measurements and included the full dispersion of the photonic crystal waveguide. Our mathematical model and the experimental findings showed a good correspondence. Our findings show that if the most commonly used slow light regime in photonic crystals is to be exploited, great care has to be taken about higher-order dispersion.

High-frequency electron drift instability in the cross-field configuration of Hall thrusters

Abstract: A systematic study of a high-frequency electron drift instability is presented. It has very large wave numbers corresponding to wavelengths close to the electron gyroradius. The three-dimensional dispersion relation is derived for a model of a crossed electric and magnetic field configuration existing in the Hall thruster. It is shown that the instability develops in packets of oblique unstable modes perpendicular to the magnetic field. The evolution of the instability is also studied for distorted electron distribution functions obtained in particle-in-cell simulations.

On the spectra of carbon nano-structures

Abstract: An explicit derivation of dispersion relations and spectra for periodic Schrodinger operators on carbon nano-structures (including graphen and all types of single-wall nano-tubes) is provided.

Multispin giant magnons

Abstract: We investigate giant magnons from classical rotating strings in two different backgrounds. First we generalize the solution of Hofman and Maldacena and investigate new magnon excitations of a spin chain which are dual to a string on RxS{sup 5} with two nonvanishing angular momenta. Allowing string dynamics along the third angle in the five sphere, we find a dispersion relation that reproduces the Hofman and Maldacena one and the one found by Dorey for the two spin case. In the second part of the paper we generalize the two 'spin' giant magnon to the case of {beta}-deformed AdS{sub 5}xS{sup 5} background. We find agreement between the dispersion relation of the rotating string and the proposed dispersion relation of the magnon bound state on the spin chain.

Stochastic Acceleration of 3He and 4He in Solar Flares by Parallel-propagating Plasma Waves: General Results

Abstract: We study the acceleration in solar flares of 3He and 4He from a thermal background by parallel-propagating plasma waves with a general broken power-law spectrum. The exact dispersion relation for a cold plasma is used to describe the relevant wave modes, and the Coulomb collision loss and escape processes are included. Under the quasi-linear approximation, the pitch-angle-averaged acceleration time of α-particles is at least 1 order of magnitude longer than that of 3He ions at low energies and starts to approach that of 3He beyond a few tens of keV nucleon-1. Because their loss and escape times are comparable, the acceleration of 4He is suppressed significantly at low energies, and the spectrum of the accelerated α-particles is always softer than that of 3He. Quantitative results depend primarily on the wave generation and damping length scales, the electron plasma to gyrofrequency ratio, and the intensity of turbulence. The model gives a reasonable account of the observed low-energy 3He and 4He fluxes and spectra in the impulsive solar energetic particle events observed with the Advanced Composition Explorer. Other acceleration processes and/or stochastic acceleration by other wave modes seem to be required to explain the occasionally observed decrease of 3He to 4He ratio at energies beyond a few MeV nucleon-1.

Frozen light in photonic crystals with degenerate band edge.

Abstract: Consider a plane monochromatic wave incident on a semi-infinite periodic structure. What happens if the normal component of the transmitted wave group velocity vanishes? At first sight, zero normal component of the transmitted wave group velocity simply implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possible outcome. Instead, the transmitted wave can appear in the form of a frozen mode with very large diverging amplitude and either zero, or purely tangential energy flux. The field amplitude in the transmitted wave can exceed that of the incident wave by several orders of magnitude. There are two qualitatively different kinds of frozen mode regime. The first one is associated with a stationary inflection point of electromagnetic dispersion relation. This phenomenon has been analyzed in our previous papers. Now, our focus is on the frozen mode regime related to a degenerate photonic band edge. An advantage of this phenomenon is that it can occur in much simpler periodic structures. This spectacular effect is extremely sensitive to the frequency and direction of propagation of the incident plane wave. These features can be very attractive in a variety of practical applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc.

Kinetic Limit for Wave Propagation in a Random Medium

Abstract: We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of the order √ e. The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit e → 0, the disorder-averaged Wigner function on the kinetic scale, time and space of order e −1 , is governed by a linear Boltzmann equation.

Excitation spectra of the spin- 1 2 triangular-lattice Heisenberg antiferromagnet

Abstract: We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-(1)/(2) triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find rotonlike minima at special wave vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [Phys. Rev. B74, 180403(R) (2006)]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a nonlinear sigma model description of the finite-temperature properties is only applicable at temperatures < 0.1J. Finally, we review recent NMR measurements on the organic compound kappa-(BEDT-TTF)(2)Cu-2(CN)(3). We argue that these are inconsistent with long-range order and a description of the low-energy excitations in terms of interacting magnons, and that therefore a Heisenberg model with only nearest-neighbor exchange does not offer an adequate description of this material.

Dispersion relations, rays and ray splitting in magnetohelioseismology.

Abstract: Local helioseismology seeks to probe the near surface regions of the Sun, and in particular of active regions. These are distinguished by their strong magnetic fields, yet current local techniques do not take proper account of this. Here, we first derive appropriate gravito-magneto-acoustic dispersion relations, and then use these to examine how acoustic rays entering regions of strong field split into fast and slow components, and the subsequent fates of each. Specifically, two types of transmission point, where wave energy can transfer from the fast to slow branch (or vice versa) are identified; one close to the equipartition level where the sound and Alfven speeds coincide, and one higher up near the acoustic cutoff turning point. This second type only exists for rays of low frequency or low l though. In accord with recent studies of fast-to-slow mode conversion from the perspective of p-modes, magnetic field inclination is found to have significant consequences for wave splitting.