Showing papers on "Group velocity published in 2006"

Ultrasonic metamaterials with negative modulus

Abstract: The emergence of artificially designed subwavelength electromagnetic materials, denoted metamaterials, has significantly broadened the range of material responses found in nature. However, the acoustic analogue to electromagnetic metamaterials has, so far, not been investigated. We report a new class of ultrasonic metamaterials consisting of an array of subwavelength Helmholtz resonators with designed acoustic inductance and capacitance. These materials have an effective dynamic modulus with negative values near the resonance frequency. As a result, these ultrasonic metamaterials can convey acoustic waves with a group velocity antiparallel to phase velocity, as observed experimentally. On the basis of homogenized-media theory, we calculated the dispersion and transmission, which agrees well with experiments near 30 kHz. As the negative dynamic modulus leads to a richness of surface states with very large wavevectors, this new class of acoustic metamaterials may offer interesting applications, such as acoustic negative refraction and superlensing below the diffraction limit.

Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial

Abstract: We investigated the propagation of femtosecond laser pulses through a metamaterial that has a negative index of refraction for wavelengths around 1.5 micrometers. From the interference fringes of a Michelson interferometer with and without the sample, we directly inferred the phase time delay. From the pulse-envelope shift, we determined the group time delay. In a spectral region, phase and group velocity are negative simultaneously. This means that both the carrier wave and the pulse envelope peak of the output pulse appear at the rear side of the sample before their input pulse counterparts have entered the front side of the sample.

Photonic crystal waveguides with semi-slow light and tailored dispersion properties

Abstract: We demonstrate a concept for tailoring the group velocity and dispersion properties for light propagating in a planar photonic crystal waveguide By perturbing the holes adjacent to the waveguide core it is possible to increase the useful bandwidth below the light-line and obtain a photonic crystal waveguide with either vanishing, positive, or negative group velocity dispersion and semi-slow light We realize experimentally a silicon-on-insulator photonic crystal waveguide having nearly constant group velocity ~c0/34 in an 11-nm bandwidth below the silica-line

Observation of Backward Pulse Propagation Through a Medium with a Negative Group Velocity

Abstract: The nature of pulse propagation through a material with a negative value of the group velocity has been mysterious, as simple models seem to predict that pulses will propagate "backward" through such a material. Using an erbium-doped optical fiber and measuring the time evolution of the pulse intensity at many points within the fiber, we demonstrate that the peak of the pulse does propagate backward inside the fiber, even though the energy flow is always in the forward direction.

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) .

Coupling into the slow light mode in slab-type photonic crystal waveguides.

Abstract: Coupling external light signals into a photonic crystal (PhC) waveguide becomes increasingly inefficient as the group velocity of the waveguiding mode slows down. We have systematically studied the efficiency of coupling in the slow light regime for samples with different truncations of the photonic lattice at the coupling interface between a strip waveguide and a PhC waveguide. An inverse power law dependence is found to best fit the experimental scaling of the coupling loss on the group index. Coupling efficiency is significantly improved up to group indices of 100 for a truncation of the lattice that favors the appearance of photonic surface states at the coupling interface in resonance with the slow light mode.

Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies.

Abstract: A one-dimensional magnetic plasmon propagating in a linear chain of single split ring resonators is proposed. The subwavelength size resonators interact mainly through exchange of conduction current, resulting in stronger coupling as compared to the corresponding magneto-inductive interaction. Finite-difference time-domain simulations in conjunction with a developed analytical theory show that efficient energy transfer with signal attenuation of less then 0.57 dB/microm and group velocity higher than 1/4c can be achieved. The proposed novel mechanism of energy transport in the nanoscale has potential applications in subwavelength transmission lines for a wide range of integrated optical devices.

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.

Slow light in photonic crystals

Abstract: The problem of slowing down light by orders of magnitude has been extensively discussed in the literature. Such a possibility can be useful in a variety of optical and microwave applications. Many qualitatively different approaches have been explored. Here we discuss how this goal can be achieved in linear dispersive media, such as photonic crystals. The existence of slowly propagating electromagnetic waves in photonic crystals is quite obvious and well known. The main problem, though, has been how to convert the input radiation into the slow mode without losing a significant portion of the incident light energy to absorption, reflection, etc. We show that the so-called frozen mode regime offers a unique solution to the above problem. Under the frozen mode regime, the incident light enters the photonic crystal with little reflection and, subsequently, is completely converted into the frozen mode with huge amplitude and almost zero group velocity. The linearity of the above effect allows the slowing of lig...

Traveltime approximations for a layered transversely isotropic medium

Abstract: We consider multiple transmitted, reflected, and converted qP-qSV-waves or multiple transmitted and reflected SH-waves in a horizontally layered medium that is transversely isotropic with a vertical symmetry axis (VTI). Traveltime and offset (horizontal distance) between a source and receiver, not necessarily in the same layer, are expressed as functions of horizontal slowness. These functions are given in terms of a Taylor series in slowness in exactly the same form as for a layered isotropic medium. The coefficients depend on the parameters of the anisotropic layers through which the wave has passed, and there is no weak anisotropy assumption. Using classical formulas, the traveltime or traveltime squared can then be expressed as a Taylor series in even powers of offset. These Taylor series give rise to a shifted hyperbola traveltime approximation and a new continued-fraction approximation, described by four parameters that match the Taylor series up to the sixth power in offset. Further approximations give several simplified continued-fraction approximations, all of which depend on three parameters: zero-offset traveltime, NMO velocity, and a heterogeneity coefficient. The approximations break down when there is a cusp in the group velocity for the qSV-wave. Numerical studies indicate that approximations of traveltime squared are generally better than those for traveltime. A new continued-fraction approximation that depends on three parameters is more accurate than the commonly used continued-fraction approximation and the shifted hyperbola.

Motion of observed structures calculated from multi-point magnetic field measurements: Application to Cluster

Abstract: A new method is described which calculates the velocity of observed, quasi-stationary structures at every moment in time from multi-point magnetic field measurements. Once the magnetic gradient tensor G=del (B) over right arrow and the time variation of the magnetic field have been estimated at every moment, the velocity can then be determined, in principle, as a function of time. One striking property of this method is that we can calculate the velocity of structures for any dimensionality: for three-dimensional structures, all three components of the velocity vector can be calculated directly; for two-dimensional (or one-dimensional) structures, we can calculate the velocity along two (or one) directions. The advantage of this method is that the velocity is determined instantaneously, point by point through any structure, and so we can see the time variation of the velocity as the spacecraft traverse the structure. In this paper, the feasibility of the method is tested by calculating the motion velocity of a three-dimensional, near cusp structure and a two-dimensional magnetotail current sheet. The results for one-dimensional structures in the magnetopause and cusp boundaries are compared to calculations for the standard techniques for analyzing discontinuities.

A multistep approach for joint modeling of surface wave dispersion and teleseismic receiver functions: Implications for lithospheric structure of the Arabian Peninsula

Abstract: [1] We present a multiple step procedure for joint modeling of surface wave group velocity dispersion curves and teleseismic receiver functions for lithospheric velocity structure. The method relies on an initial grid search for a simple crustal structure, followed by a formal iterative inversion, an additional grid search for shear wave velocity in the mantle, and finally, forward modeling of transverse isotropy to resolve Love-Rayleigh surface wave dispersion discrepancy. It considers longer-period surface wave group velocity (SWGV) dispersion, allowing for the resolution of deeper structure compared to previous joint inversions. The grid search for simple crustal structure is facilitated using a library of precomputed receiver functions and SWGV dispersion curves. The iterative inversion improves fit to the data by increasing the number of layers in the crust when necessary. In order to fit the SWGV for periods greater than about 50 s, we perform a grid search over mantle velocities including the mantle lid and low-velocity zone, keeping the crustal structure fixed to the values from the previous step. In some cases a clear Love-Rayleigh discrepancy prevents a simultaneous fit of the group velocities with an isotropic model. The Love-Rayleigh discrepancy can be resolved by allowing shear wave transverse isotropy with a vertical symmetry axis (vSH − vSV differences) in the uppermost mantle. The method is applied to 10 stations in the Arabian Peninsula sampling various tectonic environments including active continental rifting and stable regions. The resulting shear velocity models confirm rapid crustal thinning of the Arabian Shield toward the Red Sea; however, we do not find strong evidence for crustal thickening toward the Arabian Platform. Our results suggest that the mantle lithosphere thickness varies regionally but that the mantle shear velocities beneath the Arabian Shield and Red Sea coast are generally anomalously low. Furthermore, our results indicate the presence of strong polarization anisotropy (up to about 10%) in the lithospheric upper mantle, in the vicinity of, as well as farther away from, the Red Sea. Our modeling yields vSV > vSH in the southwestern part of the Arabian Peninsula, consistent with vertical flow, and vSH > vSV in the northwestern part of the Arabian Peninsula and the continental interior, consistent with horizontal flow, indicating that the mantle flow pattern is not uniform along the axis of the Red Sea.

Voltage-controlled slow light in asymmetry double quantum dots

Abstract: The authors demonstrate theoretically that there exists electromagnetically induced transparency in an asymmetric double quantum dot system using tunneling instead of pump laser. The group velocity slowdown factor is theoretically analyzed as a function of electron tunneling at different broadened linewidths. With feasible parameters for applications to a 100Gbits∕s optical network, numerical calculation infers group velocity as low as 300m∕s. The scheme is expected to be useful in constructing a variable semiconductor optical buffer based on electromagnetically induced transparency in an asymmetric double quantum dot controlled by voltage.

The effect of confinement on the stability of two-dimensional shear flows

Abstract: It has been shown recently that the instability of a two-dimensional wake increases when it is confined in the transverse direction by two flat plates. Confinement causes the transition from convective to absolute instability to occur at lower values of shear. This paper examines this effect comprehensively and concludes that it is due to the constructive interaction of modes with zero group velocity in the wake (or jet) and in the surrounding flow. Maximum instability occurs when the wavenumber of the fundamental mode in the wake (or jet) matches that of the fundamental mode in the surrounding flow. Other regions of high instability occur when the harmonics of one mode interact with the fundamental of the other. This effect is examined at density ratios from 0.001 to 1000. At each density ratio, the confinement which causes maximum absolute instability can be predicted. This study also shows that it is vital to examine the wavenumber of absolutely unstable modes in order to avoid over-predicting the absolute instability. In some situations this wavenumber is vanishingly small and the mode must be discounted on physical grounds.

Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency

Abstract: Direct time-domain measurement of tunable optical delay in a silicon resonating structure is presented. The structure is composed by a double-ring resonator, whose spectrum has a narrow transparency peak with low group velocity analogous to that in electromagnetically induced transparency. Effective group indices from 90 to 290 are obtained by tuning the resonator thermally. The measurements agree well with the theoretical analysis.

Measuring guided waves in long bones: modeling and experiments in free and immersed plates.

Abstract: Guided waves, consistent with the A0 Lamb mode, have previously been observed in bone phantoms and human long bones. Reported velocity measurements relied on line fitting of the observed wave fronts. Such an approach has limited ability to assess dispersion and is affected by interference by other wave modes. For a more robust identification of modes and determination of phase velocities, signal processing techniques using the fast Fourier transform (FFT) were investigated. The limitations of FFT because of spatial resolution were addressed to improve the precision of the measured modes. An inversion scheme was developed for determining the plate thickness from the measured velocity. Experiments were performed on free and immersed plates, mimicking bone without and with an overlying tissue. With group velocity filtering, modes could be identified reliably with precise phase velocities and thicknesses. These methods were essential for the immersed plates and they should lead to more reliable in vivo measurements.

Properties of the particle velocity field in gas-solid turbulent channel flow

Abstract: Spatial characteristics of the particle velocity field are investigated using numerical simulations of gas-solid turbulent channel flow. The carrier phase is resolved using large eddy simulation (LES) of the incompressible Navier-Stokes equations. The dispersed phase is computed using Lagrangian tracking in which particle motion is governed by the drag force. Predictions of dispersed phase transport are obtained for three particle response times in simulations with and without interparticle collisions. Spatial correlations of the particle velocity field are measured in planes parallel to the wall and exhibit a discontinuity at the origin. The discontinuity in the spatial correlations is consistent with recent work by Fevrier et al. [J. Fluid Mech., 533, 1 (2005)] that shows the velocity of a particle is comprised of a contribution from a continuous field, shared by all the particles, and a random velocity component that is not spatially correlated. Analysis of the simulation database shows that the random...

Slow light and 3D imaging with non-magnetic negative index systems.

Abstract: We demonstrate that strongly anisotropic planar dielectric systems can be used to create waveguides supporting modes with extremely slow group velocity. Furthermore, we show that such systems can be used for 3D imaging, with a potential for subwavelength resolution.

Analysis of Smith-Purcell free-electron lasers

Abstract: We present an analysis of the beam dynamics in a Smith-Purcell free-electron laser (FEL). In this system, an electron beam interacts resonantly with a copropagating surface electromagnetic mode near the grating surface. The surface mode arises as a singularity in the frequency dependence of the reflection matrix. Since the surface mode is confined very close to the grating surface, the interaction is significant only if the electrons are moving very close to the grating surface. The group velocity of the surface mode resonantly interacting with a low-energy electron beam is in the direction opposite to the electron beam. The Smith-Purcell FEL is therefore a backward wave oscillator in which, if the beam current exceeds a certain threshold known as start current, the optical intensity grows to saturation even if no mirrors are employed for feedback. We derive the coupled Maxwell-Lorentz equations for describing the interaction between the surface mode and the electron beam, starting from the slowly varying approximation and the singularity in the reflection matrix. In the linear regime, we derive an analytic expression for the start current and calculate the growth rate of optical power in time. The analysis is extended to the nonlinear regime by performing a one-dimensional time-dependent numerical simulation. Results of our numerical calculation compare well with the analytic calculation in the linear regime and show saturation behavior in the nonlinear regime. We find that a significant amount of power grows in the surface mode due to this interaction. Several ways to outcouple this power to freely propagating modes are discussed.

New solitons for the Hirota equation and generalized higher-order nonlinear Schrödinger equation with variable coefficients

Abstract: In this paper, multisoliton solutions of the Hirota equation with variable coefficients are obtained by the Darboux transformation based on the Ablowitz–Kaup–Newell–Segur technology. As an example, we discuss the evolutional behaviour of a two-soliton solution in a soliton control fibre system. The results reveal that one may control the interaction between the pulses by choosing the third-order dispersion parameters d4 and h appropriately. Meanwhile, more generalized forms of bright soliton and dark soliton solutions of generalized higher order nonlinear Schrodinger equations (GHONLSE) with variable coefficients are obtained by the extended tanh-function method. Moreover, new bright and dark combined solitary wave, kink solitary wave and M-shaped solitary wave to GHONLSE with variable coefficients are firstly reported in this paper. Especially, the term proportional to α1 resulting from the group velocity decides the group velocity and the phase shift of these new solitary waves.

Fluctuation spectra and velocity profile from Doppler backscattering on Tore Supra

Abstract: Backscattering of a microwave beam close to the cut-off allows for measurement of density fluctuations at a specified wave-number, selected by the scattering geometry , where ki is the beam wave-number at the reflection layer. On the Doppler reflectometry system installed on Tore Supra, both the scattering wave-number k⊥ and the scattering localization (r/a) can be changed during the shot owing to the steppable probing frequency and the motorized antenna. Operating in O mode, the spatial and wave-number ranges depend essentially on density profile, typically probing 0.5 < r/a < 0.95 and 2 < k < 15 cm−1. Wave number spectra are similar to those obtained with conventional scattering systems. The perpendicular fluctuation velocity in the laboratory frame is obtained from the Doppler shift of the frequency spectrum Δω = k⊥v⊥. It is dominated by the plasma Er × B velocity. In the core, the latter is mainly due to the projection of the toroidal velocity, as this is shown by comparison with measurements by charge exchange recombination spectroscopy. In the set of analysed Tore Supra ohmic and ICRH plasmas, the observed rotation is consistent with a poloidal velocity in the electron diamagnetic direction and/or a toroidal velocity in the counter current direction. The detailed structure of the velocity profile, at the edge and in different plasma regimes, allows us then to get information on the radial electric field distribution. The dynamics of the fluctuation velocity can be studied from the time frequency analysis of the signal, for investigating intermittent behaviour and transient regimes.

Analogues of nonlinear optics using terahertz Josephson plasma waves in layered superconductors

Abstract: Electromagnetic waves in layered superconductors are known as Josephson plasma waves (JPWs). An important property of JPWs is the gap in their energy spectrum: JPWs can propagate if the frequency ω is above the Josephson plasma frequency ωJ (refs 1, 2), which being in the terahertz (THz) range, is important for applications3. This feature is fuelling a growing interest in studies of JPWs (see, for example, refs 4–7). However, nonlinear (NL) JPWs have not yet been studied. It is a challenge to understand nonlinearities around the plasma frequency, where the interplay between the unusual spectrum and the nonlinearity of the JPWs is most pronounced. Here, we predict the propagation of NL JPWs with frequencies below ωJ, which is unusual for plasma-like excitations. In analogy to NL optics, these waves exhibit numerous remarkable features, including the slowing down of light (when the group velocity ∂ ω/∂ k≈0), self-focusing effects and the pumping of weaker waves by stronger ones. The nonlinearity for ω>ωJ can potentially be used for transforming continuous THz radiation into amplified pulses.

A phase reconstruction algorithm for Lamb wave based structural health monitoring of anisotropic multilayered composite plates

Abstract: Platelike structures, made of composites, are being increasingly used for fabricating aircraft wings and other aircraft substructures. Continuous monitoring of the health of these structures would aid the reliable operation of aircrafts. This paper considers the use of a Lamb wave based structural health monitoring (SHM) system to identify and locate defects in large multilayered composite plates. The SHM system comprises of a single transmitter and multiple receivers, coupled to one side of the plate that send and receive Lamb waves. The proposed algorithm processes the data collected from the receivers and generates a reconstructed image of the material state of the composite plate. The algorithm is based on phased addition in the frequency domain to compensate for the dispersion of Lamb waves. In addition, small deviations from circularity of the slowness curves of Lamb wave modes, due to anisotropy, are corrected for by assuming that the phase and group velocity directions coincide locally. Experiment...

The effects of the incoherent pumping field on the phase control of group velocity

Abstract: This paper studies the effects of the incoherent pumping field and the spontaneously generated coherence (SGC) on the phase control of group velocity. The effects of a relative phase between probe and coupling fields on the absorption and the dispersion are then discussed. It is shown that the phase dependence of the group velocity not only depends on the existence of the SGC, but also depends on the existence of the incoherent pump field. We show that for the weak probe field, and in the presence of SGC, the existence of the incoherent pump field is a necessary condition for the phase control of the dispersion, the absorption and the group index.

Laser impulse generation and interferometer detection of zero group velocity Lamb mode resonance

Abstract: In this letter, we describe experiments on the generation of the first order symmetric (S1) Lamb mode by a pulsed yttrium aluminum garnet laser. The vibration of the plate is detected at the same point by a heterodyne interferometer. The acoustic signal is dominated by the resonance at the point of the dispersion curve where the group velocity vanishes. The time decay of the signal leads to the local attenuation coefficient of the material. The spectrum exhibits a very sharp peak, the frequency of which is sensitive to the plate thickness. For a 0.49-mm-thick Duralumin plate, thickness variations as small as 0.1μm have been detected. Moving the detection point away from the source allows us to record the standing wave pattern resulting from the interference between the S1 and S2b Lamb waves having opposite wave vectors at the zero group velocity point.

Two-dimensional array of coupled nanomechanical resonators

Abstract: Two-dimensional arrays of coupled nanomechanical plate-type resonators were fabricated in single crystal silicon using e-beam lithography Collective modes were studied using a double laser setup with independent positioning of the point laser drive and interferometric motion detector The formation of a wide acoustic band has been demonstrated Localization due to disorder (mistune) was identified as a parameter that limits the propagation of the elastic waves We show that all 400 resonators in our 20×20 array participate in the extended modes and estimate group velocity and density of states Applications utilizing the resonator arrays for radio frequency signal processing are discussed