Showing papers on "Group velocity published in 2008"

Theory and simulation of the generation of whistler-mode chorus

Abstract: [1] The generation process of whistler-mode chorus emissions is analyzed by both theory and simulation. Driven by an assumed strong temperature anisotropy of energetic electrons, the initial wave growth of chorus is linear. After the linear growth phase, the wave amplitude grows nonlinearly. It is found that the seeds of chorus emissions with rising frequency are generated near the magnetic equator as a result of a nonlinear growth mechanism that depends on the wave amplitude. We derive the relativistic second-order resonance condition for a whistler-mode wave with a varying frequency. Wave trapping of resonant electrons near the equator results in the formation of an electromagnetic electron hole in the wave phase space. For a specific wave phase variation, corresponding to a rising frequency, the electron hole can form a resonant current that causes growth of a wave with a rising frequency. Seeds of chorus elements grow from the saturation level of the whistler-mode instability at the equator and then propagate away from the equator. In the frame of reference moving with the group velocity, the wave frequency is constant. The wave amplitude is amplified by the nonlinear resonant current, which is sustained by the increasing inhomogeneity of the dipole magnetic field over some distance from the equator. Chorus elements are generated successively at the equator so long as a sufficient flux of energetic electrons with a strong temperature anisotropy is present.

Basic physics of Alfvén instabilities driven by energetic particles in toroidally confined plasmasa)

Abstract: Superthermal energetic particles (EP) often drive shear Alfven waves unstable in magnetically confined plasmas. These instabilities constitute a fascinating nonlinear system where fluid and kinetic nonlinearities can appear on an equal footing. In addition to basic science, Alfven instabilities are of practical importance, as the expulsion of energetic particles can damage the walls of a confinement device. Because of rapid dispersion, shear Alfven waves that are part of the continuous spectrum are rarely destabilized. However, because the index of refraction is periodic in toroidally confined plasmas, gaps appear in the continuous spectrum. At spatial locations where the radial group velocity vanishes, weakly damped discrete modes appear in these gaps. These eigenmodes are of two types. One type is associated with frequency crossings of counterpropagating waves; the toroidal Alfven eigenmode is a prominent example. The second type is associated with an extremum of the continuous spectrum; the reversed shear Alfven eigenmode is an example of this type. In addition to these normal modes of the background plasma, when the energetic particle pressure is very large, energetic particle modes that adopt the frequency of the energetic particle population occur. Alfven instabilities of all three types occur in every toroidal magnetic confinement device with an intense energetic particle population. The energetic particles are most conveniently described by their constants of motion. Resonances occur between the orbital frequencies of the energetic particles and the wave phase velocity. If the wave resonance with the energetic particle population occurs where the gradient with respect to a constant of motion is inverted, the particles transfer energy to the wave, promoting instability. In a tokamak, the spatial gradient drive associated with inversion of the toroidal canonical angular momentum Pζ is most important. Once a mode is driven unstable, a wide variety of nonlinear dynamics is observed, ranging from steady modes that gradually saturate, to bursting behavior reminiscent of relaxation oscillations, to rapid frequency chirping. An analogy to the classic one-dimensional problem of electrostatic plasma waves explains much of this phenomenology. EP transport can be convective, as when the wave scatters the particle across a topological boundary into a loss cone, or diffusive, which occurs when islands overlap in the orbital phase space. Despite a solid qualitative understanding of possible transport mechanisms, quantitative calculations using measured mode amplitudes currently underestimate the observed fast-ion transport. Experimentally, detailed identification of nonlinear mechanisms is in its infancy. Beyond validation of theoretical models, the future of the field lies in the development of control tools. These may exploit EP instabilities for beneficial purposes, such as favorably modifying the current profile, or use modest amounts of power to govern the nonlinear dynamics in order to avoid catastrophic bursts.

Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures.

Abstract: We explore a novel mechanism for slowing down THz waves based on metallic grating structures with graded depths, whose dispersion curves and cutoff frequencies are different at different locations. Since the group velocity of spoof surface plasmons at the cutoff frequency is extremely low, THz waves are actually stopped at different positions for different frequencies. The separation between stopped waves can be tuned by changing the grade of the grating depths. This structure offers the advantage of reducing the speed of the light over an ultrawide spectral band, and the ability to operate at various temperatures, but demands a stringent requirement for the temperature stability.

New generation of massless Dirac fermions in graphene under external periodic potentials.

Abstract: We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are different from the original massless Dirac fermions. The quasiparticle wave vector (measured from the new Dirac point), the generalized pseudospin vector, and the group velocity are not collinear. We further show that with an appropriate periodic potential of triangular symmetry, there exists an energy window over which the only available states are these quasiparticles, thus providing a good system to probe experimentally the new massless Dirac fermions. The required parameters of external potentials are within the realm of laboratory conditions.

High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide

Abstract: A novel electro-optic silicon-based modulator with a bandwidth of 78GHz, a drive voltage amplitude of 1V and a length of only 80µm is proposed. Such record data allow 100Gbit/s transmission and can be achieved by exploiting a combination of several physical effects. First, we rely on the fast and strong nonlinearities of polymers infiltrated into silicon, rather than on the slower free-carrier effect in silicon. Second, we use a Mach-Zehnder interferometer with slotted slow-light waveguides for minimizing the modulator length, but nonetheless providing a long interaction time for modulation field and optical mode. Third, with this short modulator length we avoid bandwidth limitations by RC time constants. The slow-light waveguides are based on a photonic crystal. A polymer-filled narrow slot in the waveguide center forms the interaction region, where both the optical mode and the microwave modulation field are strongly confined to. The waveguides are designed to have a low optical group velocity and negligible dispersion over a 1THz bandwidth. With an adiabatic taper we significantly enhance the coupling to the slow light mode. The feasibility of broadband slow-light transmission and efficient taper coupling has been previously demonstrated by us with calculations and microwave model experiments, where fabrication-induced disorder of the photonic crystal was taken into account.

Broadband ambient noise surface wave tomography across the United States

Abstract: [1] This study presents surface wave dispersion maps across the contiguous United States determined using seismic ambient noise. Two years of ambient noise data are used from March 2003 through February 2005 observed at 203 broadband seismic stations in the US, southern Canada, and northern Mexico. Cross-correlations are computed between all station-pairs to produce empirical Green functions. At most azimuths across the US, coherent Rayleigh wave signals exist in the empirical Green functions implying that ambient noise in the frequency band of this study (5–100 s period) is sufficiently isotropically distributed in azimuth to yield largely unbiased dispersion measurements. Rayleigh and Love wave group and phase velocity curves are measured together with associated uncertainties determined from the temporal variability of the measurements. A sufficient number of measurements (>2000) is obtained between 8 and 25 s period for Love waves and 8 and 70 s period for Rayleigh waves to produce tomographic dispersion maps. Both phase and group velocity maps are presented in these period bands. Resolution is estimated to be better than 100 km across much of the US from 8–40 s period for Rayleigh waves and 8–20 s period for Love waves, which is unprecedented in a study at this spatial scale. At longer and shorter periods, resolution degrades as the number of coherent signals diminishes. The dispersion maps agree well with each other and with known geological and tectonic features and, in addition, provide new information about structures in the crust and uppermost mantle beneath much of the US.

Source inversion of W phase: speeding up seismic tsunami warning

Abstract: W phase is a long period phase arriving before S wave. It can be interpreted as superposition of the fundamental, first, second and third overtones of spheroidal modes or Rayleigh waves and has a group velocity from 4.5 to 9 km s^−1 over a period range of 100–1000 s. The amplitude of long period waves better represents the tsunami potential of an earthquake. Because of the fast group velocity of W phase, most of W phase energy is contained within a short time window after the arrival of the P wave. At a distance of 50°, W phase energy is contained within 23 min after the origin time which is the distinct advantage of using W phase for rapid tsunami warning purposes. We use a time domain deconvolution method to extract W phases from the broad-band records of global seismic networks. The bandwidth of W phase is approximately from 0.001 to 0.01 Hz, and we bandpass filter the data from 0.001 to 0.005 Hz in most cases. Having extracted W phase from the vertical component records, we perform a linear inversion using a point source to determine Mw and the source mechanism for several large earthquakes including the 2004 Sumatra–Andaman earthquake, the 2005 Nias earthquake, the 2006 Kuril Is. earthquake and the 2007 Sumatra earthquake. W phase inversion yields reliable solutions and holds promise of the use of W phase for rapid assessment of tsunami potential.

On streak breakdown in bypass transition

Abstract: Recent theoretical, numerical, and experimental investigations performed at the Department of Mechanics, KTH Stockholm, and the Department of Mechanical Engineering, Eindhoven University of Technology, are reviewed, and new material is presented to clarify the role of the boundary-layer streaks and their instability with respect to turbulent breakdown in bypass transition in a boundary layer subject to free-stream turbulence. The importance of the streak secondary-instability process for the generation of turbulent spots is clearly shown. The secondary instability manifests itself as a growing wave packet located on the low-speed streak, increasing in amplitude as it is dispersing in the streamwise direction. In particular, qualitative and quantitative data pertaining to temporal sinuous secondary instability of a steady streak, impulse responses both on a parallel and a spatially developing streak, a model problem of bypass transition, and full simulations and experiments of bypass transition itself are collected and compared. In all the flow cases considered, similar characteristics in terms of not only growth rates, group velocity, and wavelengths but also three-dimensional visualizations of the streak breakdown have been found. The wavelength of the instability is about an order of magnitude larger than the local boundary-layer displacement thickness δ∗, the group velocity about 0.8 of the free-stream velocity U∞, and the growth rate on the order of a few percent of U∞/δ∗. The characteristic structures at the breakdown are quasistreamwise vortices, located on the flanks of the low-speed region arranged in a staggered pattern.

Subnatural Linewidth Biphotons with Controllable Temporal Length

Abstract: Following the early papers of the Lukin and Kimble groups [1,2], it became apparent that it should be possible to use double-� systems for the generation of biphoton wave packets with temporal lengths that are controllable by varying the optical group velocity. Early results obtained at Stanford using a spherical magneto-optical trap (MOT) with an optical depth (OD) of about 10 [3,4] demonstrated wave packets with correlation times of about 50 ns and linewidths of about 9 MHz. In this Letter, we report the use of a two-dimensional (2D) MOT operating at an optical depth of 62 to attain major improvements in the performance of this type of biphoton source. These include generation of biphotons as long as 900 ns with linewidths as narrow as 0.75 MHz, a factor of 30 improvement in the effective dephasing rate of the nonallowed transition, a demonstrated efficiency of Stokes to anti-Stokes conversion of 74%, and operation in the regime where the temporal length of the biphoton varies inversely with the optical group velocity, thereby demonstrating that the physics suggested by Refs. [3,5] really works. This Letter also reports a sharp leading edge spike on the front edge of the generated biphoton. This spike is a SommerfeldBrillouin precursor [6] and is observed here by photon correlation. We begin by motivating the need for a source of long and narrow-band biphotons: First, to efficiently absorb the

Surface wave tomography of China from ambient seismic noise correlation

Abstract: [1] We perform ambient noise tomography of China using data from the China National Seismic Network and surrounding global and regional stations. For most of the station pairs, we retrieve good Rayleigh waveforms from ambient noise correlations using 18 months of continuous data at all distance ranges across the entire region (over 5000 km) and for periods from 70 s down to about 8 s. We obtain Rayleigh wave group velocity dispersion measurements using a frequency-time analysis method and invert for Rayleigh wave group velocity maps for periods from 8 s to 60 s. The tomographic maps display significant features that correlate with surface geology. Major basins, including Tarim, Junggar, Qadaim, Sichuan, Bohai-Wan, and Songliao, are all well delineated by slow group velocities at shorter periods (10 to 20 s). The overall trend of crustal thickening from east to west is well represented by group velocity decreases from east to west at periods around 30 s.

Local vibration of an elastic plate and zero-group velocity Lamb modes

Abstract: Elastic plates or cylinders can support guided modes with zero group velocity (ZGV) at a nonzero value of the wave number. Using laser-based ultrasonic techniques, we experimentally investigate some fascinating properties of these ZGV modes: resonance and ringing effects, backward wave propagation, interference between backward and forward modes. Then, the conditions required for the existence of ZGV Lamb modes in isotropic plates are discussed. It is shown that these modes appear in a range of Poisson's ratio about the value for which the cutoff frequency curves of modes belonging to the same family intercept, i.e., for a bulk wave velocity ratio equal to a rational number. An interpretation of this phenomenon in terms of a strong repulsion between a pair of modes having a different parity in the vicinity of the cutoff frequencies is given. Experiments performed with materials of various Poisson's ratio demonstrate that the resonance spectrum of an unloaded elastic plate, locally excited by a laser pulse, is dominated by the ZGV Lamb modes.

Soliton trapping in fiber lasers.

Abstract: We report on the soliton trapping in a fiber ring laser mode-locked with a SESAM. It was observed that solitons along the two orthogonal polarization directions of the cavity with fairly large difference in central frequency and energy could be coupled together to form a group velocity locked vector soliton. In particular, due to that each of the coupled solitons forms its own soliton sidebands, two sets of soliton sidebands could be observed on the vector soliton spectrum. Numerical simulations have well confirmed the experimental observations.

Slow photons in the fast lane in chemistry

Abstract: A driving force in the rapidly developing field of photonic crystals has been the photonic bandgap, a range of energies where the propagation of light is completely forbidden. The photonic bandgap allows the design of photonic lattices that localize, guide and bend light at sub-micron length scales, providing opportunities for the creation of miniature optical devices and integrated optical circuits to help drive the revolution in photonics. A less well known attribute of photonic crystals is their theoretical ability to slow light to a velocity of zero. This phenomenon can be achieved at the high and low energy edges of photonic stopgaps where the photonic bands are flat and light exists as a standing wave commensurate with the photonic lattice and travels at a group velocity of zero, referred to as “slow photons” herein. It has been shown theoretically that the probability of harvesting slow photons scales inversely with their group velocity. This means that a number of well known photon driven processes and devices in chemistry and physics can be enhanced by capturing this unique property of slow photons. In this paper we will look at slow photons mainly through the eye of chemistry and highlight some recent developments in this exciting and emerging field that demonstrate the potential of slow photons in materials chemistry and nanochemistry.

Multi-axial angular velocity sensor

Abstract: An angular velocity sensor for detecting angular velocity about a Z-axis in an XYZ coordinate system has a substrate oscillator, a flexible member for connecting the oscillator to a casing, a device for oscillating the oscillator in an X-axis direction, and a detection device detecting deviation of oscillation of the oscillator in a Y-axis direction for indicating the angular velocity about the Z-axis.

Making Massless Dirac Fermions from Patterned Two-Dimensional Electron Gases

Abstract: Analysis of the electronic structure of an ordinary two-dimensional electron gas (2DEG) under an appropriate external periodic potential of hexagonal symmetry reveals that massless Dirac fermions are generated near the corners of the supercell Brillouin zone. The required potential parameters are found to be achievable under or close to laboratory conditions. Moreover, the group velocity is tunable by changing either the effective mass of the 2DEG or the lattice parameter of the external potential, and it is insensitive to the potential amplitude. The finding should provide a new class of systems other than graphene for investigating and exploiting massless Dirac fermions using 2DEGs in semiconductors.

Slow Bloch modes for enhancing the absorption of light in thin films for photovoltaic cells

Abstract: This paper deals with the improvement of “light harvesting” in photovoltaic cells by using photonic nanostructures. We theoretically study a poly-3-hexylthiophene/[6,6]-phenyl-C61-butyric acid methyl ester (P3HT/PCBM) thin film periodically nanostructured in order to increase its absorption. The periodic nanostructuration allows “slow Bloch modes” (group velocity close to zero) to be coupled inside the material. The P3HT/PCBM photonic crystal parameters are adjusted to maximize the density of Bloch modes and obtain flat dispersion curves. The light-matter interaction is thus strongly enhanced, which results in a 35.6% increase of absorption in the 600–700nm spectral range.

All-optical delay line using semiconductor cavity solitons

Abstract: An all-optical delay line based on the lateral drift of cavity solitons in semiconductor microresonators is proposed and experimentally demonstrated. The functionalities of the device proposed as well as its performance is analyzed and compared with recent alternative methods based on the decrease of group velocity in the vicinity of resonances. We show that the current limitations can be overcome using broader devices with tailored material responses.

Two regimes of slow-light losses revealed by adiabatic reduction of group velocity.

Abstract: The losses in a photonic crystal waveguide were measured with a near-field microscope in the group velocity range of c/7 down to c/200. Our measurements show that the losses scale proportional to v{g};{-2} for group velocities above c/30. Below c/30, the losses are no longer described by the same power-law dependence on v{g} and the modal pattern becomes irregular, indicative of multiple scattering. The findings indicate the existence of two regimes of slow-light losses: one where a perturbative approach describes propagation with fabrication disorder and one where it breaks down.

Polarization rotation locking of vector solitons in a fiber ring laser

Abstract: Polarization rotation of vector solitons in a fiber ring laser was experimentally studied. It was observed that the period of vector soliton polarization rotation could be locked to the cavity roundtrip time or multiple of it. We further show that multiple vector solitons can be formed in a fiber laser, and all the vector solitons have the same group velocity in cavity, however, their instantaneous polarization ellipse orientations could be orthogonal.

Long‐time Solutions of the Ostrovsky Equation

Abstract: The Ostrovsky equation is a modification of the Korteweg-de Vries equation which takes account of the effects of background rotation. It is well known that the usual Korteweg-de Vries solitary wave decays and is replaced by radiating inertia gravity waves. Here we show through numerical simulations that after a long-time a localized wave packet emerges as a persistent and dominant feature. The wavenumber of the carrier wave is associated with that critical wavenumber where the underlying group velocity is a minimum (in absolute value). Based on this feature, we construct a weakly nonlinear theory leading to a higher-order nonlinear Schrodinger equations in an attempt to describe the numerically found wave packets.

Azimuthal anisotropy of Rayleigh-wave phase velocities in the east-central United States

Abstract: SUMMARY We explore the Rayleigh-wave phase velocity structure of the east-central US in a broad period range (10‐200 s). Using a recent implementation of the two-stations method, we first measure interstation dispersion curves of Rayleigh-wave phase velocities along 60 paths. We then invert our collection of dispersion curves for isotropic and azimuthally anisotropic (2� and 4� ) phase‐velocity maps. The inversion is performed by a damped, smoothed LSQR, and the output model is parametrized on a triangular grid of knots with a 140 km grid spacing. Using the isotropic component of the phase velocity maps to constrain regional variations in shear velocity and Moho-depth, we observe that over the upper-middle crust depth range (z 1 per cent), and the azimuth of the fast-propagation direction is uniform over the entire region and equal to 54 ◦ . Our results suggest that azimuthal anisotropy beneath the east-central US is vertically distributed in three distinct layers, with a different geodynamic origin for each of them.

Turbulent velocity profile in fully-developed open channel flows

Abstract: The determination of velocity profile in turbulent narrow open channels is a difficult task due to the significant effects of the anisotropic turbulence that involve the Prandtl’s second type of secondary flow occurring in the cross section. With these currents the maximum velocity appears below the free surface that is called dip phenomenon. The well-known logarithmic law describes the velocity distribution in the inner region of the turbulent boundary layer but it is not adapted to define the velocity profile in the outer region of narrow channels. This paper relies on an analysis of the Navier–Stokes equations and yields a new formulation of the vertical velocity profile in the center region of steady, fully developed turbulent flows in open channels. This formulation is able to predict time averaged primary velocity in the outer region of the turbulent boundary layer for both narrow and wide open channels. The proposed law is based on the knowledge of the aspect ratio and involves a parameter CAr depending on the position of the maximum velocity (ξdip). ξdip may be derived, either from measurements or from an empirical equation given in this paper. A wide range of longitudinal velocity profile data for narrow open channels has been used for validating the model. The agreement between the measured and the computed velocities is rather good, despite the simplification used.

Tailoring Metallodielectric Structures for Superresolution and Superguiding Applications in the Visible and Near-IR Ranges

Abstract: We discuss propagation effects in realistic, transparent, metallodielectric photonic band gap structures in the context of negative refraction and super-resolution in the visible and near infrared ranges. In the resonance tunneling regime, we find that for transverse-magnetic incident polarization, field localization effects contribute to a waveguiding phenomenon that makes it possible for the light to remain confined within a small fraction of a wavelength, without any transverse boundaries, due to the suppression of diffraction. This effect is related to negative refraction of the Poynting vector inside each metal layer, balanced by normal refraction inside the adjacent dielectric layer: The degree of field localization and material dispersion together determine the total momentum that resides within any given layer, and thus the direction of energy flow. We find that the transport of evanescent wave vectors is mediated by the excitation of quasistationary, low group velocity surface waves responsible for relatively large losses. As representative examples we consider transparent metallodielectric stacks such as $\mathrm{Ag}∕{\mathrm{TiO}}_{2}$ and $\mathrm{Ag}∕\mathrm{GaP}$ and show in detail how to obtain the optimum conditions for high transmittance of both propagating and evanescent modes for super-guiding and super-resolution applications across the visible and near IR ranges. Finally, we study the influence of gain on super-resolution. We find that the introduction of gain can compensate the losses caused by the excitation of surface plasmons, improves the resolving characteristics of the lens, and leads to gain-tunable super-resolution.

Spectral features of the geodesic acoustic mode and its interaction with turbulence in a tokamak plasmaa)

Abstract: The three-dimensional wavenumber and frequency spectrum for the geodesic acoustic mode (GAM) has been measured in the HuanLiuqi-2A tokamak for the first time. The spectrum provides definite evidence for the GAM, which is characterized by kθ=kϕ=0 and krρi≈0.04−0.09 with the full width at half-maximum Δkrρi≈0.03−0.07. The localized GAM packet is observed to propagate outward in the radial direction with nearly the same phase and group velocity. The envelopes of the radial electric field and density fluctuations are observed to be modulated by the GAM. By comparing the experimental result with that of the envelope analysis using model signals, the mechanism of the envelope modulation has been identified. The results strongly suggest that the envelope modulation of the Er fluctuations is dominantly caused by the direct regulation of the GAM during the GAM generation in the energy-conserving triad interaction, and the envelope modulation of the density fluctuations is induced by the GAM shearing effect, which...

Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide

Abstract: Nonlinear propagation experiments in GaAs photonic crystal waveguides (PCW) were performed, which exhibit a large enhancement of third order nonlinearities, due to light propagation in a slow mode regime, such as two-photon absorption (TPA), optical Kerr effect and refractive index changes due to TPA generated free-carriers. A theoretical model has been established that shows very good quantitative agreement with experimental data and demonstrates the important role that group velocity plays. These observations give a strong insight into the use of PCWs for optical switching devices.

Resonant light transport through Mie modes in photonic glasses

Abstract: The control of light transport is crucial to design and tailor new photonic devices with increased optical performance in the same manner as controlling electron transport is at the basis of semiconductor and electronic technology. In recent years, a new frontier has emerged, with the goal of controlling light propagation through interference in artificially engineered optical materials and metamaterials. Extraordinary progress has been made in the fabrication of nanophotonic structures, with many novel optical properties 1. While ordered periodic photonic media, i.e., photonic crystals, take advantage of the periodicity in the dielectric constant and the consequent long-range correlation to mold the flow of light 2,3, disordered ones, with no positional order, can still strongly affect light transport 1,4–6 and, for example, in the presence of short-range correlation, exhibit band-gap-like effects 7. Conventional nonabsorbing materials are homogeneous and nondispersive, i.e., they are clear and transparent, and phase and energy travel with the same velocity. Optical propagation is then determined by the shape of the interfaces between various such materials e.g., a curve surface boundary acts as a lens. If the material is absorptive, dispersion is introduced brought about by the KramersKronig relations whereby the phase velocity loses most of its usefulness, and group velocity at which pulses travel takes over to describe the transport of energy. In contrast, nonabsorbing but nanostructured materials can create a new class of systems in which the dispersion is controlled via light interference. Photonic band-gap materials, for instance, are systems where extinction is built up from multiple interference Bragg reflection creating a region of extinction and anomalous dispersion. In this way, the relevant velocities can be engineered, for instance, to create devices for dispersion compensation. An entirely new scenario is presented when disorder is added to the mixture. Usually, disordered media are opaque and white, i.e., nondispersive. In such a disordered medium, the group velocity can only be associated with the ballistic or unscattered component, and therefore cannot be applied to describe the transport of energy, which, for large enough optical thicknesses, is governed by the scattered light. When this regime of diffusive propagation is set up, not only phase but also group velocity fail to give an account of light transport, and a new quantity describing the transport of energy in the new diffusive regime is required. The velocity of the scattered light propagation inside disordered media needs to be defined by the velocity of the transported energy and is given by the ratio of the energy flux to the energy density in any point of the sample. This, in general, is very complex and given neither by the group velocity nor the phase velocity 8,9. The energy velocity can be drastically altered reduced in the presence of scattering resonances: in an extreme case of light diffusion in a cold atomic cloud, the atomic energy spectrum can be so resonant to the incident light that the energy velocity can be as low as a few thousand meters per second ve /c 10 �5 10.

S wave velocity structure of the Arabian Shield upper mantle from Rayleigh wave tomography

Abstract: [1] The shear wave velocity structure of the shallow upper mantle beneath the Arabian Shield was modeled by inverting Rayleigh wave phase velocity measurements between 45 and 140 s together with previously published Rayleigh wave group velocity measurements between 10 and 45 s. For measuring phase velocities, we applied a modified array method to data from several regional networks that minimizes the distortion of raypaths caused by lateral heterogeneity. The new shear wave velocity model shows a broad low-velocity region to depths of � 150 km in the mantle across the Shield and a narrower low-velocity region at depths � 150 km localized along the Red Sea coast and Makkah-Madinah-Nafud (MMN) volcanic line. The velocity reduction in the upper mantle corresponds to a temperature anomaly of � 250– 330 K. These findings, in particular the region of continuous low velocities along the Red Sea and MMN volcanic line, do not support interpretations for the origin of the Cenozoic plateau uplift and volcanism on the Shield invoking two separate plumes. When combined with images of the 410 and 660 km discontinuities, body wave tomographic models, a S wave polarization analysis, and SKS splitting results for the Arabian Peninsula, the anomalous upper mantle structure in our new velocity model can be attributed to an upwelling of warm mantle rock originating in the lower mantle under Africa that crosses through the mantle transition zone beneath Ethiopia and moves to the north and northwest under the eastern margin of the Red Sea and the Arabian Shield. In this interpretation, the difference in mean elevation between the Arabian Platform and Shield can be attributed to isostatic uplift caused by heating of the lithospheric mantle under the Shield, with the significantly higher elevations along the Red Sea coast possibly resulting also from lithospheric thinning and dynamic uplift.