Showing papers on "Group velocity published in 2003"

Observation of ultraslow light propagation in a ruby crystal at room temperature.

Abstract: We have observed slow light propagation with a group velocity as low as $57.5\ifmmode\pm\else\textpm\fi{}0.5\text{ }\mathrm{m}/\mathrm{s}$ at room temperature in a ruby crystal. A quantum coherence effect, coherent population oscillations, produces a very narrow spectral ``hole'' in the homogeneously broadened absorption profile of ruby. The resulting rapid spectral variation of the refractive index leads to a large value of the group index. We observe slow light propagation both for Gaussian-shaped light pulses and for amplitude modulated optical beams in a system that is much simpler than those previously used for generating slow light.

Stationary pulses of light in an atomic medium

Abstract: Physical processes that could facilitate coherent control of light propagation are under active exploration1,2,3,4,5. In addition to their fundamental interest, these efforts are stimulated by practical possibilities, such as the development of a quantum memory for photonic states6,7,8. Controlled localization and storage of photonic pulses may also allow novel approaches to manipulating of light via enhanced nonlinear optical processes9. Recently, electromagnetically induced transparency10 was used to reduce the group velocity of propagating light pulses11,12 and to reversibly map propagating light pulses into stationary spin excitations in atomic media13,14,15,16. Here we describe and experimentally demonstrate a technique in which light propagating in a medium of Rb atoms is converted into an excitation with localized, stationary electromagnetic energy, which can be held and released after a controllable interval. Our method creates pulses of light with stationary envelopes bound to an atomic spin coherence, offering new possibilities for photon state manipulation and nonlinear optical processes at low light levels.

Optical pulse propagation in metal nanoparticle chain waveguides

Abstract: Finite-difference time-domain simulations show direct evidence of optical pulse propagation below the diffraction limit of light along linear arrays of spherical noble metal nanoparticles with group velocities up to 0.06c. The calculated dispersion relation and group velocities correlate remarkably well with predictions from a simple point-dipole model. A change in particle shape to spheroidal particles shows up to a threefold increase in group velocity. Pulses with transverse polarization are shown to propagate with negative phase velocities antiparallel to the energy flow.

Spatio-temporal structure of storm-time chorus

Abstract: We discuss chorus emissions measured by the four Cluster spacecraft at close separations during a geomagnetically disturbed period on 18 April 2002. We analyze the lower band of chorus below one half of the electron cyclotron frequency, measured at a radial distance of 4.4 Earth's radii, within a 2000 km long source region located close to the equator. The characteristic wave vector directions in this region are nearly parallel to the field lines and the multipoint measurement demonstrates the dynamic character of the chorus source region, changing the Poynting flux direction at time scales shorter than a few seconds. The electric field waveforms of the chorus wave packets (forming separate chorus elements on power spectrograms) show a fine structure consisting of subpackets with a maximum amplitude above 30 mV/m. To study this fine structure we have used a sine-wave parametric model with a variable amplitude. The subpackets typically start with an exponential growth phase, and after reaching the saturation amplitude they often show an exponential decay phase. The duration of subpackets is variable from a few milliseconds to a few tens of milliseconds, and they appear in the waveform randomly, with no clear periodicity. The obtained growth rate (ratio of the imaginary part to the real part of the wave frequency) is highly variable from case to case with values obtained between a few thousandths and a few hundredths. The same chorus wave packets simultaneously observed on the different closely separated spacecraft appear to have a different internal subpacket structure. The characteristic scale of the subpackets can thus be lower than tens of kilometers in the plane perpendicular to the field line, or hundreds of kilometers parallel to the field line (corresponding to a characteristic time scale of few milliseconds during the propagation of the entire wave packet). Using delays of time-frequency curves obtained on different spacecraft, we have found the same propagation direction as obtained from the simultaneous Poynting flux calculations. The delays roughly correspond to the whistler-mode group velocity estimated from the cold plasma theory. We have also observed delays corresponding to antiparallel propagation directions for two neighboring chorus wave packets, less than 0.1 s apart.

The speed of information in a ‘fast-light’ optical medium

Abstract: One consequence of the special theory of relativity is that no signal can cause an effect outside the source light cone, the space-time surface on which light rays emanate from the source1. Violation of this principle of relativistic causality leads to paradoxes, such as that of an effect preceding its cause2. Recent experiments on optical pulse propagation in so-called ‘fast-light’ media—which are characterized by a wave group velocity υg exceeding the vacuum speed of light c or taking on negative values3—have led to renewed debate about the definition of the information velocity υi. One view is that υi = υg (ref. 4), which would violate causality, while another is that υi = c in all situations5, which would preserve causality. Here we find that the time to detect information propagating through a fast-light medium is slightly longer than the time required to detect the same information travelling through a vacuum, even though υg in the medium vastly exceeds c. Our observations are therefore consistent with relativistic causality and help to resolve the controversies surrounding superluminal pulse propagation.

Linear and nonlinear wave propagation in negative refraction metamaterials

Abstract: Linear and Nonlinear Wave Propagation in Negative Refraction Meta-Materials V. M. Agranovich 1,2) , Y. R. Shen 3) , R. H. Baughman 1) , A. A. Zakhidov 1) UTD-NanoTech Institute,The University of Texas at Dallas, Richardson TX, 75083-0688 USA Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow obl. 142190, Russia Physics Department, University of California, Berkeley, CA 94720 USA ABSTRACT We discuss linear and nonlinear optical wave propagation in a left-handed medium (LHM) or medium of negative refraction (NRM). We use the approach of characterizing the medium response totally by a generalized electric polarization (with a dielectric r permittivity e ( ω , k ) ) that can be decomposed into a curl and a non-curl part. The description has a one-to-one correspondence with the usual approach characterizing the LHM response with a dielectric permittivity e <0 and a magnetic permeability μ <0. The latter approach is less physically transparent in the optical frequency region because the usual definition of magnetization loses its physical meaning. Linear wave propagation in LHM or NRM is characterized by negative refraction and negative group velocity that could be clearly manifested by ultra-short pulse propagation in such a medium. Nonlinear optical effects in LHM can be predicted from the same calculations adopted for ordinary media using our general approach. I. Introduction. Over 30 years ago, Veselago [1] suggested that electromagnetic wave propagation in an isotropic medium with negative dielectric permittivity, e ( ω ) < 0 and negative magnetic permeability μ ( ω ) < 0 can exhibit very unusual properties. Since in such r r r media, the wave vector k , the electric field E , and the magnetic field H of a wave form a left-handed orthogonal set, in contrast to the right- handed orthogonal set in an ordinary medium, they are sometimes labeled as left-handed meta-materials (LHM), as opposite to the ordinary right-handed media (RHM). Among the many interesting properties of wave propagation in such media are the appearances of a Pointing vector in the direction

Light transport through the band-edge states of Fibonacci quasicrystals.

Abstract: The propagation of light in nonperiodic quasicrystals is studied by ultrashort pulse interferometry. Samples consist of multilayer dielectric structures of the Fibonacci type and are realized from porous silicon. We observe mode beating and strong pulse stretching in the light transport through these systems, and a strongly suppressed group velocity for frequencies close to a Fibonacci band gap. A theoretical description based on transfer matrix theory allows us to interpret the results in terms of Fibonacci band-edge resonances.

Periodically loaded transmission line with effective negative refractive index and negative group velocity

Abstract: We present the design and implementation of a periodically loaded transmission line, which simultaneously exhibits negative refractive index (NRI) and negative group delay (and, hence, negative group velocity). This is achieved by loading the transmission line in series with capacitors and RLC resonators and in shunt with inductors. We discuss the dispersion characteristics of such a medium and identify the frequency bands of NRI and negative group delay. The structures are theoretically studied using S-parameters simulations on truncated loaded transmission lines of different lengths, and the predicted results are compared to the measured scattering parameters of such lines printed on circuit boards using coplanar waveguide technology.

Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures

Abstract: The linear and nonlinear characteristics of optical slow-wave structures made of direct coupled Fabry–Perot and Ring Resonators are discussed. The main properties of an infinitely long slow-wave structure are derived analytically with an approach based on the Bloch theory. The spectral behaviour is periodical and closed form expressions for the bandwidth, the group velocity, the dispersion and the linear and nonlinear induced phase shift are derived. For structures of finite length the results still hold providing that proper input/output matching sections are added. In slow-wave structures most of the propagation parameters are enhanced by a factor S called the slowing ratio. In particular nonlinearities result strongly enhanced by the resonant propagation, so that slow-wave structures are likely to become a key point for all-optical processing devices. A numerical simulator has been implemented and several numerical examples of propagation are discussed. It is also shown as soliton propagation is supported by slow-wave structures, demonstrating the flexibility and potentiality of these structures in the field of the all-optical processing.

Rayleigh wave tomography of China and adjacent regions

Abstract: [1] This paper presents a tomographic study on the S wave velocity structure of China and adjacent regions. Group velocity dispersions of fundamental Rayleigh waves along more than 4000 paths were determined with frequency-time analysis. The study region was divided into a 1° × 1° grid, and velocities in between grid nodes were calculated by bilinear interpolation. The Occam's inversion scheme was adopted to invert for group velocity distributions. This method is robust and allows us to use a fine grid in model parameterization and thus helps to restore a more realistic velocity pattern. Checkerboard tests were carried out, and the lateral resolution was estimated to be 4°–6° in China and its eastern continental shelves. The resulting group velocity maps from 10 to 184 s showed good correlation with known geological and tectonic features. The pure path dispersion curves at each node were inverted for shear wave velocity structures. The three-dimensional velocity model indicates thick lithospheres in the Yangtze and Tarim platforms and hot upper mantles in Baikal and western Mongolia, coastal area and continental shelves of eastern China, and Indochina and South China Sea regions. The Tibetan Plateau has a very thick crust with a low-velocity zone in its middle. Beneath the crust a north dipping high-velocity zone, mimicking a subducting plate, reaches to 200 km in depth and reaches to the Kunlun Mountains northward. In northern Tibet a low-velocity zone immediately below the Moho extends eastward then turns southward along the eastern edge of the plateau until it connects to the vast low-velocity area in Indochina and the South China Sea.

Effects of the Solvent Refractive Index and Its Dispersion on the Radiative Decay Rate and Extinction Coefficient of a Fluorescent Solute

Abstract: It is well known that the probabilities of radiative transitions in a medium differ from those in vacuum. Excitation of a fluorescent molecule and its radiative decay are examples of radiative transitions. The rates of these processes in solution depend on the optical characteristics of the solvent. In this article the radiative decay rate and the extinction coefficient of a fluorescent molecule in solution are expressed in terms of the intrinsic properties of the fluorescent molecule (electronic transition moments) and the optical characteristics of the solvent (refractive index, group velocity of light). It is shown that the group velocity does not enter in the final expressions for the radiative decay rate and the extinction coefficient; this means that the dispersion of the refractive index has no effect on these quantities. The expressions for both the radiative decay rate and the extinction coefficient contain the refractive index of the solvent and the local field correction factor. The latter depends on the cavity model, and, for some cavity models, on the shape of the cavity. Four types of cavity models are discussed; for each model the limits of applicability are examined. Experimental evidence in support of specific cavity models is reviewed.

Ionospheric remote sensing of the Denali Earthquake Rayleigh surface waves

Abstract: [1] Using the Global Positioning System, we have detected ionospheric disturbances associated with the long-period Rayleigh waves from the 2002 Denali earthquake (Ms = 7.9). The dense California GPS networks allowed us to map the ionospheric perturbations and to compute the group velocity with a high spatial resolution above the Pacific coasts. Due to a low sampling rate, a large error in the velocity determination remains. Nonetheless, it demonstrates that bi-static remote sensing measurements of seismic waves with GPS networks can be performed. Monostatic measurements with a dedicated satellite could possibly be used to record in the ionosphere surface waves originating from large earthquakes. Such a space-based remote sensing of the local group velocity of Rayleigh surface waves would effectively complement the seismic networks for high-resolution global tomography of the Earth's lithosphere.

Effect of realistic astrophysical inputs on the phase and shape of the WIMP annual modulation signal

Abstract: The orbit of the Earth about the Sun produces an annual modulation in the WIMP direct detection rate. If the local WIMP velocity distribution is isotropic then the modulation is roughly sinusoidal with maximum in June, however if the velocity distribution is anisotropic the phase and shape of the signal can change. Motivated by conflicting claims about the effect of uncertainties in the local velocity distribution on the interpretation of the DAMA annual modulation signal (and the possibility that the form of the modulation could be used to probe the structure of the Milky Way halo), we study the dependence of the annual modulation on various astrophysical inputs. We first examine the approximations used for the Earth's motion about the Sun and the Sun's velocity with respect to the Galactic rest frame. We find that overly simplistic assumptions lead to errors of up to ten days in the phase and up to tens of per-cent in the shape of the signal, even if the velocity distribution is isotropic. Crucially, if the components of the Earth's velocity perpendicular to the motion of the Sun are neglected, then the change in the phase which occurs for anisotropic velocity distributions is missed. We then examine how the annual modulation signal varies for physically and observationally well-motivated velocity distributions. We find that the phase of the signal changes by up to 20 days and the mean value and amplitude change by up to tens of per-cent.

Oblique frozen modes in periodic layered media.

Abstract: We study the classical scattering problem of a plane electromagnetic wave incident on the surface of semi-infinite periodic stratified media incorporating anisotropic dielectric layers with special oblique orientation of the anisotropy axes. We demonstrate that an obliquely incident light, upon entering the periodic slab, gets converted into an abnormal grazing mode with huge amplitude and zero normal component of the group velocity. This mode cannot be represented as a superposition of extended and evanescent contributions. Instead, it is related to a general (non-Bloch) Floquet eigenmode with the amplitude diverging linearly with the distance from the slab boundary. Remarkably, the slab reflectivity in such a situation can be very low, which means an almost 100% conversion of the incident light into the axially frozen mode with the electromagnetic energy density exceeding that of the incident wave by several orders of magnitude. The effect can be realized at any desirable frequency, including optical and UV frequency range. The only essential physical requirement is the presence of dielectric layers with proper oblique orientation of the anisotropy axes. Some practical aspects of this phenomenon are considered.

Anisotropy correction for deviated‐well sonic logs: Application to seismic well tie

Abstract: Borehole sonic logs acquired in deviated wells penetrating the HRZ and Colville shales in the Niakuk field in Alaska's North Slope are seen to be significantly faster than vertical well logs. These differences are attributed to shale anisotropy. An iterative inversion scheme was created to invert for shale anisotropy parameters using multiple wells penetrating shale sections at different angles. The inversion involves fitting the sonic log data at a range of borehole angles to the compressional wave group velocity surface. The result is an estimate of the anisotropy parameters (e and δ) and the vertical P‐wave velocity. The results show that the shales are strongly anisotropic, with compressional‐wave anisotropy (Thomsen's parameter e) on the order of 40% and the anisotropy parameter δ (relates vertical velocity to short‐offset NMO velocity) around 10%. This large anisotropy can affect seismic imaging, AVO, and time–depth calculations.A procedure was created to estimate the anisotropy‐corrected vertical s...

Elastic waves in a functionally graded piezoelectric cylinder

Abstract: An analytical–numerical method is presented for analyzing dispersion and characteristic surface of waves in a circular cylinder composed of functionally graded piezoelectric material (FGPM). In this method, the FGPM cylinder is divided into a number of annular elements with three-nodal lines in the wall thickness. The elemental mechanical as well as electrical properties are assumed to vary linearly in the thickness direction so as to better model the spatial variation of the mechanical and electrical properties of FGPM. The associated frequency dispersion equation is developed and the phase velocity and slowness as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. The calculation examples provide a full understanding of the complex phenomena of elastic waves in FGPM cylinders.

Air-coupled acoustic imaging with zero-group-velocity Lamb modes

Abstract: A Lamb wave resonance has been found that allows unusually efficient transmission of airborne sound waves through plates. This occurs at the zero-group-velocity point at the frequency minimum of the first-order symmetric (S1) Lamb mode. At this frequency, plane waves with a range of incident angles can couple between the air and the Lamb mode in the solid plate, dominating the spectrum of transmitted focused sound beams by 10 dB or more. We use this frequency for C-scan imaging, and demonstrate the detection of both a 3.2-mm-diameter buried flaw and a subwavelength thickness changes of .005λ (1%).

Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line

Abstract: We were able to arbitrarily control the speed of a light pulse from subluminal to superluminal velocity by changing only the power of the laser for coupling coherently the single transition between $6{}^{2}{S}_{1/2}F=4$ and $6{}^{2}{P}_{3/2}{F}^{\ensuremath{'}}=5$ in the ${D}_{2}$ line of a Cs atomic vapor system. With weak coupling power, a Gaussian light pulse was propagated superluminally with a negative group velocity ${v}_{g}=\ensuremath{-}c/14400,$ which is caused by a highly anomalous dispersion related to an electromagnetically induced absorption. By increasing the coupling power at the same laser frequency, the pulses were propagated with a vacuum speed at the middle power and a subluminal group velocity ${v}_{g}=c/3000$ at high power, which is caused by a normal dispersion related to an electromagnetically induced transparency. It was also found that group velocities depend largely on polarization combinations.

Periodically loaded transmission line with effective negative refractive index and negative group velocity

Abstract: Media with negative refractive index (NRI) are expected to exhibit properties that are unusual compared to materials with a positive index of refraction. However, until recently, these properties were not experimentally observed, since no NRI material occurs naturally. Periodic structures with NRI have been constructed. Our group created artificial NRI materials by loading a cellular network of transmission lines with series capacitors and shunt inductors (Eleftheriades, G.V. et al., IEEE Trans. Microwave Theory and Techniques, vol.50, no.12, p.2702-12, 2002; Microwave and Wireless Component Lett., 2003). We have extended that work to design a medium that exhibits negative group velocity (NGV) in addition to NRI. To achieve the NGV, a resonant circuit is embedded within each loaded transmission line (LTL) unit cell. The resonance produces a region of anomalous dispersion in which the group delay, and thus the group velocity, is negative. The NGV means that the peak of the output pulse emerges from the LTL prior to the peak of the input pulse, though much reduced in magnitude. Note that the front of the output pulse does not precede the front of the input pulse; that is, the output pulse front suffers the usual positive delay. The proposed transmission line is fabricated using coplanar waveguide technology. Scattering matrix measurements verify the theoretical predictions.

Propagation of light-pulses at a negative group-velocity

Abstract: This paper deals with the apparent superluminal propagation of electromagnetic pulses in a linear dispersive medium. One specifically examines the possibility that the pulse leaving the medium may be nearly identical to the incident one (low distortion) and in significant advance of it (strongly negative group-delays). Favourable conditions are obtained in a dilute medium where the required anomalous dispersion originates in an ensemble of narrow absorption or gain lines. Analytical expressions of the advancement of the pulse centre-of-gravity and of the lowest order distortion are established from the transfer-function of the medium. The experiments already achieved with arrangements involving a single absorption-line or a gain-doublet are analysed in detail and compared. The considerable difficulties to overcome in order to attain advancements comparable to the pulse width without important distortion are pointed out. New and promising schemes involving a narrow dip in a gain profile or absorption-doublets are proposed.

Limit states of internal wave beams

Abstract: Internal gravity waves propagate away from a localized monochromatic disturbance inside beams, which develop around a St Andrew's Cross in two dimensions and around a double cone in three dimensions. The structure of the beams depends on three mechanisms, which couple together the different directions of propagation of the waves within the fluid. These mechanisms are associated with the size of the disturbance, the start-up of the motion and the viscosity of the fluid, respectively. The present paper considers each mechanism in isolation, for three-dimensional generation. The analysis is asymptotic and relies on far-field and large-time approximations. For each mechanism, three expressions of the waves are found: one, exact for an extended disturbance, that involves all the wavenumber vectors satisfying the dispersion relation; and two others, respectively uniform and non-uniform asymptotic expansions, that involve only the wavenumber vectors associated with group velocity vectors pointing toward the observer. For each mechanism, profiles of pressure and velocity are presented. A new time-independent characterization of the waves is introduced, in terms of the intensity or average energy flux; it is applied to the definition of the beam width. For an extended disturbance this width is a constant, the diameter of the disturbance. For an impulsive start-up the width increases linearly with the distance from the disturbance, and decreases in inverse proportion to the time elapsed since the start-up. For a viscous fluid the width increases as the one-third power of the distance. In all three cases, for a disturbance of multipolar order $2^n$, at constant strength, the power output varies in inverse proportion to the $(2n+1)$th power of the beam width.

Abnormal wave propagation in passive media

Abstract: Abnormal velocities in passive structures such as one-dimensional (1-D) photonic crystals and a slab having a negative index of refraction are discussed. In the case of 1-D photonic crystal, the frequency- and time-domain experiments for waves tuned to the bandgap of the photonic crystal demonstrate a positive group velocity exceeding the speed of light in vacuum (superluminal). In the case of a medium with negative index of refraction, our theoretical studies show that such a medium can support positive group and negative phase velocities (backward waves), as well as negative group and negative phase velocities. The meaning of superluminal group velocity and negative group velocity, or equally, positive superluminal group delay and negative group delay, are discussed. It is shown that despite their counterintuitive meaning there are no contradictions with the requirements of relativistic causality (Einstein causality). To clearly demonstrate this, the important subject of the "front" is reintroduced.

Light propagation in an atomic medium with steep and sign-reversible dispersion

Abstract: We show that ground-state Zeeman coherence prepared by two-photon Raman transitions in alkali atoms results in steep controllable and sign-reversible dispersion. Pulse propagation with small negative as well as positive group velocity of light (-c/5100 and c/41 000) in a Cs vapor cell is reported. Energy exchange between copropagating light components through long-lived Zeeman coherence with enhanced absorption or transmission has been observed.