Showing papers on "Group velocity published in 2000"

Dark-State Polaritons in Electromagnetically Induced Transparency

Abstract: We identify form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in electromagnetically induced transparency. The properties of dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and "trapped" in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this reversible coherent-control technique are discussed.

Gain-assisted superluminal light propagation

Abstract: Einstein's theory of special relativity and the principle of causality imply that the speed of any moving object cannot exceed that of light in a vacuum (c) Nevertheless, there exist various proposals for observing faster-than-c propagation of light pulses, using anomalous dispersion near an absorption line, nonlinear and linear gain lines, or tunnelling barriers However, in all previous experimental demonstrations, the light pulses experienced either very large absorption or severe reshaping, resulting in controversies over the interpretation Here we use gain-assisted linear anomalous dispersion to demonstrate superluminal light propagation in atomic caesium gas The group velocity of a laser pulse in this region exceeds c and can even become negative, while the shape of the pulse is preserved We measure a group-velocity index of n(g) = -310(+/- 5); in practice, this means that a light pulse propagating through the atomic vapour cell appears at the exit side so much earlier than if it had propagated the same distance in a vacuum that the peak of the pulse appears to leave the cell before entering it The observed superluminal light pulse propagation is not at odds with causality, being a direct consequence of classical interference between its different frequency components in an anomalous dispersion region

Joint inversion of receiver function and surface wave dispersion observations

Abstract: We implement a method to invert jointly teleseismic P-wave receiver functions and surface wave group and phase velocities for a mutually consistent estimate of earth structure. Receiver functions are primarily sensitive to shear wave velocity contrasts and vertical traveltimes, and surface wave dispersion measurements are sensitive to vertical shear wave velocity averages. Their combination may bridge resolution gaps associated with each individual data set. We formulate a linearized shear velocity inversion that is solved using a damped least-squares scheme that incorporates a priori smoothness constraints for velocities in adjacent layers. The data sets are equalized for the number of data points and physical units in the inversion process. The combination of information produces a relatively simple model with a minimal number of sharp velocity contrasts. We illustrate the approach using noise-free and realistic noise simulations and conclude with an inversion of observations from the Saudi Arabian Shield. Inversion results for station SODA, located in the Arabian Shield, include a crust with a sharp gradient near the surface (shear velocity changing from 1.8 to 3.5 km s−1 in 3 km) underlain by a 5-km-thick layer with a shear velocity of 3.5 km s−1 and a 27-km-thick layer with a shear velocity of 3.8 km s−1, and an upper mantle with an average shear velocity of 4.7 km s−1. The crust–mantle transition has a significant gradient, with velocity values varying from 3.8 to 4.7 km s−1 between 35 and 40 km depth. Our results are compatible with independent inversions for crustal structure using refraction data.

Velocity Modification of H I Power Spectrum

Abstract: The distribution of atomic hydrogen in the Galactic plane is usually mapped using the Doppler shift of 21 cm emission line, and this causes the modification of the observed emission spectrum. We calculate the emission spectrum in velocity slices of data (channel maps) and derive its dependence on the statistics of velocity and density fields. We find that, (1) if the density spectrum is steep, i.e., n < -3, the large k asymptotics of the emissivity spectrum are dominated by the velocity fluctuations; and (2) the velocity fluctuations make the emission spectra shallower, provided that the data slices are sufficiently thin. In other words, turbulent velocity creates small-scale structure that can erroneously be identified as clouds. The effect of thermal velocity is very similar to the change of the effective slice thickness, but the difference is that, while an increase of the slice thickness increases the amplitude of the signal, the increase of the turbulent velocity leaves the measured intensities intact while washing out fluctuations. The contribution of fluctuations in warm H I is suppressed relative to those in the cold component when the velocity channels used are narrower than the warm H I thermal velocity and small angular scale fluctuations are measured. We calculate how the spectra vary with the change of velocity slice thickness and show that the observational 21 cm data is consistent with the explanation that the intensity fluctuations within individual channel maps are generated by turbulent velocity fields. As the thickness of velocity slices increases, density fluctuations begin to dominate emissivity. This allows us to disentangle velocity and density statistics. The application of our technique to Galactic and SMC data reveals spectra of density and velocity with power law indexes close to -11/3. This is a Kolmogorov index, but the explanation of the spectrum as due to the Kolmogorov-type cascade faces substantial difficulties. We generalize our treatment for the case of a statistical study of turbulence inside individual clouds. The mathematical machinery developed is applicable to other emission lines.

Relativistic effects of light in moving media with extremely low group velocity

Abstract: A moving dielectric medium acts as an effective gravitational field on light. One can use media with extremely low group velocities [Lene Vestergaard Hau et al., Nature (London) 397, 594 (1999)] to create dielectric analogs of astronomical effects on Earth. In particular, a vortex flow imprints a long-ranging topological effect on incident light and can behave like an optical black hole.

Principles of parametric temporal imaging. I. System configurations

Abstract: The recently developed process of temporal imaging expands or compresses time waveforms while preserving the shapes of their envelope profiles. A key element in a temporal imaging system is a time lens which imparts a quadratic phase modulation to the waveform being imaged. Several methods, such as electrooptic modulation, can be used to produce the phase modulation. In this paper, we concentrate on the parametric mixing of a signal waveform with a linearly chirped optical pump as the time lens mechanism. We analyze all single-lens system configurations including sum- and difference-frequency mixing schemes with positive and negative group velocity dispersions using temporal ray diagrams as an aid in understanding their operation.

Guided wave nuances for ultrasonic nondestructive evaluation

Abstract: Recent developments in guided wave generation, reception, and mode control show that increased penetration power and sensitivity are possible. A tone burst function generator and appropriate signal processing are generally used. Variable angle beam and comb-type transducers are the key to this effort. Problems in tubing, piping, hidden corrosion detection in aging aircraft, adhesive and diffusion bonding, and ice detection are discussed. Additionally, sample configurations, inspection objectives, and logic are being developed for such sample problems as defect detection and analysis in lap splice joints, tear straps, cracks in a second layer, hidden corrosion in multiple layers, cracks from rivet holes, transverse cracking in a beam, and cracks in landing gear assembly. Theoretical and experimental aspects of guided wave analysis include phase velocity, group velocity, and attenuation dispersion curves; boundary element model analysis for reflection and transmission factor analysis; use of wave structure for defect detection sensitivity; source influence on the phase velocity spectrum, and the use of angle beam and comb transducer technology. Probe design and modeling considerations are being explored. Utilization of in-plane and out-of-plane displacement patterns on the surface and longitudinal power distribution across the structural cross-section are considered for improved sensitivity, penetration power, and resolution in nondestructive evaluation. Methods of controlling the phase velocity spectrum for mode and frequency selection are available. Such features as group velocity change, mode cut-off measurements, mode conversion, amplitude ratios of transmission, and reflection factors of specific mode and frequency as input will be introduced for their ability to be used in flaw and material characterization analysis.

Turbulent Molecular Cloud Cores: Rotational Properties

Abstract: The rotational properties of numerical models of centrally condensed, turbulent molecular cloud cores with velocity fields that are characterized by Gaussian random fields are investigated. It is shown that the observed line width-size relationship can be reproduced if the velocity power spectrum is a power law with P(k) ∝ kn and n = -3 to -4. The line-of-sight velocity maps of these cores show velocity gradients that can be interpreted as rotation. For n = -4, the deduced values of angular velocity Ω = 1.6 km s-1 pc-1×(R/0.1 pc)-0.5, and the scaling relations between Ω and the core radius R are in very good agreement with the observations. As a result of the dominance of long-wavelength modes, the cores also have a net specific angular momentum with an average value of J/M = 7 × 1020 × (R/0.1 pc)1.5 cm2 s-1 with a large spread. Their internal dimensionless rotational parameter is β ≈ 0.03, independent of the scale radius R. In general, the line-of-sight velocity gradient of an individual turbulent core does not provide a good estimate of its internal specific angular momentum. We find however that the distribution of the specific angular momenta of a large sample of cores which are described by the same power spectrum can be determined very accurately from the distribution of their line-of-sight velocity gradients Ω using the simple formula j = pΩR2, where p depends on the density distribution of the core and has to be determined from a Monte Carlo study. Our results show that for centrally condensed cores the intrinsic angular momentum is overestimated by a factor of 2-3 if p = 0.4 is used.

Measurements of phase velocity and group velocity in human calcaneus.

Abstract: Ultrasonic velocity in calcaneus correlates highly with bone mineral density, which is a good predictor of osteoporotic fracture risk. Several commercial bone sonometers perform a velocity measurement based on the transit time of a broadband pulse to assess skeletal status. This approach is somewhat problematic, however, because several authors have reported ambiguities in measurements in calcaneus. Phase velocity is an alternative that may be less dependent on device spectral characteristics. In addition, dispersion (the frequency-dependence of phase velocity) is a fundamental property worth investigating to increase understanding of interaction between ultrasound and bone. To compare two group-velocity measurement methods and one phase-velocity measurement method, a polycarbonate sample (for method validation) and 24 human calcanei were investigated in vitro . Phase velocity in calcaneus at 500 kHz was 1511 m/s ± 30 m/s (mean ± standard deviation). Average phase velocity decreased approximately linearly with frequency (−18 m/s MHz). The two group velocity measurements were comparable and tended to be slightly lower than phase velocity. The magnitude of dispersion showed little correlation with bone mineral density.

Fracture source location in thin plates using the wavelet transform of dispersive waves

Abstract: A new signal processing approach was presented for acoustic emission source location using the dispersive waves in a thin plate. For wave propagation in dispersive media, the accuracy of source location can be improved by using the arrival times of a single frequency component in the output signals at an array of sensors. The wavelet transform (WT) was used to resolve this problem. By utilizing the time-frequency data of the WT, the frequency-dependent arrival time traveling with the group velocity was shown to be easily determined. Experiments were performed using a lead break as the simulated fracture source on the surface of an aluminum plate. Two plate modes corresponding to the S/sub 0/ and A/sub 0/ Lamb waves were identified, and their group velocities were accurately measured. The source location results based on the WT method agreed well with the true locations. The WT method was also compared with the cross correlation technique, and both methods provide similar results.

All-optical switching in phase-shifted fiber Bragg grating

Abstract: A low-power all-optical-switching in a phase-shifted grating has been experimentally demonstrated at 1.55 /spl mu/m. The grating is written in a standard fiber for communication and the switching is based on the cross-phase modulation induced by an intense pump pulse on a low intensity probe. An extinction ratio of more than 6 dB has been achieved for 1 kW pulse peak power. The strong enhancement of the nonlinear effect due to the group velocity reduction and the switching polarization dependence have been theoretically investigated and experimentally confirmed.

Amplification of light and atoms in a bose-einstein condensate

Abstract: A Bose-Einstein condensate illuminated by a single off-resonant laser beam (``dressed condensate'') shows a high gain for matter waves and light. We have characterized the optical and atom-optical properties of the dressed condensate by injecting light or atoms, illuminating the key role of long-lived matter wave gratings produced by the condensate at rest and recoiling atoms. The narrow bandwidth for optical gain gave rise to an extremely slow group velocity of an amplified light pulse ( $\ensuremath{\sim}1\mathrm{m}/\mathrm{s}$).

Average Energy Flow of Optical Pulses in Dispersive Media

Abstract: The arrival time of a light pulse at a point in space is defined using a time expectation integral over the Poynting vector. The delay between pulse arrival times at two distinct points is shown to consist of two parts: a spectral superposition of group delays (inverse of group velocity) and a delay due to spectral reshaping via absorption or amplification. The result provides a context wherein group velocity is always meaningful even for broad band pulses and when the group velocity is superluminal or negative. The result imposes luminality on sharply defined pulses.

Propagation speed of evanescent modes

Abstract: The group velocity of evanescent waves (in undersized waveguides, for instance) was theoretically predicted, and has been experimentally verified, to be superluminal ${(v}_{g}gc).$ By contrast, it is known that the precursor speed in vacuum cannot be larger than c. In this paper, by computer simulations based on Maxwell equations only, we show the existence of both phenomena. In other words, we verify the actual possibility of superluminal group velocities, without violating the so-called (naive) Einstein causality.

Accelerating shear velocity in gravel-bed channels

Abstract: The behaviour of the shear velocity along a gravel-bed channel is investigated experimentally in the presence of a negative pressure gradient (accelerating flow). Different methods of estimation of the shear velocity, derived from vertical profiles of the mean longitudinal point velocity, are examined and a new method is proposed. Results show that the proposed method of estimation is comparable to the St Venant and Clauser's methods. At a specific cross section, for constant bottom slope and relative roughness, shear velocity increases with discharge.

Nonlinear theory of nonparaxial laser pulse propagation in plasma channels

Abstract: Nonparaxial propagation of ultrashort, high-power laser pulses in plasma channels is examined. In the adiabatic limit, pulse energy conservation, nonlinear group velocity, damped betatron oscillations, self-steepening, self-phase modulation, and shock formation are analyzed. In the nonadiabatic limit, the coupling of forward Raman scattering (FRS) and the self-modulation instability (SMI) is analyzed and growth rates are derived, including regimes of reduced growth. The SMI is found to dominate FRS in most regimes of interest. (c) 2000 The American Physical Society.

Advantages of calculating shear-wave velocity from surface waves with higher modes

Abstract: Summary The Rayleigh-wave phase velocity of a layered earth model is a function of frequency and four groups of earth parameters: compressional (P)-wave velocity, shear (S)-wave velocity, density, and thickness of layers. For the fundamental mode of Rayleigh waves, analysis of the Jacobian matrix for high frequencies (5-40 Hz) provides a measure of dispersion curve sensitivity to earth model parameters. S-wave velocities are the dominant influence of the four earth model parameters. With the lack of sensitivity of the Rayleigh wave to P-wave velocities and densities, estimations of these parameters can be made for a layered earth model such that dispersive data vary predominantly with S-wave velocities (Xia et al., 1999a). This thesis is valid for higher modes of Rayleigh waves as well. Experimental analysis indicates that energy of higher modes tends to become more dominant as the source distance becomes larger (Park et al., 1999a). In some cases, higher mode data are necessary since shorter wavelength components of fundamental mode Rayleigh waves are obscured by these higher frequency data where higher modes of Rayleigh waves dominate. As well, our modeling results demonstrate at least two quite exciting higher mode properties. First, for fundamental and higher mode Rayleigh wave data with the same wavelength, higher modes can “see” deeper (longer than the wavelength) than fundamental modes (normally shorter than the wavelength). Second, higher mode data can increase the resolution of the inverted S-wave velocities. A much better S-wave velocity picture can be produced from inversion of surface wave data if higher-mode data are included. Real world examples show how resolution can be improved.

Effect of rotation and relaxation times on plane waves in generalized thermo-visco-elasticity

Abstract: The generalized dynamical theory of thermo-elasticity proposed by Green and Lindsay is applied to study the propagation of harmonically time-dependent thermo-visco- elastic plane waves of assigned frequency in an infinite visco-elastic solid of Kelvin-Voigt type, when the entire medium rotates with a uniform angular velocity A more general dispersion equation is deduced to determine the effects of rotation, visco-elasticity, and relaxation time on the phase-velocity of the coupled waves The solutions for the phase velocity and attenuation coefficient are obtained for small thermo-elastic couplings by the perturbation technique Taking an appropriate material, the numerical values of the phase velocity of the waves are computed and the results are shown graphically to illustrate the

Time-domain detection of superluminal group velocity for single microwave pulses

Abstract: Single microwave pulses centered at 9.68 GHz with 100-MHz (full width at half maximum) bandwidth are used to evanescently tunnel through a one-dimensional photonic crystal. In a direct time-domain measurement, it is observed that the peak of the tunneling wave packets arrives (440+/-20) ps earlier than the companion free space (air) wave packets. Despite this superluminal behavior, Einstein causality is not violated since the earliest parts of the signal, also known as the Sommerfeld forerunner, remain exactly luminal. The frequency of oscillations and the functional form of the Sommerfeld forerunner for any causal medium are derived.

Laser pulse modulation instabilities in plasma channels

Abstract: In this paper the modulational instability associated with propagation of intense laser pulses in a partially stripped, preformed plasma channel is analyzed. In general, modulation instabilities are caused by the interplay between (anomalous) group velocity dispersion and self-phase modulation. The analysis is based on a systematic approach that includes finite-perturbation-length effects, nonlinearities, group velocity dispersion, and transverse effects. To properly include the radial variation of both the laser field and plasma channel, the source-dependent expansion method for analyzing the wave equation is employed. Matched equilibria for a laser beam propagating in a plasma channel are obtained and analyzed. Modulation of a uniform (matched) laser beam equilibrium in a plasma channel leads to a coupled pair of differential equations for the perturbed spot size and laser field amplitude. A general dispersion relation is derived and solved. Surface plots of the spatial growth rate as a function of laser beam power and the modulation wave number are presented.

Precise velocity measurement of surface acoustic waves on a bearing ball

Abstract: Using the photoacoustic effect of interference fringes scanned at the phase velocity of surface acoustic waves (SAW), we excited tone bursts of SAW with a center frequency of around 30 MHz on a 8 mm φ steel bearing ball. A surprisingly large number (around 20 turns) of round-trip propagations was observed. The time interval between the SAW at the first and the twelfth turn was as large as 93 μs, however it could be determined with a 2 ns resolution since an exact overlapping of the two wave forms was possible. Thus, we achieved a very high resolution of 0.002% in the velocity measurement, and a velocity change of 2 m/s due to the deposition of a 50-nm-thick Ag film was easily detected. Because of its noncontact nature, this method would be useful for nondestructive evaluation of bearing balls.

The velocity distribution of barotropic turbulence

Abstract: We study the statistical properties of the velocity and velocity gradient distributions in barotropic turbulence. At large enough Reynolds number, the velocity distribution becomes non-Gaussian outside the vortex cores, and its characteristics are completely determined by the properties of the far field induced by the coherent vortices. The velocity gradients are always non-Gaussian inside coherent vortices, due to the spatial velocity correlations associated with the ordered flow in the vortex cores, and become non-Gaussian also in the background turbulence at large enough Reynolds number.

Slow light

Abstract: We present a brief classical discussion of a process to reduce the group velocity of an electromagnetic pulse by many orders of magnitude

Compressional-wave velocities in attenuating media: A laboratory physical model study

Abstract: Elastic-wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material's intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol-saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high-frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self-consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

Stable laser-pulse propagation in plasma channels for GeV electron acceleration

Abstract: To achieve multi-GeV electron energies in the laser wakefield accelerator (LWFA) it is necessary to propagate an intense laser pulse long distances in plasma without disruption. A 3D envelope equation for a laser pulse in a tapered plasma channel is derived, which includes wakefields and relativistic and nonparaxial effects, such as finite pulse length and group velocity dispersion. It is shown that electron energies of approximately GeV in a plasma-channel LWFA can be achieved by using short pulses where the forward Raman and modulation nonlinearities tend to cancel. Further energy gain can be achieved by tapering the plasma density to reduce electron dephasing.

Simultaneous measurement of group and phase delay between two photons

Abstract: We report on an experiment to determine both the group and phase delays experienced by orthogonally polarized photon pairs traveling through a birefringent medium. Both types of delay are determined from the same set of coincidence-counting data. The experiment is based on an interference technique using two-photon multipath indistinguishability to produce an interference feature. Earlier work has shown that this interference feature can be used to measure the group velocity of single-photon wave packets in dielectric media. In the current work, the two-photon interferometer has been modified to produce an additional interference feature that is sensitive to the phase velocity of the light. We have used this technique to simultaneously measure the group delay in crystal quartz with a precision of 0.1 fs and the phase delay with a precision of 8 attoseconds. Our analysis clarifies the effects of group and phase delays and shows the unexpected result that dispersive temporal broadening, which is well known to be canceled for the original interferometer setup, is not canceled for this type of ‘‘postponed compensation’’ interferometer.