Showing papers on "Group velocity published in 1999"
TL;DR: The relations for the dispersion and the group velocity of the photonic band of the CROW's are obtained and it is found that they are solely characterized by coupling factor k(1) .
Abstract: We propose a new type of optical waveguide that consists of a sequence of coupled high- Q resonators. Unlike other types of optical waveguide, waveguiding in the coupled-resonator optical waveguide (CROW) is achieved through weak coupling between otherwise localized high- Q optical cavities. Employing a formalism similar to the tight-binding method in solid-state physics, we obtain the relations for the dispersion and the group velocity of the photonic band of the CROW's and find that they are solely characterized by coupling factor k 1 . We also demonstrate the possibility of highly efficient nonlinear optical frequency conversion and perfect transmission through bends in CROW's.
1,671 citations
TL;DR: In this paper, an iterative solution technique to the weighted equation proved very effective in the high frequency range when using the Levenberg-Marquardt and singular value decomposition techniques.
Abstract: The shear‐wave (S-wave) velocity of near‐surface materials (soil, rocks, pavement) and its effect on seismic‐wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh‐wave phase velocity of a layered‐earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion‐curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high‐frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high‐frequency range when using the Levenberg‐Marquardt and singular‐value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg‐Marquardt method. Synthetic examples demonstrated calculation efficiency and stability ...
1,378 citations
TL;DR: In this paper, small group velocities of order 90 m/s and large group delays of greater than 0.26 ms were observed in an optically dense hot rubidium gas ( $\ensuremath{\approx}360\mathrm{K}$).
Abstract: We report the observation of small group velocities of order 90 m/s and large group delays of greater than 0.26 ms, in an optically dense hot rubidium gas ( $\ensuremath{\approx}360\mathrm{K}$). Media of this kind yield strong nonlinear interactions between very weak optical fields and very sharp spectral features. The result is in agreement with previous studies on nonlinear spectroscopy of dense coherent media.
1,042 citations
TL;DR: In this paper, the authors investigated the dynamics of light propagation in a cell with antirelaxation wall coating and found that the observed dynamics are analogous to those in electromagnetically induced transparency.
Abstract: The dynamics of resonant light propagation in rubidium vapor in a cell with antirelaxation wall coating are investigated. We change the polarization of the input light and measure the time dependence of the polarization after the cell. The observed dynamics are shown to be analogous to those in electromagnetically induced transparency. Spectral dependence of light pulse delays is found to be similar to that of nonlinear magneto-optic rotation. Delays up to [approx]13 ms are observed, corresponding to a 8 m/s group velocity. Fields of a few microgauss are used to control the group velocity. [copyright] [ital 1999] [ital The American Physical Society ]
508 citations
TL;DR: In this paper, an analysis of the operation of a new type of laser resonator with two-dimensional distributed feedback from a photonic crystal is presented, where the gain medium consists of a 2-(4-biphenylyl)-5(4-tert-butylphenyl)-1,3,4-oxadiazole host doped with Coumarin 490 and DCM and is deposited on lithographically patterned Si/SiO2 structures.
Abstract: We report an analysis of the operation of a new type of laser resonator with two-dimensional distributed feedback from a photonic crystal. The gain medium consists of a 2-(4-biphenylyl)-5(4-tert-butylphenyl)-1,3,4-oxadiazole host doped with Coumarin 490 and DCM and is deposited on lithographically patterned Si/SiO2 structures. Bragg reflections caused by the grating diminish the group velocity of photons along some directions of crystallographic symmetry to zero, and the resulting feedback gives rise to laser oscillations. Dispersion relations for photons were calculated analytically and are used to interpret the laser emission spectra.
414 citations
TL;DR: In this article, the authors used a face-centered cubic model of lattice dynamics to calculate the group velocity of acoustic phonons in the growth direction of periodic superlattices.
Abstract: With the use of a face-centered cubic model of lattice dynamics we calculate the group velocity of acoustic phonons in the growth direction of periodic superlattices. Comparing with the case of bulk solids, this component of the phonon group velocity is reduced due to the flattening of the dispersion curves associated with Brillouin-zone folding. The results are used to estimate semiquantitatively the effects on the lattice thermal conductivity in Si/Ge and GaAs/AlAs superlattices. For a Si/Ge superlattice an order of magnitude reduction is predicted in the ratio of superlattice thermal conductivity to phonon relaxation time [consistent with the results of P. Hyldgaard and G. D. Mahan, Phys. Rev. B 56, 10 754 (1997)]. For a GaAs/AlAs superlattice the corresponding reduction is rather small, i.e., a factor of 2--3. These effects are larger for the superlattices with larger unit period, contrary to the recent measurements of thermal conductivity in superlattices.
231 citations
TL;DR: In this paper, the dynamic response of an axially accelerating, elastic, tensioned beam is investigated, where the time-dependent velocity is assumed to vary harmonically about a constant mean velocity.
229 citations
TL;DR: An analytical expression was derived for light amplification by stimulated emission in arbitrary photonic crystals, which showed and enhancement due to small group velocity, which was evaluated quantitatively for a two-dimensional crystal with a finite thickness.
Abstract: An analytical expression was derived for light amplification by stimulated emission in arbitrary photonic crystals, which showed and enhancement due to small group velocity. This enhancement was evaluated quantitatively for a two-dimensional crystal with a finite thickness, and an extremely large enhancement due to group-velocity anomaly peculiar to two- and three-dimensional crystals was found even for quite a thin crystal.
178 citations
TL;DR: In this paper, the properties of wave packets are mainly illustrated using time-lagged one-point correlation maps performed both on υ′ and wave packet envelopes, and the results show that over most regions in the Northern Hemisphere winter, with the exception of the deep Tropics and near the Aleutian low, medium-scale waves (dominant wavenumber 5-8) exhibit the characteristics of downstream development and occur within wave trains that propagate with eastward group velocities much faster than the phase speeds of individual phases of the waves.
Abstract: Gridded data produced by the ECMWF reanalysis project have been analyzed to document the properties of wave packets in the Northern Hemisphere winter midlatitude upper troposphere. Based on results from earlier investigations, 300-hPa meridional wind variations were chosen for analysis. Wave packet envelopes were also defined by performing complex demodulation on the wind data. The properties of the wave packets are mainly illustrated using time-lagged one-point correlation maps performed both on υ′ and wave packet envelopes. The results show that, over most regions in the Northern Hemisphere winter, with the exception of the deep Tropics and near the Aleutian low, medium-scale waves (dominant wavenumber 5–8) exhibit the characteristics of downstream development and occur within wave trains that propagate with eastward group velocities much faster than the phase speeds of individual phases of the waves. Their group velocity is highly correlated with the local time mean 200–400-hPa wind, while the...
151 citations
TL;DR: An experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary finds the more massive particles are found to have greater kinetic energy.
Abstract: We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3–8 times the gravitational acceleration), the probability distribution P(v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P(v)∼exp(−|v/vc|1.5), in agreement with a recent theory. The characteristic velocity vc is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy.
148 citations
TL;DR: In this article, phase-sensitive ultrashort-pulse interferometry was used to study the modification of optical pulse propagation near the photonic band edges in colloidal crystals consisting of polystyrene spheres in water.
Abstract: We have used phase-sensitive ultrashort-pulse interferometry to study the modification of optical pulse propagation near the photonic band edges in colloidal crystals consisting of polystyrene spheres in water. A strong suppression of the group velocity is found at frequencies near the $L$ gap of the fcc lattice. The group velocity dispersion diverges at the band edges and shows branches of both normal dispersion and anomalous dispersion, which can be interpreted as large changes in the effective mass, both positive and negative. We obtain excellent agreement with the dynamical diffraction theory.
TL;DR: Non-Gaussian velocity distributions are observed at low vibration amplitudes but cross over smoothly to Gaussian distributions as the amplitude is increased, demonstrating cross-correlations between fluctuations in density and temperature.
Abstract: Velocity distributions in a vibrated granular monolayer are investigated experimentally. Non-Gaussian velocity distributions are observed at low vibration amplitudes but cross over smoothly to Gaussian distributions as the amplitude is increased. Cross-correlations between fluctuations in density and temperature are present only when the velocity distributions are strongly non-Gaussian. Confining the expansion of the granular layer results in non-Gaussian velocity distributions that persist to high vibration amplitudes.
TL;DR: In this article, the authors applied the mode branch stripping (MBS) technique of van Heijst & Woodhouse (1997) to approximately 110 000 three-component seismograms and determined the optimum damping of the high-resolution phase velocity maps with a method based on crossvalidation.
Abstract: SUMMARY We apply the mode branch stripping (MBS) technique of van Heijst & Woodhouse (1997) to approximately 110 000 three-component seismograms.We select high-quality data with the reliability estimate of van Heijst & Woodhouse (1997). We assess the in£uence of diierent selection criteria and remove outliers using smooth degree-12 phase velocity maps. We present ¢nal results in terms of Rayleigh- and Love-wave fundamental-mode and overtone global high-resolution (l~40) phase velocity maps. We determine the optimum damping of the high-resolution maps with a method based on cross-validation. Our fundamental-mode phase velocity maps are generally in good agreement with previous studies, especially with Ekstro« m et al. (1997). They do, however, contain more short-wavelength structure than previous studies as we apply relatively little damping. The Rayleigh wave overtone phase velocity measurements made with MBS are of high quality in broad frequency ranges. The measurements are generally well explained by phase velocity maps, and variance reductions for some modes, after rejecting outliers, are as high as 85 per cent. We compare our global phase velocity distributions to the previous results of Stutzmann & Montagner (1994) and to phase velocity maps predicted by 3-D tomographic mantle models. Agreement of the model predictions with our Rayleigh wave phase velocity maps, in terms of both amplitude and observed structures, is good. For Love waves, the qualityof the measurements made with MBS is not as high as for Rayleigh waves.The variance reductions achieved are lower and the agreement between model predictions and our phase velocity maps is less, especially in the frequency ranges where interference between diierent mode branches is strong. Finally, as an additional check on the quality of our overtone measurements, we present a comparison of the fundamental-mode Rayleigh phase velocity distribution at 40 s and our fourth Rayleigh wave overtone phase velocity distribution at 62 s. These two modes are similarly sensitive to velocity anomalies in the top of the upper mantle. We show that the two phase velocity maps are in very close agreement.
TL;DR: In this paper, the authors used an acoustic Doppler current profiler (ADCP) to measure the mean velocity and its vertical shear in a turbulent flow using data gathered in a tidal channel.
Abstract: This paper discusses the principles of measuring the mean velocity and its vertical shear in a turbulent flow using an acoustic Doppler current profiler (ADCP), and presents an analysis of data gathered in a tidal channel. The assumption of horizontal homogeneity of the first moments is fundamental to the derivation of the mean velocity vector because the velocity is never homogeneous over the span of the beams in a turbulent flow. Two tests of this assumption are developed—a comparison of the mean error velocity against its standard deviation and against the mean speed. The fraction of the samples that pass these tests increases with increasing spatial averaging and exceeds 95% for distances longer than 55 beam separations. The statistical uncertainty of the velocity and shear vector, averaged over 10 min and longer, stems from turbulent fluctuations rather than Doppler noise. Estimation of the vertical velocity requires a correction for the bias in the measured tilt. The mean velocity and shear estimates from this natural tidal channel show more complex depth‐time variations than found in idealized one-dimensional channel flow, which seldom occurs in nature. The ADCP measurements reveal the secondary circulation, bursts of up- and downwelling, shear reversals, and transverse velocity shear.
TL;DR: In this article, the authors present an analysis with numerical examples of the following effects in the frequency range from 100 MHz to 2 GHz in order to show the frequency dependence and the effects of total electron content (TEC) of the ionosphere.
Abstract: Recently, there has been increasing interest in the use of spaceborne synthetic aperture radar (SAR) for measuring forest biomass However, it is noted that conventional SAR using C-band or higher frequencies cannot penetrate into foliage, and therefore the biomass measurements require longer wavelengths, typically P-band (500 MHz) It is also known that the ionosphere is highly dispersive, causing group delay and broadening of pulses The variance of the refractive index fluctuations due to turbulence is approximately proportional toƒ−4 In addition, the Faraday rotation due to the geomagnetic field in the ionosphere becomes significant This paper presents an analysis with numerical examples of the following effects in the frequency range from 100 MHz to 2 GHz in order to show the frequency dependence and the effects of total electron content (TEC) of the ionosphere First, the ionospheric turbulence can reduce the coherent length below the equivalent aperture size, and the azimuthal resolution becomes greater than D/2 where D is the antenna aperture size Second, the ionospheric dispersion causes a shift of the imagery due to the group velocity Third, the dispersion also creates broadening of the pulse In addition, multiple scattering due to ionospheric turbulence gives rise to pulse broadening Fourth, we consider the Faraday rotation effect and show that the ellipticity change is negligible, but the orientation angle changes significantly at P-band Numerical examples are shown using typical ionospheric parameters, turbulence spectrum, and TEC values
TL;DR: An analytical expression of the lasing threshold for arbi trary photonic crystals was derived, which showed their reduction due to small group velocities of electromagnetic eigenmodes.
Abstract: An analytical expression of the lasing threshold for arbitrary photonic crystals was derived, which showed their reduction due to small group velocities of electromagnetic eigenmodes. The lasing threshold was also evaluated numerically for a two-dimensional photonic crystal by examining the divergence of its transmission and reflection coefficients numerically. A large reduction of lasing threshold caused by a group-velocity anomaly that is peculiar to two- and three-dimensional photonic crystals was found.
TL;DR: In this article, a noncontact estimation of the thickness and elastic properties of metallic foils was attempted by quantitative analysis of velocity dispersion of laser-generated Lamb waves, which was found to agree well with the numerical solution of the Rayleigh-Lamb equation.
Abstract: Non-contact estimation of the thickness and elastic properties of metallic foils was attempted by quantitative analysis of velocity dispersion of laser-generated Lamb waves. Lamb waves were generated in stainless steel (AISI304) foils with a thickness of less than 40 μm by a Q-switched Nd:YAG laser. Both the zeroth order symmetric S0 and anti-symmetric A0 waves were monitored using a heterodyne-type laser interferometer. Dispersion of group velocity of the A0 mode was obtained by the wavelet transformation, and was found to agree well with the numerical solution of the Rayleigh–Lamb equation. A modified method to estimate both the thickness and acoustic (or elastic) properties from the sheet wave velocity and the group velocity dispersion of the A0 mode was proposed. The modified method was found to provide a correct estimate for stainless steel foils thinner than 30 μm.
TL;DR: In this paper, the authors present a second-order analysis of the pure magnetohydrodynamic equations and hybrid simulations which show that nonlinear Alfven waves traveling in different directions but with equal group velocity can generate pressure-balanced structures with wave vectors perpendicular to the background magnetic field B 0.
Abstract: In the solar wind, Alfvenic fluctuations are typically observed in association with small fluctuations of the density (ρ) and magnetic field strength (B), which tend to be anticorrelated and in approximate pressure balance. One would not expect any finite δρ and δB among pure Alfven waves propagating strictly outward from the Sun. Our paper shows how Alfven waves can nonlinearly produce structures in pressure balance. We present a second-order analysis of the pure magnetohydrodynamic equations and hybrid simulations which show that nonlinear Alfven waves traveling in different directions but with equal group velocity can generate pressure-balanced structures with wave vectors perpendicular to the background magnetic field B 0 . Homogeneous fast waves are also generated in this direction in order to satisfy initial conditions. They cannot be Landau or transit-time damped and so cause the values of B and ρ to vary with time as they beat with the pressure-balanced structures. However, we find δρδB < 0 is satisfied most of the time, and this can partly explain the tendency for anticorrelation observed in the solar wind. In directions away from the perpendicular one, Alfven waves produce driven fast waves which give constant B and ρ to second order. Homogeneous fast and slow waves are also produced in these directions but Landau damp away in large β plasmas. Thus an equilibrium or steady propagating waveform at second order can be produced where B and ρ vary only in the perpendicular direction. If transverse magnetic structures with wave vectors perpendicular to B 0 are included at the same order as the initial Alfven waves, then these evolve to pressure-balanced structures and can also coexist with the Alfven waves. However, an equilibrium is obtained generally only when these structures also have velocity fluctuations equivalent of those of the Alfven waves.
TL;DR: In this article, high-resolution reflectance and emission spectra for high-quality free-standing GaN nearly free from residual strains and impurities are analyzed based on a model exciton-polariton picture in which free A, B, and C excitons couple simultaneously to an electromagnetic wave, where the effective-mass anisotropy and the optical anisotropic are taken into account.
Abstract: High-resolution reflectance and emission spectra have been measured for high-quality free-standing GaN nearly free from residual strains and impurities. They have been analyzed based on a model exciton-polariton picture in which free A, B, and C excitons couple simultaneously to an electromagnetic wave, where the effective-mass anisotropy and the optical anisotropy are taken into account. Taking account of the free-exciton damping, we have calculated not only the dispersion relations but also the energy dependence of the imaginary part of the wave vectors for the excitonic polaritons. Furthermore, the lifetime of each polariton branch has been calculated combining the imaginary part of the polariton wave vectors and the group velocity obtained from the polariton dispersion relations. It is demonstrated that information on the polariton lifetime is indispensable for interpreting the emission spectra. A brief discussion will be given on obtained values for some physical parameters, including hole parameters.
TL;DR: In this paper, the dependence of the strength of the current on the steepness, AIMI, of the incident wave and on its propagation direction is examined as a function of α and β, the inclination of the boundary to the horizontal and the angle between the reported wave group velocity vector and the horizontal, respectively.
Abstract: Internal gravity waves propagating in a fluid of constant buoyancy frequency and approaching a uniform sloping boundary from a direction that is not in a plane normal to the boundary, and dissipating energy on reflection, generate alongslope currents. The net radiation stress or momentum flux into the breaking region is proportional to the flux of energy lost from the waves. It is supposed that the stress is balanced by a frictional boundary stress so that a steady alongslope current is generated. The dependence of the strength of the current on the steepness, AIMI, of the incident wave and on its propagation direction is examined as a function of α and β, the inclination of the boundary to the horizontal and the angle between the incident wave group velocity vector and the horizontal, respectively. Alongslope currents of several centimeters per second, generally exceeding the Lagrangian drift produced by wave reflection alone, may be generated in the ocean or in lakes. Reflection of subcritical ...
TL;DR: In this paper, the effect of SGT on group velocity measurements for fundamental Rayleigh waves and report on its dependence on period (10−200 s), source mechanism, and source depth.
TL;DR: In this paper, the velocity in turbulent convection was measured near its gas-liquid critical point by light scattering on the critical density fluctuations, and the statistics of the velocity fluctuations remained Gaussian up to the Reynolds numbers of ${10}^{5}$.
Abstract: Direct measurements of the velocity in turbulent convection of ${\mathrm{SF}}_{6}$ near its gas-liquid critical point by light scattering on the critical density fluctuations were conducted. The temperature, velocity, and cross frequency power spectra in a wide range of the Rayleigh and Prandtl numbers show scaling behavior with indices, which are rather close to the Bolgiano-Obukhov scaling in the wave number domain. The statistics of the velocity fluctuations remain Gaussian up to the Reynolds numbers of ${10}^{5}$.
TL;DR: In this article, the operation of a continuous-wave mode-locked silver gallium selenide (AgGaSe2) optical parametric oscillator (OPO) was reported.
Abstract: The operation of a continuous-wave mode-locked silver gallium selenide (AgGaSe2) optical parametric oscillator (OPO) is reported. The OPO was synchronously excited by 120-fs-long pulses of 1.55-μm radiation at a repetition rate of 82 MHz. The 1.55-μm radiation is generated by a noncritically phasematched cesium-titanyl-arsenate (CTA)-OPO pumped by a mode-locked Ti:sapphire laser. The AgGaSe2-OPO generates signal and idler radiation in the range from 1.93 μm to 2.49 μm and from 4.1 μm to 7.9 μm, respectively. Up to 67 mW of signal wave output power has been obtained. The experimentally determined pulse duration and chirp parameters are in reasonable agreement with results from a numerical model taking into account group velocity mismatch, group velocity dispersion, self phase modulation, and chirp enhancement.
TL;DR: In this paper, the authors present experimental measurements of a sidewall traveling wave in rotating Rayleigh-B\'enard convection and determine the stability and characteristics of the traveling wave state for dimensionless rotation rates.
Abstract: We present experimental measurements of a sidewall traveling wave in rotating Rayleigh-B\'enard convection. The fluid, water with Prandtl number about 6.3, was confined in a 1-cm-high cylindrical cell with radius-to-height ratio $\ensuremath{\Gamma}=5.$ We used simultaneous optical-shadowgraph, heat-transport, and local temperature measurements to determine the stability and characteristics of the traveling-wave state for dimensionless rotation rates $60l\ensuremath{\Omega}l420.$ The state is well described by the one-dimensional complex Ginzburg-Landau (CGL) equation for which the linear and nonlinear coefficients were determined for $\ensuremath{\Omega}=274.$ The Eckhaus-Benjamin-Feir-stability boundary was established and the phase-diffusion coefficient and nonlinear group velocity were determined in the stable regime. Higher-order corrections to the CGL equation were also investigated.
TL;DR: In this article, a quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field, and a straightforward procedure for exactly diagonalizing the Hamiltonian in one-, two-, or three-dimensional environments, even in the presence of longitudinal phononexciton dispersion, and an arbitrary number of resonant transitions with different frequencies.
Abstract: A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical Sellmeir equations obtained from the Drude-Lorentz model. In the homogeneous (planewave) case, we obtain the detailed quantum mode structure of the coupled polariton fields, and show that the mode expansion in all branches of the dispersion relation is completely defined by the refractive index and the group velocity for the polaritons. We demonstrate a straightforward procedure for exactly diagonalizing the Hamiltonian in one-, two-, or three-dimensional environments, even in the presence of longitudinal phonon-exciton dispersion, and an arbitrary number of resonant transitions with different frequencies. This is essential, since it is necessary to include at least one phonon (IR) and one exciton (UV) mode, in order to represent dispersion in transparent solid media accurately. Our method of diagonalization does not require an explicit solution of the dispersion relation, but relies instead on the analytic properties of Cauchy contour integrals over all possible mode frequencies. When there is longitudinal-phonon dispersion, the relevant group-velocity term is modified so that it only includes the purely electromagnetic part of the group velocity. [S1050-2947(98)05811-9].
TL;DR: In this article, the dispersion velocity of circumferential waves propagating around a thin elastic tube is determined from a time-frequency representation. And the phase velocity is also determined from the group velocity.
Abstract: The experimental measurement of the group and phase velocities of some circumferential waves propagating around a thin elastic tube is a still complex operation. In this study, we show that the dispersion velocity can be determined from a time–frequency representation. We use the Wigner–Ville method by virtue of its interesting properties. On some time–frequency images, the symmetric (S0) and antisymmetric (A1) circumferential waves are identified. The group velocity dispersion estimated from these images is compared with that computed by the proper mode theory method. A good agreement is obtained. The phase velocity is also determined from the group velocity.
01 Jan 1999
TL;DR: In this article, the authors studied the self-induced transparency (SIT) solitons of a 2π-pulse soliton and showed that the group velocity depends on the duration of the pulse, i.e., the shorter is the duration, the higher is its speed.
Abstract: A self-induced transparency (SIT) phenomenon consists in the propagation of a powerful ultrashort pulse (USP) of light through a resonance medium without the distortion and energy loss of this pulse [1–4]. This phenomenon is characterised by the continuous absorption and re-emission of electromagnetic radiation by resonant atoms of medium in such a manner that steady-state optical pulse propagates. In the ideal case the energy dissipation of the USP is invisible, and the state of the resonant medium is not varying. It means that the medium is transparent. The group velocity of a such steady-state pulse, called 2π-pulse or soliton of SIT, is less than the phase speed of light in a medium. The group velocity depends on a 2π-pulse duration: the shorter is the duration, the higher is its speed [2–5]. When two pulses of the different velocities spread in the medium, the second pulse may overtake the first and a collision will take place. After the collision, the solitons keep their shape and velocity (but in general all other parameters of solitons may alter). This fundamental property of the SIT solitons has been studied many times both theoretically and experimentally [3,6,7].
TL;DR: In this article, the envelope formalism for the description of a small-amplitude parallel-propagating Alfven wave train is tested against direct numerical simulations of the Hall-MHD equations in one space dimension where kinetic effects are neglected.
Abstract: . The envelope formalism for the description of a small-amplitude parallel-propagating Alfven wave train is tested against direct numerical simulations of the Hall-MHD equations in one space dimension where kinetic effects are neglected. It turns out that the magnetosonic-wave dynamics departs from the adiabatic approximation not only near the resonance between the speed of sound and the Alfven wave group velocity, but also when the speed of sound lies between the group and phase velocities of the Alfven wave. The modulational instability then does not anymore affect asymptotically large scales and strong nonlinear effects can develop even in the absence of the decay instability. When the Hall-MHD equations are considered in the long-wavelength limit, the weakly nonlinear dynamics is accurately reproduced by the derivative nonlinear Schrodinger equation on the expected time scale, provided no decay instabilities are present. The stronger nonlinear regime which develops at later time is captured by including the coupling to the nonlinear dynamics of the magnetosonic waves.
TL;DR: The accuracy of the group-velocity description of dispersive pulse propagation in a double-resonance Lorentz model dielectric is shown to decrease monotonically as the propagation distance increases as discussed by the authors.
Abstract: The accuracy of the group-velocity description of dispersive pulse propagation in a double-resonance Lorentz model dielectric is shown to decrease monotonically as the propagation distance increases, whereas the accuracy of the asymptotic description increases monotonically as the propagation distance increases above a single absorption depth in the medium at the pulse carrier frequency.
TL;DR: In this article, a new sensing method for measuring flow velocity distribution directly by using low-coherence interference techniques is proposed and demonstrated, where a temporally fluctuating signal, not the Doppler frequency shift, is detected.
Abstract: A new sensing method for measuring flow velocity distribution directly by using low-coherence interference techniques is proposed and demonstrated. In this method a temporally fluctuating signal, not the Doppler frequency shift, is detected. Theoretical analysis shows that a spectrum of light backscattered from a particle takes a Gaussian form whose width is simply proportional to the flow velocity. The measured velocity is in good agreement with the actual flow velocity derived from the flow rate. The dynamic range of this sensing method is governed by the frequency range of the fast-Fourier-transform processor used and is estimated to be 1.4×10-4–14 m/s. The depth position can be adjusted with an accuracy of approximately 30 μm, which is determined by the coherence length of the light source.