Group Velocity Distribution Research Articles

Dynamics of focused femtosecond laser pulse during photodisruption of crystalline lens

Propagation of laser pulses of femtosecond time duration (focused through a focusing lens inside the crystalline lens) has been investigated in this paper. Transverse beam diffraction, group velocity dispersion, graded refractive index structure of the crystalline lens, self-focusing, and photodisruption in which plasma is formed due to the high intensity of laser pulses through multiphoton ionization have been taken into account. The model equations are the modified nonlinear Schrödinger equation along with a rate equation that takes care of plasma generation. A close analysis of model equations suggests that the femtosecond laser pulse duration is critical to the breakdown in the lens. Our numerical simulations reveal that the combined effect of self-focusing and multiphoton ionization provides the breakdown threshold. During the focusing of femtosecond laser pulses, additional spatial pulse splitting arises along with temporal splitting. This splitting of laser pulses arises on account of self-focusing, laser induced breakdown, and group velocity distribution, which modifies the shape of laser pulses. The importance of the present study in cavitation bubble generation to improve the elasticity of the eye lens has also been discussed in this paper.

S-wave velocity model for several regions of the Kamchatka Peninsula from the cross correlations of ambient seismic noise

The data from the seismic networks of the Kamchatka Branch of the Geophysical Survey of the Russian Academy of Sciences are used for calculating the cross correlations of seismic noise for the stationary digital stations over 2013 and for radio telemetric stations (RTS) in the region of the Klyuchevskoy volcano over the period from January 1, 2009 to May 31, 2013. Four hundred and two correlations overall are calculated. The fundamental-mode group velocities of the Rayleigh waves are calculated in the periods ranging from 5 to 50 s. The calculations for the region of the Klyuchevskaya group of volcanoes are based on the RTS data and cover the periods from 2 to 8 s. The two-dimensional (2D) maps of group velocity distributions in different periods are constructed with the use of the algorithm of surface wave tomography (Barmin, 2001). The velocity sections for the selected Kamchatka regions are reconstructed by the dispersion curve inversion technique (Mordret, 2014). For each region, the structure of the Earth’s crust and upper mantle down to a depth of 50 km was obtained.

Rayleigh wave group velocity tomography of Gujarat region, Western India and its implications to mantle dynamics

In the present study, fundamental Rayleigh waves with varying period from 10 to 80 s are used to obtain group velocity maps in the northwest Deccan Volcanic Province of India. About 350 paths are obtained using 53 earthquakes (4.8 ≤ M ≥ 7.9) recorded by the SeisNetG (Seismic Network of Gujarat). Individual dispersion curves of group velocity of Rayleigh wave for each source-station path are estimated using multiple filter technique. These curves are used to determine lateral distribution of Rayleigh wave group velocity by tomographic inversion method. Our estimated Rayleigh group velocity at varying depths showed conspicuous corroboration with three tectonic blocks [Kachchh Rift Basin (KRB), Saurashtra Horst (SH), and Mainland Gujarat (MG)] in the region. The seismically active KRB with a thicker crust is characterized as a low velocity zone at a period varying from 10 to 30 s as indicative of mantle downwarping or sagging of the mantle beneath the KRB, while the SH and MG are found to be associated with higher group velocities, indicating the existence of the reduced crustal thickness. The trend of higher group velocity was found prevailed adjacent to the Narmada and Cambay rift basins that also correspond to the reduced crust, suggesting the processes of mantle upwarping or uplifting due to mantle upwelling. The low velocities at periods longer than 40 s beneath the KRB indicate thicker lithosphere. The known Moho depth correlates well with the observed velocities at a period of about 30 s in the Gujarat region. Our estimates of relatively lower group velocities at periods varying from 70 to 80 s may correspond to the asthenospheric flow beneath the region. It is interesting to image higher group velocity for the thinner crust beneath the Arabian Sea adjacent to the west coast of Gujarat at the period of 40 s that may correspond to the upwarped or upwelled mantle beneath the Arabian Sea. Our results have better resolution estimated by a radius of equivalent circular averaging area for each period.

High-level ab initio potential energy surface and dynamics of the F- + CH3I SN2 and proton-transfer reactions.

Bimolecular nucleophilic substitution (SN2) and proton transfer are fundamental processes in chemistry and F- + CH3I is an important prototype of these reactions. Here we develop the first full-dimensional ab initio analytical potential energy surface (PES) for the F- + CH3I system using a permutationally invariant fit of high-level composite energies obtained with the combination of the explicitly-correlated CCSD(T)-F12b method, the aug-cc-pVTZ basis, core electron correlation effects, and a relativistic effective core potential for iodine. The PES accurately describes the SN2 channel producing I- + CH3F via Walden-inversion, front-side attack, and double-inversion pathways as well as the proton-transfer channel leading to HF + CH2I-. The relative energies of the stationary points on the PES agree well with the new explicitly-correlated all-electron CCSD(T)-F12b/QZ-quality benchmark values. Quasiclassical trajectory computations on the PES show that the proton transfer becomes significant at high collision energies and double-inversion as well as front-side attack trajectories can occur. The computed broad angular distributions and hot internal energy distributions indicate the dominance of indirect mechanisms at lower collision energies, which is confirmed by analyzing the integration time and leaving group velocity distributions. Comparison with available crossed-beam experiments shows usually good agreement.

Ambient Seismic Noise Tomography of a Loess High Bank at Dunaszekcső (Hungary)

Loess high banks along the right side of the Danube in Hungary are potential subjects of landslides. Small scale ambient seismic noise tomography was used at the Dunaszekcső high bank. The aim of the study was to map near surface velocity anomalies since we assume that the formation of tension cracks—which precede landslides—are represented by low velocities. Mapping Rayleigh wave group velocity distribution can help to image intact and creviced areas and identify the most vulnerable sections. The study area lies at the top of the Castle Hill of Dunaszekcső, which was named after Castellum Lugio, a fortress of Roman origin. The presently active head scarp was formed in April 2011, and our study area was chosen to be at its surroundings. Cross-correlation functions of ambient noise recordings were used to retrieve the dispersion curves, which served as the input of the group velocity tomography. Phase cross-correlation and time-frequency phase weighted stacking was applied to calculate the cross-correlation functions. The average Rayleigh wave group velocity at the loess high bank was found to be 171 ms $$^{-1}$$ . The group velocity map at a 0.1 s period revealed a low-velocity region, whose location coincides with a highly creviced area, where slope failure takes place along a several meter wide territory. Another low velocity region was found, which might indicate a previously unknown loosened domain. The highest velocities were observed at the supposed remnants of Castellum Lugio.

Tomographic Rayleigh wave group velocities in the Central Valley, California, centered on the Sacramento/San Joaquin Delta

AbstractIf shaking from a local or regional earthquake in the San Francisco Bay region were to rupture levees in the Sacramento/San Joaquin Delta, then brackish water from San Francisco Bay would contaminate the water in the Delta: the source of freshwater for about half of California. As a prelude to a full shear‐wave velocity model that can be used in computer simulations and further seismic hazard analysis, we report on the use of ambient noise tomography to build a fundamental mode, Rayleigh wave group velocity model for the region around the Sacramento/San Joaquin Delta in the western Central Valley, California. Recordings from the vertical component of about 31 stations were processed to compute the spatial distribution of Rayleigh wave group velocities. Complex coherency between pairs of stations was stacked over 8 months to more than a year. Dispersion curves were determined from 4 to about 18 s. We calculated average group velocities for each period and inverted for deviations from the average for a matrix of cells that covered the study area. Smoothing using the first difference is applied. Cells of the model were about 5.6 km in either dimension. Checkerboard tests of resolution, which are dependent on station density, suggest that the resolving ability of the array is reasonably good within the middle of the array with resolution between 0.2 and 0.4°. Overall, low velocities in the middle of each image reflect the deeper sedimentary syncline in the Central Valley. In detail, the model shows several centers of low velocity that may be associated with gross geologic features such as faulting along the western margin of the Central Valley, oil and gas reservoirs, and large crosscutting features like the Stockton arch. At shorter periods around 5.5 s, the model's western boundary between low and high velocities closely follows regional fault geometry and the edge of a residual isostatic gravity low. In the eastern part of the valley, the boundaries of the low‐velocity zone and gravity anomaly are better aligned at longer periods (around 10.5 s) suggesting that the eastern edge of the gravity low is associated with deeper structure. There is a strong correspondence between a low in gravity near the Kirby Hills fault and low velocities from the ambient noise tomography. At longer periods, higher velocities creep in from the east and narrow the overall dimension defined by the lower velocities. Overall, there is a strong correspondence between the shape and location of low velocities in the Rayleigh wave velocity images, and geological and geophysical features.

Information propagation and equilibration in long-range Kitaev chains

We study the propagation of information through a Kitaev chain with long-range pairing interactions. Although the Lieb-Robinson bound is violated in the strict sense for long-range interacting systems, we illustrate that a major amount of information in this model still propagates ballistically on a light cone. We find a pronounced effect of the interaction range on the decay of the mutual information between spatially disconnected subsystems. A significant amount of information is shared at time-like separations. This regime is accompanied by very slow equilibration of local observables. As the Kitaev model is quasi-free, we illustrate how the distribution of quasi-particle group velocities explains the physics of this system qualitatively.

On the quantitative determination of coal seam thickness by means of in-seam seismic surveys

By means of in-seam seismic (ISS) surveys carried out at Karvina coal mine of OKD, Czech Republic, in two neighbouring panels it is shown how the distribution of coal seam thickness can be investigated if the coal seam consists of almost pure coal. The coal seam under investigation was considerably affected by erosion, which resulted in thickness changes amounting from ∼30 cm up to ∼4.40 m. First, by applying ISS-tomographic inversion to the group travel times for a constant frequency value, the distribution of the related group velocity was determined, which showed the extension of the erosions within the survey areas. By correlating the group velocity distribution with known values of the coal seam thickness along a gate, a relation in terms of a polynomial approximation between these quantities could be derived. This relation is specific for a chosen frequency value and resolves in general only some of the thickness range. For the application presented in this paper, a value of 200 Hz was chosen for the constant frequency value by which a range of coal seam thicknesses from about 100 cm to about 300 cm was resolved. This was the main objective of the surveys. For the investigation of a greater variation of coal seam thickness (or even the complete thickness distribution), the described procedure has to be repeated for different constant frequency values. The final thickness map then has to be combined from the individual results for the different constant frequency values. The thickness range that was investigated by the surveys was in good agreement with the thickness encountered by mining the panel.

Two‐mode ionospheric response and Rayleigh wave group velocity distribution reckoned from GPS measurement following Mw 7.8 Nepal earthquake on 25 April 2015

AbstractThe coseismic‐induced ionospheric total electron content (TEC) perturbations were analyzed following the Mw 7.8 Nepal earthquake (28.147°N, 84.708°E; depth ~15 km) that occurred on 25 April 2015 at 06:11:26 UTC. The ionospheric response is due to both the modes, i.e., shock acoustic waves (slow mode) and Rayleigh wave induced (fast mode). The continuous Global Positioning System (GPS) data at about 60 sites from various GPS networks have been used in the present study. All the sites within epicentral distance of ~2400 km and 70°–170° azimuth recorded the Rayleigh wave‐induced TEC response, while the sites within ~400–2200 km in the same azimuth recorded the response from both the modes. The maximum coseismic‐induced peak‐to‐peak TEC amplitude is ~1.2 total electron content unit, 1 TECU = 1016 el m−2. From Hodochron plot, the apparent Rayleigh wave velocity has been determined as ~2400 m/s on the average and the acoustic wave velocity as 1180 m/s, both these waves being discernible beyond ~1200 km of epicentral distance as also evident from Hodochron plot and wavelet spectrographs. We reckoned the Rayleigh wave group velocities using ionospheric response at selected radial pairs of stations and validated. The ionospheric response distribution seen mainly depending on the epicentral distance, satellite geometry, directivity of radiation pattern, and the upper crustal heterogeneity. This study highlights the characteristics of ionospheric response consequent to the 2015 Nepal earthquake.

Anomalous dispersion properties of TM waves in subwavelength metallic waveguides loaded by uniaxial metamaterials

Abstract Dispersion properties of transverse magnetic (TM) waves in a subwavelength metallic waveguide loaded by uniaxial metamaterials are investigated, based on two kinds of uniaxial metamaterials with different orientations of optical axis. The numerical results show that the existence of fundamental TM 0 mode and high-order TM modes in the waveguide system is dependent on the orientation of optical axis. In addition, their anomalous dispersion properties are clarified. When the orientation of optical axis is selected properly, there are two branches of dispersion curves for each high-order mode—one is normal dispersion and another belongs to anomalous dispersion, showing a transition from a backward wave to a forward one with the increase of working frequency. Moreover, the group velocity and energy flow distribution for TM 1 mode are also demonstrated. These properties may have potential applications in optical information storage, integrated optics and nanophotonic devices.

Rayleigh wave group velocity distributions for East Asia using ambient seismic noise

AbstractVertical component data from 206 broadband seismometer stations from Korean networks Korean Institute of Geoscience and Mineral Resources and Korea Meteorological Administration, the Japanese F‐net network, and the Chinese New China Digital Seismograph Network and Northeast China Extended Seismic Array network are collected for the year 2011, and the ambient seismic noise is analyzed. Rayleigh wave group velocity distribution maps are created in the period range 10 to 70 s. Our results are largely consistent with previous studies of the area but provide greater detail in the Korean peninsula and the Sea of Japan. Low group velocities are observed in the Ulleung basin, and the Chubu‐Kanto and Kyushu regions in Japan. At 10 s period, sediment basins in the Sea of Japan appear as low group velocity regions relative to higher group velocity continental regions. At periods longer than 40 s, a low group velocity region emerges in the Ulleung basin region, and is bounded by the Korean peninsula.

Structural model of the lithosphere–asthenosphere system beneath the Qinghai–Tibet Plateau and its adjacent areas

The deep structure of the lithosphere–asthenosphere system, as imaged from geophysical data, of the Qinghai–Tibet Plateau, the highest on the Earth, provides important clues in understanding its orogenic processes. Here we reconstruct the main features of the structure of the crust and upper mantle from surface wave tomography in the Qinghai–Tibet Plateau and its adjacent areas, in order to understand the modality of the convergence and collision process between the Indian and Eurasian plates. Based on Rayleigh waves dispersion theory, we collected long period and broad-band seismic data from the global and regional seismic networks surrounding the study area (20°N–50°N, 70°E–110°E). After applying instrument response calibration and filtering, group velocities of the fundamental mode of Rayleigh waves are measured using the frequency–time analysis (FTAN). Combining the published dispersion data, a 2-D surface-wave tomography method is applied to calculate the lateral variations of group velocity distribution at different periods, in the range from 8s to 150s. The Hedgehog non-linear inversion method is performed to obtain shear wave velocity (Vs) versus depth models of the crust and upper mantle for 181 cells, with size 2°×2°. In order to identify the cellular representative models, we applied the local smoothness optimization method (LSO). Fairly detailed structural models of the lithosphere–asthenosphere system have been defined. The Vs models demonstrate the lateral variation of the thickness of the metasomatic lid between the south and north of the Bangong–Nujiang Suture (BNS) and the west and east of Tibet. The variation in thickness of the metasomatic lid may suggest that the leading edge of the subducting Indian slab reaches up to BNS.

Anomalous dispersion and group velocity properties in subwavelength uniaxial metamaterial waveguide with metal cladding

We investigate propagation behavior of electromagnetic waves in a slab uniaxial metamaterial waveguide with metal cladding and discuss the dispersion relation, group velocity and energy flux distribution of transverse electric guided modes in two kinds of uniaxial metamaterial waveguides with different orientations of optical axis in detail. The numerical results show that there exist anomalous dispersion properties such as backward modes existing in low-frequency range, and the group velocity can be negative or approach zero. If the orientation of optical axis is selected properly, each guided mode has two dispersion curves—one is normal dispersion and another belongs to anomalous dispersion and shows a transition from a backward mode to a forward one with the angular frequency increasing. In addition, the condition of the existence of cutoff frequency is clarified. These properties may have potential applications in optical information storage, optical communication, integrated optics and nanophotonic devices.

Spectral properties of a two dimensional photonic crystal with quasi-integrable geometry

In this paper we study the statistical properties of the allowed frequencies for electromagnetic waves propagating in two-dimensional photonic crystals with quasi-integrable geometry. We compute the level spacing, group velocity, and curvature distributions (P(s), P(v), and P(c), respectively) and compare them with the corresponding random matrix theory predictions. Due to the quasi-integrability of the crystal we observe signatures of intermediate statistics in P(s) and P(c) for high refractive index contrasts.

Tight focusing of radially polarized vortex laser pulse

The tight focusing of femtosecond radially polarized vortex laser pulse by a high numerical aperture objective is investigated in this paper. Based on Richards-Wolf vectorial diffraction theory, the electric field and the group velocity of the radially polarized vortex femtosecond laser pulse are studied in great detail. It finds that the femtosecond radially polarized vortex laser pulse can travel at various group velocities near the focus, that is, slower or faster than light velocity in vacuum, depending on the numerical aperture of the focusing objective system. Moreover, the effect of spherical aberration of objective, topological charge and time duration of the radially polarized vortex laser pulse on the group velocity distribution near the focus is discussed.

Ambient seismic noise Rayleigh wave tomography for the Pannonian basin

We studied the Rayleigh wave group velocities beneath Hungary using ambient seismic noise tomography. Noise data were gathered from 17 broadband seismological stations in and around the Pannonian basin. The cross-correlation method was used to calculate the Green’s functions. Group velocities belonging to the fundamental mode Rayleigh waves were determined by multiple filter technique. We measured the dispersion curves for each station pair in a period range of 7–28 s and computed maps of group velocity distribution using a 2D tomography method. The group velocity maps of 7–14 s periods correlate well with sedimentary thickness and regional geology. Velocity anomalies observed at longer periods reflect the effect of the crustal and mantle structural features.

Direct Excitation of Propagating Spin Waves by Focused Ultrashort Optical Pulses

An all-optical experiment long utilized to image phonons excited by ultrashort optical pulses has been applied to a magnetic sample. In addition to circular ripples due to surface acoustic waves, we observe an X-shaped pattern formed by propagating spin waves. The emission of spin waves from the optical pulse epicenter in the form of collimated beams is qualitatively reproduced by micromagnetic simulations. We explain the observed pattern in terms of the group velocity distribution of Damon-Eshbach magnetostatic spin waves in the reciprocal space and the wave vector spectrum of the focused ultrafast laser pulse.

Multiatomic mirror for perfect reflection of single photons in a wide band of frequency

A resonant two level atom doped in one dimensional waveguide behaves as a mirror, but this single-atom "mirror" can only reflect single photon perfectly at a specific frequency. For a one dimensional coupled-resonator waveguide, we propose to extend the perfect reflection region from a specific frequency to a wide band by placing many atoms individually in the resonators in a finite coordinate region of the waveguide. Such a doped resonator array promises us to control the propagation of a practical photon wave packet with certain momentum distribution instead of a single photon, which is ideally represented by a plane wave with specific momentum. The studies based on the discrete-coordinate scattering theory display that such hybrid structure indeed provides a near-perfect reflection for single photon in a wide band. We also calculated photon group velocity distribution, which shows that the perfect reflection with wide band exactly corresponds to the stopping light region.

Rayleigh wave group velocity distribution in Ningxia

In this article, seven months ambient noise data and 10 events recorded at seven digital stations from the Ningxia (宁夏) regional seismic network and 5 500-t controlled source explosion data recorded by 15 temporary and 7 permanent seismic stations are used to measure dispersion curves of fundamental mode Rayleigh waves. The study region was divided into grids with 0.1°×0.1°; group velocity distributions of Rayleigh waves from 6–22 s were determined with the Occam’s inversion technique. These velocity distribution maps show the lateral velocity variations in the study area, and the velocity structures are correlated with surface geology and tectonic units. The Yinchuan (银川) basin is clearly featured with low velocities, and the Helan (贺兰) Mountain and southern mountain areas are revealed with high velocities.

Crustal velocity structures beneath North China revealed by ambient noise tomography

We collected continuous noise waveform data from January 2007 to February 2008 recorded by 190 broadband and 10 very broadband stations of the North China Seismic Array. The study region is divided into grid with interval 0.25°×0.25°, and group velocity distribution maps between 4 s and 30 s are obtained using ambient noise tomography method. The lateral resolution is estimated to be 20–50 km for most of the study area. We construct a 3-D S wave velocity model by inverting the pure path dispersion curve at each grid using a genetic algorithm with smoothing constraint. The crustal structure observed in the model includes sedimentary basins such as North China basin, Yanqing-Huailai basin and Datong basin. A well-defined low velocity zone is observed in the Beijing-Tianjin-Tangshan region in 22–30 km depth range, which may be related to the upwelling of hot mantle material. The high velocity zone near Datong, Shuozhou and Qingshuihe within the depth range of 1–23 km reveals stable characteristics of Ordos block. The Taihangshan front fault extends to 12 km depth at least.