Showing papers on "Group velocity published in 2009"

Seismic tomography with the reversible jump algorithm

Abstract: SUMMARY The reversible jump algorithm is a statistical method for Bayesian inference with a variable number of unknowns. Here, we apply this method to the seismic tomography problem. The approach lets us consider the issue of model parametrization (i.e. the way of discretizing the velocity field) as part of the inversion process. The model is parametrized using Voronoi cells with mobile geometry and number. The size, position and shape of the cells defining the velocity model are directly determined by the data. The inverse problem is tackled within a Bayesian framework and explicit regularization of model parameters is not required. The mobile position and number of cells means that global damping procedures, controlled by an optimal regularization parameter, are avoided. Many velocity models with variable numbers of cells are generated via a transdimensional Markov chain and information is extracted from the ensemble as a whole. As an aid to interpretation we visualize the expected earth model that is obtained via Monte Carlo integration in a straightforward manner. The procedure is particularly adept at imaging rapid changes or discontinuities in wave speed. While each velocity model in the final ensemble consists of many discontinuities at cell boundaries, these are smoothed out in the averaged ensemble solution while those required by the data are reinforced. The ensemble of models can also be used to produce uncertainty estimates and experiments with synthetic data suggest that they represent actual uncertainty surprisingly well. We use the fast marching method in order to iteratively update the ray geometry and account for the non-linearity of the problem. The method is tested here with synthetic data in a 2-D application and compared with a subspace method that is a more standard matrix-based inversion scheme. Preliminary results illustrate the advantages of the reversible jump algorithm. A real data example is also shown where a tomographic image of Rayleigh wave group velocity for the Australian continent is constructed together with uncertainty estimates.

Controlling the Velocity of Light Pulses

Abstract: It is now possible to exercise a high degree of control over the velocity at which light pulses pass through material media. This velocity, known as the group velocity, can be made to be very different from the speed of light in a vacuum c. Specifically, the group velocity of light can be made much smaller than c, greater than c, or even negative. We present a survey of methods for establishing extreme values of the group velocity, concentrating especially on methods that work in room-temperature solids. We also describe some applications of slow light.

Generation of vorticity and velocity dispersion by orbit crossing

Abstract: We study the generation of vorticity and velocity dispersion by orbit crossing using cosmological numerical simulations, and calculate the backreaction of these effects on the evolution of large-scale density and velocity divergence power spectra. We use Delaunay tessellations to define the velocity field, showing that the power spectra of velocity divergence and vorticity measured in this way are unbiased and have better noise properties than for standard interpolation methods that deal with mass-weighted velocities. We show that high resolution simulations are required to recover the correct large-scale vorticity power spectrum, while poor resolution can spuriously amplify its amplitude by more than 1 order of magnitude. We measure the scalar and vector modes of the stress tensor induced by orbit crossing using an adaptive technique, showing that its vector modes lead, when input into the vorticity evolution equation, to the same vorticity power spectrum obtained from the Delaunay method. We incorporate orbit-crossing corrections to the evolution of large-scale density and velocity fields in perturbation theory by using the measured stress tensor modes. We find that at large scales (k{approx_equal}0.1h Mpc{sup -1}) vector modes have very little effect in the density power spectrum, while scalar modes (velocity dispersion) can induce percent-level correctionsmore » at z=0, particularly in the velocity divergence power spectrum. In addition, we show that the velocity power spectrum is smaller than predicted by linear theory until well into the nonlinear regime, with little contribution from virial velocities.« less

Electromagnetically induced transparency and slow light in an array of metallic nanoparticles

Abstract: We present a classical analog of electromagnetically induced transparency occurring when light is absorbed by a two-dimensional lattice of metallic spheres mounted on an asymmetric dielectric waveguide. The transparency is manifested as a spectral hole within the surface-plasmon absorption peak of the metallic spheres and is a result of destructive interference of the waveguide modes with incident radiation. The presence of transparency windows is accompanied by slow light effect wherein the group velocity is reduced by a factor of 6000. At the same time, the minimum length for storing a bit of information is of the order of 100 nm. The proposed setup is a much easier means to achieve transparency and slow light compared to existing atomic, solid-state, and photonic systems and allows for the realization of ultracompact optical delay lines and buffers.

Tomography of the Alpine region from observations of seismic ambient noise

Abstract: We use correlations of the ambient seismic noise to study the crust in western Europe. Cross correlation of 1 year of noise recorded at 150 three components broadband stations yields more than 3 000 Rayleigh wave group velocity measurements. These measurements are used to construct Rayleigh group velocity maps of the Alpine region and surrounding area in the 5–80 s period band. In the 5–10 s period band, the seismic noise recorded in Europe is dominated by surface waves originating from the Northern Atlantic ocean. This anisotropy of the noise and the uneven station distribution affect the azimuthal distribution of the paths where we obtain reliable group velocity measurements. As a consequence our group velocity models have better resolution in the northeast direction than in the southwest direction. Finally we invert the resulting Rayleigh wave group velocity maps to determine the Moho depth. Our results are in good agreement with the result of the numerous active experiments in the Alps and provide a continuous image of the Alpine structure.

Slow and fast light: fundamentals and applications

Abstract: We review progress in the development of methods for controlling the group velocity of light. These methods allow one to create situations in which the group velocity of light is much smaller than the velocity of light in vacuum c, in which the group velocity is greater than c, or in which the group velocity is negative. We present a survey of methods for establishing extreme values of the group velocity, concentrating especially on methods that can work in room temperature solids. We also describe some of the applications of slow and fast light that are currently under development.

Disorder-induced coherent scattering in slow-light photonic crystal waveguides.

Abstract: Light transmission measurements and frequency-delay reflectometry maps for GaAs photonic crystal membranes are presented and analyzed, showing the transition from propagation with a well-defined group velocity to a regime completely dominated by disorder-induced coherent scattering. Employing a self-consistent optical scattering theory, with only statistical functions to describe the structural disorder, we obtain excellent agreement with the experiments using no fitting parameters. Our experiments and theory together provide clear physical insight into naturally occurring light localization and multiple coherent-scattering phenomena in slow-light waveguides.

Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration

Abstract: We present a technique based on the selective liquid infiltration of photonic crystal (PhC) waveguides to produce very small dispersion slow light over a substantial bandwidth. We numerically demonstrate that this approach allows one to control the group velocity (from c/20 to c/110) from a single PhC waveguide design, simply by choosing the index of the liquid to infiltrate. In addition, we show that this method is tolerant to deviations in the PhC parameters such as the hole size, which relaxes the constraint on the PhC fabrication accuracy as compared to previous structural-based methods for slow light dispersion engineering.

Disorder-Induced Multiple Scattering in Photonic-Crystal Waveguides

Abstract: In this Letter, we study slow-light transport in photonic-crystal waveguides in the presence of structural imperfections. In contrast with previous theoretical works that rely on perturbation theories, the present formalism takes into account multiple scattering and localization effects. It allows for a quantitative prediction of the main statistical transport coefficients, including averaged values as well as probability distributions. In particular, we evidence that, as the group velocity decreases, the attenuation probability distribution exhibits a rapid broadening that one should consider for designing slow-light devices.

Magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface

Abstract: Steady two-dimensional stagnation-point flow of an electrically conducting power-law fluid over a stretching surface is investigated when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. We have discussed the uniqueness of the solution except when the ratio of free stream velocity and stretching velocity is equal to 1. The effect of magnetic field on the flow characteristic is explored numerically and it is concluded that the velocity at a point decreases/increases with increase in the magnetic field when the free stream velocity is less/greater than the stretching velocity. It is further observed that for a given value of magnetic parameter M, the dimensionless shear stress coefficient | F ″ ( 0 ) | increases with increase in power-law index n when the value of the ratio of free stream velocity and stretching velocity is close to 1 but not equal to 1. But when the value of this ratio further differs from 1, the variation of | F ″ ( 0 ) | with n is non-monotonic.

What is negative refraction

Abstract: We review various published definitions associated with the phenomenon of negative phase velocity propagation of electromagnetic waves in meta-media, as observed through negative refraction. For the principal definition, based on the Poynting vector and the wave vector having negative scalar product, we summarise the various material constraints that have been derived. The distinction between criteria based on the Poynting vector and the group velocity are considered, both in respect of causality, and in the context of moving media. Instances where a fully covariant definition is necessary are also identified, and compared with other results from the extant literature. Satisfaction of the NPV propagation criterion is also considered for surface plasmons.

Phase-dependent electromagnetically induced transparency and its dispersion properties in a four-level quantum well system

Abstract: The four-level inverted-Y configuration realizable in an asymmetric quantum well system interacting with four fields is studied to demonstrate the phenomenon of phase-dependent electromagnetically induced transparency (EIT) in this system. The system is studied under various parametric conditions to demonstrate the controllability of EIT, dispersion properties, and group velocity.

Joint inversion of surface wave velocity and gravity observations and its application to central Asian basins shear velocity structure

Abstract: [1] We implement and apply a method to the jointly inverted of surface wave group velocities and gravity anomalies observations. Surface wave dispersion measurements are sensitive to seismic shear wave velocities, and the gravity measurements supply constraints on rock density variations. Our goal is to obtain a self-consistent three-dimensional shear velocity–density model with increased resolution of shallow geologic structures. We apply the method to investigate the structure of the crust and upper mantle beneath two large central Asian sedimentary basins: the Tarim and Junggar. The basins have thick sediment sections that produce substantial regional gravity variations (up to several hundred milligals). We used gravity observations extracted from the global gravity model derived from the Gravity Recovery and Climate Experiment (GRACE) satellite mission. We combine the gravity anomalies with high-resolution surface wave slowness tomographic maps that provide group velocity dispersion values in the period range between 8 and 100 s for a grid of locations across central Asia. To integrate these data, we use a relationship between seismic velocity and density constructed through the combination of two empirical relations. One determined by Nafe and Drake, most appropriate for sedimentary rocks, and a linear Birch's law, more applicable to denser rocks (the basement). An iterative, damped least squares inversion including smoothing is used to jointly model both data sets, using shear velocity variations as the primary model parameters. Results show high upper mantle shear velocities beneath the Tarim basin and suggest differences in lower crust and upper mantle shear velocities between the eastern and western Tarim.

THz surface wave collapse on coated metal surfaces

Abstract: The Zenneck THz surface wave (Z-TSW) on metals is discussed with respect to its difficulty in generation and measurement. The spatial collapse of the extent of the Z-TSW evanescent field, upon the addition of a sub-wavelength dielectric layer on the metal surface, is explained by a simple model, in good agreement with exact analytical theory. Experimental measurements of the THz surface wave on an aluminum surface covered with a 12.5 µm thick dielectric layer have completely characterized the resultant single-mode dielectric layer THz surface wave (DL-TSW). The measured frequency-dependent exponential fall-off of the evanescent wave from the surface agrees well with theory. The DL-TSW frequency-dependent absorption coefficient, phase velocity, group velocity and group velocity dispersion have been obtained. These guided-wave parameters compare favorably with other guided wave structures.

Soliton trapping of dispersive waves in tapered optical fibers.

Abstract: We show that trapping of dispersive waves by solitons is significantly enhanced in tapered optical fibers as compared with nontapered fibers. For the trapping process to occur, the soliton must be decelerating; in nontapered fiber, the cause of soliton deceleration is Raman self-scattering to spectral regions of lower group velocity. It is shown here that deceleration of the soliton due to the changing group velocities in a tapered optical fiber also enables and enhances the trapping process, independently of Raman gain. This explains the enhanced blue spectral extension observed for supercontinuum generation in tapered optical fibers. This result also indicates that trapping of dispersive waves by solitons will also be possible in fibers or waveguides made from materials with negligible Raman self-scattering.

Coexistence of polarization-locked and polarization-rotating vector solitons in a fiber laser with SESAM.

Abstract: We report the experimental observation of the coexistence of polarization-locked vector solitons (PLVSs) and polarization-rotating vector solitons (PRVSs) in a fiber laser mode locked with a semiconductor saturable absorber mirror. It was found experimentally that interaction between the PLVSs in a fiber laser could lead to formation of bound states of PRVSs. Moreover, the bound PRVSs as a unit have the same group velocity as that of the PLVSs in the cavity.

Multicarrier Light Source With Flattened Spectrum Using Phase Modulators and Dispersion Medium

Abstract: This paper describes a phase-locked multicarrier light source that employs a continuous wave (CW) light source, two phase modulators, and a dispersion medium. A sinusoidal phase modulation (PM) with a modulation index of ?/4 and a group velocity dispersion of ±1/(4?fm 2), where fm is the modulation frequency, are applied to a CW light followed by a large sinusoidal PM. This configuration provides a multicarrier light with a flattened optical power spectrum for any modulation index of the second PM. By adopting a chirped fiber Bragg grating (FBG) as a dispersion medium instead of a long normal dispersion fiber, we can increase the stability of the optical output spectrum and reduce the size of the multicarrier light generator. We have built a prototype with this configuration that generates a 61-carrier light with a 25 GHz interval and a power deviation of less than 8 dB.

Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law

Abstract: Through a combined theoretical and experimental study of disorder-induced incoherent scattering losses in slow-light photonic crystal slab waveguides, we show the importance of Bloch mode reshaping and multiple scattering. We describe a convenient and fully three-dimensional theoretical treatment of disorder-induced extrinsic scattering, including the calculation of backscatter and out-of-plane losses per unit cell, and the extrapolation of the unit-cell loss to the loss for an entire disordered waveguide. The theoretical predictions, which are also compared with recent measurements on dispersion engineered silicon waveguides, demonstrate the failure of the Beer-Lambert law due to multiple scattering. We also explain why the previously assumed group velocity scalings of disorder-induced loss break down in general.

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

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

Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides.

Abstract: We investigate the nonlinear response of photonic crystal waveguides with suppressed two-photon absorption. A moderate decrease of the group velocity (~c/6 to c/15, a factor of 2.5) results in a dramatic (×30) enhancement of three-photon absorption well beyond the expected scaling, ∝1/vg3. This non-trivial scaling of the effective nonlinear coefficients results from pulse compression, which further enhances the optical field beyond that of purely slow-group velocity interactions. These observations are enabled in mm-long slow-light photonic crystal waveguides owing to the strong anomalous group-velocity dispersion and positive chirp. Our numerical physical model matches measurements remarkably.

Light transport regimes in slow light photonic crystal waveguides

Abstract: The dispersive properties of waves are strongly affected by inevitable residual disorder in man-made propagating media, in particular in the slow wave regime. By a direct measurement of the dispersion curve in k space, we show that the nature of the guided modes in real photonic crystal waveguides undergoes an abrupt transition in the vicinity of a band edge. Such a transition that is not highlighted by standard optical transmission measurement, defines the limit where k can be considered as a good quantum number. In the framework of a mean-field theory we propose a qualitative description of this effect and attribute it to the transition from the “dispersive” regime to the diffusive regime. In particular we prove that a scaling law exists between the strength of the disorder and the group velocity. As a result, for group velocities vg smaller than c / 25 the diffusive contribution to the light transport is predominant. In this regime the group velocity vg loses its relevance and the energy transport velocity vE is the proper light speed to consider.

Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials

Abstract: The planewave response of a linear passive material generally cannot be characterized by a single scalar refractive index, as directionality of energy flow and multiple wave vectors may need to be considered. This is especially significant for materials which support negative refraction, negative phase velocity, and counterposition. By means of a numerical example based on a commonly studied bianisotropic material, our theoretical investigation revealed that (i) negative (positive) refraction can arise even though the phase velocity is positive (negative), (ii) counterposition can arise in instances of positive and negative refraction, (iii) the phase velocity and time-averaged Poynting vectors can be mutually orthogonal, and (iv) whether or not negative refraction occurs can depend on the state of polarization and angle of incidence. A further numerical example revealed that negative phase velocity and positive refraction can coexist even in a simple isotropic dielectric material.

Non-local Ponderomotive Nonlinearity in Plasmonic

Abstract: We analyze an inherent nonlinearity of Surface Plasmon Polaritons at the interface of Fermi-Dirac metal plasma, stemming from the depletion of electron density in high-field intensity regions. The derived optical nonlinear coefficients are comparable to the experimental values for metals. We calculate the dispersion relations for the nonlinear propagation of high-intensity Surface Plasmon Polaritons, predicting a nonlinear induced cutoff and vanishing group velocity.

Influence of the anisotropy on zero-group velocity Lamb modes.

Abstract: Guided waves in a free isotropic plate (symmetric Sn and antisymmetric An Lamb modes) exhibit a resonant behavior at frequencies where their group velocity vanishes while their phase velocity remains finite. Previous studies of this phenomenon were limited to isotropic materials. In this paper, the optical generation and detection of these zero-group velocity (ZGV) Lamb modes in an anisotropic plate is investigated. With a circular laser source, multiple local resonances were observed on a silicon wafer. Experiments performed with a line source demonstrated that the frequency and the amplitude of these resonances depend on the line orientation. A comparison between experimental and theoretical dispersion curves for waves propagating along the [100] and [110] directions of the silicon crystal verified that these resonances occur at the minimum frequency of the S1 and A2 Lamb modes. Simulations indicated that it is possible to deduce the three elastic constants of the plate material with good accuracy from ...

Slow Wave Phenomena in Photonic Crystals

Abstract: Slow light in photonic crystals and other periodic structures is associated with stationary points of the photonic dispersion relation, where the group velocity of light vanishes. We show that in certain cases, the vanishing group velocity is accompanied by the so-called frozen mode regime, when the incident light can be completely converted into the slow mode with huge diverging amplitude. The frozen mode regime is a qualitatively new wave phenomenon -- it does not reduce to any known electromagnetic resonance. Formally, the frozen mode regime is not a resonance, in a sense that it is not particularly sensitive to the size and shape of the photonic crystal. The frozen mode regime is more robust and powerful, compared to any known slow-wave resonance. It has much higher tolerance to absorption and structural imperfections.

Midcrustal low‐velocity layer beneath the central Himalaya and southern Tibet revealed by ambient noise array tomography

Abstract: [1] Ambient noise tomography has been becoming an important tool to image the shallow lithospheric structure of the Earth. Using 2 months of ambient noise data from 20 stations of the Himalayan Nepal Tibet Seismic Experiment, we investigate the upper and middle crustal structure in the central Himalaya and southern Tibet. About 120 interstation Rayleigh wave empirical Green's functions with sufficient signal-to-noise ratio are obtained and used for group velocity dispersion analysis in the period range 6–25 s using frequency-time analysis technique. The obtained dispersion data are then used to construct 2-D group velocity maps. At the short periods from 9 to 15 s, the distribution of Rayleigh wave velocities delineates several distinct low- and high-velocity zones separated mainly by geological boundaries. The high group velocity zone is located mainly around regions with plutonic rocks, and the low group velocity zone is located around regions with sedimentary or metasedimentary rocks. Finally, we invert for the shear velocity structure in the upper and middle crust along a N-S trending cross section at the longitude 86.5°E. We observe a clear low-velocity layer in the middle crust (about 10–25 km depth) distributed on both sides of the Indus Yarlung Suture zone. The existence of this midcrustal low-velocity zone suggests a mechanically weaker middle crust beneath the central Himalaya and southern Tibet, which might decouple the upper crustal deformation from that of the lower crust in the Tibetan-Himalayan orogenic processes.

Wave-turbulence approach of supercontinuum generation: Influence of self-steepening and higher-order dispersion

Abstract: We analyze the influence of self-steepening and higher-order dispersion on the process of optical wave thermalization. This study is aimed at developing a thermodynamic formulation of supercontinuum generation in photonic crystal fibers. In the highly nonlinear regime of supercontinuum generation, the optical field exhibits a turbulent dynamics that may be described by the kinetic wave theory. In this respect, the phenomenon of spectral broadening inherent to supercontinuum generation may be interpreted as a natural process of thermalization, which is characterized by an irreversible evolution of the optical field toward a thermodynamic equilibrium state. The numerical simulations show that, under certain conditions, the intensity of the field spontaneously concentrates around two specific frequencies. The theory reveals that these particular frequencies are selected in such a way that the corresponding wave packets propagate with the same group velocity, which is shown to also match the average group velocity of the optical field. This ``velocity-locking'' effect and the underlying process of spectral fission are interpreted in the light of a fundamental property of statistical equilibrium thermodynamics. It is shown that a velocity locking is required, in the sense that it prevents ``a macroscopic internal motion in the wave system.'' Furthermore, the kinetic wave theory sheds light on the role of self-steepening in the incoherent regime of supercontinuum generation. A family of equilibrium spectra is derived in the presence of self-steepening. They are found in quantitative agreement with the numerical simulations of the generalized nonlinear Schr\"odinger equation, without adjustable parameters.