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Showing papers on "Brillouin zone published in 2003"


Journal ArticleDOI
TL;DR: In this article, the spin-fermion model near the antiferromagnetic instability in two dimensions was analyzed and it was shown that λ scales with the spin correlation length and diverges at criticality, implying that the conventional perturbative expansion breaks down.
Abstract: We present the full analysis of the normal state properties of the spin-fermion model near the antiferromagnetic instability in two dimensions. The model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies—an effective spin-fermion interaction g¯ and an energy ωsf below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ2 ∝ g¯/ωsf. We show that λ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We develop a novel approach to the problem—the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavours—which allows us to explicitly account for all terms which diverge as powers of λ, and treat the remaining, O(log λ) terms...

355 citations


Journal ArticleDOI
TL;DR: Application of the transfer-matrix technique to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method.
Abstract: Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method.

298 citations


Journal ArticleDOI
TL;DR: A comprehensive and up-to-date review of the main physical properties (such as energy profiles, localization, scale laws, multifractal analysis, transmission spectra, transmission fingerprints, electronic structures, magnetization curves and thermodynamic properties) of the elementary excitations that can propagate in multilayered structures with constituents arranged in a quasiperiodic fashion is presented in this article.

254 citations


Journal ArticleDOI
TL;DR: In this paper, the optical absorption spectra of graphite and carbon nanotubes are calculated for a single-wall carbon nanophase and the chirality dependence of the absorption matrix element is analyzed analytically.
Abstract: The optical absorption spectra of \ensuremath{\pi} electrons are calculated for graphite and carbon nanotubes. Particular attention is paid to the processes contributing to the optical absorption as a function of the electron wave vector k and light polarization direction. The optical absorption amplitude around the K point in the Brillouin zone has a node in the two-dimensional Brillouin zone of graphite. The formula for the absorption scattering matrix around the K point is given analytically by expanding the matrix element into a Taylor series. The chirality dependence of the absorption matrix element of a single-wall carbon nanotube is presented.

253 citations


Journal ArticleDOI
TL;DR: In this article, the authors review the theoretical results of the interaction effects in the energy dispersion of the Bloch wave and in the linear stability of such waves and show that the lowest Bloch band develops a loop at the edge of the Brillouin zone.
Abstract: Superflow of a Bose–Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results of the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau–Zener tunnelling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making a transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.

232 citations


Journal ArticleDOI
TL;DR: Dielectric periodic media can possess a complex photonic band structure with allowed bands displaying strong dispersion and anisotropy, and it is shown that for some frequencies the form of iso-frequency contours mimics theform of the first Brillouin zone of the crystal.
Abstract: Dielectric periodic media can possess a complex photonic band structure with allowed bands displaying strong dispersion and anisotropy. We show that for some frequencies the form of iso-frequency contours mimics the form of the first Brillouin zone of the crystal. A wide angular range of flat dispersion exists for such frequencies. The regions of iso-frequency contours with near-zero curvature cancel out diffraction of the light beam, leading to a self-guided beam.

219 citations


Journal ArticleDOI
TL;DR: In this paper, the formation of the pseudogap in a polystyrene crystal is studied by means of reflectivity and transmission spectra, and a characterization of the photonic band structure in the hexagonal facet of the Brillouin zone is made using angle resolved reflectivity measurements.
Abstract: Artificial opals consisting of polystyrene spheres ordered into a fcc lattice are grown with control over the orientation and thickness. A thorough study of the formation of the pseudogap in these structures is carried out by means of reflectivity and transmission spectra. Special attention is paid to discriminating those features inherent to the photonic crystal, and those to the substrate on which the crystal is grown. Further, a characterization of the photonic band structure in the hexagonal facet of the Brillouin zone is made using angle resolved reflectivity measurements.

199 citations


Journal ArticleDOI
TL;DR: It is shown that the ideal strength of a metal has been shown to be dictated by instabilities in the acoustic phonon spectra, and further suggests that shear failure is an inherent property of aluminum even in an initially dislocation-free perfect crystal.
Abstract: We have calculated the phonon spectra of aluminum as a function of strain using density functional perturbation theory for $⟨110⟩$, $⟨100⟩$, and $⟨111⟩$ uniaxial tension, as well as relaxed $⟨112⟩{111}$ shear. In all four cases, phonon instabilities occur at points away from the center of the Brillouin zone and intrude before the material becomes unstable according to elastic stability criteria. This is the first time the ideal strength of a metal has been shown to be dictated by instabilities in the acoustic phonon spectra. We go on to describe the crystallography of the unstable modes, all of which are shear in character. This work further suggests that shear failure is an inherent property of aluminum even in an initially dislocation-free perfect crystal.

190 citations


Journal ArticleDOI
TL;DR: In this paper, the phonons in boron nitride nanotubes using density functional perturbation theory in the local density approximation were evaluated based on the nonsymmorphic rod-group symmetry of the tubes, the Raman and infrared-active modes at the G point of the one-dimensional Brillouin zone were evaluated.
Abstract: We present an extensive first-principles study of the phonons in boron nitride nanotubes using density functional perturbation theory in the local density approximation. Based on the nonsymmorphic rod-group symmetry of the tubes, the Raman- and infrared-active modes at the G point of the one-dimensional Brillouin zone are evaluated. For zigzag and chiral nanotubes, the set of infrared-active modes is a subset of the Raman-active modes. In particular, the radial breathing mode is not only Raman but also infrared active. However, for armchair tubes, the sets of infrared- and Raman-active modes are disjoint. This may serve to spectroscopically distinguish between macroscopic samples of zigzag-chiral and armchair nanotubes. We present the frequencies of the active modes of zigzag, chiral, and armchair tubes as a function of the tube diameter and compare the results with the frequencies obtained by the zone-folding method, i.e., the rolling of a single hexagonal BN sheet into a tube. Except for the high-frequency tangential modes, the zone-folding results are in very good agreement with the ab initio calculations. The radial breathing mode frequency can be derived by folding a sheet of finite width. Finally, we show that the effects of bundling on the phonon frequencies are small. This demonstrates that the obtained results for isolated BN tubes may serve as a basis for an accurate assignment of phonon modes in spectroscopic measurements.

177 citations


Journal ArticleDOI
TL;DR: In this paper, the authors review the theoretical results on the interaction effects in the energy dispersion of the Bloch wave and in the linear stability of such waves and discuss the experimental implications of their findings.
Abstract: Superflow of Bose-Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results on the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau-Zener tunneling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.

170 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the band structure of a Bose-Einstein condensate in a one-dimensional periodic potential by calculating stationary solutions of the Gross-Pitaevskii equation, which have the form of Bloch waves.
Abstract: We investigate the band structure of a Bose-Einstein condensate in a one-dimensional periodic potential by calculating stationary solutions of the Gross-Pitaevskii equation, which have the form of Bloch waves. We demonstrate that loops (``swallow tails'') in the band structure occur both at the Brillouin zone boundary and at the center of the zone, and they are therefore a generic feature. A physical interpretation of the swallow tails in terms of periodic solitons is given. The linear stability of the solutions is investigated as a function of the strength of the mean-field interaction, the magnitude of the periodic potential, and the wave vector of the condensate. The regions of energetic and dynamical stability are identified by considering the behavior of the Gross-Pitaevskii energy functional for small deviations of the condensate wave function from a stationary state. It is also shown how for long-wavelength disturbances the stability criteria may be obtained within a hydrodynamic approach.

Journal ArticleDOI
TL;DR: Experimental data are presented which show that spin-polarized electron energy loss spectroscopy can be used to measure spin-wave dispersion curves of ultrathin ferromagnetic films up to the surface Brillouin zone boundary.
Abstract: The realm of high energy, large wave vector spin waves in ultrathin films and at surfaces is unexplored because a suitable method was not available up to now. We present experimental data for an 8 ML thick Co film deposited on Cu(001) which show that spin-polarized electron energy loss spectroscopy can be used to measure spin-wave dispersion curves of ultrathin ferromagnetic films up to the surface Brillouin zone boundary.

Journal ArticleDOI
TL;DR: It is shown that in the range of the experiment, the orientational time is depending on a unique parameter built on temperature and density, and this parameter appears to be always of the same order of magnitude.
Abstract: Transverse Brillouin spectra of orthoterphenyl are measured in the (250-305 K; 0.1-100 MPa) temperature-pressure range, which corresponds to the supercooled phase of this organic glass former. We show that the analysis of these spectra combined with an extrapolation of the reorientation times under pressure leads to an estimate of the static shear viscosity in a pressure range whose validity extends beyond the range of the Brillouin measurements. The relative contributions of temperature and of density to the change of this reorientation time measured along an isobar are extracted from our results in a large temperature range extending from the liquid to the low temperature supercooled state. They appear to be always of the same order of magnitude. It is also shown that in the range of the experiment, the orientational time is depending on a unique parameter built on temperature and density.

01 May 2003
TL;DR: In this paper, the authors investigated the band structure of a Bose-Einstein condensate in a one-dimensional periodic potential by calculating stationary solutions of the Gross-Pitaevskii equation, which have the form of Bloch waves.
Abstract: We investigate the band structure of a Bose-Einstein condensate in a one-dimensional periodic potential by calculating stationary solutions of the Gross-Pitaevskii equation, which have the form of Bloch waves. We demonstrate that loops (``swallow tails'') in the band structure occur both at the Brillouin zone boundary and at the center of the zone, and they are therefore a generic feature. A physical interpretation of the swallow tails in terms of periodic solitons is given. The linear stability of the solutions is investigated as a function of the strength of the mean-field interaction, the magnitude of the periodic potential, and the wave vector of the condensate. The regions of energetic and dynamical stability are identified by considering the behavior of the Gross-Pitaevskii energy functional for small deviations of the condensate wave function from a stationary state. It is also shown how for long-wavelength disturbances the stability criteria may be obtained within a hydrodynamic approach.

Journal ArticleDOI
TL;DR: This is the first Brillouin observation of acoustic mode quantization in a nanoparticle arising from spatial confinement and the distinct spectral peaks measured afford an unambiguous assignment of seven surface and inner acoustic modes.
Abstract: The vibrational modes in three-dimensional ordered arrays of unembedded ${\mathrm{S}\mathrm{i}\mathrm{O}}_{2}$ nanospheres have been studied by Brillouin light scattering. Multiple distinct Brillouin peaks are observed whose frequencies are found to be inversely proportional to the diameter ($\ensuremath{\approx}200--340\text{ }\text{ }\mathrm{n}\mathrm{m}$) of the nanospheres, in agreement with Lamb's theory. This is the first Brillouin observation of acoustic mode quantization in a nanoparticle arising from spatial confinement. The distinct spectral peaks measured afford an unambiguous assignment of seven surface and inner acoustic modes. Interestingly, the relative intensities and polarization dependence of the Brillouin spectrum do not agree with the predictions made for Raman scattering.

Journal ArticleDOI
TL;DR: In this paper, the authors show that the phenomenon of modulational instability in arrays of Bose-Einstein condensates confined to optical lattices gives rise to coherent spatial structures of localized excitations.
Abstract: We show that the phenomenon of modulational instability in arrays of Bose-Einstein condensates confined to optical lattices gives rise to coherent spatial structures of localized excitations. These excitations represent thin disks in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with condensed atoms of much greater density compared to surrounding array sites. Aspects of the developed pattern depend on the initial distribution function of the condensate over the optical lattice, corresponding to particular points of the Brillouin zone. The long-time behavior of the spatial structures emerging due to modulational instability is characterized by the periodic recurrence to the initial low-density state in a finite optical lattice. We propose a simple way to retain the localized spatial structures with high atomic concentration, which may be of interest for applications. Theoretical model, based on the multiple scale expansion, describes the basic features of the phenomenon. Results of numerical simulations confirm the analytical predictions.

Journal ArticleDOI
TL;DR: In this paper, a correlation-based continuous-wave technique for high spatial resolution and distributed dynamic strain measurements using stimulated Brillouin scattering is presented, which has successfully measured dynamic strain from a 5-cm vibrating section, at a sampling rate of 8.8 Hz with a strain accuracy of about
Abstract: Conventional fiber Brillouin-based strain sensors are capable of distributed sensing, making them advantageous over fiber Bragg grating-based sensors for structural monitoring applications. However, Brillouin sensors have low spatial resolution and are inappropriate for dynamic strain measurements as they have large measurement times of several minutes. We present a correlation-based continuous-wave technique for high spatial resolution and distributed dynamic strain measurements using stimulated Brillouin scattering. Using our technique, we have successfully measured dynamic strain from a 5-cm vibrating section, at a sampling rate of 8.8 Hz with a strain accuracy of about /spl plusmn/38 /spl mu//spl epsiv/.

Journal ArticleDOI
TL;DR: In this article, a force field for modeling calcium carbonate has been derived that corrects deficiencies of previous models, which correctly reproduces the structure of the gas phase species, as predicted from ab initio calculations, as well as the bulk structure and properties of calcite and aragonite.
Abstract: A new force field for modeling calcium carbonate has been derived that corrects deficiencies of previous models. The model correctly reproduces the structure of the gas phase species, as predicted from ab initio calculations, as well as the bulk structure and properties of calcite and aragonite. With this new model, a (2 × 1) reconstruction is predicted to occur for the dominant (1014) surface of calcite, involving rotation of half of the surface carbonate anions. This reconstruction matches the results of low energy electron diffraction measured in vacuo and provides the first independent verification of this observation, as well as yielding the atomic detail of the nature of the reconstruction. While there is only a small exothermic energy associated with the formation of the supercell, the presence of an imaginary phonon mode at (1/2, 0) in the two-dimensional Brillouin zone for a single surface cell verifies the existence of the reconstruction.

Journal ArticleDOI
TL;DR: It is shown that the origin of the previously reported unusual kink on the low frequency transverse phonon dispersion curve (known as the "waterfall effect") depends on the choice of the Brillouin zone and that the relation of q(wf) to the size of the polar nanoregions is highly improbable.
Abstract: We have undertaken an inelastic neutron scattering study of the perovskite relaxor ferroelectric Pb(Zn(1/3)Nb(2/3))O3 with 8% PbTiO3 (PZN-8%PT) in order to elucidate the origin of the previously reported unusual kink on the low frequency transverse phonon dispersion curve (known as the "waterfall effect"). We show that its position (q(wf)) depends on the choice of the Brillouin zone and that the relation of q(wf) to the size of the polar nanoregions is highly improbable. The waterfall phenomenon is explained in the framework of a simple model of coupled damped harmonic oscillators representing the acoustic and optic phonon branches.

Journal ArticleDOI
Jianfeng Xu1, Xiaobin Ren1, Wenping Gong1, Rui Dai1, Dahe Liu1 
TL;DR: The results show that the bulk viscosity of water can be determined directly from Brillouin-scattering measurements, which has a high signal-to-noise ratio and high accuracy.
Abstract: The aim is to develop a rapid and direct method for measuring the bulk viscosity of a liquid as a function of temperature. Brillouin scattering of a laser beam in fresh water and salt water at different temperatures has been studied. The results show that there exists a close temperature-dependent relationship among the Brillouin frequency shift, the Brillouin linewidth, and the bulk viscosity of water. Thus the bulk viscosity of water can be determined directly from Brillouin-scattering measurements. The method has a high signal-to-noise ratio and high accuracy.

Journal ArticleDOI
TL;DR: In this article, the long-range dipolar interactions in a crystalline cubic polar semiconducting nanowire give rise to an important splitting of the Raman-active transverse optic (TO) and longitudinal optic (LO) phonons at the center of the Brillouin zone.
Abstract: We show that the long-range dipolar interactions in a crystalline cubic polar semiconducting nanowire give rise to an important splitting of the Raman-active transverse optic (TO) and longitudinal optic (LO) phonons at the center of the Brillouin zone The dipole sums that determine the two LO and two TO phonon frequencies in the nanowire are sensitive to the aspect ratio (L/D), where L and D are the length and diameter, respectively In the limit L/D →∞, we predict the phonon frequencies for several important polar semiconducting nanowires Our calculated results are also compared with Raman scattering data obtained on crystalline GaP and GaAs semiconducting wires

Journal ArticleDOI
TL;DR: In this article, the authors used first-order Raman scattering to determine the zone-center phonons and their dependence on structural attributes such as stress, chemical composition, impurities, and doping.
Abstract: We present a selection of our contributions to basic research on the lattice dynamical properties of groupIII nitrides and their alloys. We used first-order Raman scattering to determine the zone-center phonons and their dependence on structural attributes such as stress, chemical composition, impurities, and doping. Results on the angular dispersion of the polar modes, strain distribution, coupled LO-phonon plasmon modes, multi-mode behavior in AlxGa1–xN, and the quantitative determination of the phase purity of cubic and hexagonal GaN are shown. Second-order Raman-scattering experiments on GaN and AlN provide information on the vibrational states throughout the entire Brillouin zone. Based on a comparison of experimental data and calculated phonon-dispersion curves we assigned the observed structures to particular phonon branches and points in the Brillouin zone. We also discuss the behavior of the optical modes under large hydrostatic pressure.

Journal ArticleDOI
TL;DR: This work uses the nonlocalized, fluctuating source model for the stimulated Brillouin scattering to get the exact spectrum of the Stokes wave in optical fibers with attenuation loss and gives for the first time an approximate solution for standard steady-state BrillouIn equations.
Abstract: We first use the nonlocalized, fluctuating source model for the stimulated Brillouin scattering to get the exact spectrum of the Stokes wave in optical fibers with attenuation loss. A new relation for the evaluation of the critical pump power (or Brillouin threshold) depending on the fiber length is then introduced, which should be more precise than the well-known Smith formula. Furthermore, we give for the first time, to the best of our knowledge, an approximate solution for standard steady-state Brillouin equations, which consists of two simple relations.

Journal ArticleDOI
TL;DR: In this article, the second-order elastic moduli of tetragonal hen egg-white lysozyme crystals were determined as a function of relative humidity (RH) by Brillouin scattering.

Journal ArticleDOI
TL;DR: In this article, the optical properties of 3,4,9,10 perylene-tetracarboxylic-dianhydride (PTCDA) were investigated with a model allowing for the transfer of the electronic excitation between different molecular sites in the crystal, resulting from the interactions between the molecular higher occupied to lower unoccupied molecular orbital transition dipoles.
Abstract: The optical properties of 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) in the monoclinic $\ensuremath{\alpha}$ phase are investigated with a model allowing for the transfer of the electronic excitation between different molecular sites in the crystal, resulting from the interactions between the molecular higher occupied to lower unoccupied molecular orbital transition dipoles. Due to the large extension of the molecules with respect to the intermolecular distances, the calculation has to account for the delocalization of the transition charge density over the carbon and oxygen atoms involved in both orbitals. Applying these microscopic ingredients to a calculation of the dispersion of the Frenkel excitons, it can be shown that the dielectric tensor is related to excitons at the $\ensuremath{\Gamma}$ point of the Brillouin zone and the photoluminescence to vertical recombination starting from the minimum of the Frenkel exciton dispersion at the surface of the Brillouin zone. The calculated results agree both with the extinction coefficient measured on polycrystalline thin films and with the dominating low-temperature photoluminescence decay channel observed on single crystals of $\ensuremath{\alpha}$-PTCDA.

Journal ArticleDOI
TL;DR: The high pressure behavior of SnO 2 has been examined by Brillouin and Raman scattering spectroscopy to pressures of 30 GPa at ambient temperature as discussed by the authors, and the elastic constants c 1 1, c 1 2, c 4 4, and c 6 6 were determined as a function of pressure to 13 GPa.
Abstract: The high-pressure behavior of SnO 2 has been examined by Brillouin and Raman scattering spectroscopy to pressures of 30 GPa at ambient temperature. The elastic constants c 1 1 , c 1 2 , c 4 4 , and c 6 6 of rutile-type SnO 2 were determined as a function of pressure to 13 GPa by Brillouin spectroscopy and the Raman-active modes have been measured up to 30 GPa. The transition from the rutile- to the CaCl 2 -type structure was observed. The Raman-active soft mode and the elastic soft mode behavior were fit to an order parameter model with bilinear coupling of the Raman-active order parameter and the elastic strain. It is shown that the pressure dependence of the Raman-active soft mode is controlled in part by the characteristic frequencies of the two coupled soft modes. No further indications for soft-mode-driven phase transitions at higher pressures were found.

Journal ArticleDOI
TL;DR: In this article, the Curie temperature in the diluted magnetic semiconductor (Ga12x2yMnxAsy) As alloys, where the compensation effect by As antisites is taken into account, was determined from first principles.
Abstract: We have determined from first principles the Curie temperature in the diluted magnetic semiconductor (Ga12x2yMnxAsy) As alloys, where the compensation effect by As antisites is taken into account. The disorder due to random positions of Mn impurities and As antisites is taken into account in the framework of the coherent potential approximation. We demonstrate that a simple mean-field approximation~MFA! already gets Tc accurately. In particular, it is shown that the calculated Tc in the random-phase approximation and Monte Carlo simulations differ only weakly from the MFA values. The reason is that a proper treatment of the disorder beyond the virtual-crystal approximation leads, in this doped material, to a flat magnon dispersion in a large part of the Brillouin zone.

Book ChapterDOI
01 Jan 2003
TL;DR: In this article, a light scattering process is said to be stimulated if the fluctuations are induced by the presence of the light field, which is called stimulated Brillouin scattering (SBS).
Abstract: Publisher Summary A light scattering process is said to be stimulated if the fluctuations are induced by the presence of the light field. Stimulated light scattering is typically very much more efficient than spontaneous light scattering. Stimulated Brillouin scattering (SBS) process leads to amplification of a Stokes wave propagating in any direction except for the propagation direction of the laser wave. However, SBS is usually observed only in the backwards direction, because the spatial overlap of the laser and Stokes beams is largest under these conditions. Electrostriction is also important both as a mechanism leading to a third-order nonlinear optical response and as a coupling mechanism that leads to stimulated Brillouin scattering. The scattering of light from isobaric density fluctuations that are driven by the process of electrostriction leads to electrostrictive stimulated Rayleigh scattering, whereas the scattering of light from isobaric density fluctuations that are driven by the process of optical absorption leads to thermal stimulated Rayleigh scattering.

Journal ArticleDOI
TL;DR: This work is able to measure the anisotropy, or the trigonal warping effect, in the phonon dispersion relations around the hexagonal corner of the Brillouin zone of graphite.
Abstract: The one-dimensional structure of carbon nanotubes leads to quantum confinement of the wave vectors for the electronic states, thus making the double resonance Raman process selective, not only of the magnitude, but also of the direction of the phonon wave vectors. This additional selectivity allows us to reconstruct the phonon dispersion relations of 2D graphite, by probing individual single wall carbon nanotubes of different chiralities by resonance Raman spectroscopy, and using different laser excitation energies. In particular, we are able to measure the anisotropy, or the trigonal warping effect, in the phonon dispersion relations around the hexagonal corner of the Brillouin zone of graphite.

Journal ArticleDOI
TL;DR: In this article, the number and the nature of the relaxation processes active in this prototype glass forming system in the high frequency region were investigated. But the results were limited to the GHz frequency region, while the contributions coming from intramolecular channels are negligible.
Abstract: Brillouin scattering has been used to measure the dynamic structure factor of glycerol as a function of temperature from the high temperature liquid to the glassy state. Our investigation aims at understanding the number and the nature of the relaxation processes active in this prototype glass forming system in the high frequency region. The associated character of glycerol is reflected by a rather simple relaxation pattern, while the contributions coming from intramolecular channels are negligible in the GHz frequency region. The temperature behavior of the characteristic frequency and lifetime of the longitudinal acoustic modes is analyzed, suggesting that a phenomenological model which only includes the structural (α) process and the unrelaxed viscosity is able to catch the leading contributions to the dynamics of the density fluctuations. This ansatz is also supported by a combined analysis of light and inelastic x-ray scattering spectra. The temperature dependence of the characteristic time of the α-...