Brillouin Lines Research Articles

Light scattering and sound propagation in a chemically reacting binary gas mixture

The aim of this paper is to study time-dependent problems like sound propagation and light scattering in binary mixtures undergoing a simple reversible symmetric reaction—of the type A+A⇌B+B—close to the final stage of the chemical reaction where the system tends to chemical equilibrium. The molecules of the gas are modeled as rigid spheres and—apart from the binding (or formation) energy of the molecules—the internal degrees of freedom were not taken into account. The hydrodynamic description is based on the conservation laws of mass, momentum and energy closed by the constitutive equations for the pressure tensor, heat flux vector, diffusion velocity and rate of reaction which correspond to the Navier–Stokes law and generalized laws of Fourier, Fick and Arrhenius, respectively. For the problem of sound propagation it is shown how endothermic and exothermic reactions have influence on the phase speed and on the attenuation coefficient, whereas for the problem of light scattering, their influences on the width of the Rayleigh and Brillouin lines and the position of the Brillouin peak are analyzed.

Origin of spectral hole burning in Brillouin fiber amplifiers and generators

We show theoretically that the spectral hole burning recently observed in Brillouin fiber amplifiers and generators can be interpreted without invoking an inhomogeneous broadening of the Brillouin line. By using the three-wave model of stimulated Brillouin scattering (SBS), we first investigate the linear response of a Brillouin fiber amplifier to a weak amplitude modulation of the injected signal wave. The transfer functions that fully characterize this response are analytically calculated. The fact that they may exhibit a dip is shown to be due both to the gain saturation and to the coupling between the pump and signal perturbations that counterpropagate around the steady-state intensity profiles. These transfer functions also appropriately characterize the way through which noisy perturbations are filtered in SBS fiber generators. The spectral hole burning observed in generators is thus simply connected to spectral hole burning studied in SBS amplifiers.

Melting Temperature, Brillouin Shift, and Density of States of Nanocrystals

The amplitude of displacement of atoms due to scattering at the surface is calculated. It is found that the zero-point vibrational correction to the mean-square displacement varies as the inverse square of the nanocrystal size and the temperature-dependent part also varies with the nanocrystal size. The melting temperature is found to depend on the nanocrystal size so that smaller melting temperature is obtained for smaller nanocrystals. The phonon−phonon scattering is found to shift the Brillouin line such that as the crystal size reduces, it moves toward the Rayleigh line. The phonon density of states is found to be larger for nanocrystals than for the bulk crystals as it depends on the inverse square of the nanocrystal size.

Constant loss in Brillouin spectra of polymers

AbstractThe polarized (VV) and depolarized (VH) light scattering spectra of polyisobutylene, poly(methyl methacrylate), and glycerol were measured in the gigahertz frequency range at temperatures below and above the glass transition. Both VV and VH spectra exhibit a significant constant loss contribution that appears as a frequency‐independent imaginary part of the susceptibility spectrum. Existence of the frequency‐independent susceptibility in VV spectra below the Brillouin lines suggests that the constant loss also appears in mechanical relaxation in the gigahertz frequency range. Intensity of the constant loss increases strongly with temperature. Analysis of the spectra and literature data suggests that the constant loss can be general for many glass‐forming systems, but it is hidden in many cases by other relaxation contributions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 201–209, 2002

Resonant Brillouin Scattering of Exciton-Polaritons in β-ZnP2

The secondary emission spectra of β-ZnP 2 under the resonant excitation in the 1 s exciton region were investigated in detail. Several scattering lines with the Stokes shifts of less than 6 meV were found. By analyzing the experimental results using a model based on the exciton-polariton picture, we attributed the observed scattering lines to the Brillouin lines. The sound velocities of the LA and TA phonons were derived to be v LA =4.8 (±0.2)×10 5 cm/s and v TA =2.8 (±0.2)×10 5 cm/s, respectively. The resonant enhancement of the Brillouin lines was observed around the transverse exciton energy E T , which reflects high transmissivity and a small group velocity of the exciton-polaritons at E T . We also found that the Rayleigh scattering line was resonantly enhanced between the longitudinal exciton energy E L and E T due to the surface roughness, which explains the drastic reduction of the luminescence from the lower branch polaritons in intensity reported earlier. The excitation energy dependence of the Brillouin line width is also discussed.

Unusual features of long-range density fluctuations in glass-forming organic liquids: a Rayleigh and Rayleigh-Brillouin light scattering study.

A new feature of glass-forming liquids, i.e., long-range density fluctuations of the order of 100 nm, has been extensively characterized by means of static light scattering, photon correlation spectroscopy and Rayleigh-Brillouin spectroscopy in orthoterphenyl (OTP) and 1,1-di(4(')-methoxy-5(')methyl-phenyl)-cyclohexane (BMMPC). These long-range density fluctuations result in the following unusual features observed in a light scattering experiment, which are not described by the existing theories: (i) strong q-dependent isotropic excess Rayleigh intensity, (ii) additional slow component in the polarized photon correlation function, and (iii) high Landau-Placzek ratio. These unusual features are equilibrium properties of the glass-forming liquids and depend only on temperature, provided that the sample has been equilibrated long enough. The temperature-dependent equilibration times were measured for BMMPC and are about 11 orders of magnitude longer than the alpha process. It was found that the glass-forming liquid OTP may occur in two states: with and without long-range density fluctuations ("clusters"). We have characterized the two states by static and dynamic light scattering in the temperature range from T(g) to T(g)+200 K. The relaxation times of the alpha process as well as the parameters of the Brillouin line are identical in both OTP with and without clusters. The alpha process (density fluctuations) in OTP was characterized by measuring either the polarized (VV) or depolarized (VH) correlation function, which are practically identical and q-independent. This feature, which is commonly observed in glass-forming liquids, is not fully explained by the existing theories.

Brillouin scattering study of molten zinc chloride.

Polarized and depolarized Brillouin scattering experiments on molten ZnCl2 were performed between 300 and 600 degrees C in different geometries. VV spectra measured in backscattering and small angle scattering were analyzed with conventional viscoelastic theory using either a Debye or a Cole-Davidson model for the memory function. We also analyzed in the same way the temperature dependence of the transverse Brillouin lines detected in a 90 degrees VH geometry. We show that the Cole-Davidson memory function yields a consistent interpretation of all the spectra. The resulting shear and longitudinal relaxation times are equal within their error bars, and are about 2.5 times smaller than the alpha relaxation time previously determined. The static shear viscosity values deduced from the analysis of the propagating transverse waves agree, at all temperatures, with the measured viscosity values.

Spatial resolution enhancement of a Brillouin-distributed sensor using a novel signal processing method

It is known that the ultimate spatial resolution for a Brillouin-based sensor is limited by the lifetime of the phonons in the fiber that mediate the Brillouin loss process. At optical pulse widths less than 10 ns (corresponding to one meter spatial resolution) the Brillouin line width is considerably broadened, causing a severe penalty in resolving the Brillouin frequency shift. Around 5 ns the Brillouin line width is too broad to allow an accurate frequency determination. The fiber optics group at the University of New Brunswick, Canada, has recently developed an automated system for strain measurements in a distributed sensing system that uses a novel signal processing technique to measure strain at resolutions finer than the Brillouin line width limit. Strain has been resolved to 20 /spl mu//spl epsiv/ at 500 mm and to 40 /spl mu//spl epsiv/ at 250 mm.

Characterization of the Brillouin-loss spectrum of single-mode fibers by use of very short (<10-ns) pulses

The characterization of the Brillouin-loss spectrum of single-mode fibers with very short (<10-ns) pulses has been studied. It was found that the Brillouin-loss signal intensity is linearly related to the duration of the pump pulse used to obtain the spectrum. In contrast with the uniform trend of the signal, three distinct behaviors were observed in the spectral linewidth. At long pulse durations the linewidth was constant at approximately 40 MHz. Pulse durations of the order of the phonon lifetime resulted in a broader spectrum, reaching a maximum width of ~100 MHz at 5 ns. Reducing the pulse duration further resulted in a sudden narrowing of the Brillouin line.

Brillouin light scattering of a fragile glass former: O-terphenyl

Abstract We report Brillouin scattering measurements of the fragile glass former o-terphenyl over a wide temperature range covering the normal and the supercooled liquid phase down to the glass temperature. The velocity dispersion and the absorption of the longitudinal sound waves are reported and compared with literature data. The presence of both a residual sound speed dispersion in the hot liquid phase and a strongly asymmetric shape of the Brillouin line width curve in the high-temperature region indicates the existence of two relaxation phenomena: a structural and a fast secondary relaxation. This picture is consistent with the classication of o-terphenyl as a non-associated liquid, as emerges from the analysis of the temperature behaviour of the ratio of the experimental to the classically calculated sound wave absorption.

Mechanical and photoelastic properties of oriented poly-4-methyl-1-pentene investigated by Brillouin spectroscopy

The elastic constants C11, C13, C33 and C44 of oriented poly-4-methyl-1-pentane (P4M1P) films were measured with Brillouin scattering. The photoelastic constants p11, p13, p31 and p33 were measured by evaluating the integral intensities of the phonon lines. The correlation of the photoelastic constants p13 and p31 with the degree of stretching was determined by evaluating the relative integral intensities of the Brillouin lines with the phonon propagation vector into and perpendicular to the stress direction. The other photoelastic constants were measured by comparing the angle-dependent relative integral intensities of the transverse and longitudinal Brillouin lines. The elastic constants, as well as birefringence, were surprisingly found to be unaffacted by further stretching of the sample above the necking region. The density was constant for all degrees of stretching. The photoelastic constants p11 and p33 showed significant variation during deformation. The results have been compared with former measurements of polypropylene (PP) by Cavanaugh and Wang. Because the elastic constants are unchanged during deformation, the modulation of the intensities is due to the variation of the photoelastic constants for this material.

A light-scattering study of 1-4 cis - trans polybutadiene

Light-scattering measurements on 1-4 polybutadiene of two molecular weights have been carried out using two different tandem Fabry - Pérot interferometers in the back-scattering and scattering geometries. The Rayleigh - Brillouin spectrum has been measured at different temperatures through the glass transition. Relaxation times and sound velocities have been fitted to a hydrodynamic formula, with as few independent parameters as possible. Comparison with previous measurements shows that the Brillouin relaxation times do not follow the structural or relaxation. Forcing the fit either with the times of the process or with a high-frequency relaxation channel does not yield satisfactory results. The only processes arising on a similar timescale and with comparable activation energies are intra-chain conformational changes rates as computed by molecular dynamics. A possible mechanism linking these conformational changes to the damping of the Brillouin lines is suggested.

Similar elastic behaviour in mhseo4crystals near the superionic transition

Abstract Brillouin scattering investigations in NH4-, Rb- and CsHSeO4 are reported near their superionic transition. A similar elastic behaviour is observed, consisting of strong downward jumps of elastic constants C11, C22 and C33, at the transition, and broadenings of the corresponding Brillouin lines above the transition. No pretransitional evolutions occur in both phases.

Low-frequency light-scattering spectroscopy of powders

Light-scattering spectra of powders of transparent materials were found to exhibit a characteristic band at frequencies below ∼1 cm−1. This band was observed in all powdered materials studied, including enzymes, organic and inorganic crystals, and glass. We interpret the band as a superposition of Brillouin lines produced in combined elastic and inelastic scattering events. A theoretical expression is deduced for the spectrum that is in good agreement with the experiments.

Elastic properties of silicate melts up to 2350 K from Brillouin scattering

Compressional wave velocities (Vp) have been determined up to 2350 K on CaSiO3, MgSiO3, CaMgSi2O6, CaAl2Si2O8 and Ca3Al2Si3O12 glasses and melts from Brillouin‐scattering experiments made with a 180° backscattering geometry. At the glass transition, the decrease of Vp with increasing temperatures becomes much stronger and the width of the Brillouin lines begins to increase markedly. At the highest temperatures investigated, Vp is similar to the relaxed values determined in acoustic measurements for several of these melts. This indicates that the configurational degrees of freedom of these liquids have become accessible within the very short timescale of Brillouin scattering experiments: equilibrium compressibilities of silicate melts can thus be determined with this technique. Our measurements also suggest that the shear modulus at infinite frequency of silicate melts could vary with either temperature or composition more strongly than assumed currently.

Resonance Brillouin scattering from quantized exciton-polaritons in ultrathin epitaxial layers of ZnSe

Resonant Brillouin scattering in ultrathin MBE-grown epitaxial layers of ZnSe with thicknesses from 50 to 200 nm is esployed to investigate the properties of the 1s exciton-polariton states. The effective masses are found different from that in bulk ZnSe caused by the energetic decoupling of heavy- and light-hole states due to strain. In the 50 nm sample the momentum selection rule is relaxed, leading to broad Brillouin lines that show fine structure due to the phonon quantization in these layers, whereby dilatation and flexural phonon modes are involved in the scattering.

Phase transitions in the superionic protonic conductor CsHSeO 4 investigated by Brillouin spectroscopy

A Brillouin investigation in CsHSeO 4 has been performed over the temperature range 20–165 °C which includes two phase transitions, in particular the transition to the superionic phase near T s = 129 °C. We observed strong discontinuities for elastic constants C 11, C 22 and C 33 at T s and a broadening of the Brillouin lines above T s . The results are discussed on the basis of a linear coupling between strains and mobile protons.

Development of a distributed sensing technique using Brillouin scattering

This paper reviews the developments of a distributed strain and temperature sensing technique that uses Brillouin scattering in single-mode optical fibers. This technique is based on strain- and temperature-induced changes in the Brillouin frequency shift. Several approaches for measuring the weak Brillouin line are compared. >

Structural changes and elastic properties in aerogels investigated by Brillouin scattering

Silica aerogels with different microstructures were synthesized by one-step and two-step process. Acoustic waves in these materials were studied by Brillouin scattering. As expected, propagative phonons are observed for high-density samples. However, for some two-step samples an asymmetric profile of the Brillouin line is found which was not observed in previous investigations. This behaviour is attributed to some relaxation process coupled to the phonons. After an oxidation heat treatment these relaxations disappear. For low-density samples, the crossover to fracton modes is investigated. Values of the sound velocities, ν 0, are compared for different series of samples and the data are correlated to structural information.

A model of low-frequency Raman scattering in glasses: Comparison of Brillouin and Raman data

A model of the low-frequency Raman scattering intensity in glasses is proposed, which describes the spectrum in the region of the boson peak, typical of glasses. The model considers the boson peak as a result of first-order light scattering by harmonic quasilocalized vibrations. The amplitude, frequency, and polarization dependence of the light on the vibrational coupling coefficient C(ω) are estimated. The model predicts a linear frequency dependence of C(ω) in the region of the boson peak and the depolarization ratio as a function of the relative contribution of the longitudinal and transverse-type motions which comprise these quasilocal vibrational modes. Low-frequency Raman and Brillouin measurements have been made on SiO2 glass in order to check the predictions of the model regarding the amplitude and integrated intensity of the boson peak. The estimated ratio of these values to those of the Brillouin lines are in good agreement with experiment. Comparison of the theoretical and experimental values of the depolarization ratio for the boson peak shows a predominance of the transverse-type atomic motions in the low-frequency quasilocalized vibrational modes in glasses.