Line width, Brillouin

During a second step we carried out measurements of the Brillouin position and Brillouin line width which are related to the sound velocity and sound absorption. We use the method of Zamir, et al. ° With our current setup, the Rayleigh line provides us with the apparatus window function from where the FSR and the finesse for each spectrum are measured. During a second step we carried out measurements of the Brillouin position and Brillouin line width which are related to the sound velocity and sound absorption. We use the method of Zamir, etal. °... 

Due to the small value of the Brillouin shifts and their line widths, experimental techniques involve interferometric devices. However, resolution is not all. perhaps the more important quality is the contrast, i.e., the ability to... 

K. The resonance was saturated at 6.8 GHz, producing a phonon bottle-neck in which the effective temperature of the resonant phonons was raised to 150K. The bandwidth was 270 MHz, of the same order as the unsaturated line width of the cerium resonance. Measurements of Brillouin scattering in CaW04 containing Nd are described by Geschwind (1972). 

The intermediate relaxation limit in which >e = structural relaxation contributes heavily to the line width of the Brillouin lines. The relaxation processes can be resolved by means of the Fabry-Perot interferometry (24). Figure 5... 

Fig. 5. Polarized Rayleigh-Brillouin spectrum of amorphous PnHMA taken with a Burleigh plane Fabry-Perot interferometer using a free spectral range of 12.4 GHz at 295 K. The two Brillouin peaks are shifted from the incident frequency by the product of the wave vector q and the sound velocity u. The line width of the Brillouin peaks is related to the attenuation of the sound waves. PnHMA.

The Brillouin components shown in Fig. 2 have a width which is determined partly by the resolving power of the interferometer and partly by mechanisms which lead to damping of acoustic modes in the sample. The instrumental width is usually allowed for by a convolution method so as to obtain the true line width. This numerical procedure is one of the largest sources of inaccuracy in this experiment. Each line in the pair has a true half width at half maximum given by (5) ... 

The next two temis (Lorentzians) arise from the mechanical part of the density fluctuations, the pressure fluctuations at constant entropy. These are the adiabatic sound modes (l/y)exp[-FA t ]cos[co(A) t ] with (D(k) = ck, and lead to the two spectral lines (Lorentzians) which are shifted in frequency by -ck (Stokes line) and +ck (anti-Stokes line). These are known as the Brillouin-Mandehtarn, doublet. The half-width at... 

The spectrum consists of three components. The first term represents an unshifted line called the Rayleigh line, which is a Lorentzian with a halfwidth at half-maximum given by Acoc(q) = Dpq2. The next two terms represent a doublet called the Brillouin doublet. These are two Lorentzian lines shifted symmetrically from the origin by co = csq, each having half-width at half-maximum, AcoB(q) = Tq2. 

Physically, the Brillouin spectrum arises from the inelastic interaction between a photon and the hydrodynamics modes of the fluid. The doublets can be regarded as the Stokes and anti-Stokes translational Raman spectrum of the liquid. These lines arise due to the inelastic collision between the photon and the fluid, in which the photon gains or loses energy to the phonons (the propagating sound modes in the fluid) and thus suffer a frequency shift. The width of the band gives the lifetime ( 2r)-1 of a classical phonon of wavenumber q. The Rayleigh band, on the other hand, represents the... 

Poole, Liesegang, Leckey, and Jenkin (1975) have reviewed published band calculations for the alkali halides and tabulated the corresponding parameters obtained by various methods. Pantclidcs (1975c) has used an empirical LCAO method that is similar to that described for cesium chloride in Chapter 2 (see Fig. 2-2), to obtain a universal one-parameter form for the upper valence bands in the rocksalt structure. This study did not assume only one important interatomic matrix clement, as we did in Chapter 2, but assumed that all interatomic matrix elements scale as d with universal parameters. Thus it follows that all systems would have bands of exactly the same form but of varying scale. That form is shown in Fig. 14-2. Rocksalt and zincblende have the same Brillouin Zone and symmetry lines, which were shown in Fig. 3.6. The total band width was given by... 

Ii3/2 multiplets. Frequencies and polarization vectors of phonons in the LiYp4 crystal were obtained at 8000 points in the irreducible part of the Brillouin zone using the rigid ion model of lattice dynamics derived on the basis of neutron scattering data. Matrix elements of electronic operators Vds) were calculated with the wave functions obtained from the crystal-field calculation. The inverse lifetimes of the crystal-field sublevels determine the widths of corresponding absorption lines. 

Above about 0.5 GHz, Brillouin scattering provides an elegant technique of measuring phonon mean free paths (which are inversely proportional to the sound attenuation coefficient) by evaluating the width of the Brillouin lines [53]. However, as a result of finite spectrometer resolution and contrast, this method is limited to aerogel densities above 180 kg/m. ... 

The Raman scattering of single-crystal graphite was found to contain a single narrow band (G-mode) at 1575 cm, that is assigned to the planar mode of the Brillouin zone center. However, jp -hybridized carbon, that is, single-crystal diamond, demonstrates a single first-order peak in the Raman spectrum, a narrow symmetric line at the frequency of 1332.5 cm (with a peak width of about 2.0 cm" ), which derives from the transverse TO phonon of symmetry. At... 

Figure 5-1. Backscattering Brillouin spectra for six silica aerogel densities (in kg/m ).The relative intensities, not adjusted for sample turbidity, are otherwise significant. IW is the full instrumental width at half-height. The central portion of the spectra, affected by the elastic line, was removedfor clarity. (Reprinted figure with permission from [E. Courtens etaL, Phys. Rev. Lett. 58, 128 (1987)]. Copyright (1987) by the American Physical Society.)...

Fig. 7. Typical diagram of the spectrum of scattered light as measured by a Fabry Perot interferometer showing the Rayleigh line (center) and the Brillouin doublet. From the frequency shift and the width of the Brillouin bands one can obtain the storage and loss moduli fin- compresacHKil waves exxuring at hypersonic frequencies...

---