Brillouin lines

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. °... 

Figure 5. Brillouin spectral 20°C. Notice the overlap between Brillouin 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. ... 

Thus, the choice of an incident radiation Aj defines k , whereas the choice of a scattering angle (usually 90° or 180") unambiguously determines and, henceforth, the Brillouin shifi related to each of the three acoustic modes with their own velocities. Typically, for an incident visible radiation, and a material characterized by an index of refraction about 1.5 and sound velocities of a few km/s, the Brillouin shift lies in the range of 10-30 GHz (0.33-1 cm ) in backscattering geometry. Obviously, the study of Brillouin lines requires a more consequent resoiution than the one of a conventional Raman spectrometer. 

In the absence of any perturbation by other modes, the Brillouin lines can be described by a damped oscillator profile derived from the imaginary part ("(< ) of the oscillator susceptibility ... 

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... 

Of considerable interest is the ratio of the intensity of light scattered in the central Rayleigh line to that scattered in the Brillouin line. The central line comes about because of incoherent or random fluctuations in the density whUe the Brillouin line is due to scattering from coherent thermaUy excited sound waves which are adiabatic fluctuations. 

Fig. 8. Li t scattering spectra of polyethyl methacrylate in the gigacycle region recorded immediately below the glass transition (solid line) and immediately above (dashed line) (75). The Rayleigh component is reduced by a factor of 10. The unusually high ratio of the Rayleigh line to the Brillouin line and the sharp change atr, has been shown to be due to inhomogeneities present in the sample (see text)...

Fig. 9 shows the shift in frequency of the Brillouin components as a function of temperature at a constant scattering angle of 90° C in PMMA. The change in the Brillouin lines is due to a change in the velocity of the hypersonic waves with temperature. At 90° C the sound waves or phonons have a wavelength of /I = 30(X) A. Using this value and the value of 1.491 for n, the index of refraction, it was found that at 20° the measured sound frequency of 9.58 x 10 Hz multiplied by A yielded a value of k = 287 x 10 cm/sec which is within 10% of the published ultrasonic values. 

Rayleigh scattering). The intensity of the Rayleigh line relative to the intensity of the Brillouin lines is given by the Landau-Placzek ratio... 

The width, r, (half width at half maximum) of the Brillouin lines is proportional to the sound attenuation coefficient. 

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