Rayleigh line width

Fig, 26. Experimental dispersion curve of the Kr monolayer and measured line width broadening As of the Kr creation phonon peaks. The solid line in the dispersion plot is the clean Pt(lll) Rayleigh phonon dispersion curve and the dashed line the longitudinal phonon bulk band edge of the Pt(l 11) substrate, both in the r Mn azimuth which is coincident with the r Kk, azimuth. 

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. 

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. °... 

Auciujlions arc usuatty dominani. Under Ihesc condi-lioiis. Ihe widlh of the Rayleigh line is directly proportional to the translational diffusion cocflictcnt DpThe 1)1.S mcthtxl uses optical mixing techniques and correlation analvsis to obtain these diffusion coelTicients. The line widths (I H to I MH/) arc too small to be measured by conventional spectrometers and even interferometers. 

In the foriniila for the Rayleigh eenlral line width (Equation 2.3- 162)... 

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.

As shown in Fig. 1, the representation l p) also eliminates the central part of the Rayleigh line. However, an intensity maximum is observed at very low frequencies. The exact position of this maximum depends on the width of the Rayleigh line. Thus, this low-frequency maximum in the I (P) representation reflects the relaxational processes in the liquid. 

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...

We consider the situation in which the frequency of the exciting light is far from any molecular resonance (o> cdk) Then in Eq. (44) we may remove the frequency-dependent terms from the summation over all vibrational states fc Utilizing the closure relation X k) k = 1, we see that in Eq. (44), X (k f) = (/ /), which vanishes in the harmonic oscillator approximation unless I =/ Thus, far from a molecular resonance, the term A contributes only to the Rayleigh line. If, alternately, we consider in term A those states in which either K or I is actually a metal state (Figure 19a), we might expect resonant contributions to the intensity, and we cannot carry out the sum over vibrational states if the laser width is less than vibrational spacings. In the latter case, a... 

X X z location of line center in cm -1 pressure of sample gas multiplied by optical path length distance from center of line image expressed in Rayleigh widths... 

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... 

Figure 33. Surface phonon dispersion for W(OOl) in the FM portion of the SBZ showing the measured Rayleigh wave (R) and longitudinal (L) modes. The data in the upper panel were obtained at 1200 K, while in the lower panel the data shown by open circles were obtained at 500 K and those represented by closed circles were obtained at 300 K. The edges of the transverse acoustic (TA) and longitudinal acoustic (LA) bulk bands are given by the hatched lines. The vertical lines in the lower panel denote the widths in the energy transfer distributions of these points. (Reproduced from Figs. 10 and 13 of Ref. 110, with permission.)...

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