Raman scattering isotropic

Unlike the typical laser source, the zero-point blackbody field is spectrally white , providing all colours, CO2, that seek out all co - CO2 = coj resonances available in a given sample. Thus all possible Raman lines can be seen with a single incident source at tOp Such multiplex capability is now found in the Class II spectroscopies where broadband excitation is obtained either by using modeless lasers, or a femtosecond pulse, which on first principles must be spectrally broad [32]. Another distinction between a coherent laser source and the blackbody radiation is that the zero-point field is spatially isotropic. By perfonuing the simple wavevector algebra for SR, we find that the scattered radiation is isotropic as well. This concept of spatial incoherence will be used to explain a certain stimulated Raman scattering event in a subsequent section. 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

In the conclusion of the present chapter we show how comparison of NMR and Raman scattering data allows one to test formulae (3.23) and (3.24) and extract information about the relative effectiveness of dephasing and rotational relaxation. In particular, spectral broadening in nitrogen caused by dephasing is so small that it may be ignored in a relatively rarefied gas when spectrum collapse proceeds. This is just what we are going to do in the next sections devoted to the impact theory of the isotropic Raman spectrum transformation. 

In the pioneering work the same information was extracted from the extremum position assuming it is independent of y [143]. This is actually the case when isotropic scattering is studied by the CARS spectroscopy method [134]. The characteristic feature of the method is that it measures o(ico) 2 not the real part of Ko(icu), as conventional Raman scattering does. This is insignificant for symmetric Lorentzian contours, but not for the asymmetric spectra observed in rarefied gas. These CARS spectra are different from Raman ones both in shape and width until the spectrum collapses and its asymmetry disappears. In particular, it turns out that... 

Burshtein A. I., Storozhev A. V. The quantum theory of collapse of the isotropic Raman scattering spectrum, Chem. Phys. 135, 381-9 (1989). 

Sala J. P., Bonamy J., Robert D., Lavorel B., Millot G., Berger H. A rotational thermalization model for the calculation of collisionally narrowed isotropic Raman scattering spectra - application to the SRS N2 Q-branch, Chem. Phys. 106, 427-39 (1986). 

A review article has been published on depolarized Raman spectroscopy in molten salts, and it is discussed briefly here for the case of molten nitrates. Polarized (VV) and depolarized (HV) Raman scattering of the 1050 cm" line was used. The intensity of the isotropic part of the... 

Additionally, the description of LC involves an analysis of order. In particular, a sharp drop of the order parameter to B is observed when a transition takes place from the LC phase into the isotropic phase. The order parameter can be measured experimentally in a number of ways, such as diamagnetism, birefringence, Raman scattering, NMR, and EPR. 

This was first investigated by Huang n). Long-wave optical phonons are those with small k values. A polar phonon is an infrared-active phonon. Polar phonons therefore can only be observed in the Raman effect for crystals having no center of symmetry in the elementary cell. For centro-symmetric crystals the rule of mutual exclusion applies infrared-active phonons are forbidden in Raman scattering and vice versa. The elementary cells of NaCl and LiF have a center of symmetry, but GaP has none. The following considerations may therefore be applied to GaP as an example. This crystal has two atoms in the elementary cell and is cubic. It can be treated as an optically isotropic medium. 

For a purely isotropic Raman scattering tensor, the depolarization ratio will be zero since the scattered light from such a system must have a polarization parallel to the incident beam. This is evident when equation equation (5.29) is used in equation (5.30) so that [21],... 

This expression is identical in form to equation (5.20). In the case of Raman scattering, however, it is necessary to compute the average Raman tensor, (. For a transversely isotropic system, the segment is free to spin about the r. axis, and the vector ni is averaged over the unit circle normal to r . In addition to (n() = 0 and equation (5.22), we require the result,... 

Figure 3. Calculated band profiles of Stokes vibrational Raman scattering from Nt at 2000 K assuming a triangular slit function with FWHM = 5.0 cm 1. The bottom curve includes the isotropic part of the Q-branch only. The top curve is a more exact calculation including O- and S-branch scattering, the anisotropic part of the Q-branch and line-strength corrections owing to centrifugal distortion. The base lines have been shifted vertically for clarity.

A remedy obviously should be available using polarization tricks. In conventional Raman spectroscopy, the isotropic and anisotropic components are deduced from linear combinations of the polarized and depolarized spectra, while a nonresonant part is not clearly recognized (41). In frequency-domain CARS it is known how to suppress the nonresonant contribution and solely measure resonant scattering (isotropic plus anisotropic part) (42). In time-domain CARS, polarization interference can do an even better job with three magic cases (derived in Refs. 35,39). These authors derived explicit expressions for the coupling factors F in Equations (2)-(4) ... 

Corresponding lineshape data of the isotropic component of spontaneous Raman scattering are presented in Fig. 8b. Knowing T2 within 30 fs (Fig. 5), the measured lineshape (experimental points) is readily plotted versus normalized frequency units Aco x T2. Comparison with the computed lineshapes [Fourier transformation of Equation (9)] leads to 350 100 fs for rc, in good agreement with the time-domain results. Combining the measurements, one arrives at rc = 330 70 fs (45). 

Ordinary Raman scattering intensity (far from resonance) can be expressed in terms of two invariants the isotropic transition polarizability a, and the anisotropic transition polarizability... 

T. Bancewicz and S. Kielich. Isotropic Raman scattering for non-totally symmetric vibrations of correlated molecules with intrinsic optical anisotropy. J. Chem. Phys., 75 107-109 (1981). 

D. P. Shelton and G. C. Tabisz. Binary collision induced light scattering by isotropic molecular gases II. Molecular spectra and induced rotational Raman scattering. Molec. Phys., 40 299-308 (1980). 

Several complementary techniques exist for the experimental study of dephasing, and here we will underline only the differences between them. The simplest experimental access to dephasing is by spontaneous Raman scattering. A laser of frequency scattered light at to, around cuj = frequency resolved. The isotropic Raman scattering cross section is directly related to the vibrational correlation function... 

Under conditions in which the material is isotropic only, the odd nonlinear susceptibilities contribute to TPA. The even terms vanish because orientation is required. Therefore, the lowest nonlinear absorption is described by the imaginary part of y° corresponding to Stokes-Raman, anti-Stokes-Raman scattering, and TPA [16, 22, 23, 35, 45, 50, 53, 70, 73, 280, 281],... 

Whereas the dielectric constant probes essentially the R-dependence of the isotropic polarizability, the collison induced depolarized Raman scattering depends on the increment in the anisotropy of the polarizability with varying R. Depolarized Raman scattering of noble gases has first been observed by MacTague and Bim-baum in 1968, and later investigated for many gases . Very recently also polarized Raman intensities have been measured for NCj and He ... 

The temperature dependence on the IR absorption and Raman scattering bandwidths of some fundamental modes of Aj, B, and B2 symmetries of thiophene has been investigated in the region 400-1600 cm <81CPH251>. The spectroscopic study was carried out in the liquid phase which requires simultaneous investigation of the bands. Results show that the IR and anisotropic Raman bandwidths increase with increasing temperature and more so in the latter case. The rotational diffusion coefficients obtained from the bandwidths indicate that the rotational and vibrational relaxation phenomena occur simultaneously. The IR and isotropic and anisotropic Raman band profiles of the Aj symmetry mode have also been studied in the liquid phase <81CPH265>. 

One final procedure for minimizing substrate Raman scattering interference in thin polycrystalline films deposited on silica is based upon the polarization properties of the scattered light (16). Inherent molecular disorder present in vitreous silica substrates results in marked polarization anisotropy of the Raman-scattered light from the substrate. Raman scattering from a deposited polycrystalline film is isotropic since the individual randomly-oriented grains act to scramble the... 

Schmidt, M., Brodin, A., Jacobsson, R, Olsson, M., and Maurer, R H. J., Quasi-elastic Raman scattering and free volume in isotropic pressure-densihed atactic poly(methyl methacrylate) glasses, J. Chem. Phys., 112, 1020-1028. (2000b). 

Raman scattering is envisaged as the process of reradiation of scattered light by dipoles induced (P) in the molecules by the incident light and modulated by the vibrations of the molecules (a.3). In normal Raman scattering by molecules in isotropic media, the dipoles are simply those that result from the action of the electric field component, E, of the incident light on the molecules,... 

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