Raman theoretical background

The first observation of the stimulated Raman effect was reported by Woodbury and Ng 215) j e effect was then thoroughly studied by several authors 216-218) and its theoretical background developed 219.220) (see also the review articles by Zubov et a/.22D). The stimulated Raman effect can be described as a parametric process where the coupling between a light wave at the Stokes frequency (Os and an optical phonon (vibrational wave) at cOy is produced by a pump field at col = (Oj + ojy. 

The theoretical background which will be needed to calculate the excited state distortions from electronic and Raman spectra is discussed in this section. We will use the time-dependent theory because it provides both a powerful quantitative calculational method and an intuitive physical picture [42,46-50]. The method shows in a simple way the inter-relationship between Raman and electronic spectroscopy. It demonstrates that the intensity of a peak in a resonance Raman spectrum provides detailed information about the displacement of the excited state potential surface along the normal mode giving rise to the peak [42,48]. It can also be used to calculate distortions from the intensities of vibronic peaks in electronic spectra [49]. For harmonic oscillators, the time-dependent theory is mathematically equivalent to the familiar Franck-Condon calculation [48]. 

The theoretical background for the Scatter Correction is that the scattering intensity is a function of the wavenumber (Rayleigh s v -law, see Section 5.7). The effect increases with the spectral distance of the line of interest from the wavenumber of the excitation laser. To correct this the Raman intensity data are multiplied point-by-point by ... 

Since the theoretical background and practical implementation of vibrational spectroscopy are described elsewhere in this encyclopedia, the emphasis here will be on the extension of Raman and infrared spectroscopy to the microscopic realm. It should be noted that many of the methods described here are applicable to other microspectroscopic methods, especially those based on optical phenomena such as fluorescence. 

The information required for predicting and/or analyzing spectra in the field of vibrational spectroscopy are vibrational frequencies and the corresponding intensities. While the former are univocally defined, the definition of the latter depends on the technique considered (infrared, vibrational circular dichroism, and Raman). For the extended theoretical background of the various spectroscopies, we refer interested readers to well-established textbooks [59, 60, 205,... 

While the present first volume contains much of the theoretical background, the emphasis in [1.35] is on experimental techniques, the interpretation of experimental results and the discussion of a number of phenomena which are directly related to phonons. Correspondingly, the second volume will contain a number of rather short chapters and its style will be somewhat different from this volume by exchanging depth for breadth in many places. It is planned to introduce the reader into the following topics Infrared, Raman and Bril-louin spectroscopy, interaction of X-rays with phonons, inelastic neutron scattering and some other techniques of interest. Phenomena such as piezoelectricity, ferroelectricity, melting and thermal conductivity will be given a qualitative discussion. The book will also contain some newer developments ... 

Fig. 6. Theoretical approximation of Raman spectra for x v polarization of Las Sr NiC single crystal at T = 5 K. Solid line is the experimental spectrum, dashed line is the calculated two-magnon hand, dotted line is a sum of some reasonable spectral shapes to fit line at 720 cm 1 and wide background, open circles represent total fitting spectrum.

Figure 8. Nitrogen concentration vs. temperature, determined from Raman data at position shown in Hi-air turbulent diffusion flame. The solid theoretical curve, corresponding to adiabatic conditions, was obtained by replotting the information in Figure 7. The theoretical point for stoichiometric combustion ( = 1) is shown on this curve as a filled-in circle. These Raman data were not corrected for optical background at the Raman spectral band position.

The purpose of this section is to provide some background to the theories by introducing theoretical expressions for Raman scattering intensities and outlining some of the more important features of the various theories classical electromagnetic enhancement (EM enhancement) and nonclassical contributions (chemical effects). 

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