The Depolarization Ratio

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], 

The off diagonal elements, a yz and a, will be zero for an isotropic Raman 

In a system comprised of many molecules, the measured intensity will be an average over all the Raman scatterers in the sample, and this is accounted for by the angular brackets in equation (5.31). Since this average is over the square of the derived polarizabil- 

Measuring the depolarization ratio, therefore, provides a direct, spectroscopic determination of the structure and dynamics of vibrational modes. Furthermore, this experiment can be used to determine the parameter e, which must be known for quantitative measurements of the order parameters in oriented systems. 

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Additional mfomiation about the vibration ean be obtained tln-ough the depolarization ratio. This is the ratio of the intensity of seattered light that is polarized in a plane perpendieular to the ineident radiation relative to that the seattered light that is polarized parallel to the ineident polarization, p For totally synnnetrie... 

Thus one predicts that the depolarization ratio for excitation with natural light should be... 

In analogy with the depolarization ratio for linearly polarized light, the ratio of the two above quantities is known as the reversal coefficient, R(Q, given by... 

The Raman spectrum can be used to give additional information regarding the symmetry properties of vibrations. This information derives from the measurement of the depolarization ratio p for each Raman band. The quantity p is a measure of the degree to which the polarization properties of the incident radiation may be changed after scattering... 

An approach simpler than the "general" method has been used by Bower and coworkers [52,53] and has proved to be useful to determine the order parameters of uniaxially oriented polymers. This approach, called "cylindrical" method, requires a smaller number of spectra that are easily measurable, but it assumes that the Raman tensor associated with the vibrational mode under study is cylindrical. In such case, at — a2 — a so that the depolarization ratio R so of an... 

Finally, Frisk et al. have proposed a third method, the "depolarization" method, that does not need the assumption of a cylindrical Raman tensor [56]. A randomly oriented sample is again necessary but the depolarization ratio takes the general form... 

The measurement of four independent spectra then leads to the complete resolution of the system, assuming that the depolarization ratio is the same for the oriented and isotropic samples. 

Silk fibers, a basic system with a uniaxial symmetry, have also been investigated by Raman spectromicroscopy [63] that is one of the rare techniques capable of providing molecular data on such small (3-10 pm diameter) single filaments. The amide I band of the silk proteins has been particularly studied to determine the molecular orientation using the cylindrical Raman tensor approximation. In this work, it was assumed that Co Ci, C2 and the a parameter was determined from an isotropic sample using the following expression of the depolarization ratio... 

Beattie, I.R., Ozin, G.A., and Perry, R.O., Gas phase Raman spectra of P4, P2, As4 and As2. Resonance fluorescence spectrum of 80Se2. Resonance fluores-cence-Raman effects in the gas-phase spectra of sulfur and iodine. Effect of pressure on the depolarization ratios for iodine,. Chem. Soc., Perkin I, 2071, 1970. 

The anisotropy of the polarizability is described by the tensor invariant y2, which determines the depolarization ratio. This invariant y2 is averaged over all configurations of the chain molecule treated in the RIS approximation, interdependenca of rotations about neighboring bonds is taken into account. 

In addition to the intensity and frequency of the Raman lines, the polarization character of the lines can be measured. In fact, what led Sir C. V. Raman to believe that he was observing a new phenomenon was the unique polarization properties of this new radiation. Usually, the observations are made perpendicular to the incident beam, which is plane-polarized, as at (a) in Fig. 15. The depolarization ratio p is defined as the intensity ratio of the two polarized components of the scattered light that are respectively parallel and perpendicular to the direction of the (polarized) incident beam when the polarization of the incident beam is perpendicular to the plane of propagation and observation (p = I /ll). 

One of the limitations of the PRS method is that it is not trivial to determine the incipient lesion depth. This parameter is clinically relevant as it can guide the clinician in the treatment decision-making process. Furthermore, one additional challenge facing the use of the depolarization ratio of the Vi POJ3 mode as a marker for early caries formation is the speed required to complete a full... 

The dependence of the light scattering patterns on a wide variety of variables may be explored, i.e. size, angle, intensity or combination of intensities such as the depolarization ratio i2/ii or the polarization (i2-ii)/(i2+ii) ... 

The experiment shown in Figure 5.6 shows the basic experiment defining the depolarization ratio. Here incident light, E(. polarized parallel to the y axis is brought to the sample... 

Besides being always Raman active, the totally symmetric vibrational modes can also be readily identified in the spectrum. As shown in Fig. 7.3.2, the scattered Raman radiation can be resolved into two intensity components, /l and 7. The ratio of these two intensities is called the depolarization ratio p ... 

Here, T is the observed line width (Av << F), 7d is the peak-to-valley intensity in the difference spectrum, and To is the peak height of the Raman line. Although this equation is for Lorentzian-shaped bands, the results are approximately the same for Gaussian-shaped bands (the constant 0.385 becomes 0.350). In the case of carbon disulfide-benzene mixtures, the smallest shift observed was -0.06 cm-1, and the associated error was 0.02 cm-1 (77). A convenient rotating system that can be used for (1) difference spectroscopy, (2) normal rotating sample techniques (solid and solution), and (3) automatic scanning of the depolarization ratios as a function of the wave number has been designed (45). 

Moving to higher-order echo experiments, it has been shown that the infrared echo is inescapably affected by rotation as well as dephasing (38). The full polarization and rotation dependence of the Raman echo has not been explored. However, if the vibrator has a purely isotropic Raman cross section, i.e., the depolarization ratio p = 0, the analysis is simple. The Raman echo is completely independent of rotational dynamics. This fact gives the Raman echo a significant advantage over the infrared echo for many systems. 

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