Polarization dependencies of absorption bands

The crystal structures of transition metal compounds and minerals have either cubic or lower symmetries. The cations may occur in regular octahedral (or tetrahedral) sites or be present in distorted coordination polyhedra in the crystal structures. When cations are located in low-symmetry coordination environments in non-cubic minerals, different absorption spectrum profiles may result when linearly polarized light is transmitted through single crystals of the anisotropic phases. Such polarization dependence of absorption bands is illustrated by the spectra ofFe2+ in gillespite (fig. 3.3) and of Fe3+in yellow sapphire (fig. 3.16). 

The solid curve in Fig. 31 shows the frequency dependence of absorption [Eq. (255)]. We see the shoulder in the R-band region (at x 2) and the main (librational) absorption peak at x 5.5. This dependence (solid curve) agrees with the experimental data [42, 51] (a more detailed analysis is given in the next section). If the vibration lifetime r b were twice as large, we would get an unreasonably large and narrow R-peak (dashed curve). On the other hand, if the parameter, v were twice as large, the intensity of the R-band would increase unreasonably (dash-and-dotted curve). This example shows convincingly that the form of the FIR water spectra sharply determines the parameters (25 lb) of our polarization model. 

A qualitative explanation for the polarization dependence of the absorption bands is as follows. According to eq. (4.1) the probability, P of a transition is proportional to the square of the integral... 

Figure 3.25. Thickness dependence of absorption depth (AT = 1 - T) for (a) vjox. P) vroy> and (c) VLQz bands in transmission spectra of standing film of anisotropic inorganic material (Table 3.3) at several angles of incidence (a, c) for p-polarization p) for s-polarization. Dashed lines are calculated according to thin-film approximation Equation (1.98). Reprinted, by permission, from K. Yamamoto and FI. Ishida, Appl. Opt. 34, 4177 (1995), p. 4181, Fig. 6. Copyright 1995 Optical Society of America.

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