Scattered light, polarization

From a theoretical perspective, since the designation of the lab-fixed axes is arbitrary, what is relevant is the relative orientation of the polarizations of the excitation and scattered light. Thus the line shape for excitation light polarized along axis p, and scattered light polarized along axis q (p or q denote X, Y, or Z axes in the lab frame) is called Ipq(co). When p = q this is lyy, and when p q this is IVH. Mixed quantum/classical formulae for Ipq(co) are identical to those for the IR spectmm, except mPi is replaced by apqP which is the pq tensor element of the transition polarizability for chromophore i. Thus we have, for example [6],... 

Each of the resonances appearing in the spectra are identified and characterized by the type (TE or TM), mode number n, and mode order 5 (i.e., TE J. Allowances were made in the fit for a small amount of scattered light polarized perpendicular to the scattering plane (due to imperfect alignment of the polarizer) and a small change in the particle radius due to evaporation during the experiment. Once the resonances are identified there are no adjustable parameters in the simulation of an excitation spectrum of a... 

Thus the intensity of scattering should vary essentially as T — T ) (fig. 2.5.5) and the ratio of the scattered light polarized along z to that polarized along X should be 4/3. Both these predictions have been verified quantitatively for... 

Polar diagram of the intensity of scattered light (polarization is still in the x-z plane)... 

If the incident light is natural (unpolarized), the depolarization ratio may be computed by considering the scattered light to represent the sum of the intensities of observations made parallel and perpendicular to the incident electric vector of a polarized beam. That part of the light from the parallel observation, being unpolarized, contributes one-half its intensity to the scattered light polarized, respectively, parallel and perpendicular to ... 

The second kind of experiment to be discussed here is Raman spectroscopy, which can be viewed as a consequence of effect 3. However, the theory of the Raman effect is made somewhat more complicated by the use of polarized incident and scattered radiation in modern laser Raman studies as a technique to extract more information. Suppose the incident radiation is polarized in the Z direction the usual arrangement is to measure both the intensity of scattered light polarized in the Z direction and the scattered light polarized perpendicular to Z (call it X). We consider only these two geometries, since no additional information is ordinarily obtained from other polarizations, at least for fluids where the range of the correlations (or molecular size) is small compared to the wavelength of the light used. 

Let the direction of propagation of the incident radiation be the z axis and the direction of observation be perpendicular to the z axis in the xy plane (see Fig. 1.33). The depolarization ratio p is defined as the ratio of the intensity of scattered light polarized perpendicular to the xy plane /j to that polarized parallel to the xy plane /.i. 

For a circularly polarized light experiment, one can measure the cross sections for either right (r) or left (1) polarized scattered light. Suppose that right polarized light is made incident on a Raman active sample. The general expressions for the Raman cross sections are [176]... 

At 20 = 0°, the scattering comprises both components of polarization of the incident beam at 29 = 90°, the scattering comprises only one half of the incident beam. Consequently, the scattered light at 90° will be plane polarized. 

The sin 0 terms in Eqs. (10.25) and (10.26) arise from the consideration of polarized light. The light scattered by polarized incident light is also polarized in the same direction, so the term 1 + cos 0 in Eq. (10.30) describes the overall polarization of the scattered light. Before we lose sight of the individual contributions to this, it will be helpful to consider this polarization somewhat further. This is done in the following example. 

The intensity of the vertically polarized scattered light is proportional to sin 0 which, in polar coordinates, is described by a figure 8-shaped curve centered at the origin and having maximum values of 1 at 0 = 90°, Because 0 is symmetrical with respect to the z axis, this component of scattered light is described in three dimensions by a doughnut-shaped surface in which the hole has shrunk to a point - centered symmetrically in the xy plane. 

Along the z axis, sin 0 contributes nothing but sin 0,, = 1. so the net scattered light is horizontally polarized. 

The arrangement illustrated in Figure 1 is commonly used for angular characterization of scattered light. The light source is usually a laser. The incident beam may be unpolarized, or it can be linearly polarized with provisions for rotating the plane of polarization. Typically the plane of polarization is perpendicular to the plane of... 

Polarization effects are another feature of Raman spectroscopy that improves the assignment of bands and enables the determination of molecular orientation. Analysis of the polarized and non-polarized bands of isotropic phases enables determination of the symmetry of the respective vibrations. For aligned molecules in crystals or at surfaces it is possible to measure the dependence of up to six independent Raman spectra on the polarization and direction of propagation of incident and scattered light relative to the molecular or crystal axes. 

Fig. 3—Measurement of surface by HDI surface reflectance analyzer. In electromagnetic radiation (light), the polarization direction is defined as the direction of the electric field vector. The incident polarization of the light can be controlled. The instrument uses a variety of detectors to analyze the reflected polarization state of the light. (U.S. Patent 6,134,011). (a) Plane of the disk The SRA uses a fixed 60 degree (from the surface normal) angle of incidence. The plane of incidence is the same as the paper plane (b) Pit on a surface detected by reflected light channels of HDI instrument (c) Scratches on disk surface measured by HDI surface reflectance analyzer (d) Particles on the surface of disk detected by reflected light (black spot) and by scattered light (white spot) [8].

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