Circularly polarized light definition

Analogous to the definitions of linear birefringence and linear dichroism following equations (2.15) and (2.21), the form of equation (2.30) suggests the following optical anisotropies for circularly polarized light ... 

It was seen in Chapter 8 that circular polarizers are required components in several pola-rimeter designs. By definition, a circular polarizer will extinguish circularly polarized light of one sense (either left- or right-circularly polarized light), but allow the other circular polarization to pass. 

Large gium values are indicative of large discrimination of these optically active species between left and right circularly polarized light. This can be seen, for example, by rearranging the definition of gahs [see eq. (3)3 to solve for the relative absorption of the two polarizations. 

For the definition of the asymmetry factors gx, see Appendix A.) The first tei is the Stevenson and Verdieck result [27] (for circularly polarized light, AUI = 1 The second term describes the enantiomeric excess due to the true magnetochin anisotropy. 

Electronic circular dichroism (CD) results from different absorption (molar absorption coefficient i and e ) of left- and right-circularly polarized light by the electronic subsystem of the molecule. CD has the same electronic origin as ordinary absorption. Therefore, CD spectra are interpreted in terms of the same concepts as absorption spectra, namely electronic transitions and excited states of definite chromophores For the discussions of electronic structures and excitations of complex chromophores molecular orbital (MO) theory provides an adequate framework. 

The optical purity is usually, but not always, equal to enantiomer excess. In order for the two to be equal, it is necessary that there be no aggregation. It is possible, for example, that a homochiral or heterochiral dimer (see Glossary, Section 1.6, for definitions) would refract the circularly polarized light differently than the monomer (or each other). In 1968 [19] Krow and Hill showed that the specific rotation of (S)-2-ethyl-2-methylsuccinic acid (85% ee) varies markedly with concentration, and even changes from levorotatory to dextrorotatory upon dilution. In 1969 [20], Horeau followed up on Krow and Hill s observation, and showed that the optical purity (at constant concentration) and enantiomer excess of (5)-2-ethyl-2-methylsuccinic acid were unequal except when enantiomerically pure or completely racemic. This deviation from linearity is known as the Horeau effect, and its possible occurence should be remembered when determining enantiomeric purity by polarimetry. 

FIGURE 1 Definition and sign of the d term., Non-polarized light 1 and r, left and right circularly polarized light. 

Figure 2. The linear polarized laser light is converted to circularly polarized light by a A/4 wave plate and then is linearly repolarized in the desired direetion by a eomputer controlled polarizer. The exeitation beam passes through a pinhole and reaehes the sample. The windows of the eryostat had to be carefully checked at the experimental temperature for depolarization properties. The lower part clarifies the definitions and orientations of the properties discussed in the text. Figure adapted from Ref. 1.

The imaginary part of the complex refractive indices for left and right circularly polarized light relates to circular dichroism, that is differential absorption for light of different circular polarizations. It is treated in a similar manner to linear dichroism, except that the definition of principal components follows a different convention. For linear birefringence and dichroism the principal values of the complex refractive index relate to the electric field polarization direction which is transverse to the propagation... 

Note -. In the above definition of right and left circularly polarized light, we adopt the convention frequently used in optics, that is, from the point of view of an observer looking at the light head on. For R, the observer will see a clockwise rotation of the electric field vector, while for L, the observer will see a counterclockwise rotation of the electric field vector. This is also the convention used in Chapter 4 when we discussed circularly polarized fight in the context of the optical properties of cholesteric liquid crystals. 

The fundamental scattering mechanism responsible for ROA was discovered by Atkins and Barron (1969), who showed that interference between the waves scattered via the polarizability and optical activity tensors of the molecule yields a dependence of the scattered intensity on the degree of circular polarization of the incident light and to a circular component in the scattered light. Barron and Buckingham (1971) subsequently developed a more definitive version of the theory and introduced a definition of the dimensionless circular intensity difference (CID),... 

Figure 3 The Faraday Effect within magnetic optical rotatory dispersion (MORD) spectroscopy. A plane polarized beam is rotated by a magnetic field applied parallel to the axis of propagation. The rotation is defined as positive if the beam is rotated to the right in a clockwise direction when viewed toward the sonrce (a). The original definition of Icp and rep within CD spectroscopy — light plane polarized in the j/z-plane can be described in mathematical terms as being comprised of left or right circularly polarized components of equal phase and amplitude (b). The perspective is depicted schematically toward the source. (Reprinted from Mack, Stillman and Kobayashi, Elsevier 2007)...

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