Completely polarized light

In order to be able to apply Eq. (2.2) in practice, let us consider how we can determine the cyclic components E9 of the vector E for completely polarized light. 

Simultaneous application of Eqs. (2.6) and (2.8) makes it possible to find G(0, ip) in explicit form for any case of interaction between completely polarized light and a transition dipole moment of a molecule. 

Thus, for completely polarized light (2.4) gives p =, for unpolarized light p = 0, and partially polarized 0 < /> < 1. It is often convenient to use the degree of linear polarization ... 

In the case of a molecule that is free to explore a wide range of orientations rapidly, compared with the lifetime of the excited state, the emission will be essentially depolarized and r = 0 since fy = However, if the molecule experiences some degree of hindered rotation or alignment, r will be non-zero. For completely polarized light, for example scattered polarized laser light, r = 1. Note that the absorption and emission dipoles for typical fluorophores are never perfectly parallel and so some degree of depolarization is intrinsic even for a rota-tionally frozen molecule (hence the use of scattered light in this example). 

For completely polarized light, the normalized Stokes parameters satisfy the condition + 52 + 51 = 5o = l. Therefore the point with the coordinates (Si,S2,S3) is on the surface of a unit sphere in 3-D space. This sphere is known as the Poincare sphere and is shown in Figure 3.6. 

Figure 6.21 Schematic representation of light polarization (a) natural light, (b) partly polarized light and (c) completely polarized light.

We have recently initiated our investigation of blends by examining the compatibility between our modified polymer sample 4 and poly(methyl methacrylate). Mixtures with a composition of between 10% and 30% of sample 4 yield compatible blends which are transparent under a polarized light microscope, and are characterized by a single Tg. Mixtures richer than 60% of 4 undergo complete phase separation. 

Isotropic samples will have no effect on the polarized light no matter how the crystal is oriented, since all crystal axes are completely equivalent. This effect is known as complete or isotropic extinction (Fig. 3a). Noncrystalline, amorphous samples will exhibit the same effect. 

Addition of hydroxide occurs as a rapid follow-up reaction. Even if the alkyl halide was chiral before the carbocation formed, racemization occurs about the central carbon atom because the hydroxide can bond to the planar central carbon from either side (see Figure 8.17(b)). Statistically, equal numbers of each racemate are formed, so the angle through which the plane polarized light rotated during reaction will, therefore, decrease toward 0°, when reaction is complete. 

When following the (dual-route) reaction of a secondary halide with hydroxide ion, we find that the angle 9 through which plane polarized light is rotated will decrease, as for primary and tertiary halides, but will not reach zero at completion. In fact, the final angle will have a value between 0° and 6>finai because of the mixtures of products, itself a function of the mixture of SnI and Sn2 reaction pathways. 

A rigorous and complete mathematical treatment of the polarization of light and the interaction of light with oriented matter is outside the scope of this chapter. These subjects have been thoroughly dealt with before and can be found in a number of comprehensive texts [29-32] the reader is referred to the excellent book by Michl and Thulstrup [3] for a more detailed treatment of optical spectroscopy with polarized light. Here, a conventional, qualitative representation is given to establish the nomenclature and conventions to be used and to facilitate the understanding of the concepts presented. 

Then the moment induced by the electric vector of the incident light is parallel to that vector resulting in complete polarization of the scattered radiation. The A lg i>(CO) mode of the hexacarbonyls provides a pertinent example08. Suppose we have a set of coupled vibrators, equidistant from some origin. Then it must be possible to express the basis functions for the vibrations in terms of spherical harmonics, for the former are orthogonal and the latter comprise a complete set. The polarization of a totally symmetric vibration will be determined by its overlap with the spherically symmetrical term which may be taken as r2 = x2 + y1 + z2. Because of the orthogo-... 

Let us now differentiate between structures which are asymmetric and dissymmetric. The word asymmetric conveys the idea that the molecule is completely devoid of the elements of symmetry. Dissymmetric on the other hand means not completely devoid of elements of symmetry but possessing so few elements of symmetry that on the whole it will posses two structures which will be the mirror images of each other. Therefore to avoid confusion the term asymmetric is used to cover examples which rotate the plane polarized light. The two forms of an optically active compound are called enantiometers or enantiomorphs or optical antipodes. They are also said to have enantiomeric relationship to each other. 

A complete analysis of the IR spectra of thienothiophenes 1 and 2 in the gaseous, liquid, and crystalline states was carried out by Kimel feld et a/. The following isotopically substituted compounds were also studied 2-deuterothieno[2,3-h]thiophene (l-2d), 2-deuterothieno[3,2-I)]-thiophene (2-2d), 2,5-dideuterothieno[2,3-h]thiophene (l-2,5-d2), and 2,5-dideuterothieno[3,2-h]thiophene (2-2,5-dj). The IR spectra of oriented polycrystalline films of all compounds were measured in polarized light, and Raman spectra of liquid thienothiophenes 1, l-2d, and 1-2,5-dj, of crystals of thienothiophenes 2 and 2-2,5-d2 and melts of thienothiophenes 2 and 2-2d were analyzed. The planar structure of point-group Cj, for thienothiophene 1 in the liquid and gaseous states was assumed. Then the thirty vibrations of compounds 1 and l-2,5-d2 can be divided into four symmetry classes Aj (11), Bj (10), A2 (4), and B2 (5) the vibrations of molecule (l-2d) (C, symmetry) are divided into two classes A (21) and A" (9). 

Although the ellipsometric parameters completely specify a monochromatic wave of given frequency and are readily visualized, they are not particularly conducive to understanding the transformations of polarized light. Moreover, they are difficult to measure directly (with the exception of irradiance, which can easily be measured with a suitable detector) and are not adaptable to a... 

We may represent a beam of arbitrary polarization, including partially polarized light, by a column vector, the Stokes vector, the four elements of which are the Stokes parameters. In general, the state of polarization of a beam is changed on interaction with an optical element (e.g., polarizer, retarder, reflector, scatterer). Thus, it is possible to represent such optical elements by a 4 X 4 matrix (Mueller, 1948). The Mueller matrix describes the relation between incident and transmitted Stokes vectors by incident is meant before interaction with the optical element, and by transmitted is meant after interaction. As an example, consider the Mueller matrix for an ideal linear polarizer. Such a polarizer transmits, without change of amplitude, only electric field components parallel to a particular axis called the transmission axis. Electric field components in other directions are completely removed from the transmitted beam by some means which we need not explicitly consider. The relation between incident field components (E, E i) and field components ( l, E () transmitted by the polarizer is... 

A beam of light is monochromatic if all photons have the same energy (the same frequency or wavelength in the wave picture). A beam of light is completely polarized if all the photons have parallel electric and magnetic vectors (E and H). 

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