Partially polarized light

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... 

Quantitative treatments of partially polarized light can be found in the texts by Born and Wolf [2], and Azzam and Bashara [5]. In this monograph, the light will be assumed to be perfectly polarized. It should be noted, however, that in many experimental situations depolarization can readily occur and care must be taken to either account for it, or to minimize this possibility. The most common source of depolarization in optical rhe-ometry is multiple scattering by such systems as dense suspensions and liquid crystals. 

Figure 4.4. Optical microscope image for composites containing 0.05 wt % SWNT and 2 wt% clay under partial polarized light condition (a) and schematic illustration for clay assisted dispersion of SWNT (b). Reprinted with permission from ref (41).

In a very recent work [316] the emission of (partially) polarized light from highly ordered a6T films with large grain size is reported. With ITO substrates and A1 top electrodes a quantum efficiency of about 10 is found (Table 13,10). 

One may wonder why two widely used measures exist for the same phenomenon. Both P and r have a rational origin. Consider partially polarized light traveling along thex-a us (Figure 10.2), and assume that one measures the intensities h and /y with the detector and polarizer positioned on the. v-axis. The polarization of this light is defined as the fraction of the light that is linearly polarized. Specifically,... 

If the orientation of the polcirizer is parallel to the plane of polarization of light, the intensity of the transmitted polarized light will be maximum. This intensity will be zero if the polarizer orientation is perpendicular to the plane of polarized light (Figure 8.31). Therefore, for a partially polarized light, the polarization P, may be given by the relationship... 

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