Plane-polarized beam

Circular dichroism arises from the same optically active transitions responsible for the Cotton effects observed in ORD curves, but unlike ORD it is an absorption, not a dispersion, phenomenon. Hence, the CD effect is restricted to the region of the transition and can be interpreted more straightforwardly. Both ORD and CD can best be understood if one imagines the incident plane-polarized beam resolved into two in-phase circularly polarized beams whose vectors rotate in opposite directions. A difference in index of refraction between the left and right circularly polarized beams results in rotation of the transmitted plane polarized beam while differential absorption of the two circularly polarized beams results in depolarization of the transmitted beam, so that an incident plane-polarized beam whose frequency is within that of an optically active absorption band becomes both rotated and elliptically polarized upon passage through the sample. This depolarization effect is CD, and the measured parameter is (et — er), the difference in extinction coefficient between the left and right circularly polarized beams. The data is usually recorded as the specific ellipticity, defined as ... 

A typical experimental ellipsometer is illustrated in Figure 3.7. Monochromatic light, typically from a continuous wave laser, e.g. a He-Ne laser, is plane polarized (the angle of polarization is given by p) and impinges on a surface. A compensator is then used to convert the elliptically polarized reflected beam to a plane polarized beam (with a being the angle of polarization). The analyzer then determines the... 

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 source (a). The original definition of Icp and rep within CD spectroscopy—fight plane polarized in the yz-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)...

The successful development of a chiral detector based on optical rotation measurement hinges on the use of the Faraday effect. If a plane polarized beam of light passes through a medium that is... 

It is most important to note that in many cases of harmonic emission, a more completely index-symmetric form of the polarizability tensor is implicated. Consider once again the prototypical example of optical nonlinearity afforded by harmonic generation. When any harmonic is generated from a plane-polarized beam, in an isotropic medium, it produces photons with the same polarization vector as the incident light. In such a case the radiation tensor pyk becomes fully index-symmetric, and arguments similar to those given above show that only the fully index-symmetric part of the hyperpolarizability tensor, 3p(—2m co, co), can be involved. This does not mean that the tensor itself is inherently fully index-symmetric, but it does mean that experiments of the kind described cannot determine the extent of any index antisymmetry. 

FIGURE 19-4 Equivalency of a plane-polarized beam to two J. I) circularly polarized beams of radiation. 

A beam of unpolarized light of intensity I is equivalent to two plane polarized beams, each of intensity I/2, polarized in mutually perpendicular directions, and incoherent in phase. Therefore, for a vertically polarized incident beam of unit intensity, the scattered intensity at 90° in the horizontal plane is twice as great as for an unpolarized incident beam of the same total intensity for in the latter case, only half the total intensity contributes to scattering in the horizontal plane at 90°. (For further discussion see Sinclair (1947).) For a system of small isotropic particles, there is of course no horizontal component in this direction as will be seen later, this is true also for scattering from iso-... 

The observed signal-to-noise power ratio for these experiments was found to behave in accordance with the theoretical expression obtained for parallel, plane-polarized beams incident on a quantum-noise-limited detector under ideal conditions [7.4-7], i.e.. 

When ordinary light is passed through a polarizer, the polarizer interacts with the electric field so that the electric field of the light that emerges from the polarizer (and the magnetic field perpendicular to it) is oscillating only in one plane. Such light is called pUme-polarized lig ht (Fig. If the plane-polarized beam encounters a filter with... 

As shown in Figure 9 A plane-polarized light is formed from two plane-polarized beams whose phase difference Aq> equals zero. If a phase shift of 90° (A(p = 7i/2) is chosen, as shown in Fig-... 

The ratio of absorbances at the 1256 and 1220 cm bands is measured when the electric vector of the plane-polarized beam at normal incidence is parallel to and perpendicular to an arbitrary reference direction. The reference direction is usually chosen as the direction of stretch (tape drawing) and, hence, tape longitudinal axis, at which the band intensity is maximum. The dichroic ratio of an absorption band is determined by placing the polarizer at the light source. Orientation function (/<, or/a ) is calculated using the Samuels (6) relationship ... 

From the second point above, we can imderstand that the value of Aa is very small. How then do we measure it to get the CD spectrum Ideal situation would be to fill a constant path-length cell with a solution of particul concentration C and then measure absorbance due to the left and right components (A and A individually and then arrive at the difference (A - A ) by subtracting one from another. In actual practice a plane polarized beam is passed throu a quarter-wave plate which is rotated from +45° to -45° producing first d and then I circularly pol2irized light. A spectrophotometer then measures the periodic variation in the transmittance when the incident radiation experiences periodic changes in the handedness. If we use the relationship between A and T,... 

Figure 6-12a shows a few of the vectors depicted in Figure 6-1 lb at the instant the wave is at its maximum. The vector in any one plane, say XY as depicted in Figure 6-12a. can be resolved into two mutually perpendicular components AB and CO as shown in Figure 6-12b. If the two components for all of the planes shown in Figure 6-12a arc combined, the resultant has the appearance shown in Figure 6-12c. Removal of one of the two resultant planes of vibration in Figure 6-12c produces a beam that is plane polarized. The resultant electric vector of a plane-polarized beam then occupies...

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