Degree of circularity

Figure 12. The degree of circular polarization i3 measured behind the experimental chamber on two optically similar branches fed by the same undulator pair of the UE56/2 beamUne at BESSY II. Data taken from Ref. [55].

It is revealing to look at an example of such data in Fig. 12. The UE56/2 beamline has two nominally identical branches with replicated optical paths, but that have been used for different experiments. The measurements show a high degree of circular polarization, [531 > 98%, except near carbon K edge where the polarization reduces, but only on one branch. It is postulated that this is a consequence of carbon contamination on a beamline optic in that branch. These results demonstrate the necessity to be alert to such possible causes of degradation and to perform polarization checks where possible rather than rely on theoretical predictions. 

Unfortunately, in the VUV region no polarimetry data are available, but calculations indicate the degree of circular polarization achieved by the wiggler may be 80%, estimated to be no worse than 70% delivered at the experimental chamber [95, 96]. In PECD experiments, we have calibrated the polarization state by deduction from cross-comparison of results at a few fixed energies previously studied on the SU5 beamline where accurate polarimetry data was available [36]. Because the horizontal magnetic field array in the insertion device is electromagnetic, fast current reversal to switch left- and right-handed elliptical polarizations is possible, with the usual potential benefit for dichroism measurements. 

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),... 

For geometrical reasons the degree of circular polarization of the rf field is 100% only along the cylinder axis of the cavity. However, it has been shown that for samples with diameters < 6 mm the contribution of the counter-rotating component to the nuclear transition probability is less than 1%43. ... 

Note that the cross polarization is zero and incident unpolarized light does not acquire a degree of circular polarization upon scattering. 

If such light is incident on a medium described by the matrix (14.4), the degree of circular polarization of the scattered light is... 

A necessary condition for the correctness of the multiple-scattering explanation of the observed circular polarization is that scattering by noctilucent cloud particles does not appreciably reduce the degree of circular polarization of the incident light. That this is so for randomly oriented Rayleigh ellipsoids is readily shown. M in (5.52) is nearly unity for ice ellipsoids, so to good approximation... 

Both Vms//ms and /ms//0 must be about 0.2 or higher if the highest values of circular polarization are the result of multiple scattering if they both are about 0.07, the multiple scattering explanation is consistent with the lowest observed values. To put it another way, Fms//0 must be not less than the observed degree of circular polarization this is at least plausible—there are no strong reasons for rejecting it—but it has yet to be demonstrated unequivocally. 

There are several possible explanations for the circular polarization data they are in error the particles are small, aligned, and highly absorbing the light illuminating the clouds has acquired a degree of circular polarization by multiple scattering. 

Small degrees of circular polarization (V/I) in starlight, usually less than 1%, have been observed in recent years the polarization modulation technique for observing such polarization was discussed in Section 13.7. There are at least two mechanisms for circularly polarizing starlight. 

Figure 2.28 Comparison of the Raman and ROA bands of - -)- P)-1,4-dimethylenespiro-pentane (a) in substance and (b) as a 20% by volume solution in trideuterioacetoni-trile measured in backscattering for the 1650 to 1830cm 1 region. From bottom to top Raman, ROA, degree of circularity. The relative scattering intensities in substance and trideu-terioacetonitrile solution were normalized so that the largest peak in the measured Raman spectra, vibration 8 at 609 cm-1, has the same height. The experimental parameters are as in Figure 2.27.

Analogous g-values may be defined for the degree of circular polarization in emission [or circularly polarized photoluminescence (CPPL)] and circularly polarized electroluminescence (CPEL), eg. gCppL = 2(JL - 1R)/(1L + 1r), where IL and IR denote the intensity of left- and right-handed circularly polarized emission, respectively. CPPL should not be confused with fluorescence-detected CD. 

Fig. 2.6. Geometry for the calculation of the degree of circularity of fluorescence C at excitation by lefthanded circularly polarized light.

In the presence of such processes the degree of circularity of fluorescence depends simultaneously on two ratios - To/Ti and ro/T2. ... 

Table 3.5. The dependence of the intensity, anisotropy of polarization degree of polarization V and degree of circularity C on the pumping parameter x at the classical limit J — oo...

Table 3.6. Expressions for anisotropy of polarization 1Z(J), degree of polarization V J) and degree of circularity C(J) for all types of dipole transitions, J being the quantum number of the initial level. Summation is over M from — J to J. 

Fig. 3.12. Measured [369] values of degree of circularity C as dependent on the excitation power density w.

Fig. 4.4. The geometry adopted in the calculation of the degree of circularity C = (Ir — Ii)/(Ir + h) under elliptically polarized excitation.

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