Elliptical polarization

Another very important property of synchrotron radiation is its very high degree of polarization. The radiation is predominantly polarized with the electric field vector parallel to the acceleration vector. Thus, in the plane of the orbit, the radiation is 100% plane-polarized. Elliptical polarization can be obtained by going away from the plane however, intensities also decrease significantly. 

Finally, let us note that P2 and P4 are invariant for rotations of the polarization axes with respect to the propagation axis OZ. The quantity w2 is called the wave helicity. The polarization ellipticity is associated with m2, the obliquity with raj. 

The electronic Schrodinger equation for the hJ ion can be solved by transforming to a coordinate system that is called confocal polar elliptical coordinates. One coordinate is f = (rA + rB)/rAB, the second coordinate isp = (rA — rB)/rAB, and the third coordinate is the angle , the same angle as in spherical polar coordinates. The solutions to the electronic Schrodinger equation are products of three factors ... 

In ellipsometry monochromatic light such as from a He-Ne laser, is passed through a polarizer, rotated by passing through a compensator before it impinges on the interface to be studied [142]. The reflected beam will be elliptically polarized and is measured by a polarization analyzer. In null ellipsometry, the polarizer, compensator, and analyzer are rotated to produce maximum extinction. The phase shift between the parallel and perpendicular components A and the ratio of the amplitudes of these components, tan are related to the polarizer and analyzer angles p and a, respectively. The changes in A and when a film is present can be related in an implicit form to the complex index of refraction and thickness of the film. 

Synchrotron radiation provides a convenient source of tunable VUV and SXR radiation. Natural synchrotron radiation, emitted by relativistic electrons, is linearly polarized in the plane of their orbit, which is traditionally the configuration used to collect the radiation. However, it is well known that the polarization becomes elliptical if observed above or below the plane of the orbit. 

The circular polarization (CIPO) beamline at the Elettra synchrotron (Trieste, Italy) operates in the VUV-SXR range with radiation from a combination permanent magnet-electromagnetic elliptical wiggler [94, 95]. This does not achieve full circular polarization in the VUV region, but rather an elliptical output with principal axis lying in the horizontal plane (ii > 0, 2 = 0, < 1). 

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. 

FIGURE 27.25 Elliptic polarization resulting from the superposition of two linear components of different phase and amplitude. (From Muller, 1973, with permission from Wiley-VCH.)... 

As discussed above, the reflection of linearly polarized light from a surface generally produces elliptically polarized light, because the parallel and perpendicular components are reflected with different efficiencies and different phase shifts. These changes in intensity and phase angle can be analyzed to characterize the reflecting system. This approach is called ellipsometry. 

MCP experiments were performed at AR-NE1 station of KEK (National Laboratory of High Energy Physics), Japan, using circularly polarized X-rays with the incident X- ray energy of 60 keV emitted from the elliptical multipole wiggler. Figures 1 and 2 show MCPs ofUSe and UTe, which have been measured at 150 and 80 K, respectively. 

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