Elliptically polarized

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. 

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. 

In ellipsometric spectroscopy, an elliptically polarized light is allowed to reflect on the interface and the change in ellipticity and phase angle are determined from complex reflectivity. 

With Xi and x2 as defined before, (3 = 0 denotes linear polarization at an angle a to the x-axis (3 = 7t/2 and a = n/4 denote circular polarization, and arbitrary a and (3 correspond to elliptical polarization. 

Optically active chromophores show different absorption for left and right circular polarized light (where the orientation of the polarized light changes periodically). These substances modify a circular polarized beam in such a way that the light is elliptically polarized after leaving the sample, an effect called circular dichroism. 

Figure 7.1. Electric field vectors of incident and evanescent light for the p-polarization, showing the phase lag Sp and the elliptical polarization of the evanescent field in the plane of propagation. Both the incident and evanescent field vectors, shown here below and above the interface for pictorial clarity, refer to the z = 0 position.

Equation (2.78) describes an ellipse, the vibration ellipse (Fig. 2.11). If A = 0 (or B = 0), the vibration ellipse is just a straight line, and the wave is said to be linearly polarized , the vector B then specifies the direction of vibration. (The term plane polarized is also used, but it has become less fashionable in recent years.)If A = B and A B = 0, the vibration ellipse is a circle, and the wave is said to be circularly polarized. In general, a monochromatic wave of the form (2.77) is elliptically polarized. 

If the incident light is obliquely polarized at an angle of 45° to the scattering plane, the scattered light will, in general, be elliptically polarized, although the azimuth of the vibration ellipse need not be 45°. The amount of rotation of the azimuth, as well as the ellipticity, depends not only on the particle characteristics but also on the direction in which the light is scattered. 

Smith, D. Y., 1976. Comments on the dispersion relations for the complex refractive index of circularly and elliptically polarized light, J. Opt. Soc. Am., 66, 454-460. 

These later form a three-dimensional Stokes vector S [13-15] whose tip moves over the surface of a Poincare sphere as the radiation passes without attenuation along the optical axis. Figure 5.1 shows the connection between polarization and points on the Poincare sphere. Right circular polarization is represented by the north pole, left circular polarization by the south pole, linear polarizations by points in the equatorial plane, and elliptical polarization by the points between the poles and the equatorial plane. 

Fig. 7.57. Perspective view of the x and y components of an elliptically polarized wave. The ellipse results as a resolute of the two components. (Reprinted from R. A. Serway, C. J. Moses, and C. A. Moyer, Modem Physics, Saunders College Publishing, 1997, p. 208.)...

Adding LCP and RCP components of different amplitudes, yields elliptically polarized light. The major axis of the ellipsoid is the sum of amplitudes AR and AL, and the minor axis is their difference, as shown in Fig. 5. The ellipticity 0 is defined as the arctangent of the ratio of the minor axis to the major axis ... 

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