Polarized light, elliptically

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. 

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. 

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.

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. 

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 ... 

Fig. 5. Elliptically polarized light emerging toward the observer through a circularly dichroic sample. The sign is defined by the chemical convention that

Metallic reflectors do not produce plane-polarization, but when plane-polarized light falls on a polished metal, its vibration is in general changed from a rectilinear to an elliptic one, and the light is said to be elliptically polarized. 

When plane-polarized light traverses a crystal exhibiting double refraction, such as calcite, at right angles to its axis, it is transformed into elliptically polarized, or even circularly polarized, light. 

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