Circularly and Elliptically Polarized Light

The endpoint of the electric field vector of elliptically polarized light describes a distorted helix, and the change in time at a given point corresponds to an ellipse. The ratio of the minor and major axes is given by tan 0 where 6 is the ellipticity of the light. 

If linearly polarized light of a wavelength that is not being absorbed passes through an optically active sample, the polarization plane is rotated by an angle a due to the different refractive indices r their effect 

In the following it will be assumed that the sample has the same properties in all directions, that is, that it is isotropic. For anisotropic samples the description of optical activity is much more complicated.  

---

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. 

Let us consider a polarized light it is characterized by its wave vector k and polarization (light vector) E or B (they are perpendicular Figure 11.4). We shall consider plane, circular and elliptical polarization as defined in Table 11.2. 

Both parameters distinguish the degree of helicity of the incident radiation. For instance, rj assumes the value of unity for plane polarized light and zero for circularly polarized light, and may therefore be regarded as a direct measure of the degree of ellipticity of the laser beam. However, only (, which is zero for plane polarized light, differentiates the sense of handedness in circular or elliptical polarizations, and for the circularly polarized cases we have... 

Because of absorption, the intensity of the plane-polarized light will also decrease exponentially with distance. In optically active media, the two components El and Er will, therefore, not only show different velocities but they will also be absorbed to a different extent. This phenomenon is termed circular dichroism (CD). The head of the resulting vector E will appear to move on an ellipse. Thus, elliptically polarized light is produced from linearly polarized light in a medium showing circular dichroism. 

Fig. 5.11 Principles of CD As in ORD, linearly polarized light can be considered as the superposition of circularly polarized light of opposite direction of rotation but equal amplitude and phase. Differences in absorption of left and right polarized light lead to elliptic polarization of the transmitted light.

---