5.1 Double Refraction

When some incident beam hits the interface separating two transparent media, it may happen that two transmitted beams are generated; when this is the case, at least one of the two media is anisotropic. This phenomenon was first observed in 1669 by the Dane Erasmus Bartholimus who called it double refraction. Media in which double refraction occurs are said to be birefringent. As early as 1690, using his famous construction of refracted beams, Huygens could give an interpretation of the principal aspects of birefringence.

When crossing an anisotropic material limited by two planar interfaces, a parallel beam of natural (unpolarized) light generates two transmitted beams, they are linearly polarized along two mutually orthogonal directions which are labeled (1) and (2) in Figures 5.1 and 5.2, and which are determined by the orientation of the material.

Figure 5.1: Transmission of a parallel beam of natural (unpolarized) light by an anisotropic plate. Two transmitted beams are observed, they have two mutual linear and orthogonal polarizations, along directions that are determined by the orientation of the plate. Since the two sides of the plate are parallel, the two transmitted beams and the incident beam are also, respectively, parallel.

Figure 5.2: Transmission of a parallel beam with a linear polarization parallel to one of the privileged directions of vibration. Only one transmitted beam is observed.

When the two sides of the anisotropic sample are planar and parallel, the two emerging beams are parallel to the incident beam. In the...