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Chapter 4:
Double Refraction and Applications

4.1 Introduction

When an unpolarized light beam enters an anisotropic medium such as calcite, it usually splits into two linearly polarized beams. One of the beams obeys Snell's law of refraction and is known as the ordinary ray (o ray). The second beam, which, in general, does not obey Snell's law, is known as the extraordinary ray (e ray). These two waves are linearly polarized and, in general, propagate with different wave and ray velocities (wave velocity is also referred to as phase velocity), and hence are characterized by different refractive indices. This phenomenon is known as double refraction, or birefringence, which is of great importance and is used to realize several polarization-based devices. In this chapter, we will discuss plane wave propagation in an anisotropic medium and some applications.

4.2 Anisotropic Media

The difference between an isotropic and an anisotropic medium lies in the relationship between the displacement vector D and the electric vector E. In an isotropic medium, D is in the same direction as E, and we can write


where ε is the dielectric permittivity of the medium. On the other hand, in an anisotropic medium, D is not, in general, in the direction of E, and the relationship between D and E can be written in the form


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