As we saw in Chapter 5, electromagnetic waves in isotropic materials are transverse, their electric and magnetic field vectors E and H being normal to the direction of propagation k. The direction of E or rather, as we shall see later, the electric displacement field D, is called the polarization direction, and for any given direction of propagation there are two independent polarization vectors, which can be in any two mutually orthogonal directions normal to k. However, when the medium through which the wave travels is anisotropic, which means that its properties depend on orientation, the choice of the polarization vectors is not arbitrary, and the velocities of the two waves may be different. A material that supports two distinct propagation vectors is called birefringent.
In this chapter, we shall learn:
about the various types of polarized plane waves that can propagate – linear, circular and elliptical – and how they are produced;
how an anisotropic optical material can be described by a dielectric tensor ∈, which relates the fields D and E within the material;
a simple geometrical representation of wave propagation in an anisotropic material, the n-surface, which allows the wave propagation properties to be easily visualized;
how Maxwell's equations are written in an anisotropic material, and how they lead to two particular orthogonally polarized plane-wave solutions;