Polarization and anisotropic media

Abstract

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; […]