Symmetry and the Optical Properties of Crystals

Abstract

As beams of electromagnetic light waves travel through a crystal their properties may change due to their interaction with the material. In some cases these changes depend on the direction of travel in the crystal. In these cases the material is said to be optically anisotropic. The reason for this is that the structure of the crystal controls the ability of the electrons on the atoms of the crystal to respond to the influence of an electromagnetic wave. The light wave propagates through the crystal because its electric field induces the electrons on the atoms of the crystal to oscillate. If the crystal structure allows the electrons to oscillate more easily in one direction than another, then the speed of the light wave propagating in one direction will be greater than that of a light wave propagating in the other direction. This effect is called birefringence or double refraction. It can occur naturally due to the anisotropy of the crystal or it can be induced by an external source such as an electric field (electrooptic effect) or stress (photoelastic effect). Also the properties of the crystal may cause the light waves to exhibit optical activity which is a rotation of the direction of polarization. Because of the directional nature of these properties, the symmetry of the crystal plays an important role in determining the physical effects and it is possible to use transformation tensor formalism similar to that discussed in Chap. 3 to treat these optical properties. These properties have important applications in different types of light modulator devices used in a variety of optical systems. This chapter deals with “linear” optical properties while nonlinear optical effects are discussed in chap. 6