Light propagation in anisotropic materials and electro-optical effects: tutorial on the use of eigenvalue problems, tensors, and symmetries

Abstract

The properties of anisotropic materials are used in many optical components such as waveplates or polarizing beamsplitters. In particular, anisotropic materials that possess electro-optical properties allow the realization of actively controllable optical components like optical switches, phase shifters, or modulators. Hence, understanding and computation of light propagation in anisotropic materials with electro-optical effects are crucial in optical science and technology. On the one hand this tutorial stresses the use of eigenvalue problems to explain qualitatively and to compute quantitatively important properties such as polarization. On the other hand it discusses the mathematical model of both electro-optical effects, namely, the Pockels and the DC Kerr effect. This tutorial describes the basic concepts in a consistent tensor language, shows how the tensors are conveniently summarized in matrices, and points out that these matrices do not transform like tensors. The tensor approach clarifies how symmetry arguments affect tensor components. Further, this paper derives the more accurate nonlinear relationship between the refractive index and the externally applied electric field.