Principles of Electromagnetic Waves and Materials, 2nd Edition

12Optical Waves in Anisotropic Crystals

An optical crystal is an anisotopic dielectric and the dielectric tensor of such a crystal in a coordinate system that coincides with the principal axes of the crystal will have zero off-diagonal elements and is given by

(12.1)$$\overline{\mathrm{\epsilon }}=\left[\begin{array}{ccc}\hfill {\mathrm{\epsilon }}_1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill {\mathrm{\epsilon }}_2\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill {\mathrm{\epsilon }}_3\hfill \end{array}\right].$$

The principal refractive indices of the crystal are given by

(12.2)$$n_j={\left(\frac{{\mathrm{\epsilon }}_j}{{\mathrm{\epsilon }}_0}\right)}^{1/2},j=1,2,3.$$

The crystals are classified as biaxial, uniaxial, or isotropic depending on the number of equalities involving the principal refractive indices:

(12.3)$$n_1\ne n_2\ne n_3\left(\text{biaxial crystal}\right),$$

(12.4)$$n_1=n_2=n_{\text{o}},n_3=n_{\text{e}}\left(\text{uniaxial crystal}\right),$$

(12.5)$$n_1=n_2=n_3=n_{\text{o}}\left(\text{isotropic crystal}\right).$$

Properties of wave propagation in isotropic crystals are discussed in Chapter 2. In the following section, we discuss wave ...