 Plane wave in an anisotropic dielectric

For $D_i={\epsilon }_{ij}{E}_j$, $B=\mu H$, and a plane wave with electric polarization $e$, the source-free Maxwell equations implyIf $e$ is an eigenvector of $\epsilon$, then $e\perp k$, the dispersion relation is $|k{|}^2={\omega }^2\mu {\epsilon }_e$, and the Poynting vector is parallel to $k$.