Plane wave in an anisotropic dielectric
= Plane wave in an anisotropic dielectric
For $D_i=\varepsilon_{ij}E_j$, $B=\mu H$, and a plane wave with electric polarization $e$, the source-free Maxwell equations imply
$$
k\times(k\times e)+\omega^2\mu\varepsilon e=0.
$$
If $e$ is an eigenvector of $\varepsilon$, then $e\perp k$, the dispersion relation is $|k|^2=\omega^2\mu\varepsilon_e$, and the <Poynting vector> is parallel to $k$.