Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 36A / d / Solution

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 $k$.

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 Incoming links: Plane wave in an anisotropic dielectric