  We solve time-harmonic Maxwell's equations in anisotropic, spatially
homogeneous media in intersections of $L^p$-spaces. The material laws are
time-independent. The analysis requires Fourier restriction-extension estimates
for perturbations of Fresnel's wave surface. This surface can be decomposed
into finitely many components of the following three types: smooth surfaces
with non-vanishing Gaussian curvature, smooth surfaces with Gaussian curvature
vanishing along one-dimensional submanifolds, but without flat points, and
surfaces with conical singularities. Our estimates are based on new
Bochner-Riesz estimates with negative index for non-elliptic surfaces.
