  The paper determines and classifies the spectrum of a non-self-adjoint
operator pencil generated by the time-harmonic Maxwell problem with a nonlinear
dependence on the frequency for the case of two homogeneous materials joined at
a planar interface. We study spatially one-dimensional and two-dimensional
reductions in the whole space $\mathbb{R}$ and $\mathbb{R}^2$. The dependence
on the spectral parameter, i.e. the frequency, is in the dielectric function
and we make no assumptions on its form. These function values determine the
spectral sets. In order to allow also for non-conservative media, the
dielectric function is allowed to be complex, yielding a non-self-adjoint
problem. The whole spectrum consists of eigenvalues and the essential spectrum,
but the various standard types of essential spectra do not coincide in all
cases. The main tool for determining the essential spectra are Weyl sequences.
