  We study the strongly singular volume integral equation that describes the
scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We
consider the case of a cylindrical obstacle and fields invariant along the axis
of the cylinder, which allows the reduction to two-dimensional problems. With
this simplification, we can refine the analysis of the essential spectrum of
the volume integral operator started in a previous paper (M. Costabel, E.
Darrigrand, H. Sakly: The essential spectrum of the volume integral operator in
electromagnetic scattering by a homogeneous body, Comptes Rendus Mathematique,
350 (2012), pp. 193-197) and obtain results for non-smooth domains that were
previously available only for smooth domains. It turns out that in the TE case,
the magnetic contrast has no influence on the Fredholm properties of the
problem. As a byproduct of the choice that exists between a vectorial and a
scalar volume integral equation, we discover new results about the symmetry of
the spectrum of the double layer boundary integral operator on Lipschitz
domains.
