  In this paper we consider the transmission eigenvalue problem for Maxwell's
equations corresponding to non-magnetic inhomogeneities with contrast in
electric permittivity that has fixed sign (only) in a neighborhood of the
boundary. We study this problem in the framework of semiclassical analysis and
relate the transmission eigenvalues to the spectrum of a Hilbert-Schmidt
operator. Under the additional assumption that the contrast is constant in a
neighborhood of the boundary, we prove that the set of transmission eigenvalues
is discrete, infinite and without finite accumulation points. A notion of
generalized eigenfunctions is introduced and a denseness result is obtained in
an appropriate solution space.
