  In this paper we consider the transmission eigenvalue problem for Maxwell's
equations corresponding to non-magnetic inhomogeneities with contrast in
electric permittivity that changes sign inside its support. We formulate the
transmission eigenvalue problem as an equivalent homogeneous system of boundary
integral equation, and assuming that the contrast is constant near the boundary
of the support of the inhomogeneity, we prove that the operator associated with
this system is Fredholm of index zero and depends analytically on the wave
number. Then we show the existence of wave numbers that are not transmission
eigenvalues which by an application of the analytic Fredholm theory implies
that the set of transmission eigenvalues is discrete with positive infinity as
the only accumulation point.
