  In this paper, we develop a new representation for outgoing solutions to the
time harmonic Maxwell equations in unbounded domains in $\bbR^3.$ This
representation leads to a Fredholm integral equation of the second kind for
solving the problem of scattering from a perfect conductor, which does not
suffer from spurious resonances or low frequency breakdown, although it
requires the inversion of the scalar surface Laplacian on the domain boundary.
In the course of our analysis, we give a new proof of the existence of
non-trivial families of time harmonic solutions with vanishing normal
components that arise when the boundary of the domain is not simply connected.
We refer to these as $k$-Neumann fields, since they generalize, to non-zero
wave numbers, the classical harmonic Neumann fields. The existence of
$k$-harmonic fields was established earlier by Kress.
