  A recent problem of interest in inverse problems has been the study of
eigenvalue problems arising from scattering theory and their potential use as
target signatures in nondestructive testing of materials. Towards this pursuit
we introduce a new eigenvalue problem related to Maxwell's equations that is
generated from a comparison of measured scattering data to that of a
non-standard auxiliary scattering problem. This choice of auxiliary problem
permits the application of regularity results for Maxwell's equations in order
to show that a related interior transmission problem possesses the Fredholm
property, which is used to establish that the eigenvalues are discrete. We
investigate the properties of this new class of eigenvalues and show that the
eigenvalues may be determined from measured scattering data, concluding with a
simple demonstration of this fact.
