Inverse medium scattering problems for electromagnetic waves

Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in R-3. In this paper, existence and uniqueness of the variational problem for forward scattering are established. An energy estimate for the scattered field with a uniform bound with respect to the wavenumber is obtained in the case of low frequency on which the Born approximation is based. A continuation method for the inverse medium scattering problem, which reconstructs the scatterer of an inhomogeneous medium from boundary measurements of the scattered wave, is developed. The algorithm requires multifrequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the wavenumber k by solving one forward problem and one adjoint problem of Maxwell's equations.