Inverse medium scattering for electromagnetic wave propagation

This thesis focuses on the study of continuation methods for solving inverse medium scattering problems from electromagnetic wave propagation.; The first considers a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in R3 . 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 multi-frequency 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.; In part two, we consider the inverse medium scattering problem for Helmholtz's equation at fixed frequency. A new continuation method for the inverse medium scattering is developed. The algorithm requires only single-frequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the spatial frequency of a one-parameter family of plane waves by solving one forward and one adjoint problem of the Helmholtz equation.