Wave Splitting in Direct and Inverse Scattering Problems

The focus of this thesis is on the use of wave splitting in electromagnetic direct and inverse scattering problems. Wave splitting offers a decomposition of wave fields into appropriate input and output wave constituents. Several different wave splittings are studied including one-dimensional, multi-dimensional energy-flux, and multi-dimensional locally exact wave splittings. The Bremmer series is naturally connected to wave splitting as a method to decompose a complex scattering problem into a sequence of single scattering problems. The one-dimensional Bremmer series is reviewed and time-domain convergence is shown for the acoustic locally exact wave splitting. The emphasis of the inverse scattering problems is on the identification of the spatial structure of complex medium models in multi-dimensions from time-domain data. The parameter identification is determined in an iterative fashion with a conjugate-gradient algorithm where the least-squares error of the output field is minimized. The gradient is determined from the solution of an additional adjoint problem. The energy-flux split fields are shown to give a good representation of the boundary fields in the inverse scattering problem. Several multi-parameter identifications are performed in two spatial dimensions. A detailed analysis is included about electromagnetic modeling. The non-unique-ness of the instantaneous response and the long-time behavior is specially emphasized. Finally, time-reversal mirrors and time-reversal cavities are discussed