On the identification of defects in a periodic waveguide from far field data

The aim of this paper is to apply the linear sampling method and the factorization method to retrieve some defects in a known periodic 2D waveguide from scattering data. More precisely, some far field approximations of these two sampling methods are derived. They amount to considering the so-called propagating Floquet modes as incident waves. The efficiency of the far field formulation of the linear sampling method is shown with the help of some numerical experiments.