We consider the problem of determining the shape of a 2d object from measurements of the electromagnetic far-field it scattered. We develop couplings by considering sampling methods and shape optimization methods in the framework of perfect conductors and dielectric objects. After finding the shape gradients (first or second order) and/or topological gradient and performing scilab/Fortran numerical tests in both frameworks, this thesis allowed to build an accurate and robust LSM-DGLS2-GT coupling with a moderate computational cost. We also investigate other types of functionals to minimize and calculate the second shape gradient (which is difficult to obtain in a convenient form for implementation) in order to get a better convergence rate.
