Optimal shape design of blazed diffraction gratings

The problem of designing a periodic interface between two materials in such a way that time-harmonic waves diffracted from the interface have a specif ied far-field pattern is studied. A minimization problem for the interface is formulated, and it is shown tha t solutions of constrained bounded variation exist. The differentiability o f the cost functional is then studied, with no restrictions on the smoothne ss of the interface. Some computational issues are discussed, and finally t he results of some numerical experiments are presented.