Variational methods for diffractive optics modelling (Q2758021)

This paper gives an overview on the electromagnetic modeling and optimization of diffraction gratings. These optical devices are periodic in one or two space dimensions and the diffraction problem can be reduced to weak formulations in a periodic cell. These formulations incorporate the transmission conditions on material interfaces and nonlocal boundary operators reflecting the conditions of radiation at infinity. Using variational methods long standing problems concerning the well-posedness for non-smooth geometries could be solved recently. The authors discuss direct problems for periodic and biperiodic gratings and finite-element approximations of the time-harmonic Maxwell equations for such structures.NEWLINENEWLINENEWLINEThis approach is also applicable to inverse and optimal design problems. This is shown for the inverse problem of determining shapes from scattered fields as well as for finding the optimal designs for surface-relief gratings.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00050].