Optimal shape design for a layered periodic structure

by Flanagan, Michael Brady

A multi-layered periodic structure is investigated

for optimal shape design in diffraction gratings. A periodic dielectric material is used as the scattering profile for a planar incident wave.

Designing optimal profiles for scattering is a type of inverse problem. The ability to fabricate such materials on the order of the wavelength

of the incoming light is key for design strategies. We compute a finite element

approximation on a variational setup of the forward problem. On the inverse and optimal design problem, we discuss the stability of the designs and develop computational strategies based on a level-set evolutionary approach.