FEM and its generalization for the diffraction by polygonal profile gratings

For the numerical computation of the efficiencies for optical gratings, there exists a huge variety of algorithms. Dealing with a boundary value problem for an elliptic partial differential equation, the application of finite element methods (FEM) is natural also. However, the oscillatory nature of the electromagnetic fields requires some modifications. The resulting FEM program can be used as a part of an algorithm to design optimal gratings.