A Boundary Perturbation Method for Vector Electromagnetic Scattering from Families of Doubly Periodic Gratings

In this paper the authors extend their previous work on Boundary Perturbation methods for scattering calculations from families of diffraction gratings to three dimensions and the full vector electromagnetic Maxwell equations. This extension is non-trivial in both its algorithmic implementation (not only are new terms added to the recursions, but also the full, coupled, vector Maxwell equations must be simulated) and in the size of the relevant computer simulations. Not only do we give details of the implementation of the method, but also provide results of numerical simulations.