A high-order perturbation of surfaces method for vector electromagnetic scattering by doubly layered periodic crossed gratings

The accurate simulation of scattering of electromagnetic waves in three dimensions by a diffraction grating is crucial in many applications of engineering and scientific interest. In this contribution we present a novel High-Order Perturbation of Surfaces method for the numerical approximation of vector electromagnetic scattering by a doubly periodic layered medium. For this we restate the governing time harmonic Maxwell equations as vector Helmholtz equations which are coupled by transmission boundary conditions at the layer interface. We then apply the method of Transformed Field Expansions which delivers a Fourier collocation, Legendre-Galerkin, Boundary Perturbation approach to solve the problem in transformed coordinates. A sequence of numerical simulations demonstrate the efficient and robust spectral convergence which can be achieved with the proposed algorithm.