High-Order Perturbation of Surfaces Approach to Fokas Integral Equations: Maxwell Equations

The accurate simulation of linear electromagnetic scattering by diffraction gratings is crucial in several technologies of scientific interest. In this contribution we describe a High Order Perturbation of Surfaces (HOPS) algorithm built upon a class of Integral Equations due to the analysis of Fokas and collaborators, now widely known as the Unified Transform Method. The unknowns in this formalism are boundary quantities (the electric field and current at the layer interface) which are an order of magnitude fewer than standard volumetric approaches such as Finite Differences and Finite Elements. Our numerical experiments show the efficiency, fidelity, and high order accuracy of our algorithm.