A Stable High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method for the Numerical Solution of Grating Scattering Problems

The scattering of electromagnetic radiation by a layered periodic diffraction grating is an important model in engineering and the sciences. The numerical simulation of this experiment has been widely explored in the literature and we advocate for a novel interfacial method which is perturbative in nature. More specifically, we extend a recently developed High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation algorithm to utilize a stabilized numerical scheme which also suggests a rigorous convergence result. An implementation of this algorithm is described, validated, and utilized in a sequence of challenging and physically relevant numerical experiments.