Numerical Solution of Diffraction Problems: A High-Order Perturbation of Surfaces and Asymptotic Waveform Evaluation Method

The rapid and robust simulation of linear waves interacting with layered periodic media is a crucial capability in many areas of scientific and engineering interest. High-order perturbation of surfaces (HOPS) algorithms are interfacial methods which recursively estimate scattering quantities via perturbation in the interface shape heights/slopes. For a single incidence wavelength such methods are the most efficient available in the parameterized setting we consider here. In the current contribution we generalize one of these HOPS schemes by incorporating a further expansion in the wavelength about a base configuration which constitutes an “asymptotic waveform evaluation” (AWE). We not only provide a detailed specification of the algorithm, but also verify the scheme and point out its benefits and shortcomings. With numerical experiments we show the remarkable efficiency, fidelity, and high-order accuracy one can achieve with an implementation of this algorithm.