Joint Geometry/Frequency Analyticity of Fields Scattered by Periodic Layered Media
Published in SIAM Journal on Mathematical Analysis, 2023
Abstract: The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High–Order Perturbation of Surfaces/Asymptotic Waveform Evaluation (HOPS/AWE) methods for numerically simulating scattering returns from periodic diffraction gratings. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a periodic two–layer structure. Furthermore, we establish joint analyticity of these solutions with respect to both geometry and frequency perturbations. This result provides hypotheses under which a rigorous numerical analysis could be conducted on our recently developed HOPS/AWE algorithm.
Recommended citation: M. Kehoe and D. P. Nicholls, “Joint Geometry/Frequency Analyticity of Fields Scattered by Periodic Layered Media,” SIAM Journal on Mathematical Analysis, Volume 55, Issue 3, 1737-1765 (2023). http://matthewshawnkehoe.github.io/files/hops_awe_analyticity.pdf