JOINT GEOMETRY/FREQUENCY ANALYTICITY OF FIELDS SCATTERED BY PERIODIC LAYERED MEDIA

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 nec-essary 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 pe-riodic 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 un-der which a rigorous numerical analysis could be conducted on our recently developed HOPS/AWE algorithm.