On analyticity of linear waves scattered by a layered medium (Q2013923)

The scattering of linear waves by periodic structures is considered. It is a crucial phenomenon in many branches of engineering and applied physics. The author establishes rigorous analytic results which are needed for the numerical analysis of a method called High-Order Perturbation of Surfaces method which is used for simulating linear waves by periodic structures. More precisely, he proves existence and uniqueness of solutions to a system of partial differential equations which are used to model the interaction of linear waves with a multi-layered periodic structure in three dimensions. Hence, these results provide hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the following methods: Operator Expansions by Milder, Field Expansions by Bruno \& Reitich, and Transformed Field Expansions by Nicholls \& Reitich.