Mathematical studies in rigorous grating theory

Abstract

We consider the diffraction of a time-harmonic wave incident upon a grating (or periodic) structure. We study mathematical issues that arise in the direct modeling, inverse, and optimal design problems. Particular attention is paid to the variational approach and to finite-element methods. For the direct problem various results on existence, uniqueness, and numerical approximations of solutions are presented. Convergence properties of the variational method and sensitivity to TM polarization are examined. Our recent research on inverse diffraction problems and optimal design problems is also discussed.