On uniqueness in electromagnetic scattering from biperiodic structures
1 Center for Industrial Mathematics,
University of Bremen, 28359
2 DEFI, INRIA Saclay–Ile-de-France and Ecole Polytechnique, 91128 Palaiseau, France.
Revised: 30 August 2012
Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional non-trapping assumptions on the material parameter, this identity allows us to establish uniqueness of solution for all positive wave numbers.
Mathematics Subject Classification: 35A02
Key words: Biperiodic scattering / uniqueness / electromagnetic waves
© EDP Sciences, SMAI, 2013