Lechleiter, Armin; Nguyen, Dinh-Liem
On uniqueness in electromagnetic scattering from biperiodic structures
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) no. 4 , p. 1167-1184
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Zbl 1282.78022 | MR 3082293
doi : 10.1051/m2an/2012063
URL stable : http://www.numdam.org/item?id=M2AN_2013__47_4_1167_0

Classification:  35A02
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.

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