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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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.
@article{M2AN_2013__47_4_1167_0,
     author = {Lechleiter, Armin and Nguyen, Dinh-Liem},
     title = {On uniqueness in electromagnetic scattering from biperiodic structures},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {4},
     year = {2013},
     pages = {1167-1184},
     doi = {10.1051/m2an/2012063},
     zbl = {1282.78022},
     mrnumber = {3082293},
     language = {en},
     url = {http://http://www.numdam.org/item/M2AN_2013__47_4_1167_0}
}
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, pp. 1167-1184. doi : 10.1051/m2an/2012063. http://www.numdam.org/item/M2AN_2013__47_4_1167_0/

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