Geodesic
On uniqueness in electromagnetic scattering from biperiodic structures
ESAIM: Mathematical Modelling and Numerical Analysis , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 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.

DOI : 10.1051/m2an/2012063
Classification : 35A02
Keywords: biperiodic scattering, uniqueness, electromagnetic waves 
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     title = {On uniqueness in electromagnetic scattering from biperiodic structures},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1167--1184},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {4},
     year = {2013},
     doi = {10.1051/m2an/2012063},
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     zbl = {1282.78022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012063/}
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Lechleiter, Armin; Nguyen, Dinh-Liem. On uniqueness in electromagnetic scattering from biperiodic structures. ESAIM: Mathematical Modelling and Numerical Analysis , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 1167-1184. doi: 10.1051/m2an/2012063

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