| Issue |
ESAIM: M2AN
Volume 47, Number 4, July-August 2013
|
|
|---|---|---|
| Page(s) | 1167 - 1184 | |
| DOI | https://doi.org/10.1051/m2an/2012063 | |
| Published online | 17 June 2013 | |
On uniqueness in electromagnetic scattering from biperiodic structures
1 Center for Industrial Mathematics,
University of Bremen, 28359
Bremen, Germany.
lechleiter@math.uni-bremen.de
2 DEFI, INRIA Saclay–Ile-de-France and
Ecole Polytechnique, 91128
Palaiseau, France.
dnguyen@cmap.polytechnique.fr
Received:
3
January
2012
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
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