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On uniqueness in electromagnetic scattering from biperiodicstructures

Published online by Cambridge University Press:  17 June 2013

Armin Lechleiter and
Dinh-Liem Nguyen
Armin Lechleiter
Affiliation:
Center for Industrial Mathematics, University of Bremen, 28359 Bremen, Germany. . lechleiter@math.uni-bremen.de
Dinh-Liem Nguyen
Affiliation:
DEFI, INRIA Saclay–Ile-de-France and Ecole Polytechnique, 91128 Palaiseau, France. ; dnguyen@cmap.polytechnique.fr

Abstract

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Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectricstructure mounted on a perfectly conducting plate in three dimensions. Given thatuniqueness of solution holds, existence of solution follows from a well-known Fredholmframework for the variational formulation of the problem in a suitable Sobolev space. Inthis paper, we derive a Rellich identity for a solution to this variational problem undersuitable smoothness conditions on the material parameter. Under additional non-trappingassumptions on the material parameter, this identity allows us to establish uniqueness ofsolution for all positive wave numbers.

Keywords

Biperiodic scatteringuniquenesselectromagnetic waves

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