On Uniqueness in Electromagnetic Scattering from Biperiodic Structures

Details On Uniqueness in Electromagnetic Scattering from Biperiodic Structures On Uniqueness in Electromagnetic Scattering from Biperiodic Structures

2012-01-03

arxiv.org/abs/1201.0690v2

Mathematics

Analysis of PDEs

19 pages

Scientific paper

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 wave numbers.

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