WIAS Preprint No. 1019, (2005)

Uniqueness in determining polygonal periodic structures


  • Elschner, Johannes
  • Yamamoto, Masahiro

2010 Mathematics Subject Classification

  • 78A46 35R30


  • Diffraction grating, periodic Helmholtz equation, inverse Dirichlet and Neumann problems, polygonal grating profile


We consider the inverse problem of recovering a two-dimensional perfectly reflecting diffraction grating from scattered waves measured above the structure. We establish the uniqueness within the class of general polygonal grating profiles by a minimal number of incoming plane waves, without excluding Rayleigh frequencies and further geometric constraints on the profile. This extends and improves the uniqueness results of [10].

Appeared in

  • Z. Anal. Anwendungen 26 (2007) pp. 165-177

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