Uniqueness theorems for an inverse problem in a doubly periodic structure
           (This paper is submitted for publication to Inverse Problems.)

Habib AMMARI 
Centre de Mathematiques Appliquees - CNRS URA 756,
Ecole Polytechnique, 91128 Palaiseau Cedex, France.


Consider an electromagnetic plane wave incident on a biperiodic
 structure in $\RR^3$. The inverse problem is to determine
the shape of the structure from the scattered field. In this paper,
  uniqueness theorems are proved
by  applying the uniqueness theorem of Cauchy-Kowalewska, by extending
Isakov approach and using a result on local
injectivity of maps between finite-dimensional spaces.



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