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Math. Nachr. 216 (2002), 0 { 0 Maxwell's Equations in Periodic Chiral Structures
 

Summary: Math. Nachr. 216 (2002), 0 { 0
Maxwell's Equations in Periodic Chiral Structures
By Habib Ammari in Palaiseau, Gang Bao in East Lansing
(Received )
Abstract. Consider a time-harmonic electromagnetic plane wave incident on a biperiodic
structure in R 3 . The periodic structure separates two homogeneous regions. The medium inside the
structure is chiral and heterogeneous. In general, wave propagation in the chiral medium is governed
by Maxwell's equations together with the Drude-Born-Fedorov (constitutive) equations. In this paper,
the di raction problem is formulated in a bounded domain by introducing a pair of transparent
boundary conditions. It is then shown that for all but possibly a discrete set of parameters, there is
a unique quasi-periodic weak solution to the di raction problem. Our proof is based on the Hodge
decomposition, a compact imbedding result, and the Lax-Milgram Lemma. In addition, an energy
conservation for the weak solution is also shown.
1. Introduction
Consider a time-harmonic electromagnetic plane wave incident on a biperiodic struc-
ture in R 3 . The periodic structure separates two homogeneous regions. The medium
inside the structure is chiral and heterogeneous. The di raction problem is then to
predict energy distributions of the re ected and transmitted waves. In this paper, we
study some mathematical aspects of the di raction problem.
Recently, there has been a considerable interest in the study of scattering and di rac-

  

Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique

 

Collections: Mathematics