 
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 timeharmonic 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 DrudeBornFedorov (constitutive) equations. In this paper,
the diraction 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 quasiperiodic weak solution to the diraction problem. Our proof is based on the Hodge
decomposition, a compact imbedding result, and the LaxMilgram Lemma. In addition, an energy
conservation for the weak solution is also shown.
1. Introduction
Consider a timeharmonic 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 diraction problem is then to
predict energy distributions of the re
ected and transmitted waves. In this paper, we
study some mathematical aspects of the diraction problem.
Recently, there has been a considerable interest in the study of scattering and dirac
