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Maxwell's equations in periodic chiral structures

โœ Scribed by Habib Ammari; Gang Bao

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
208 KB
Volume
251
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Abstract

Consider a timeโ€“harmonic electromagnetic plane wave incident on a biperiodic structure in โ„^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 Drudeโ€“ Bornโ€“Fedorov (constitutive) equations. In this paper, the diffraction 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 quasiโ€“periodic weak solution to the diffraction problem. Our proof is based on the Hodge decomposition, a compact imbedding result, and the Laxโ€“Milgram Lemma. In addition, an energy conservation for the weak solution is also shown.

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