Abstract
AbstractConsider a time–harmonic electromagnetic plane wave incident on a biperiodic structure in ℝ3. 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 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 quasi–periodic weak solution to the diffraction 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.
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