Analysis of the diffraction from chiral gratings (Q2758028)

This paper gives an introduction to electromagnetic wave propagation in chiral materials and studies the diffraction in periodic chiral structures which separate two homogeneous chiral regions. Electromagnetic wave propagation is governed by Maxwell's equation and a set of constitutive relations coupling electric and magnetic fields. After introducing the Drude-Born-Fedorov constitutive equations the authors formulate the radiation conditions for biperiodic structures. These conditions are based on the Bohren decomposition of fields inside homogeneous chiral media. This allows to formulate transparent boundary conditions and to reduce the diffraction problem to a variational formulation in a bounded domain. Using Hodge decomposition and a new compact imbedding result the authors prove the well-posedness of the problem. It is shown that for all but possibly a discrete set of frequencies the diffraction problem has a unique quasiperiodic weak solution.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00050].