WIAS Preprint No. 751, (2002)

On the diffraction by biperiodic anisotropic structures


  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 35Q60 78A45 35J50 35J20


  • Maxwell equations, diffraction, strongly elliptic variational formulation, existence and uniqueness of solutions


This paper studies the scattering of electromagnetic waves by a nonmagnetic biperiodic structure. The structure consists of anisotropic optical materials and separates two regions with constant dielectric coefficients. The time harmonic Maxwell equations are transformed to an equivalent strongly elliptic variational problem for the magnetic field in a bounded biperiodic cell with nonlocal boundary conditions. This guarantees the existence of quasiperiodic magnetic fields in 𝐻1 and electric fields in 𝐻(curl) solving Maxwell's equations. The uniqueness is proved for all frequencies excluding possibly a discrete set. The analytic dependence of these solutions on frequency and incident angles is studied.

Appeared in

  • Applicable Analysis, 82 (2003), pp. 75-92

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