WIAS Preprint No. 1694, (2012)

Scattering of time-harmonic electromagnetic plane waves by perfectly conducting diffraction gratings


  • Hu, Guanghui
  • Rathsfeld, Andreas

2010 Mathematics Subject Classification

  • 78A45 35J20 35R30 78A46


  • Electromagnetic scattering, diffraction gratings, variational approach, mortar technique, non-uniqueness


Consider scattering of time-harmonic electromagnetic plane waves by a doubly periodic surface in $R^3$. The medium above the surface is supposed to be homogeneous and isotropic with a constant dielectric coefficient, while below is a perfectly conducting material. This paper is concerned with the existence of quasiperiodic solutions for any frequency of incidence. Based on an equivalent variational formulation established by the mortar technique of Nitsche, we verify the existence of solutions for a broad class of incident waves including plane waves, under the assumption that the grating profile is a Lipschitz biperiodic surface. Our solvability result covers the resonance case where a Rayleigh frequency is allowed. Non-uniqueness examples are also presented in the resonance case and the TE or TM polarization case for classical gratings.

Appeared in

  • IMA J. Appl. Math., 80 (2015) pp. 508--532.

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