WIAS Preprint No. 1469, (2009)

Solving conical diffraction with integral equations


  • Goray, Leonid I.
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 78A45 78M15 65N38 35J05 35Q60 45F15


  • Diffraction, periodic structure, integral equation method, oblique incidence, energy conservation, numerical tests




Off-plane scattering of time-harmonic plane waves by a diffraction grating with arbitrary conductivity and general border profile is considered in a rigorous electromagnetic formulation. The integral equations for conical diffraction were obtained using the boundary integrals of the single and double layer potentials including the tangential derivative of single layer potentials interpreted as singular integrals. We derive an important formula for the calculation of the absorption in conical diffraction. Some rules which are expedient for the numerical implementation of the theory are presented. The efficiencies and polarization angles compared with those obtained by Lifeng Li for transmission and reflection gratings are in a good agreement. The code developed and tested is found to be accurate and efficient for solving off-plane diffraction problems including high-conductive surfaces, borders with edges, real border profiles, and gratings working at short wavelengths.

Appeared in

  • J. Opt. Soc. Amer. A, 27 (2010) pp. 585--597 under new title: Solving conical diffraction grating problems with integral equations

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