WIAS Preprint No. 586, (2000)

Conical diffraction by periodic structures: Variation of interfaces and gradient formulas


  • Elschner, Johannes
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 78A45 35J20 49J20


  • Conical diffraction, shape optimization, Helmholtz equation




This paper studies the dependence of solutions to conical diffraction problems upon geometric parameters of non-smooth profiles and interfaces between different materials of diffractive gratings. This problem arises in the design of those optical devices to diffract time-harmonic oblique incident plane waves to a specified far-field pattern. We prove the stability of solutions and give analytic formulas for the derivatives of reflection and transmission coefficients with respect to Lipschitz perturbations of interfaces. These derivatives are expressible as contour integrals involving the direct and adjoint solutions of conical diffraction problems.

Appeared in

  • Math. Nachr. 252 (2003), pp. 24-42

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