WIAS Preprint No. 538, (1999)

Diffraction in Periodic Structures and Optimal Design of Binary Gratings II. Gradient Formulas for TM Polarization


  • Elschner, Johannes
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 78A45 35J20 49J20


  • Diffraction problems, Helmholtz equation, shape optimization




This paper provides the mathematical foundation of analytic formulae for derivatives of TM reflection and transmission coefficients of diffraction gratings with respect to geometric parameters of non-smooth grating profiles and interfaces. This problem arises in optimal design problems for those optical devices studied in Part I. The derivatives can be expressed by contour integrals involving the direct and adjoint solutions of TM diffraction problems.

Appeared in

  • The Siegfried Proessdorf Memorial Volume, Oper. Theory: Adv. Appl., Vol. 121, pp. 89-108, Birkhaeuser, Basel, 2001

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