WIAS Preprint No. 588, (2000)

Direct and inverse problems for diffractive structures - optimization of binary gratings


  • Elschner, Johannes
  • Hinder, Rainer
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 78-99 78A45 35J20 65N30 49J20


  • Diffraction by periodic structures, Helmholtz equation, transmission problems, strongly elliptic variational formulation, generalized FEM, optimal design problems, gradient methods




The goal of the project is to provide flexible analytical and numerical tools for the optimal design of binary and multilevel gratings occurring in many applications in micro-optics. The direct modeling of these diffractive elements has to rely on rigorous grating theory, which is based on Maxwell's equations. We developed efficient and accurate direct solvers using a variational approach together with a generalized finite element method which appears to be well adapted to rather general diffractive structures as well as complex materials. The optimal design problem is solved by minimization algorithms based on gradient descent and the exact calculation of gradients with respect to the geometry parameters of the grating.

Appeared in

  • Mathematics - Key Technology for the Future II, Springer, Berlin, 2003

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