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Direct and Inverse Problems for Diffractive Structures — Optimization of Binary Gratings

In: Mathematics — Key Technology for the Future

Author

Listed:
  • Johannes Elschner

    (Weierstraß-Institut für Angewandte Analysis und Stochastik)

  • Rainer Hinder

    (Weierstraß-Institut für Angewandte Analysis und Stochastik)

  • Günther Schmidt

    (Weierstraß-Institut für Angewandte Analysis und Stochastik)

Abstract

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 modelling 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.

Suggested Citation

  • Johannes Elschner & Rainer Hinder & Günther Schmidt, 2003. "Direct and Inverse Problems for Diffractive Structures — Optimization of Binary Gratings," Springer Books, in: Willi Jäger & Hans-Joachim Krebs (ed.), Mathematics — Key Technology for the Future, pages 293-304, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55753-8_24
    DOI: 10.1007/978-3-642-55753-8_24
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