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Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs

Please always quote using this URN: urn:nbn:de:0297-zib-57249
  • Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters.

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Author:Martin Hammerschmidt, Carlo Barth, Jan Pomplun, Sven BurgerORCiD, Christiane Becker, Frank Schmidt
Document Type:ZIB-Report
Tag:finite element method; optical metrology; parameter estimation; photonic crystals; reduced basis method; rigorous optical modeling
MSC-Classification:46-XX FUNCTIONAL ANALYSIS (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx)
65-XX NUMERICAL ANALYSIS
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80)
CCS-Classification:G. Mathematics of Computing
PACS-Classification:40.00.00 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS
Date of first Publication:2016/02/02
Series (Serial Number):ZIB-Report (16-06)
ISSN:1438-0064
Published in:Appeared in: Proc. SPIE 9756
DOI:https://doi.org/10.1117/12.2212482
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