The computation of eigenmodes of Maxwell's equations is one of the central tasks in the design of photonic crystal devices. In applications it is often desirable to model semi-infinite and finite structures. Thus problems to be discussed are coupled interior-exterior problems. The aim of this project is to treat the unbounded outer domain with the new pole condition approach and to solve the interior problem with adaptive finite elements.For more information see the MATHEON D9 page

• L. Zschiedrich, S. Burger, J. Pomplun, F. Schmidt
  Goal oriented adaptive finite element method for precise simulation of optical components
  In: Proc. SPIE, Integrated Optics: Devices, Materials, and Technologies XI,  Y. Sidorin and Ch. A. Waechter  (ed) ,  Vol. 6475,   64750H (2007)
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• J. Pomplun, R. Holzlöhner, S. Burger, L. Zschiedrich, F. Schmidt
  FEM investigation of leaky modes in hollow core photonic crystal fibers
  In: Proc. SPIE, Photonic Crystal Materials and Devices VI,  A. Adibi, S.-Y. Lin and A. Scherer  (ed) ,  Vol. 6480,   64800M (2007)
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• L.  Zschiedrich, S.  Burger, B.  Kettner, F.  Schmidt
  Advanced Finite Element Method for Nano-Resonators
  In: Physics and Simulation of Optoelectronic Devices XIV,  M. Osinski and F. Henneberger and Y. Arakawa  (ed) Proc. SPIE,  Vol. 6115,   164-174 (2006)
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• L.  Zschiedrich, R.  Klose, A.  Schädle, F.  Schmidt
  A new finite element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D
  J. Comput. Appl. Math.,  Vol. 188,   12-32 (2006)
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• S.  Burger, R.  Klose, A.  Schädle, F.  Schmidt, L.  Zschiedrich
  Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3D photonic crystal structures
  In: Scientific Computing in Electrical Engineering,  A. M. Anile and G. Ali and G. Mascali  (ed) Springer Verlag,   169-175 (2006)
• F.  Schmidt, S.  Burger, A.  Schädle, R.  Klose
  Finite element methods for optical device design
  In: Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices,   57-58 (2005)
• R.  Klose, S.  Burger, F.  Schmidt, L.  Zschiedrich
  A multilevel method for the computation of eigenmodes in 3D photonic crystals
  In: Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic Devices,   61-62 (2005)
• L.  Zschiedrich, S.  Burger, R.  Klose, A.  Schädle, F.  Schmidt
  JCMmode: an adaptive finite element solver for the computation of leaky modes
  In: Integrated Optics: Devices, Materials, and Technologies IX,  Y. Sidorin and C. A. Wächter  (ed) Proc. SPIE,  Vol. 5728,   192-202 (2005)
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• S. Burger, R.  Klose, A.  Schädle, F.  Schmidt, L.  Zschiedrich
  FEM modelling of 3D photonic crystals and photonic crystal waveguides
  In: Integrated Optics: Devices, Materials, and Technologies IX,  Y. Sidorin and C. A. Wächter  (ed) Proc. SPIE,  Vol. 5728,   164-173 (2005)
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• S.  Burger, F.  Schmidt, L.  Zschiedrich
  A fast and efficient Finite-Element Solver for 2D and 3D Photonic Band-Gap Problems
  In: Dig. LEOS/IEEE 2003 Summer Topicals,   75 (2003)