This project is concerned with nonlinear models in the frequency domain, which cover parametric processes such as four-wave mixing, self-phase modulation, cross-phase modulation and frequency doubling, and with radiation losses. In particular we aim to investigate these effects in photonic-crystal waveguides with an extension of a few wavelengths. We consider instantaneous quadratic and cubic space dependent nonlinearities in combination with a space dependent permittivity. This leads to highly nonlinear coupled partial differential equations. To achieve a realistic model of real devices, taking into account also radiation losses (leaky modes), we consider the finite extensions of the components. This requires transparent boundary conditions to approximate radiation conditions at infinity. For the direct numerical simulation of the partial differential equations, we adapt our finite-element based code to the simulation of three-dimensional nonlinear photonic crystal devices. The main focus in the computational part of our work will be the development of fast and reliable iterative solvers for the arising high dimensional nonlinear problems with regard to transparent boundary conditions. This part of the project is a continuation of our work on finite element methods for three-dimensional linear photonic crystal devices.

• J. Pomplun, S. Burger, F. Schmidt, A. Schliwa, D. Bimberg, A. Pietrzak, H. Wenzel, G. Erbert
  Finite element simulation of the optical modes of semiconductor lasers
  phys. stat. sol. (b),  Vol. 247,   846-853 (2010)
• D. Lockau, L. Zschiedrich, S. Burger
  Accurate simulation of light transmission through subwavelength apertures in metal films
  J. Opt. A: Pure Appl. Opt.,  Vol. 11,   114013 (2009)
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• 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, S. Burger, L. Zschiedrich, F. Schmidt
  Adaptive finite element method for simulation of optical nano structures
  phys. stat. sol. (b),  Vol. 244,   3419-3434 (2007)
• G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, P. S. J. Russell
  Models for guidance in kagome-structured hollow-core photonic crystal fibres
  Optics Express,  Vol. 15,   12680 (2007)
• F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, F. Schmidt
  The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks
  In: Modeling Aspects in Optical Metrology,  H. Bosse  (ed) Proc. SPIE,  Vol. 6617,   66171A (2007)
• J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, U. Dersch
  Finite element analysis of EUV lithography
  In: Modeling Aspects in Optical Metrology,  H. Bosse  (ed) Proc. SPIE,  Vol. 6617,   661718 (2007)
• S. Burger, L. Zschiedrich, F. Schmidt, R. Köhle, B. Küchler, C. Nölscher
  EMF Simulations of Isolated and Periodic 3D Photomask Patterns
  In: Photomask TechnologyProc. SPIE,  Vol. 6730,   6630 (2007)
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• S. Burger, L. Zschiedrich, F. Schmidt, R. Köhle, T. Henkel, B. Küchler, C. Nölscher
  3D Simulations of Electromagnetic Fields in Nanostructures
  In: Modeling Aspects in Optical Metrology,  H. Bosse  (ed) Proc. SPIE,  Vol. 6617,   66170V (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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• D. Michaelis, C. Wächter, S. Burger, L.  Zschiedrich, A. Bräuer
  Micro-optically assisted high index waveguide coupling
  Appl. Opt.,  Vol. 45,   1831-1838 (2006)
• J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze
  Rigorous FEM-Simulation of EUV-Masks: Influence of Shape and Material Parameters
  In: Photomask Technology,  P. M. Martin and R. J. Naber  (ed) Proc. SPIE,  Vol. 6349,   63493D (2006)
• S. Burger, A. Schädle, L. Zschiedrich, F. Schmidt
  Advanced FEM Analysis of Nano-Optical Devices
  In: Nanophotonics,  D. L. Andrews and J.-M. Nunzi and A. Ostendorf  (ed) Proc. SPIE,  Vol. 6195,   72-82 (2006)
• S. Burger, R. Köhle, L. Zschiedrich, H. Nguyen, F. Schmidt, R. März, C. Nölscher
  Rigorous Simulation of 3D Masks
  In: Photomask Technology,  P. M. Martin and R. J. Naber  (ed) Proc. SPIE,  Vol. 6349,   63494Z (2006)
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• R. Holzlöhner, S. Burger, P. J. Roberts, J. Pomplun
  Efficient optimization of hollow-core photonic crystal fiber design using the finite-element method
  J. Europ. Opt. Soc: Rap. Comm.,  Vol. 1,   06011 (2006)
• 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)
• L.  Zschiedrich, S.  Burger, A.  Schädle, F.  Schmidt
  Domain decomposition method for electromagnetic scattering problems
  In: Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices,   55-56 (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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• C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, C. M. Soukoulis
  Magnetic metamaterials at telecommunication and visible frequencies
  Phys. Rev. Lett.,  Vol. 95,   203901 (2005)
  URL  
• T. Kalkbrenner, U.  Hakanson, A.  Schädle, S.  Burger, C.  Henkel, V.  Sandoghdar
  Optical microscopy using the spectral modifications of a nano-antenna
  Phys. Rev. Lett.,  Vol. 95,   200801 (2005)
  URL   Preprint  
• S. Burger, L. Zschiedrich, R. Klose, A. Schädle, F. Schmidt, C. Enkrich, S. Linden, M. Wegener, C. M. Soukoulis
  Numerical Investigation of Light Scattering off Split-Ring Resonators
  In: Metamaterials,  T. Szoplik and E. Özbay and C. M. Soukoulis and N. I. Zheludev  (ed) Proc. SPIE,  Vol. 5955,   18-26 (2005)
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• S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, C. Nölscher
  Benchmark of FEM, Waveguide and FDTD Algorithms for Rigorous Mask Simulation
  In: Photomask Technology,  J. T. Weed and P. M. Martin  (ed) Proc. SPIE,  Vol. 5992,   378-389 (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, R.  Klose, R.  März, A.  Schädle, F.  Schmidt, L.  Zschiedrich
  Efficient Finite Element Methods for the Design of Microoptical Components
  In: Proc. Microoptics Conf. 2004,   J8 (2004)
• R. März, S. Burger, A. Forchel, H. Heidrich, O. Hess, D. Michaelis, K. Wandel, R. Wehrspohn
  High-contrast planar photonic crystals
  In: Nanophotonics for Communication,  M. Lipson et al.  (ed) Proc. SPIE,  Vol. 5597,   68-81 (2004)
• R. März, S. Burger, S. Golka, A. Forchel, C. Herrmann, C. Jamois, D. Michaelis, K. Wandel
  Planar High Index-Contrast Photonic Crystals for Telecom Applications
  In: Photonic Crystals - Advances in Design, Fabrication and Characterization,  K. Busch et al.  (ed) Wiley-VCH,   308-329 (2004)
• T. Hohage, F. Schmidt
  On the Numerical Solution of Nonlinear Schrödinger equations in fiber optics
   (02-04) ZIB  ZIB Report (2002)
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