TY - THES A1 - Zschiedrich, Lin T1 - Transparent boundary conditions for Maxwell's equations: Numerical concepts beyond the PML method N2 - Optical technologies are ubiquitously used in hi-tech devices. As a common feature of such devices one finds structures with dimensions in the order of the wavelength of the used light. To design and produce such devices, the wave nature of light must be taken into account. Accordingly, robust simulation tools are required which are based on rigorously solving Maxwell's equations, the governing equations of light propagation within macroscopic media. This thesis contributes to the modeling and the numerical computation of light scattering problems: Light scattering problems are typically posed on the entire space. The Perfectly-Matched -Layer method (PML) is widely used to restrict the simulation problem onto a bounded computational domain. We propose an adaptive PML method which exhibits a good convergence even for critical problems where standard PML implementations fail. Besides the computation of the near field, that is the electromagnetic field within the computational domain, it is of major interest to evaluate the electromagnetic field in the exterior domain and to compute the far field. So far, this was numerically only possible for simple geometries such as homogeneous exterior domains or layered media. To deal with more complicated devices, for example with waveguide inhomogeneities, we develop an evaluation formula based on the PML solution which allows for an exterior domain field evaluation in a half space above the device. Finally, we generalize the PML method to problems with multiply structured exterior domains. The term “multiply structured exterior domain” is defined in this thesis and means that the exterior domain exhibits several half-infinite structures. Mathematically, this gives rise to various complications. For example, no analytical solutions to Maxwell's equations for standard light sources are available in the exterior domain, which are needed to describe the incoming field in a light scattering problem. To tackle this we propose a new light scattering problem formulation which fits well into the PML method framework and which may be regarded as an extension of classical contributions by Sommerfeld, Wiener and Hopf. An exterior domain evaluation formula for multiply structured exterior domains with an extended illumination is derived as well. KW - transparent boundary conditions KW - electromagnetic scattering KW - Maxwell's equations KW - perfectly matched layers KW - PML KW - Wiener-Hopf techniques Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:188-fudissthesis000000013994-8 ER - TY - GEN A1 - Schädle, Achim A1 - Zschiedrich, Lin T1 - Additive Schwarz method for scattering problems using the PML method at interfaces N2 - Scattering problems in integrated optics can be modeled in simple cases by the Helmholtz equation. The computational domain is truncated by a non-reflecting boundary condition. We investigate Schwarz algorithms with a sort of DtN operator, realized by the PML-method, at the interfaces of the sub-domains as an iterative solver. T3 - ZIB-Report - 05-27 KW - perfectly matched layer KW - Helmholtz equation KW - scattering KW - domain decomposition Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8613 ER - TY - GEN A1 - Schädle, Achim A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Klose, Roland A1 - Schmidt, Frank T1 - Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures N2 - We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer. T3 - ZIB-Report - 06-04 KW - domain decomposition KW - conical diffraction KW - electro-magnetic scattering KW - Maxwell's equations KW - Lithography KW - finite elements Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8984 ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Pomplun, Jan A1 - Schmidt, Frank T1 - Finite-element based electromagnetic field simulations: Benchmark results for isolated structures T2 - Proc. SPIE Y1 - 2013 U6 - https://doi.org/10.1117/12.2026213 VL - 8880 SP - 88801Z ER - TY - CHAP A1 - Pomplun, Jan A1 - Burger, Sven A1 - Rozova, Maria A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Finite element simulation of optical modes in VCSELs T2 - Numerical Simulation of Optoelectronic Devices (NUSOD), 11th International Conference on Y1 - 2011 U6 - https://doi.org/10.1109/NUSOD.2011.6041170 SP - 119 EP - 120 ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Schmidt, Frank A1 - Pomplun, Jan A1 - Burger, Sven T1 - Finite elements for nano-optics applications T2 - Proc. Europ. Opt. Soc. Ann. Meet. 2016 (EOSAM) Y1 - 2016 SN - 978-1-5108-4796-5 SP - 178 ER - TY - JOUR A1 - Schneider, Philipp-Immanuel A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Using Gaussian process regression for efficient parameter reconstruction JF - Proc. SPIE Y1 - 2019 U6 - https://doi.org/10.1117/12.2513268 VL - 10959 SP - 1095911 ER - TY - JOUR A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - An auxiliary field approach for computing optical resonances in dispersive media JF - J. Eur. Opt. Soc.-Rapid Y1 - 2019 U6 - https://doi.org/10.1186/s41476-019-0098-z VL - 15 SP - 3 ER - TY - JOUR A1 - Kewes, Günter A1 - Binkowski, Felix A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Benson, Oliver T1 - Heuristic Modeling of Strong Coupling in Plasmonic Resonators JF - ACS Photonics Y1 - 2018 U6 - https://doi.org/10.1021/acsphotonics.8b00766 VL - 5 SP - 4089 ER - TY - JOUR A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - A Riesz-projection-based method for nonlinear eigenvalue problems JF - J. Comput. Phys. Y1 - 2020 U6 - https://doi.org/10.1016/j.jcp.2020.109678 VL - 419 SP - 109678 ER - TY - JOUR A1 - Lalanne, P. A1 - Yan, W. A1 - Gras, A. A1 - Sauvan, C. A1 - Hugonin, J.-P. A1 - Besbes, M. A1 - Demésy, G. A1 - Truong, M. D. A1 - Gralak, B. A1 - Zolla, F. A1 - Nicolet, A. A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Zimmerling, J. A1 - Remis, R. A1 - Urbach, H. Paul A1 - Liu, H. T. A1 - Weiss, T. T1 - Quasinormal mode solvers for resonators with dispersive materials JF - J. Opt. Soc. Am. A Y1 - 2019 U6 - https://doi.org/10.1364/JOSAA.36.000686 VL - 36 SP - 686 ER - TY - JOUR A1 - Ledentsov, Jr., Nikolay A1 - Shchukin, Vitaly A1 - Kropp, Jörg-R. A1 - Zschiedrich, Lin A1 - Schmidt, Frank A1 - Ledentsov, Jr., Nikolay T1 - Resonant cavity light–emitting diodes based on dielectric passive cavity structures JF - Proc. SPIE Y1 - 2017 U6 - https://doi.org/10.1117/12.2253089 VL - 10124 SP - 101240O ER - TY - JOUR A1 - Hiremath, Kirankumar A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Numerical solution of nonlocal hydrodynamic Drude model for arbitrary shaped nano-plasmonic structures using Nedelec finite elements JF - J. Comp. Phys. Y1 - 2012 U6 - https://doi.org/10.1016/j.jcp.2012.05.013 VL - 231 IS - 17 SP - 5890 EP - 5896 ER - TY - CHAP A1 - Hohage, Thorsten A1 - Schmidt, Frank A1 - Zschiedrich, Lin ED - Michielsen, Bas ED - Decavèle, Francine T1 - A new method for the solution of scattering problems T2 - Proceedings of the JEE’02 Symposium Y1 - 2002 SP - 251 EP - 256 PB - ONERA CY - Toulouse ER - TY - JOUR A1 - Hohage, Thorsten A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Solving Time-Harmonic Scattering Problems Based on the Pole Condition I: Theory JF - SIAM J. Math. Anal. Y1 - 2003 U6 - https://doi.org/10.1137/S0036141002406473 VL - 35 IS - 1 SP - 183 EP - 210 ER - TY - JOUR A1 - Hohage, Thorsten A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Solving Time-Harmonic Scattering Problems Based on the Pole Condition II: Convergence of the PML Method JF - SIAM J. Math. Anal. Y1 - 2003 U6 - https://doi.org/10.1137/S0036141002406485 VL - 35 IS - 3 SP - 547 EP - 560 ER - TY - JOUR A1 - Enkrich, Christian A1 - Wegener, M. A1 - Linden, S. A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank A1 - Zhou, C. A1 - Koschny, T. A1 - Soukoulis, C. T1 - Magnetic metamaterials at telecommunication and visible frequencies JF - Phys. Rev. Lett. Y1 - 2005 U6 - https://doi.org/10.1103/PhysRevLett.95.203901 VL - 95 SP - 203901 ER - TY - JOUR A1 - Lockau, D. A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Accurate simulation of light transmission through subwavelength apertures in metal films JF - J. Opt. A Y1 - 2009 U6 - https://doi.org/10.1088/1464-4258/11/11/114013 VL - 11 SP - 114013 ER - TY - CHAP A1 - Lockau, D. A1 - Zschiedrich, Lin A1 - Schmidt, Frank A1 - Burger, Sven A1 - Rech, Bernd T1 - Efficient simulation of plasmonic structures for solar cells T2 - International Workshop on Optical Waveguide Theory and Numerical Modelling Y1 - 2009 VL - XVIII SP - 48 PB - Fraunhofer Institute for Applied Optics and Precision Engineering ER - TY - CHAP A1 - Lockau, D. A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schmidt, Frank A1 - Ruske, F. A1 - Rech, Bernd T1 - Rigorous optical simulation of light management in crystalline silicon thin film solar cells with rough interface textures T2 - Physics and Simulation of Optoelectronic Devices XIX Y1 - 2011 U6 - https://doi.org/10.1117/12.874967 VL - 7933 SP - 79330M PB - Proc. SPIE ER - TY - JOUR A1 - Michaelis, D. A1 - Wächter, Christoph A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Bräuer, Andreas T1 - Micro-optically assisted high index waveguide coupling JF - Appl. Opt. Y1 - 2006 U6 - https://doi.org/10.1364/AO.45.001831 VL - 45 SP - 1831 EP - 1838 ER - TY - CHAP A1 - Klose, Roland A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - A multilevel method for the computation of eigenmodes in 3D photonic crystals T2 - Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic Devices Y1 - 2005 U6 - https://doi.org/10.1109/NUSOD.2005.1518135 SP - 61 EP - 62 ER - TY - CHAP A1 - Kleemann, B. A1 - Kurz, J. A1 - Hetzler, J. A1 - Pomplun, Jan A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Fast online inverse scattering with Reduced Basis Method (RBM) for a 3D phase grating with specific line roughness T2 - Modelling Aspects in Optical Metrology III Y1 - 2011 U6 - https://doi.org/10.1117/12.889364 VL - 8083 SP - 808309 PB - Proc. SPIE ER - TY - CHAP A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schmidt, Frank T1 - Reduced basis method for computational lithography T2 - Photomask Technology Y1 - 2009 U6 - https://doi.org/10.1117/12.829639 VL - 7488 SP - 74882B PB - Proc. SPIE ER - TY - CHAP A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin A1 - Scholze, Frank ED - Martin, P. ED - Naber, R. T1 - Rigorous FEM-Simulation of EUV-Masks: Influence of shape and material parameters T2 - Photomask Technology Y1 - 2006 U6 - https://doi.org/10.1117/12.686828 VL - 6349 SP - 63493D PB - Proc. SPIE ER - TY - CHAP A1 - Schädle, Achim A1 - Zschiedrich, Lin ED - Widlund, Olof ED - Keyes, David T1 - Additive Schwarz method for scattering problems using the PML method at interfaces T2 - Domain Decomposition Methods in Science and Engineering XVI Y1 - 2007 VL - 55 SP - 205 EP - 212 PB - Springer ER - TY - JOUR A1 - Schädle, Achim A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Klose, Roland A1 - Schmidt, Frank T1 - Domain Decomposition Method for Maxwell’s Equations JF - J. Comput. Phys. Y1 - 2007 U6 - https://doi.org/10.1016/j.jcp.2007.04.017 VL - 226 SP - 477 EP - 493 ER - TY - CHAP A1 - Schmidt, Frank A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Fast online simulation of 3D nanophotonic structures by the reduced basis method T2 - Integrated Optics: Devices, Materials, and Technologies XV Y1 - 2011 U6 - https://doi.org/10.1117/12.874726 VL - 7941 SP - 79410G PB - Proc. SPIE ER - TY - CHAP A1 - Schmidt, Frank A1 - Friese, T. A1 - Zschiedrich, Lin A1 - Deuflhard, Peter T1 - Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design T2 - Mathematics - Key Technology for the Future Y1 - 2003 UR - http://www.zib.de/Publications/Reports/ZR-00-54.pdf SP - 270 EP - 292 PB - Springer ER - TY - JOUR A1 - Schmidt, Frank A1 - Hohage, Thorsten A1 - Klose, Roland A1 - Schädle, Achim A1 - Zschiedrich, Lin T1 - Pole condition: A numerical method for Helmholtz-type scattering problems with inhomogeneous exterior domain JF - J. Comput. Appl. Math. Y1 - 2008 U6 - https://doi.org/10.1016/j.cam.2007.04.046 VL - 218 IS - 1 SP - 61 EP - 69 ER - TY - CHAP A1 - Rozova, Maria A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Schmidt, Frank A1 - Burger, Sven T1 - 3D finite element simulation of optical modes in VCSELs T2 - Proc. SPIE Y1 - 2012 U6 - https://doi.org/10.1117/12.906372 VL - 8255 SP - 82550K ER - TY - JOUR A1 - Ruprecht, Daniel A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Transparent boundary conditions for time-dependent problems JF - SIAM J. Sci. Comput. Y1 - 2008 U6 - https://doi.org/10.1137/070692637 VL - 30 IS - 5 SP - 2358 EP - 2385 ER - TY - CHAP A1 - Schmidt, Frank A1 - Burger, Sven A1 - Pomplun, Jan A1 - Zschiedrich, Lin ED - Greiner, Christoph ED - Wächter, Christoph T1 - Advanced FEM analysis of optical waveguides: algorithms and applications T2 - Integrated Optics Y1 - 2008 U6 - https://doi.org/10.1117/12.765720 VL - 6896 SP - 689602 PB - SPIE ER - TY - JOUR A1 - Pomplun, Jan A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Adaptive finite element method for simulation of optical nano structures JF - Phys. Status Solidi B Y1 - 2007 U6 - https://doi.org/10.1002/pssb.200743192 VL - 244 SP - 3419 EP - 3434 ER - TY - CHAP A1 - Pomplun, Jan A1 - Holzlöhner, Ronald A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank ED - Adibi, Ali ED - Scherer, Axel ED - Lin, Shawn-Yu T1 - FEM investigation of leaky modes in hollow core photonic crystal fibers T2 - Proc. SPIE, Photonic Crystal Materials and Devices VI Y1 - 2007 UR - http://arxiv.org/pdf/physics/0702165 VL - 6480 SP - 64800M ER - TY - CHAP A1 - Pomplun, Jan A1 - Schmidt, Frank A1 - Burger, Sven A1 - Zschiedrich, Lin T1 - Adaptive Reduced Basis Method for Optical Scattering Problems T2 - Integrated Photonics Research, Silicon and Nanophotonics Y1 - 2010 U6 - https://doi.org/10.1364/IPRSN.2010.IWD4 SP - IWD4 PB - OSA ER - TY - JOUR A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Klose, Roland A1 - Schmidt, Frank A1 - Burger, Sven T1 - Finite element simulation of radiation losses in photonic crystal fibers JF - phys. stat. sol. (a) Y1 - 2007 U6 - https://doi.org/10.1002/pssa.200776414 VL - 204 IS - 11 SP - 3822 EP - 3837 ER - TY - CHAP A1 - Pomplun, Jan A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Reduced basis method for real-time inverse scatterometry T2 - Modelling Aspects in Optical Metrology III Y1 - 2011 U6 - https://doi.org/10.1117/12.889892 VL - 8083 SP - 808308 PB - Proc. SPIE ER - TY - CHAP A1 - Pomplun, Jan A1 - Wenzel, Hans A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Rozova, Maria A1 - Schmidt, Frank A1 - Crump, Paul A1 - Ekhteraei, Hossein A1 - Schultz, Christoph M. A1 - Erbert, Götz T1 - Thermo-optical simulation of high-power diode lasers T2 - Proc. SPIE Y1 - 2012 U6 - https://doi.org/10.1117/12.909330 VL - 8255 SP - 825510 ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Kettner, Benjamin A1 - Schmidt, Frank T1 - Advanced Finite Element Method for Nano-Resonators T2 - Proc. SPIE Y1 - 2006 U6 - https://doi.org/10.1117/12.646252 VL - 6115 SP - 611515 ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank ED - Sidorin, Y. ED - Wächter, Christoph T1 - JCMmode: an adaptive finite element solver for the computation of leaky modes T2 - Integrated Optics: Devices, Materials, and Technologies IX Y1 - 2005 U6 - https://doi.org/10.1117/12.590372 VL - 5728 SP - 192 EP - 202 PB - Proc. SPIE ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank ED - Sidorin, Y. ED - Waechter, Ch. T1 - Goal oriented adaptive finite element method for precise simulation of optical components T2 - Proc. SPIE, Integrated Optics Y1 - 2007 UR - http://arxiv.org/pdf/physics/0702128 VL - 6475 SP - 64750H ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schädle, Achim A1 - Schmidt, Frank ED - Levinson, Harry ED - Dusa, Mircea T1 - A rigorous finite-element domain decomposition method for electromagnetic near field simulations T2 - Optical Microlithography XXI Y1 - 2008 U6 - https://doi.org/10.1117/12.771989 VL - 6924 PB - SPIE ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schädle, Achim A1 - Schmidt, Frank T1 - Domain decomposition method for electromagnetic scattering problems: application to EUV lithography T2 - Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices Y1 - 2005 U6 - https://doi.org/10.1109/NUSOD.2005.1518132 SP - 55 EP - 56 ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Greiner, Horst A1 - Pomplun, Jan A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Schmidt, Frank T1 - FEM simulations of light extraction from nanostructured organic light-emitting diodes T2 - Renewable Energy and the Environment Optics and Photonics Congress Y1 - 2012 U6 - https://doi.org/10.1364/SOLED.2012.LT2B.5 SP - LT2B.5 PB - Optical Society of America ER - TY - JOUR A1 - Zschiedrich, Lin A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank T1 - A new finite element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D JF - J. Comput. Appl. Math. Y1 - 2006 U6 - https://doi.org/10.1016/j.cam.2005.03.047 VL - 188 SP - 12 EP - 32 ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Schmidt, Frank ED - Horiuchi, Toshiyuki T1 - Finite element simulation of light propagation in non-periodic mask patterns T2 - Photomask and Next-Generation Lithography Mask Technology XV Y1 - 2008 UR - http://arxiv.org/pdf/0804.2587v1 VL - 7028 PB - SPIE ER - TY - CHAP A1 - Wong, G. A1 - Kang, M. A1 - Lee, H. A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Biancalana, F. A1 - Russell, P. T1 - Strongly Twisted Solid-Core PCF: A One-Dimensional Chiral Metamaterial T2 - Frontiers in Optics Y1 - 2011 U6 - https://doi.org/10.1364/FIO.2011.FMG3 SP - FMG3 PB - Optical Society of America ER - TY - CHAP A1 - Tyminski, Jacek A1 - Popescu, Raluca A1 - Burger, Sven A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Matsuyama, Tomoyuki A1 - Noda, Tomoya ED - Conley, W. T1 - Finite element models of lithographic mask topography T2 - Proc. SPIE Y1 - 2012 U6 - https://doi.org/10.1117/12.916957 VL - 8326 SP - 83261B ER - TY - JOUR A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Pomplun, Jan A1 - Blome, Mark A1 - Schmidt, Frank T1 - Advanced finite-element methods for design and analysis of nano-optical structures: Applications JF - Proc. SPIE Y1 - 2013 U6 - https://doi.org/10.1117/12.2001094 VL - 8642 SP - 864205 ER - TY - JOUR A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Pomplun, Jan A1 - Schmidt, Frank A1 - Bodermann, Bernd T1 - Fast simulation method for parameter reconstruction in optical metrology JF - Proc. SPIE Y1 - 2013 U6 - https://doi.org/10.1117/12.2011154 VL - 8681 SP - 868119 ER - TY - JOUR A1 - Zschiedrich, Lin A1 - Greiner, Horst A1 - Burger, Sven A1 - Schmidt, Frank T1 - Numerical analysis of nanostructures for enhanced light extraction from OLEDs JF - Proc. SPIE Y1 - 2013 U6 - https://doi.org/10.1117/12.2001132 VL - 8641 SP - 86410B ER -