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 -