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 - 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 - 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 - 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 - 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 - Schmidt, Frank A1 - Burger, Sven A1 - Schädle, Achim A1 - Klose, Roland T1 - Finite element methods for optical device design T2 - Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices Y1 - 2005 U6 - https://doi.org/10.1109/NUSOD.2005.1518133 SP - 57 EP - 58 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 - 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 - 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 T2 - Nanophotonic Materials: Photonic Crystals, Plasmonics, and Metamaterials Y1 - 2008 U6 - https://doi.org/10.1002/9783527621880.ch17 SP - 313 EP - 331 PB - Wiley-VCH ER - TY - GEN A1 - Burger, Sven A1 - Klose, Roland A1 - Schädle, Achim A1 - Zschiedrich, Lin T1 - HelmPole - A finite element solver for scattering problems on unbounded domains: Implementation based on PML N2 - The solution of scattering problems described by the Helmholtz equation on unbounded domains is of importance for a wide variety of applications, for example in electromagnetics and acoustics. An implementation of a solver for scattering problems based on the programming language Matlab is introduced. The solver relies on the finite-element-method and on the perfectly-matched-layer-method, which allows for the simulation of scattering problems on complex geometries surrounded by inhomogeneous exterior domains. This report gives a number of detailed examples and can be understood as a user manual to the freely accessible code of the solver HelmPole. T3 - ZIB-Report - 03-38 KW - Helmholtz equation KW - finite element method KW - perfectly matched layer Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7609 ER - TY - GEN 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 N2 - In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer. T3 - ZIB-Report - 03-44 KW - transparent boundary conditions KW - perfectly matched layer KW - pole condition Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7662 ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Enkrich, Christian A1 - Linden, S. A1 - Wegener, M. A1 - Soukoulis, C. ED - Szoplik, T. ED - Özbay, E. ED - Soukoulis, C. ED - Zheludev, N. T1 - Numerical Investigation of Light Scattering off Split-Ring Resonators T2 - Metamaterials Y1 - 2005 U6 - https://doi.org/10.1117/12.622184 VL - 5955 SP - 18 EP - 26 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schädle, Achim A1 - Klose, Roland A1 - Kettner, Benjamin A1 - Pomplun, Jan A1 - Pollok, T. A1 - Schmidt, Frank T1 - Advanced FEM Analysis of Nano-Optical Devices T2 - Proc. Symposium on Photonics Technologies for the 7th Framework Programme Y1 - 2006 ER - TY - CHAP A1 - Burger, Sven A1 - Klose, Roland A1 - März, Reinhard A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Efficient Finite Element Methods for the Design of Microoptical Components T2 - Proc. Microoptics Conf. 2004 Y1 - 2004 ER - TY - CHAP A1 - Burger, Sven A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin ED - Sidorin, Y. ED - Wächter, Christoph T1 - FEM modelling of 3D photonic crystals and photonic crystal waveguides T2 - Integrated Optics : Devices, Materials and Technologies IX Y1 - 2005 U6 - https://doi.org/10.1117/12.585895 VL - 5728 SP - 164 EP - 173 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3D photonic crystal structures T2 - Scientific Computing in Electrical Engineering Y1 - 2006 U6 - https://doi.org/10.1007/978-3-540-32862-9_24 SP - 169 EP - 175 PB - Springer Verlag ER -