TY - GEN A1 - Schmidt, Frank T1 - Simultaneous Computation of the Lowest Eigenvalue and Eigenvectors of the Helmholtz Equation N2 - This report collects a number of proposals to determine the lowest eigensolutions of the scalar Helmholtz equation. The basic routine of all discussed algorithms is the standard Rayleigh quotient minimization process. The minimization is performed in a direct multilevel manner, and a subspace iteration is used to determine simultaneously a couple of eigensolutions. As smoother the nonlinear Gauß-Seidel, the nonlinear conjugate gradient method and a preconditioned version of this method are compared with respect to their efficiency. The numerical examples are based on realistic 1D and 2D models of integrated optics components. T3 - ZIB-Report - TR-95-13 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5281 ER - TY - GEN A1 - Friese, Tilman A1 - Schmidt, Frank A1 - Yevick, David T1 - Transparent Boundary Conditions for a Wide-Angle Approximation of the One-Way Helmholtz Equation N2 - We present nonlocal discrete transparent boundary conditions for a fourth-order wide-angle approximation of the two-dimensional Helmholtz equation. The boundary conditions are exact in the sense that they supply the same discrete solution on a bounded interior domain as would be obtained by considering the problem on the entire unbounded domain with zero boundary conditions at infinity. The proposed algorithm results in an unconditionally stable propagation method. Numerical examples from optics illustrate the efficiency of our approach. T3 - ZIB-Report - SC-99-45 KW - Helmholtz equation KW - Wide-angle approximation KW - Transparent boundary conditions KW - Finite-element method Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4345 ER - TY - GEN A1 - Schmidt, Frank A1 - Friese, Tilmann A1 - Yevick, David T1 - Transparent Boundary Conditions for Split-Step Pade Approximations of the One-Way Helmholtz Equation N2 - In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by Schmidt and Deuflhard {[}Comp. Math. Appl. 29 (1995) 53-76{]} and Schmidt and Yevick {[}J. Comput. Phys. 134 (1997) 96-107{]} to propagation methods based on arbitrary Pad\'e approximations to the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition which then yields an unconditionally stable propagation method. T3 - ZIB-Report - SC-99-46 KW - Helmholtz equation KW - Wide-angle approximation KW - Pad/'e split step approximation KW - Transparent boundary conditions KW - Finite-element method Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4353 ER - TY - GEN A1 - Deuflhard, Peter A1 - Friese, Tilmann A1 - Schmidt, Frank T1 - A Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation N2 - The paper is motivated by the need for a fast robust adaptive multigrid method to solve complex Helmholtz eigenvalue problems arising from the design of optical chips. A nonlinear multigrid method is developed, which can be regarded as an extension of a previous adaptive Rayleigh quotient minimization method for selfadjoint Helmholtz eigenproblems. Since the complex Helmholtz operator is just a compact nonselfadjoint perturbation of a selfadjoint operator, linear algebra techniques like Schur decomposition can be extended from the finite dimensional case. The efficiency of the derived adaptive nonlinear multigrid method is illustrated by computations for a technologically relevant integrated optics component containing Multi Quantum Well Layers. T3 - ZIB-Report - SC-97-55 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3240 ER - TY - GEN A1 - Schmidt, Frank T1 - Construction of Discrete Transparent Boundary Conditions for Schrödinger-Type Equations N2 - We present a general technique for constructing nonlocal transparent boundary conditions for time-discretized one-dimensional Schrödinger type equations. The main tool of construction is the discrete counterpart to Mikusi\'nski's continuous algebraic operator approach. Existing techniques are simplified and generalized. Both adaptive time-steps and time-dependent exterior potentials are taken into account. T3 - ZIB-Report - SC-97-60 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3292 ER - TY - JOUR A1 - Blome, Mark A1 - McPeak, Kevin A1 - Burger, Sven A1 - Schmidt, Frank A1 - Norris, David T1 - Back-reflector design in thin-film silicon solar cells by rigorous 3D light propagation modeling JF - COMPEL: Int. J. Comput. Mathem. Electr. Electron. Eng. Y1 - 2014 U6 - https://doi.org/10.1108/COMPEL-12-2012-0367 VL - 33 IS - 4 SP - 1282 EP - 1295 ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank A1 - Evanschitzky, Peter A1 - Erdmann, Andreas ED - Kawahira, H. ED - Zurbrick, L. S. T1 - Benchmark of rigorous methods for electromagnetic field simulation T2 - Photomask Technology Y1 - 2008 UR - http://dx.doi.org/10.1117/12.801248 U6 - https://doi.org/10.1117/12.801248 VL - 7122 SP - 71221 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Pomplun, Jan A1 - Schmidt, Frank ED - Bodermann, Bernd T1 - Rigorous simulations of 3D patterns on extreme ultraviolet lithography masks T2 - Modelling Aspects in Optical Metrology III Y1 - 2011 U6 - https://doi.org/10.1117/12.889831 VL - 8083 SP - 80831B PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap T2 - Physics and Simulation of Optoelectronic Devices XIX Y1 - 2011 U6 - https://doi.org/10.1117/12.875044 VL - 7933 SP - 79330T PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Kettner, Benjamin A1 - Schmidt, Frank ED - Hergert, W. ED - Wriedt, T. T1 - FEM simulation of light scattering by nonspherical objects T2 - Mie Theory 1908 – 2008 Y1 - 2008 SP - 82 EP - 83 PB - Universität Bremen 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 - Pomplun, Jan A1 - Schmidt, Frank A1 - Kettner, Benjamin A1 - Lockau, D. T1 - 3D Finite-Element Simulations of Enhanced Light Transmission Through Arrays of Holes in Metal Films T2 - Numerical Methods in Optical Metrology Y1 - 2009 U6 - https://doi.org/10.1117/12.827543 VL - 7390 SP - 73900H PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Pomplun, Jan A1 - Schmidt, Frank T1 - Finite element method for accurate 3D simulation of plasmonic waveguides T2 - Integrated Optics: Devices, Materials, and Technologies XIV Y1 - 2010 U6 - https://doi.org/10.1117/12.841995 VL - 7604 SP - 76040F PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Pomplun, Jan A1 - Schmidt, Frank T1 - JCMsuite: An Adaptive FEM Solver for Precise Simulations in Nano-Optics T2 - Integrated Photonics and Nanophotonics Research and Applications Y1 - 2008 U6 - https://doi.org/10.1364/IPNRA.2008.ITuE4 SP - ITuE4 PB - Optical Society of America ER - TY - JOUR A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - FEM Simulation of Plasmon Laser Resonances JF - AIP Conference Proceedings Y1 - 2010 U6 - https://doi.org/10.1063/1.3498131 VL - 1281 SP - 1613 EP - 1616 PB - AIP 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 - Zschiedrich, Lin A1 - Schmidt, Frank A1 - Köhle, Roderick A1 - Henkel, Thomas A1 - Küchler, Bernd A1 - Nölscher, Christoph ED - Bosse, Harald T1 - 3D simulations of electromagnetic fields in nanostructures using the time-harmonic finite-element method T2 - Modeling Aspects in Optical Metrology Y1 - 2007 U6 - https://doi.org/10.1117/12.726236 VL - 6617 SP - 66170V PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank A1 - Köhle, Roderick A1 - Küchler, Bernd A1 - Nölscher, Christoph T1 - EMF Simulations of Isolated and Periodic 3D Photomask Patterns T2 - Photomask Technology Y1 - 2007 UR - http://arxiv.org/pdf/0709.3934 VL - 6730 SP - 6630 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Köhle, Roderick A1 - Zschiedrich, Lin A1 - Gao, W. A1 - Schmidt, Frank A1 - März, Reinhard A1 - Nölscher, Christoph ED - Weed, J. ED - Martin, P. T1 - Benchmark of FEM, Waveguide and FDTD Algorithms for Rigorous Mask Simulation T2 - Photomask Technology Y1 - 2005 U6 - https://doi.org/10.1117/12.631696 VL - 5992 SP - 378 EP - 389 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Lockau, D. A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Finite-element simulations of light propagation through subwavelength apertures in metal films T2 - International Workshop on Optical Waveguide Theory and Numerical Modelling Y1 - 2009 VL - XVIII SP - 59 PB - Fraunhofer Institute for Applied Optics and Precision Engineering ER - TY - CHAP A1 - Burger, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank ED - Bhushan, B. T1 - Finite Element Methods for Computational Nano-optics T2 - Encyclopedia of Nanotechnology Y1 - 2012 U6 - https://doi.org/10.1007/978-90-481-9751-4_17 SP - 837 EP - 843 PB - Springer Netherlands ER -