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 - JOUR A1 - Schmidt, Frank A1 - März, Reinhard T1 - On the Reference Wave Vector of Paraxial Helmholtz Equations JF - IEEE Journal of Lightwave Technology Y1 - 1996 VL - 14 SP - 2395 EP - 2400 ER - TY - JOUR A1 - Schmidt, Frank A1 - Nolting, Hans-Peter T1 - Adaptive Multilevel Beam Propagation Method JF - IEEE Photonics Technology Letter Y1 - 1992 VL - 4 SP - 1381 EP - 1383 ER - TY - CHAP A1 - Schmidt, Frank A1 - Nolting, Hans-Peter T1 - An Adaptive Approach to a Beam Propagation Method T2 - Integrated Photonics Research Y1 - 1992 SP - 302 EP - 303 CY - New Orleans, Louisiana, USA ER - TY - CHAP A1 - Schädle, Achim A1 - Ruprecht, Daniel A1 - Schmidt, Frank ED - et.al., N. Biggs T1 - Transparent boundary conditions - the pole condition approach T2 - Proceedings of Waves 2007 Y1 - 2007 SP - 301 EP - 303 ER - TY - JOUR A1 - Schmidt, Frank A1 - Yevick, David T1 - Discrete Transparent Boundary Conditions for Schrödinger-Type Equations JF - J. Comput. Phys. Y1 - 1997 U6 - https://doi.org/10.1006/jcph.1997.5675 VL - 134 IS - 1 SP - 96 EP - 107 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 - Schmidt, Frank A1 - Deuflhard, Peter T1 - Discrete Transparent Boundary Conditions for Fresnel’s Equation T2 - Integrated Photonics Research Y1 - 1994 SP - 45 EP - 47 CY - San Francisco, California, USA ER - TY - JOUR A1 - Schmidt, Frank A1 - Deuflhard, Peter T1 - Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel’s Equation. JF - Comput. Math. Appl. Y1 - 1995 VL - 29 SP - 53 EP - 76 ER - TY - CHAP A1 - Schmidt, Frank ED - Bermúdez, A. ED - Gómez, D. ED - Hazard, C. ED - Joly, P. ED - Roberts, J. T1 - Discrete Nonreflecting Boundary Conditions for the Helmholtz equation T2 - Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation Y1 - 2000 UR - http://www.zib.de/Publications/Reports/ZR-00-06.pdf SP - 921 EP - 925 CY - Waves 2000, Santiago de Compostella, Spain ER - TY - THES A1 - Schmidt, Frank T1 - Solution of Interior-Exterior Helmholtz-Type Problems Based on the Pole Condition Concept Y1 - 2002 UR - http://www.zib.de/PaperWeb/abstracts/ZR-02-45 ER - TY - JOUR A1 - Schmidt, Frank T1 - Pole Condition: A new Approach to Solve Scattering Problems JF - Oberwolfach Report Y1 - 2004 VL - 1 IS - 1 SP - 615 EP - 617 PB - Mathematisches Forschungsinstitut Oberwolfach ER - TY - THES A1 - Schmidt, Frank T1 - Ingenieurmäßige Berechnung der Feldausbreitung in optischen Bauelementen der Lichtwellenleitertechnik Y1 - 1989 ER - TY - JOUR A1 - Schmidt, Frank T1 - Simulation und Herstellung von Faserschleifkopplern JF - Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin, R. Math./Naturwiss. Y1 - 1990 VL - 39 IS - 2 SP - 115 EP - 118 ER - TY - JOUR A1 - Schmidt, Frank T1 - An Adaptive Approach to the Numerical Solution of Fresnel’s Wave Equation. JF - IEEE Journal of Lightwave Technology Y1 - 1993 VL - 11 IS - 9 SP - 1425 EP - 1435 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 - JOUR A1 - Yevick, David A1 - Friese, T. A1 - Schmidt, Frank T1 - A Comparison of Transparent Boundary Conditions for the Fresnel Equation JF - J. Comput. Phys. Y1 - 2001 VL - 168 IS - 2 SP - 433 EP - 444 ER - TY - JOUR A1 - Yevick, David A1 - Yu, J. A1 - Schmidt, Frank T1 - Analytic Studies of Absorbing and Impedance-Matched Boundary Layers JF - IEEE Photonics Technology Letters Y1 - 1997 U6 - https://doi.org/10.1109/68.554499 VL - 9 SP - 73 EP - 75 ER - TY - JOUR A1 - Arellano, Cristina A1 - Mingaleev, Sergei F. A1 - Koltchanov, Igor A1 - Richter, Andre A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Efficient design of photonic integrated circuits (PICs) by combining device- and circuit- level simulation tools JF - Proc. SPIE Y1 - 2013 U6 - https://doi.org/10.1117/12.2004378 VL - 8627 SP - 862711 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 - Hammerschmidt, Martin A1 - Lockau, Daniel A1 - Burger, Sven A1 - Schmidt, Frank A1 - Schwanke, Christoph A1 - Kirner, Simon A1 - Calnan, Sonya A1 - Stannowski, Bernd A1 - Rech, Bernd T1 - FEM-based optical modeling of silicon thin-film tandem solar cells with randomly textured interfaces in 3D JF - Proc. SPIE Y1 - 2013 U6 - https://doi.org/10.1117/12.2001789 VL - 8620 SP - 86201H 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 - TY - JOUR A1 - Becker, Christiane A1 - Lockau, Daniel A1 - Sontheimer, Tobias A1 - Schubert-Bischoff, Peter A1 - Rudigier-Voigt, Eveline A1 - Bockmeyer, Matthias A1 - Schmidt, Frank A1 - Rech, Bernd T1 - Large-area 2D periodic crystalline silicon nanodome arrays on nanoimprinted glass exhibiting photonic band structure effects JF - Nanotechnology Y1 - 2012 U6 - https://doi.org/10.1088/0957-4484/23/13/135302 VL - 23 IS - 13 SP - 135302 ER - TY - JOUR A1 - Lockau, Daniel A1 - Sontheimer, Tobias A1 - Becker, Christiane A1 - Rudigier-Voigt, Eveline A1 - Schmidt, Frank A1 - Rech, Bernd T1 - Nanophotonic light trapping in 3-dimensional thin-film silicon architectures JF - Opt. Express Y1 - 2013 U6 - https://doi.org/10.1364/OE.21.000A42 VL - 21 SP - A42 ER - TY - JOUR A1 - Lockau, Daniel A1 - Sontheimer, Tobias A1 - Preidel, Veit A1 - Becker, Christiane A1 - Ruske, Florian A1 - Schmidt, Frank A1 - Rech, Bernd T1 - Optical properties and Limits of a Large-Area Periodic Nanophotonic Light Trapping Design for Polycrystalline Silicon Thin Film Solar Cells JF - MRS Proceedings Y1 - 2013 U6 - https://doi.org/10.1557/opl.2013.28 VL - 1493 SP - 59 EP - 64 ER - TY - CHAP A1 - Wohlfeil, Benjamin A1 - Burger, Sven A1 - Stamatiadis, Christos A1 - Pomplun, Jan A1 - Schmidt, Frank A1 - Zimmermann, Lars A1 - Petermann, Klaus T1 - Numerical Simulation of Grating Couplers for Mode Multiplexed Systems T2 - Proc. SPIE Y1 - 2014 U6 - https://doi.org/10.1117/12.2044461 VL - 8988 SP - 89880K ER - TY - CHAP A1 - Zschiedrich, Lin A1 - März, Reinhard A1 - Burger, Sven A1 - Schmidt, Frank T1 - Efficient 3D Finite Element Simulation of Fiber-Chip Coupling T2 - Integrated Photonics Research and Applications/Nanophotonics Y1 - 2006 U6 - https://doi.org/10.1364/IPRA.2006.ITuF1 SP - ITuF1 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 - CHAP A1 - Wenzel, Hans A1 - Crump, Paul A1 - Ekhteraei, Hossein A1 - Schultz, Christoph M. A1 - Pomplun, Jan A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank A1 - Erbert, Götz T1 - Theoretical and experimental analysis of the lateral modes of high-power broad-area lasers T2 - Numerical Simulation of Optoelectronic Devices Y1 - 2011 U6 - https://doi.org/10.1109/NUSOD.2011.6041183 SP - 143 EP - 144 ER - TY - JOUR A1 - Sontheimer, Tobias A1 - Preidel, Veit A1 - Lockau, Daniel A1 - Back, Franziska A1 - Rudigier-Voigt, Eveline A1 - Löchel, Bernd A1 - Erko, Alexei A1 - Schmidt, Frank A1 - Schnegg, Alexander A1 - Lips, Klaus A1 - Becker, Christiane A1 - Rech, Bernd T1 - Correlation between structural and opto-electronic characteristics of crystalline Si microhole arrays for photonic light management JF - Journal of Applied Physics Y1 - 2013 U6 - https://doi.org/10.1063/1.4829008 VL - 114 IS - 17 SP - 173513 PB - AIP Publishing ER - TY - JOUR A1 - Lockau, Daniel A1 - Sontheimer, Tobias A1 - Preidel, Veit A1 - Ruske, Florian A1 - Hammerschmidt, Martin A1 - Becker, Christiane A1 - Schmidt, Frank A1 - Rech, Bernd T1 - Advanced microhole arrays for light trapping in thin film silicon solar cells JF - Solar Energy Materials and Solar Cells Y1 - 2014 U6 - https://doi.org/10.1016/j.solmat.2013.11.024 VL - 125 SP - 298 EP - 304 ER - TY - JOUR A1 - Kirner, Simon A1 - Hammerschmidt, Martin A1 - Schwanke, Christoph A1 - Lockau, Daniel A1 - Calnan, Sonya A1 - Frijnts, Tim A1 - Neubert, Sebastian A1 - Schöpke, Andreas A1 - Schmidt, Frank A1 - Zollondz, Jens-Hendrik A1 - Heidelberg, Andreas A1 - Stannowski, Bernd A1 - Rech, Bernd A1 - Schlatmann, Rutger T1 - Implications of TCO Topography on Intermediate Reflector Design for a-Si/μc-Si Tandem Solar Cells — Experiments and Rigorous Optical Simulations JF - IEEE Journal of Photovoltaics Y1 - 2014 U6 - https://doi.org/10.1109/JPHOTOV.2013.2279204 VL - 4 IS - 1 SP - 10 EP - 15 ER - TY - CHAP A1 - Hammerschmidt, Martin A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Adaptive sampling strategies for effcient parameter scans in nano-photonic device simulations T2 - Proc. SPIE Y1 - 2014 U6 - https://doi.org/10.1117/12.2036363 VL - 8980 SP - 89801O PB - SPIE ER - TY - CHAP A1 - Hammerschmidt, Martin A1 - Lockau, Daniel A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Optical modelling of incoherent substrate light-trapping in silicon thin film multi-junction solar cells with finite elements and domain decomposition T2 - Proc. SPIE: Physics and Simulation of Optoelectronic Devices XXII Y1 - 2014 U6 - https://doi.org/10.1117/12.2036346 VL - 8980 SP - 898007 PB - SPIE ER - TY - CHAP A1 - Jäger, Klaus A1 - Barth, Carlo A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Burger, Sven A1 - Schmidt, Frank A1 - Becker, Christiane ED - European Society for Quantum Solar Energy Conversion, T1 - Sinusoidal Nanotextures for Enhanced Light Management in Thin-Film Solar Cells T2 - 28th Workshop on Quantum Solar Energy Conversion - (QUANTSOL) Y1 - 2016 ER - TY - JOUR A1 - Jäger, Klaus A1 - Köppel, Grit A1 - Barth, Carlo A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Burger, Sven A1 - Schmidt, Frank A1 - Becker, Christiane T1 - Sinusoidal gratings for optimized light management in c-Si thin-film solar cells JF - Proc. SPIE Y1 - 2016 U6 - https://doi.org/10.1117/12.2225459 VL - 9898 SP - 989808 ER - TY - CHAP A1 - Kantner, Markus A1 - Höhne, Theresa A1 - Koprucki, Thomas A1 - Burger, Sven A1 - Wünsche, Hans-Jürgen A1 - Schmidt, Frank A1 - Mielke, Alexander A1 - Bandelow, Uwe ED - Kneissl, Michael ED - Knorr, Andreas ED - Reitzenstein, Stephan ED - Hoffmann, Axel T1 - Multi-dimensional modeling and simulation of semiconductor nanophotonic devices T2 - Semiconductor Nanophotonics Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-35656-9_7 VL - 194 SP - 241 EP - 283 PB - Springer CY - Cham ER - TY - CHAP A1 - Hiremath, Kirankumar A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schmidt, Frank T1 - Finite elements based numerical solution of nonlocal hydrodynamic Drude model of nano-plasmonic scatterers T2 - 12th International Conference on Fiber Optics and Photonics Y1 - 2014 U6 - https://doi.org/10.1364/PHOTONICS.2014.M3D.4 SP - M3D.4 ER - TY - GEN A1 - Deuflhard, Peter A1 - Friese, Tilmann A1 - Schmidt, Frank A1 - März, Reinhard A1 - Nolting, Hans-Peter T1 - Effiziente Eigenmodenberechnung für den Entwurf integriert-optischer Chips N2 - {\bf Efficient eigenmode computation for the design of integrated optical chips.}The paper deals with adaptive multigrid methods for 2D Helmholtz eigenvalue problems arising in the design of integrated optical chips. Typical features of the technological problem are its geometric complexity, its multiscale structure, the possible occurrence of eigenvalue clusters, and the necessity of quite stringent required relative error tolerances. For reasons of sheer computational complexity, multigrid methods must be used to solve the discretized eigenvalue problems and adaptive grids must be automatically constructed to avoid an undesirable blow-up of the required number of nodes for these accuracies. In view of the problem specifications, an adaptive multigrid method based on Rayleigh quotient minimization, simultaneous eigenspace iteration, and conjugate gradient method as smoother is carefully selected. Its performance in the numerical simulation of a component of a rather recent optical chip (heterodyne receiver of HHI) is documented. T3 - ZIB-Report - SC-96-02 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2131 ER - TY - GEN A1 - Schmidt, Frank A1 - Yevick, David T1 - Discrete Transparent Boundary Conditions for Schrödinger-Type Equations N2 - We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schrödinger-type equations. Our method supplies boundary conditions for the $\theta$-family of implicit one-step discretizations of Schrödinger's equation in time. The use of Mikusi\'nski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner. T3 - ZIB-Report - SC-96-17 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2289 ER - TY - GEN A1 - Schmidt, Frank A1 - März, Reinhard T1 - On the Reference Wave Vector pf Paraxial Helmholtz Equations N2 - The reference wave vector of the paraxial Helmholtz equation is determined using various strategies which result all in similar expressions. The effort for its evaluation is so small that the reference wave vector can be adapted for each propagation step of an arbitrary BPM-algorithm. T3 - ZIB-Report - SC-94-38 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1660 ER - TY - GEN A1 - Deuflhard, Peter A1 - Schmidt, Frank T1 - Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation. N2 - The paper presents a construction scheme of deriving transparent , i. e. reflection-free, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schrödinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions. T3 - ZIB-Report - SC-93-24 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1205 ER - TY - GEN A1 - Schmidt, Frank T1 - An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation. N2 - An adaptive approach to the numerical solution of the wave propagation in integrated optics devices with 1D cross sections is described. First, Fresnel's approximation of the exact wave equation resulting from Maxwell's equations is considered. A criterion to estimate the validity of this approximation is derived. Fresnel's wave equation being formally equivalent to Schroedinger's equation uniquely defines an initial-boundary-value problem, which is solved numerically by a stepwise calculation of the propagating field. Discretization in longitudinal direction first with stepsize control leads to a stationary subproblem for the transversal field distribution, which is then handled by an adaptive finite element method. Thus full adaptivity of the algorithm is realized. The numerical examples are concentrated on taper structures playing an essential role in integrated optics devices for telecommunication systems. T3 - ZIB-Report - SC-91-12 Y1 - 1991 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-628 ER - TY - GEN A1 - Schmidt, Frank T1 - Computation of Discrete Transparent Boundary Conditions for the 2D Helmholtz Equation N2 - We present a family of nonlocal transparent boundary conditions for the 2D Helmholtz equation. The whole domain, on which the Helmholtz equation is defined, is decomposed into an interior and an exterior domain. The corresponding interior Helmholtz problem is formulated as a variational problem in standard manner, representing a boundary value problem, whereas the exterior problem is posed as an initial value problem in the radial variable. This problem is then solved approximately by means of the Laplace transformation. The derived boundary conditions are asymptotically correct, model inhomogeneous exterior domains and are simple to implement. T3 - ZIB-Report - SC-97-64 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3330 ER - TY - GEN A1 - Schmidt, Frank T1 - An Alternative Derivation of the Exact DtN-Map on a Circle N2 - The paper supplies an alternative derivation of the exact boundary conditions needed for the solution of time-harmonic acoustic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior domain problem as an initial value problem with initial data given on the boundary of a disc or sphere. The solution of the exterior domain problem is obtained via Laplace transformation techniques, where the asymptotic Sommerfeld radiation condition is reformulated accordingly. T3 - ZIB-Report - SC-98-32 KW - Helmholtz equation KW - Dirichlet-to-Neumann map KW - Sommerfeld radiation condition Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3752 ER - TY - BOOK A1 - Abbink, Erwin A1 - Bärmann, Andreas A1 - Bešinovic, Nikola A1 - Bohlin, Markus A1 - Cacchiani, Valentina A1 - Caimi, Gabrio A1 - de Fabris, Stefano A1 - Dollevoet, Twan A1 - Fischer, Frank A1 - Fügenschuh, Armin A1 - Galli, Laura A1 - Goverde, Rob M.P. A1 - Hansmann, Ronny A1 - Homfeld, Henning A1 - Huisman, Dennis A1 - Johann, Marc A1 - Klug, Torsten A1 - Törnquist Krasemann, Johanna A1 - Kroon, Leo A1 - Lamorgese, Leonardo A1 - Liers, Frauke A1 - Mannino, Carlo A1 - Medeossi, Giorgio A1 - Pacciarelli, Dario A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Schmidt, Marie A1 - Schöbel, Anita A1 - Schülldorf, Hanno A1 - Stieber, Anke A1 - Stiller, Sebastian A1 - Toth, Paolo A1 - Zimmermann, Uwe ED - Borndörfer, Ralf ED - Klug, Torsten ED - Lamorgese, Leonardo ED - Mannino, Carlo ED - Reuther, Markus ED - Schlechte, Thomas T1 - Handbook of Optimization in the Railway Industry N2 - This book promotes the use of mathematical optimization and operations research methods in rail transportation. The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art. There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational. These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning. Individual chapters cover: Simulation Capacity Assessment Network Design Train Routing Robust Timetabling Event Scheduling Track Allocation Blocking Shunting Rolling Stock Crew Scheduling Dispatching Delay Propagation Y1 - 2018 SN - 978-3-319-72152-1 U6 - https://doi.org/10.1007/978-3-319-72153-8 VL - 268 PB - Springer Verlag ER - TY - THES A1 - Schmidt, Frank T1 - A New Approach to Coupled Interior-Exterior Helmholtz-Type Problems: Theory and Algorithms N2 - The work presents a new approach to the numerical solution of time-harmonic and time-dependent scattering problems. We replace Sommerfeld's radiation condition valid for the Helmholtz equation by a more general concept called pole condition. The pole condition is based on the Laplace transform of the exterior solution and allows a characterization of outgoing waves. Both new insight into the analysis of scattering problems as well as new numerical algorithms are obtained. T3 - ZIB-Report - 02-45 KW - Pole condition KW - Helmholtz equation KW - Wide angle one-way equation KW - Schroedinger equation KW - Transparent boundary conditions KW - Unbounded domains KW - Fini Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7128 ER - TY - GEN A1 - Cordes, Frank A1 - Weber, Marcus A1 - Schmidt-Ehrenberg, Johannes T1 - Metastable Conformations via successive Perron-Cluster Cluster Analysis of dihedrals N2 - Decomposition of the high dimensional conformational space of bio-molecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-cluster cluster analysis of a Markov process that generates the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ''curse of dimension''. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ''curse of dimension'', the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ''a posteriori'' criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol. T3 - ZIB-Report - 02-40 KW - metastability KW - Perron-Cluster Cluster Analysis KW - curse of dimension KW - Hybrid Monte Carlo KW - significant dihedrals Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7074 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 - GEN A1 - May, Andreas A1 - Eisenhardt, Steffen A1 - Schmidt-Ehrenberg, Johannes A1 - Cordes, Frank T1 - Rigid body docking for Virtual Screening N2 - A recently developed algorithm allows Rigid Body Docking of ligands to proteins, regardless of the accessibility and location of the binding site. The Docking procedure is divided into three subsequent optimization phases, two of which utilize rigid body dynamics. The last one is applied with the ligand already positioned inside the binding pocket and accounts for full flexibility. Initially, a combination of geometrical and force-field based methods is used as a Coarse Docking strategy, considering only Lennard-Jones interactions between the target and pharmaceutically relevant atoms or functional groups. The protein is subjected to a Hot Spot Analysis, which reveals points of high affinity in the protein environment towards these groups. The hot spots are distributed into different subsets according to their group affiliation. The ligand is described as a complementary point set, consisting of the same subsets. Both sets are matched in $\mathrm{I\!R}^{3}$, by superimposing members of the same subsets. In the first instance, steric inhibition is nearly neglected, preventing the system's trajectory from trapping in local minima and thus from finding false positive solutions. Hence the exact location of the binding site can be determined fast and reliably without any additional information. Subsequently, errors resulting from approximations are minimized via finetuning, this time considering both Lennard-Jones and Coulomb forces. Finally, the potential energy of the whole complex is minimized. In a first evaluation, results are rated by a reduced scoring function considering only noncovalent interaction energies. Exemplary Screening results will be given for specific ligands. T3 - ZIB-Report - 03-47 KW - docking KW - point matching KW - identification of active sites Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7690 ER - TY - GEN A1 - Yevick, David A1 - Friese, Tilmann A1 - Schmidt, Frank T1 - A Comparison of Transparent Boundary Conditions for the Fresnel Equation N2 - We establish the relationship between the transparent boundary condition (BPP) of Baskakov and Popov [Wave Motion 14 (1991) 121-128] and Pakpadakis et. al. [J. Acoust. Soc. Am. 92 (1992) 2030-2038] and a second boundary condition (SDY) introduced by Schmidt and Deuflhard [Comp. Math. Appl. 29 (1995) 53-76] and Schmidt and Yevick [J. Compu. Phys. 134 (1997) 96-107], that is explicitly tailored to the form of the underlying numerical propagation scheme. Our analysis demonstrates that if the domain is first discretized in the propagation direction, the SDY expression can be obtained by applying the exact sequence of steps used to derive the BPP procedure. The BPP method is thus an approximate realization of the computationally far simpler and unconditionally stable SDY boundary condition. T3 - ZIB-Report - 00-05 KW - Fresnel equation KW - transparent boundary condition Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5738 ER - TY - GEN A1 - Schmidt, Frank T1 - Discrete Nonreflecting Boundary Conditions for the Helmholtz Equation N2 - We derive exact discrete nonreflecting boundary conditions for time-harmonic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior problem as an initial value problem with initial data given on the boundary of the computational domain. The solution of the exterior problem is obtained via Laplace transformation techniques which supply the boundary conditions in terms of discrete Dirichlet-to-Neumann operators. T3 - ZIB-Report - 00-06 KW - Helmholtz equation KW - transparent boundary consitions KW - finite element method Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5744 ER - 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 - TY - CHAP A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - A fast and efficient Finite-Element Solver for 2D and 3D Photonic Band-Gap Problems T2 - Dig. LEOS/IEEE 2003 Summer Topicals Y1 - 2003 U6 - https://doi.org/10.1109/LEOSST.2003.1224282 SP - 75 ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - 3D FEM Simulations of High-Q Resonances in Photonic Crystal Microcavities T2 - Integrated Photonics Research, Silicon and Nanophotonics Y1 - 2010 U6 - https://doi.org/10.1364/IPRSN.2010.IWB7 SP - IWB7 PB - OSA ER - TY - CHAP A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin ED - Jena, Friedrich-Schiller-Universität T1 - FEM simulation of resonances in low-Q cavities for plasmon lasers T2 - International Workshop on Photonic Nanomaterials Y1 - 2010 SN - 978-3-00-031358-5 SP - 36 ER - TY - CHAP A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Numerical investigation of optical resonances in circular grating resonators T2 - Silicon Photonics V Y1 - 2010 U6 - https://doi.org/10.1117/12.842061 VL - 7606 SP - 760610 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Numerical Investigation of Photonic Crystal Microcavities in Silicon-on-Insulator Waveguides T2 - Photonic and Phononic Crystal Materials and Devices X Y1 - 2010 U6 - https://doi.org/10.1117/12.841867 VL - 7609 SP - 76091Q PB - Proc. SPIE ER - TY - CHAP A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schmidt, Frank A1 - Tyminski, Jacek A1 - Flagello, Donis A1 - Toshiharu, N. T1 - Reduced basis method for source mask optimization T2 - Photomask Technology Y1 - 2010 U6 - https://doi.org/10.1117/12.866101 VL - 7823 SP - 78230E PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Schädle, Achim A1 - Zschiedrich, Lin A1 - Schmidt, Frank ED - Andrews, David L. ED - Nunzi, Jean-Michel ED - Ostendorf, Andreas T1 - Advanced FEM Analysis of Nano-Optical Devices T2 - Nanophotonics Y1 - 2006 U6 - https://doi.org/10.1117/12.662942 VL - 6195 SP - 72 EP - 82 PB - Proc. SPIE 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 - TY - CHAP A1 - Burger, Sven A1 - Kleemann, B. A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Finite-Element Simulations of Light Propagation through Circular Subwavelength Apertures T2 - Microtechnologies for the New Millenium Y1 - 2009 U6 - https://doi.org/10.1117/12.822828 VL - 7366 SP - 736621 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Köhle, Roderick A1 - Zschiedrich, Lin A1 - Nguyen, H. A1 - Schmidt, Frank A1 - März, Reinhard A1 - Nölscher, Christoph ED - Martin, P. ED - Naber, R. T1 - Rigorous Simulation of 3D Masks T2 - Photomask Technology Y1 - 2006 UR - http://arxiv.org/pdf/physics/0610218 VL - 6349 SP - 63494Z PB - Proc. SPIE ER - TY - CHAP A1 - Deuflhard, Peter A1 - Friese, T. A1 - Schmidt, Frank A1 - März, Reinhard A1 - Nolting, Hans-Peter ED - et al. Hoffmann, K.-H. T1 - Effiziente Eigenmodenberechnung für den Entwurf integriert-optischer Chips T2 - Mathematik - Schlüsseltechnologie für die Zukunft Y1 - 1996 SP - 267 EP - 279 PB - Springer Verlag ER - TY - GEN A1 - Gutsche, Philipp A1 - Judd, Thomas A1 - Schmidt, Frank T1 - A convergence study of different Rigorous Coupled Wave Analysis (RCWA) approaches to time-harmonic electromagnetic scattering problems with applications to nanooptical structures T2 - Verhandlungen der Deutschen Physikalischen Gesellschaft (DPG-Frühjahrstagung Berlin 2014) N2 - Reliable numerical simulations of nano-optical structures are the key for design and pre-fabrication processes in diverse disciplines such as lithography in semiconductor industries, spectroscopy of biological molecules, optimization of quantum dot cavities for single-photon sources, and computation of atomic forces like the Casimir Effect. For these purposes a variety of different methods, e.g. FDTD, FEM and RCWA, are in use. On the one hand, FDTD and FEM are investigated intensively - both in mathematics and numerical experiments - and their approximations and convergence properties are well known. On the other hand, there is a lack of these insights in RCWA. In spite of this, RCWA is commonly used to simulate a wide range of systems. We review historical and modern contributions to convergence improvements with respect to RCWA from the early sugesstions to modern developments. We study the convergence rates of the open-source software S4 and analyze the algorithmic properties in detail. Furthermore, we compare RCWA and FEM simulations for different classes of problems including 1D-binary gratings and 2D-periodic photonic crystals. Y1 - 2014 ER - TY - CHAP A1 - Burger, Sven A1 - Gutsche, Philipp A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank A1 - Wohlfeil, Benjamin A1 - Zschiedrich, Lin T1 - Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures T2 - Proc. SPIE Y1 - 2015 U6 - https://doi.org/10.1117/12.2190119 VL - 9630 SP - 96300S ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schmidt, Frank T1 - Reduced basis method for Maxwell's equations with resonance phenomena T2 - Proc. SPIE N2 - Rigorous optical simulations of 3-dimensional nano-photonic structures are an important tool in the analysis and optimization of scattering properties of nano-photonic devices or parameter reconstruction. To construct geometrically accurate models of complex structured nano-photonic devices the finite element method (FEM) is ideally suited due to its flexibility in the geometrical modeling and superior convergence properties. Reduced order models such as the reduced basis method (RBM) allow to construct self-adaptive, error-controlled, very low dimensional approximations for input-output relationships which can be evaluated orders of magnitude faster than the full model. This is advantageous in applications requiring the solution of Maxwell's equations for multiple parameters or a single parameter but in real time. We present a reduced basis method for 3D Maxwell's equations based on the finite element method which allows variations of geometric as well as material and frequency parameters. We demonstrate accuracy and efficiency of the method for a light scattering problem exhibiting a resonance in the electric field. T3 - ZIB-Report - 15-37 KW - reduced basis method KW - finite element method KW - maxwell equation KW - photonic crystal KW - nano-photonics Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55687 SN - 1438-0064 VL - 9630 SP - 96300R ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Pomplun, Jan A1 - Herrmann, Sven A1 - Schmidt, Frank T1 - hp-finite element method for simulating light scattering from complex 3D structures T2 - Proc. SPIE Y1 - 2015 U6 - https://doi.org/10.1117/12.2085795 VL - 9424 SP - 94240Z ER - TY - JOUR A1 - Shchukin, Vitaly A1 - Ledentsov, Jr., Nikolay A1 - Kropp, Jörg-R. A1 - Steinle, Gunther A1 - Ledentsov, Jr., Nikolay A1 - Burger, Sven A1 - Schmidt, Frank T1 - Single-Mode Vertical Cavity Surface Emitting Laser via Oxide-Aperture-Engineering of Leakage of High Order Transverse Modes JF - IEEE J. Quant. Electron. Y1 - 2014 U6 - https://doi.org/10.1109/JQE.2014.2364544 VL - 50 IS - 12 SP - 990 EP - 995 ER - TY - BOOK A1 - Lavrinenko, Andrei A1 - Laegsgaard, Jesper A1 - Gregersen, Niels A1 - Schmidt, Frank A1 - Soendergaard, Thomas ED - Wyant, James C. T1 - Numerical Methods in Photonics Y1 - 2014 SN - 9781466563889 PB - CRC Press ER -