TY - CHAP A1 - Gschrey, Manuel A1 - Seifried, Marc A1 - Krüger, Luzy A1 - Schmidt, Ronny A1 - Schulze, Jan-Hindrick A1 - Heindel, Tobias A1 - Burger, Sven A1 - Rodt, Sven A1 - Schmidt, Frank A1 - Strittmatter, Andre A1 - Reitzenstein, Stephan T1 - Boosting the photon-extraction efficiency of nanophotonic structures by deterministic microlenses T2 - CLEO: 2014 Y1 - 2014 U6 - https://doi.org/10.1364/CLEO_QELS.2014.FF2K.2 SP - FF2K.2 PB - Optical Society of America ER - TY - GEN A1 - Amiranashvili, Shalva A1 - Bandelow, Uwe A1 - Blome, Mark A1 - Burger, Sven A1 - Schmidt, Frank A1 - Schmidt, Kersten A1 - Zschiedrich, Lin ED - Deuflhard, Peter ED - et al., T1 - Nanophotonics and nonlinear fiber optics T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 U6 - https://doi.org/10.4171/137 VL - 1 SP - 257 EP - 275 PB - European Mathematical Society ER - TY - CHAP A1 - Thoma, Alexander A1 - Schnauber, Peter A1 - Gschrey, Manuel A1 - Schmidt, Ronny A1 - Wohlfeil, Benjamin A1 - Seifried, Marc A1 - Schulze, Jan-Hindrick A1 - Burger, Sven A1 - Schmidt, Frank A1 - Strittmatter, Andre A1 - Rodt, Sven A1 - Heindel, Tobias A1 - Reitzenstein, Stephan T1 - Indistinguishable Photons from Deterministic Quantum Dot Microlenses T2 - European Conference on Lasers and Electro-Optics - European Quantum Electronics Conference Y1 - 2015 U6 - https://doi.org/10.1364/IPRSN.2015.IS4A.6 SP - EA_8_5 ER - TY - CHAP A1 - Gschrey, Manuel A1 - Seifried, Marc A1 - Krüger, Luzy A1 - Schmidt, Ronny A1 - Schulze, Jan-Hindrick A1 - Heindel, Tobias A1 - Burger, Sven A1 - Rodt, Sven A1 - Schmidt, Frank A1 - Strittmatter, Andre A1 - Reitzenstein, Stephan T1 - Advanced Quantum Light Sources: Modelling and Realization by Deterministic Nanofabrication Technologies T2 - Integrated Photonics Research, Silicon and Nanophotonics Y1 - 2014 U6 - https://doi.org/10.1364/IPRSN.2014.IW1A.3 VL - IPRSN SP - IW1A.3 ER - TY - JOUR A1 - Gschrey, Manuel A1 - Thoma, Alexander A1 - Schnauber, Peter A1 - Seifried, Marc A1 - Schmidt, Ronny A1 - Wohlfeil, Benjamin A1 - Krüger, Luzy A1 - Schulze, Jan-Hindrick A1 - Heindel, Tobias A1 - Burger, Sven A1 - Schmidt, Frank A1 - Strittmatter, Andre A1 - Rodt, Sven A1 - Reitzenstein, Stephan T1 - Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography JF - Nature Communications Y1 - 2015 U6 - https://doi.org/10.1038/ncomms8662 VL - 6 SP - 7662 ER - TY - CHAP A1 - Thoma, Alexander A1 - Schnauber, Peter A1 - Gschrey, Manuel A1 - Schmidt, Ronny A1 - Wohlfeil, Benjamin A1 - Seifried, Marc A1 - Schulze, Jan-Hindrick A1 - Burger, Sven A1 - Schmidt, Frank A1 - Strittmatter, Andre A1 - Rodt, Sven A1 - Heindel, Tobias A1 - Reitzenstein, Stephan T1 - Indistinguishable Photons from Deterministically Fabricated Quantum Dot Microlenses T2 - Advanced Photonics Y1 - 2015 U6 - https://doi.org/10.1364/IPRSN.2015.IS4A.6 SP - IS4A.6 ER - TY - CHAP A1 - Scholze, Frank A1 - Laubis, Christian A1 - Dersch, Uwe A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank ED - Bosse, Harald T1 - The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks T2 - Modeling Aspects in Optical Metrology Y1 - 2007 VL - 6617 SP - 66171A PB - Proc. SPIE ER - TY - CHAP A1 - Scholze, Frank A1 - Laubis, Christian A1 - Ulm, Gerhard A1 - Dersch, Uwe A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank ED - Schellenberg, Frank T1 - Evaluation of EUV scatterometry for CD characterization of EUV masks using rigorous FEM-simulation T2 - Emerging Lithographic Technologies XII Y1 - 2008 VL - 6921 PB - SPIE ER - TY - CHAP A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank A1 - Scholze, Frank A1 - Laubis, Christian A1 - Dersch, Uwe ED - Horiuchi, Toshiyuki T1 - Metrology of EUV masks by EUV-scatterometry and finite element analysis T2 - Photomask and Next-Generation Lithography Mask Technology XV Y1 - 2008 VL - 7028 PB - 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 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank A1 - Scholze, Frank A1 - Laubis, Christian A1 - Dersch, Uwe ED - Bosse, Harald T1 - Finite element analysis of EUV lithography T2 - Modeling Aspects in Optical Metrology Y1 - 2007 U6 - https://doi.org/10.1117/12.726156 VL - 6617 SP - 661718 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Pomplun, Jan A1 - Schmidt, Frank A1 - Kato, Akiko A1 - Laubis, Christian A1 - Scholze, Frank T1 - Investigation of 3D Patterns on EUV Masks by Means of Scatterometry and Comparison to Numerical Simulations T2 - Photomask Technology 2011 Y1 - 2011 U6 - https://doi.org/10.1117/12.896839 VL - 8166 SP - 81661Q PB - Proc. SPIE 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 - Hohage, Thorsten A1 - Schmidt, Frank T1 - On the Numerical Solution of Nonlinear Schrödinger type equations in fiber optics N2 - The aim of this paper is to develop fast methods for the solution of nonlinear Schrödinger type equations in fiber optics. Using the method of lines we have to solve a stiff system of ordinary differential equations where the eigenvalues of the Jacobian are close to the imaginary axis. This is usually done by a Split Step method. Here we consider the extrapolation of Split Step methods with adaptive order and step size control. For more complicated nonlinearities, in particular stimulated Raman scattering, Split Step methods are less efficient since symmetry is either destroyed or requires much additional effort. In this case we use implicit Runge Kutta formulas of Gauß type. The key point for the efficient implementation of these methods is that the system of nonlinear algebraic equations can be solved without setting up the Jacobian. The proposed methods are compared to other methods, in particular exponential integrators, the method of Marcuse, and the method of Blow and Wood. T3 - ZIB-Report - 02-04 KW - nonlinear Schroedinger equation KW - split step methods KW - extrapolation KW - collocation methods Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6715 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 - Hohage, Thorsten A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Solving time-harmonic scattering problems based on the pole condition: Convergence of the PML method N2 - In this paper we study the PML method for Helmholtz-type scattering problems with radially symmetric potential. The PML method consists in surrounding the computational domain by a \textbf{P}erfectly \textbf{M}atched sponge \textbf{L}ayer. We prove that the approximate solution obtained by the PML method converges exponentially fast to the true solution in the computational domain as the thickness of the sponge layer tends to infinity. This is a generalization of results by Lassas and Somersalo based on boundary integral eqaution techniques. Here we use techniques based on the pole condition instead. This makes it possible to treat problems without an explicitly known fundamental solution. T3 - ZIB-Report - 01-23 KW - transparent boundary conditions KW - PML KW - pole condition Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6494 ER - TY - GEN A1 - Hohage, Thorsten A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - A new method for the solution of scattering problems N2 - We present a new efficient algorithm for the solution of direct time-harmonic scattering problems based on the Laplace transform. This method does not rely on an explicit knowledge of a Green function or a series representation of the solution, and it can be used for the solution of problems with radially symmetric potentials and problems with waveguides. The starting point is an alternative characterization of outgoing waves called \emph{pole condition}, which is equivalent to Sommerfeld's radiation condition for problems with radially symmetric potentials. We obtain a new representation formula, which can be used for a numerical evaluation of the exterior field in a postprocessing step. Based on previous theoretical studies, we discuss the numerical realization of our algorithm and compare its performance to the PML method. T3 - ZIB-Report - 02-01 KW - transparent boundary conditions KW - inhomogeneous exterior domains KW - Laplace transform Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6683 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 - 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 - Ruprecht, Daniel A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Transparent boundary conditons for time-dependent problems N2 - A new approach to derive transparent boundary conditions (TBCs) for wave, Schrödinger, heat and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physical reasonable and unreasonable solutions by the location of the singularities of the spatial Laplace transform of the exterior solution. To obtain a numerical algorithm, a Möbius transform is applied to map the Laplace transform onto the unit disc. In the transformed coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the power series are derived. These are coupled to the equation in the interior, and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients. T3 - ZIB-Report - 07-12 KW - transparent boundary condition KW - non-reflecting boundary condition KW - pole condition KW - wave equation KW - Schrödinger equation KW - drift diffusion equation Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9558 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 - 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 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 - 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 - 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 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 - 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 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 - 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 - GEN A1 - Schmidt, Frank A1 - Friese, Tilmann A1 - Zschiedrich, Lin A1 - Deuflhard, Peter T1 - Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design N2 - This paper has been motivated by the need for a fast robust adaptive multigrid method to solve the vectorial Maxwell eigenvalue problem arising from the design of optical chips. Our nonlinear multigrid methods are based on a previous method for the scalar Helmholtz equation, which must be modified to cope with the null space of the Maxwell operator due to the divergence condition. We present two different approaches. First, we present a multigrid algorithm based on an edge element discretization of time-harmonic Maxwell's equations, including the divergence condition. Second, an explicit elimination of longitudinal magnetic components leads to a nodal discretization known to avoid discrete \emph{spurious modes} also and a vectorial eigenvalue problem, for which we present a multigrid solver. Numerical examples show that the edge element discretization clearly outperforms the nodal element approach. T3 - ZIB-Report - 00-54 KW - Maxwell's equations KW - eigenvalue problem KW - edge elements KW - multigrid methods KW - waveguide KW - optical chip design Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6228 ER - TY - GEN A1 - Hohage, Thorsten A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Solving time-harmonic scattering problems based on the condition: Theory N2 - The pole condition is a general concept for the theoretical analysis and the numerical solution of a variety of wave propagation problems. It says that the Laplace transform of the physical solution in radial direction has no poles in the lower complex half-plane. In the present paper we show that for the Helmholtz equation with a radially symmetric potential the pole condition is equivalent to Sommerfeld's radiation condition. Moreover, a new representation formula based on the pole condition is derived and used to prove existence, uniqueness and asymptotic properties of solutions. This lays the foundations of a promising new algorithm to solve time-harmonic scattering problems numerically and provides a new approach for analyzing existing algorithms such as the Perfectly Matched Layer (PML) method and the Bayliss-Gunzburger-Turkel (BGT) algorithm. T3 - ZIB-Report - 01-01 KW - transparent boundary conditions KW - Laplace transform KW - Sommerfeld radiation condition Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6279 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 - 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 - 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 - 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 - 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 - JOUR A1 - Schmidt, Frank A1 - Friese, T. A1 - Yevick, David T1 - Transparent Boundary Conditions for Split-Step Padé Approximations of the One-Way Helmholtz equation JF - J. Comp. Phys Y1 - 2001 VL - 170 SP - 696 EP - 719 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 - Gottschling, K. T1 - Improved Method of Mode Determination in Planar Optical Waveguides Using Line Transmission Approach JF - J. Opt. Commun. Y1 - 1992 VL - 12 IS - 3 SP - 112 EP - 114 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 - 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 - Pomplun, Jan A1 - Schmidt, Frank T1 - Accelerated a posteriori error estimation for the reduced basis method with application to 3D electromagnetic scattering problems JF - SIAM J. Sci. Comput. Y1 - 2010 U6 - https://doi.org/10.1137/090760271 VL - 32 SP - 498 EP - 520 ER - TY - CHAP A1 - Pomplun, Jan A1 - Schmidt, Frank T1 - Reduced basis method for fast and robust simulation of electromagnetic scattering problems T2 - Numerical Methods in Optical Metrology Y1 - 2009 U6 - https://doi.org/10.1117/12.827588 VL - 7390 SP - 73900I 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 - Philippow, E. A1 - Schmidt, Frank T1 - Besondere Lösungen in harmonisch erregten Ferroresonanz-Kreisen T2 - 4. Internationales Symposium Theoretische Elektrotechnik Ilmenau Y1 - 1987 VL - 2 SP - 26 EP - 32 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 - 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 - JOUR A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank A1 - Schliwa, Andrei A1 - Bimberg, Dieter A1 - Pietrzak, Agnieszka A1 - Wenzel, Hans A1 - Erbert, Götz T1 - Finite element simulation of the optical modes of semiconductor lasers JF - Phys. Status Solidi B Y1 - 2010 U6 - https://doi.org/10.1002/pssb.200945451 VL - 247 SP - 846 EP - 853 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 T1 - Reduced Basis Method for Electromagnetic Field Computations T2 - Scientific Computing in Electrical Engineering SCEE 2008 Y1 - 2010 U6 - https://doi.org/10.1007/978-3-642-12294-1_12 SP - 85 PB - Springer Berlin Heidelberg ER - TY - CHAP A1 - Pomplun, Jan A1 - Schmidt, Frank T1 - Reduced Basis Method for Nano Optical Simulations T2 - Integrated Photonics and Nanophotonics Research and Applications Y1 - 2008 SP - IWD7 PB - Optical Society of America 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 - 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 - Schmidt, Frank ED - G. C. Righini, D. T1 - Phase-adaptive basis functions for a multilevel finite element solution of the paraxial wave equation T2 - Euro-Opto Series Y1 - 1994 SP - 57 EP - 61 CY - Lindau, Germany ER - TY - JOUR A1 - Schmidt, Frank T1 - Computation of Discrete Transparent Boundary Conditions for the 2D Helmholtz equation JF - Optical and Quantum Electronics Y1 - 1998 VL - 30 IS - 5,6 SP - 427 EP - 441 ER - TY - CHAP A1 - Schmidt, Frank T1 - Simulation of Scattering and Reflection Problems via Solution of the 2D Helmholtz Equation T2 - Integrated Photonics Research Y1 - 1998 VL - 4 SP - 408 EP - 410 ER - TY - JOUR A1 - Schmidt, Frank T1 - Construction of Discrete Transparent Boundary Conditions for Schrödinger-Type equations JF - Surv. Math. Ind. Y1 - 1999 VL - 9 SP - 87 EP - 100 ER - TY - JOUR A1 - Richter, Marten A1 - Schlosser, Felix A1 - Schoth, Mario A1 - Burger, Sven A1 - Schmidt, Frank A1 - Knorr, Andreas A1 - Mukamel, Shaul T1 - Reconstruction of the wave functions of coupled nanoscopic emitters using a coherent optical technique JF - Phys. Rev. B Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevB.86.085308 VL - 86 SP - 085308 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 - 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 - 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 - 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 - CHAP A1 - Friese, T. A1 - Deuflhard, Peter A1 - Schmidt, Frank ED - Lai, Choi-Hong ED - Bjørstad, Petter E. ED - Cross, Mark ED - Widlund, Olof T1 - A Multigrid Method for the Complex Helmholtz Eigenvalue Problem T2 - Procs. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering (DD11), UK Y1 - 1999 SP - 19 EP - 26 PB - DDM.org ER - TY - JOUR A1 - Friese, T. A1 - Schmidt, Frank A1 - Yevick, David T1 - Transparent boundary conditions for a wide-angle approximation of the one-way Helmholtz equation JF - J. Comput. Phys. Y1 - 2000 U6 - https://doi.org/10.1006/jcph.2000.6637 VL - 165 IS - 2 SP - 645 EP - 659 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 - 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 - Linden, S. A1 - Enkrich, Christian A1 - Dolling, G. A1 - Klein, M. A1 - Zhou, J. A1 - Koschny, T. A1 - Soukoulis, C. A1 - Burger, Sven A1 - Schmidt, Frank A1 - Wegener, M. T1 - Photonic metamaterials: Magnetism at Optical Frequencies JF - IEEE Journal of Selected Topics in Quantum Electronics Y1 - 2006 U6 - https://doi.org/10.1109/JSTQE.2006.880600 VL - 12 IS - 6 SP - 1097 EP - 1105 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 - 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 - 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 - 3D optical modeling of thin-film a-Si/mc-Si tandem solar cells with random textured interfaces using FEM T2 - Renewable Energy and the Environment Optics and Photonics Congress Y1 - 2012 U6 - https://doi.org/10.1364/E2.2012.JM5A.15 SP - JM5A.15 PB - Optical Society of America ER - TY - JOUR A1 - Karl, M. A1 - Kettner, Benjamin A1 - Burger, Sven A1 - Schmidt, Frank A1 - Kalt, H. A1 - Hetterich, M. T1 - Dependencies of micro-pillar cavity quality factors calculated with finite element methods JF - Optics Express Y1 - 2009 UR - http://dx.doi.org/10.1364/OE.17.001144 U6 - https://doi.org/10.1364/OE.17.001144 VL - 17 SP - 1144 ER - TY - CHAP A1 - Kettner, Benjamin A1 - Schmidt, Frank T1 - The pole condition as transparent boundary condition for resonance problems T2 - Physics and Simulation of Optoelectronic Devices XIX Y1 - 2011 U6 - https://doi.org/10.1117/12.874752 VL - 7933 SP - 79331B PB - Proc. SPIE 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 - 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 - 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 - 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 - 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 - 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 - Becker, Christiane A1 - Xavier, Jolly A1 - Preidel, Veit A1 - Wyss, Philippe A1 - Sontheimer, Tobias A1 - Rech, Bernd A1 - Probst, Jürgen A1 - Hülsen, Christoph A1 - Löchel, Bernd A1 - Erko, Alexei A1 - Burger, Sven A1 - Schmidt, Frank A1 - Back, Franziska A1 - Rudigier-Voigt, Eveline T1 - Nanophotonic light trapping in polycrystalline silicon thin-film solar cells using periodically nanoimprint-structured glass substrates T2 - Proc. SPIE Y1 - 2013 U6 - https://doi.org/10.1117/12.2023871 VL - 8824 SP - 88240D 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 - 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 - TY - CHAP A1 - Manley, Phillip A1 - Schmidt, Frank A1 - Schmid, Martina T1 - Light extraction from plasmonic particles with dielectric shells and overcoatings T2 - Renewable Energy and the Environment Y1 - 2013 U6 - https://doi.org/10.1364/PV.2013.PW3B.7 SP - PW3B.7 PB - Optical Society of America ER - TY - CHAP A1 - Ledentsov, Jr., Nikolay A1 - Shchukin, Vitaly A1 - Ledentsov, Jr., Nikolay A1 - Kropp, Jörg-R. A1 - Burger, Sven A1 - Schmidt, Frank T1 - New Generation of Vertical-Cavity Surface-Emitting Lasers for Optical Interconnects T2 - Future Trends in Microelectronics: Journey into the Unknown Y1 - 2016 U6 - https://doi.org/10.1002/9781119069225.ch3-5 PB - John Wiley & Sons ER - TY - CHAP A1 - Schmidt, Frank ED - Piprek, Joachim T1 - Photonics T2 - Handbook of Optoelectronic Device Modeling and Simulation Y1 - 2017 SN - 9781498749381 PB - CRC Press ER - TY - JOUR A1 - Gutsche, Philipp A1 - Poulikakos, Lisa A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Schmidt, Frank T1 - Time-harmonic optical chirality in inhomogeneous space JF - Proc. SPIE Y1 - 2016 U6 - https://doi.org/10.1117/12.2209551 VL - 9756 SP - 97560X ER - TY - GEN A1 - Gutsche, Philipp A1 - Poulikakos, Lisa A1 - Burger, Sven A1 - Hammerschmidt, Martin A1 - Schmidt, Frank T1 - Optical chirality: conservation law in arbitrary space T2 - 606. WE-Heraeus-Seminar on Nanophotonics and Complex Spatial Modes of Light N2 - The introduction of the near-field quantity of optical chirality has emerged in various numerical and few experimental studies of local chirality enhancement due to its relation to the excitation rate of chiral molecules. This time-even pseudoscalar has been dismissed as being a higher-order version of helicity. Nevertheless, we revisit the derivation of the underlying conservation law and define optical chirality in media similar to. We identify the mechanism of chirality conversion by either inhomogeneous or anisotropic space to complement the conservation of optical chirality. The conservation law of optical chirality in arbitrary space enables the extension of the concept of polarization to the near-field where no distiniguished propagation direction of light is present. We show that the connection of electromagnetic energy and optical chirality provide the ability to define a circular polarization basis in time-harmonic near-field analysis. In order to illustrate our theory, we present electromagnetic field simulations of simple as well as more complex nanostructures. Results using the well-known far-field polarization concept are readily reproduced and extended from the point of view of chirality conversion. Y1 - 2016 ER - TY - JOUR A1 - Hammerschmidt, Martin A1 - Barth, Carlo A1 - Pomplun, Jan A1 - Burger, Sven A1 - Becker, Christiane A1 - Schmidt, Frank T1 - Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs JF - Proc. SPIE N2 - Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters. Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58187 VL - 9756 SP - 97561R ER - TY - JOUR A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Model order reduction for the time-harmonic Maxwell equation applied to complex nanostructures JF - Proc. SPIE N2 - Fields such as optical metrology and computational lithography require fast and efficient methods for solving the time-harmonic Maxwell's equation. Highly accurate geometrical modelling and numerical accuracy at low computational costs are a prerequisite for any simulation study of complex nano-structured photonic devices. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem based on the hp-adaptive finite element solver JCMsuite capable of handling geometric and non-geometric parameter dependencies allowing for online evaluations in milliseconds. We apply the RBM to compute light-scattering at optical wavelengths of periodic arrays of fin field-effect transistors (FinFETs) where geometrical properties such as the width and height of the fin and gate can vary in a large range. Y1 - 2016 U6 - https://doi.org/10.1117/12.2212367 VL - 9742 SP - 97420M ER - TY - GEN A1 - Gutsche, Philipp A1 - Läuter, Matthias A1 - Schmidt, Frank T1 - Parameter-dependent Parallel Block Sparse Arnoldi and Döhler Algorithms on Distributed Systems N2 - We summarize the basics and first results of the analyses within our ZIB Bridge Project and give an outlook on further studies broadening the usage of hardware acceleration within the Finite Element Method (FEM) based solution of Maxwell’s equations. T3 - ZIB-Report - 16-15 KW - Generalized Eigenvalue Problem KW - Many Integrated Core Coprocessor (MIC) KW - Finite Element Method Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58202 SN - 1438-0064 ER - TY - JOUR A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Reduced basis method for electromagnetic scattering problem: a case study for FinFETs JF - Optical and Quantum Electronics N2 - Optical 3D simulations in many-query and real-time contexts require new solution strategies. We study an adaptive, error controlled reduced basis method for solving parametrized time-harmonic optical scattering problems. Application fields are, among others, design and optimization problems of nano-optical devices as well as inverse problems for parameter reconstructions occurring e. g. in optical metrology. The reduced basis method pre- sented here relies on a finite element modeling of the scattering problem with parametrization of materials, geometries and sources. Y1 - 2016 U6 - https://doi.org/10.1007/s11082-016-0530-1 VL - 48 SP - 250 ER - TY - JOUR A1 - Jäger, Klaus A1 - Barth, Carlo A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Burger, Sven A1 - Schmidt, Frank A1 - Becker, Christiane T1 - Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells JF - Opt. Express Y1 - 2016 U6 - https://doi.org/10.1364/OE.24.00A569 VL - 24 SP - A569 ER - TY - JOUR A1 - Ledentsov, Jr., Nikolay A1 - Shchukin, Vitaly A1 - Kropp, Jörg-R. A1 - Burger, Sven A1 - Schmidt, Frank A1 - Ledentsov, Jr., Nikolay T1 - Direct visualization of the in-plane leakage of high-order transverse modes in vertical-cavity surface-emitting lasers mediated by oxide-aperture engineering JF - Proc. SPIE Y1 - 2016 U6 - https://doi.org/10.1117/12.2208909 VL - 9766 SP - 976608 ER - TY - JOUR A1 - Pomplun, Jan A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Gutsche, Philipp A1 - Schmidt, Frank T1 - Method for fast computation of angular light scattering spectra from 2D periodic arrays JF - Proc. SPIE Y1 - 2016 U6 - https://doi.org/10.1117/12.2219666 VL - 9778 SP - 977839 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 - JOUR A1 - Ruprecht, Daniel A1 - Schädle, Achim A1 - Schmidt, Frank T1 - Transparent boundary conditions based on the pole condition for time-dependent, two-dimensional problems JF - Numerical Methods for Partial Differential Equations Y1 - 2013 U6 - https://doi.org/10.1002/num.21759 VL - 29 IS - 4 SP - 1367 EP - 1390 ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Adaptive sampling strategies for efficient parameter scans in nano-photonic device simulations N2 - Rigorous optical simulations are an important tool in optimizing scattering properties of nano-photonic devices and are used, for example, in solar cell optimization. The finite element method (FEM) yields rigorous, time-harmonic, high accuracy solutions of the full 3D vectorial Maxwell's equations [1] and furthermore allows for great flexibility and accuracy in the geometrical modeling of these often complex shaped 3D nano-structures. A major drawback of frequency domain methods is the limitation of single frequency evaluations. For example the accurate computation of the short circuit current density of an amorphous silicon / micro-crystalline multi-junction thin film solar cell may require the solution of Maxwell's equations for over a hundred different wavelengths if an equidistant sampling strategy is employed. Also in optical metrology, wavelength scans are frequently used to reconstruct unknown geometrical and material properties of optical systems numerically from measured scatterometric data. In our contribution we present several adaptive numerical integration and sampling routines and study their efficiency in the context of the determination of generation rate profiles of solar cells. We show that these strategies lead to a reduction in the computational effort without loss of accuracy. We discuss the employment of tangential information in a Hermite interpolation scheme to achieve similar accuracy on coarser grids. We explore the usability of these strategies for scatterometry and solar cell simulations. T3 - ZIB-Report - 14-20 KW - finite element method KW - optical simulations KW - adaptive sampling KW - optical metrology KW - parameter scans KW - solar cells Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50395 SN - 1438-0064 ER - TY - GEN 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 N2 - In many experimentally realized applications, e.g. photonic crystals, solar cells and light-emitting diodes, nano-photonic systems are coupled to a thick substrate layer, which in certain cases has to be included as a part of the optical system. The finite element method (FEM) yields rigorous, high accuracy solutions of full 3D vectorial Maxwell's equations [1] and allows for great flexibility and accuracy in the geometrical modelling. Time-harmonic FEM solvers have been combined with Fourier methods in domain decomposition algorithms to compute coherent solutions of these coupled system. [2,3] The basic idea of a domain decomposition approach lies in a decomposition of the domain into smaller subdomains, separate calculations of the solutions and coupling of these solutions on adjacent subdomains. In experiments light sources are often not perfectly monochromatic and hence a comparision to simulation results might only be justified if the simulation results, which include interference patterns in the substrate, are spectrally averaged. In this contribution we present a scattering matrix domain decomposition algorithm for Maxwell's equations based on FEM. We study its convergence and advantages in the context of optical simulations of silicon thin film multi-junction solar cells. This allows for substrate light-trapping to be included in optical simulations and leads to a more realistic estimation of light path enhancement factors in thin-film devices near the band edge. T3 - ZIB-Report - 14-21 KW - finite element method KW - rigorous optical modeling KW - domain decomposition KW - multi-junction solar cells KW - thin-film silicon solar cells KW - incoherent layers KW - incoherent light-trapping Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50410 SN - 1438-0064 ER - TY - CHAP A1 - Lockau, Daniel A1 - Hammerschmidt, Martin A1 - Haschke, Jan A1 - Blome, Mark A1 - Ruske, Florian A1 - Schmidt, Frank A1 - Rech, Bernd T1 - A comparison of scattering and non-scattering anti-reflection designs for back contacted polycrystalline thin film silicon solar cells in superstrate configuration T2 - Proc. SPIE Y1 - 2014 U6 - https://doi.org/10.1117/12.2052362 VL - 9140 SP - 914006 ER - TY - GEN A1 - Lockau, Daniel A1 - Hammerschmidt, Martin A1 - Blome, Mark A1 - Schmidt, Frank ED - Deuflhard, Peter ED - et al., T1 - Optics of thin film solar cells T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 U6 - https://doi.org/10.4171/137 VL - 1 SP - 278 EP - 279 PB - European Mathematical Society ER - TY - CHAP A1 - Manley, Phillip A1 - Burger, Sven A1 - Schmidt, Frank A1 - Schmid, Martina ED - Sakabe, Shuji ED - Lienau, Christoph ED - Grunwald, Rüdiger T1 - Design Principles for Plasmonic Nanoparticle Devices T2 - Progress in Nonlinear Nano-Optics Y1 - 2015 UR - http://www.springer.com/978-3-319-12216-8 U6 - https://doi.org/10.1007/978-3-319-12217-5_13 VL - XXI SP - 223 EP - 247 PB - Springer ET - Nano-Optics and Nanophotonics 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 - 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 - Schlosser, Felix A1 - Schoth, Mario A1 - Burger, Sven A1 - Schmidt, Frank A1 - Knorr, Andreas A1 - Mukamel, S. A1 - Richter, Marten T1 - Ultrafast nonlinear spectroscopy with spatially confined fields JF - AIP Conference Proceedings Y1 - 2011 U6 - https://doi.org/10.1063/1.3644223 VL - 1398 SP - 94 EP - 96 PB - AIP ER - TY - CHAP A1 - Schlosser, Felix A1 - Schoth, Mario A1 - Burger, Sven A1 - Schmidt, Frank A1 - Knorr, Andreas A1 - Mukamel, Shaul A1 - Richter, Marten T1 - Coherent Nonlinear Spectroscopy with Spatiotemporally Controlled Fields T2 - CLEO/QELS Y1 - 2012 U6 - https://doi.org/10.1364/QELS.2012.QF3D.6 SP - QF3D.6 PB - Optical Society of America ER - TY - CHAP A1 - Schlosser, Felix A1 - Schoth, Mario A1 - Hiremath, Kirankumar A1 - Burger, Sven A1 - Schmidt, Frank A1 - Knorr, Andreas A1 - Mukamel, Shaul A1 - Richter, Marten T1 - Combining nanooptical fields and coherent spectroscopy on systems with delocalized excitons T2 - Proc. SPIE Y1 - 2012 U6 - https://doi.org/10.1117/12.906671 VL - 8260 SP - 82601V 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 - THES A1 - Schmidt, Frank T1 - Untersuchung heteronomer Differentialgleichungen mit Hilfe des Analogrechners Y1 - 1986 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 - Yevick, David T1 - Discrete Transparent Boundary Conditions for the Fresnel Equation T2 - Proceedings of the 8th European Conference on Integrated Optics Y1 - 1997 SP - 222 EP - 225 CY - Royal Institute of Technology, Stockholm, Sweden 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 - 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 - 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 - Ledentsov, Jr., Nikolay A1 - Kropp, Jörg-R. A1 - Shchukin, Vitaly A1 - Steinle, Gunther A1 - Ledentsov, Jr., Nikolay A1 - Turkiewicz, Jarek P. A1 - Wu, Bo A1 - Shaofeng, Qiu A1 - Ma, Yanan A1 - Zhiyong, Feng A1 - Burger, Sven A1 - Schmidt, Frank A1 - Caspar, Christoph A1 - Freund, Ronald A1 - Choquette, Kent D. T1 - High-speed modulation, wavelength, and mode control in vertical-cavity surface-emitting lasers T2 - Proc. SPIE Y1 - 2015 U6 - https://doi.org/10.1117/12.2082951 VL - 9381 SP - 93810F ER - TY - CHAP A1 - Shchukin, Vitaly A1 - Ledentsov, Jr., Nikolay A1 - Kropp, Jörg-R. A1 - Steinle, Gunther A1 - Ledentsov, Jr., Nikolay A1 - Choquette, Kent D. A1 - Burger, Sven A1 - Schmidt, Frank T1 - Engineering of optical modes in vertical-cavity microresonators by aperture placement: applications to single-mode and near-field lasers T2 - Proc. SPIE Y1 - 2015 U6 - https://doi.org/10.1117/12.2077012 VL - 9381 SP - 93810V 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 - 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 - CHAP A1 - Burger, Sven A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank T1 - Reduced basis methods for optimization of nano-photonic devices T2 - Proc. Int. Conf. Numerical Simulation of Optoelectronic Devices (NUSOD) Y1 - 2015 U6 - https://doi.org/10.1109/NUSOD.2015.7292871 SP - 159 ER - TY - JOUR A1 - Ledentsov, Jr., Nikolay A1 - Shchukin, Vitaly A1 - Ledentsov, Jr., Nikolay A1 - Kropp, Jörg-R. A1 - Burger, Sven A1 - Schmidt, Frank T1 - Direct Evidence of the Leaky Emission in Oxide-Confined Vertical Cavity Lasers JF - IEEE J. Quant. Electron. Y1 - 2016 U6 - https://doi.org/10.1109/JQE.2016.2518081 VL - 52 IS - 3 SP - 2400207 ER - TY - CHAP A1 - Jäger, Klaus A1 - Barth, Carlo A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Burger, Sven A1 - Schmidt, Frank A1 - Becker, Christiane T1 - Sinusoidal Nanotextures for Coupling Light into c-Si Thin-Film Solar Cells T2 - Light, Energy and the Environement 2015 Y1 - 2015 U6 - https://doi.org/10.1364/PV.2015.PTu4B.3 SP - PTu4B.3 ER - TY - CHAP A1 - Barth, Carlo A1 - Jäger, Klaus A1 - Burger, Sven A1 - Hammerschmidt, Martin A1 - Schmidt, Frank A1 - Becker, Christiane T1 - Design of Photonic Crystals with Near-Surface Field Enhancement T2 - Light, Energy and the Environement 2015 Y1 - 2015 U6 - https://doi.org/10.1364/PV.2015.JTu5A.9 SP - JTu5A.9 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 - 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 - 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 - 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 - 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 - 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 - Barth, Carlo A1 - Roder, Sebastian A1 - Brodoceanu, Daniel A1 - Kraus, Tobias A1 - Burger, Sven A1 - Hammerschmidt, Martin A1 - Schmidt, Frank A1 - Becker, Christiane T1 - Increased fluorescence of PbS quantum dots on photonic crystal slab structures T2 - Proc. Europ. Opt. Soc. Ann. Meet. 2016 (EOSAM) Y1 - 2016 SN - 978-1-5108-4796-5 SP - 181 ER - TY - CHAP A1 - Hammerschmidt, Martin A1 - Barth, Carlo A1 - Burger, Sven A1 - Becker, Christiane A1 - Schmidt, Frank T1 - Determining 2D photonic crystal geometries from reflectance spectra with a reduced basis method T2 - Proc. Europ. Opt. Soc. Ann. Meet. 2016 (EOSAM) Y1 - 2016 SN - 978-1-5108-4796-5 SP - 281 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 - 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 - GEN A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Model order reduction for the time-harmonic Maxwell equation applied to complex nanostructures T2 - Proc. SPIE N2 - Fields such as optical metrology and computational lithography require fast and efficient methods for solving the time-harmonic Maxwell’s equation. Highly accurate geometrical modeling and numerical accuracy atcomputational costs are a prerequisite for any simulation study of complex nano-structured photonic devices. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem based on the hp-adaptive finite element solver JCMsuite capable of handling geometric and non-geometric parameter dependencies allowing for online evaluations in milliseconds. We apply the RBM to compute light-scatteringoptical wavelengths off periodic arrays of fin field-effect transistors (FinFETs) where geometrical properties such as the width and height of the fin and gate can vary in a large range. T3 - ZIB-Report - 16-05 KW - reduced basis method KW - finite element method KW - rigorous optical modeling KW - reduced order models KW - electromagnetic field solver Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57239 SN - 1438-0064 VL - 9742 SP - 97420M ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Barth, Carlo A1 - Pomplun, Jan A1 - Burger, Sven A1 - Becker, Christiane A1 - Schmidt, Frank T1 - Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs N2 - Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters. T3 - ZIB-Report - 16-06 KW - finite element method KW - rigorous optical modeling KW - photonic crystals KW - reduced basis method KW - parameter estimation KW - optical metrology Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57249 SN - 1438-0064 ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Burger, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank T1 - Reduced basis method for the optimization of nano-photonic devices N2 - Optical 3D simulations in many-query and real-time contexts require new solution strategies. We study an adaptive, error controlled reduced basis method for solving parametrized time-harmonic optical scattering problems. Application fields are, among others, design and optimization problems of nano-optical devices as well as inverse problems for parameter reconstructions occuring e. g. in optical metrology. The reduced basis method presented here relies on a finite element modeling of the scattering problem with parametrization of materials, geometries and sources. T3 - ZIB-Report - 16-10 KW - reduced basis method KW - model reduction KW - optical critical dimension metrology KW - electromagnetic field solver Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57556 SN - 1438-0064 ER - TY - JOUR A1 - Lang, Annemarie A1 - Helfmeier, Sarah A1 - Stefanowski, Jonathan A1 - Kuppe, Aditi A1 - Sunkara, Vikram A1 - Pfeiffenberger, Moritz A1 - Wolter, Angelique A1 - Damerau, Alexandra A1 - Hemmati-Sadeghi, Shabnam A1 - Ringe, Jochen A1 - Haag, Rainer A1 - Hauser, Anja E. A1 - Löhning, Max A1 - Perka, Carsten A1 - Duda, Georg A1 - Hoff, Paula A1 - Schmidt-Bleek, Katharina A1 - Gaber, Timo A1 - Buttgereit, Frank T1 - HIF-stabilization prevents delayed fracture healing JF - bioarxiv Y1 - 2020 U6 - https://doi.org/10.1101/2020.07.02.182832 ER -