@misc{Schmidt1995, author = {Schmidt, Frank}, title = {Simultaneous Computation of the Lowest Eigenvalue and Eigenvectors of the Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5281}, number = {TR-95-13}, year = {1995}, abstract = {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.}, language = {en} } @misc{FrieseSchmidtYevick1999, author = {Friese, Tilman and Schmidt, Frank and Yevick, David}, title = {Transparent Boundary Conditions for a Wide-Angle Approximation of the One-Way Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4345}, number = {SC-99-45}, year = {1999}, abstract = {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.}, language = {en} } @misc{SchmidtFrieseYevick1999, author = {Schmidt, Frank and Friese, Tilmann and Yevick, David}, title = {Transparent Boundary Conditions for Split-Step Pade Approximations of the One-Way Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4353}, number = {SC-99-46}, year = {1999}, abstract = {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.}, language = {en} } @misc{DeuflhardFrieseSchmidt1997, author = {Deuflhard, Peter and Friese, Tilmann and Schmidt, Frank}, title = {A Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3240}, number = {SC-97-55}, year = {1997}, abstract = {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.}, language = {en} } @misc{Schmidt1997, author = {Schmidt, Frank}, title = {Construction of Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3292}, number = {SC-97-60}, year = {1997}, abstract = {We present a general technique for constructing nonlocal transparent boundary conditions for time-discretized one-dimensional Schr{\"o}dinger 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.}, language = {en} } @article{BlomeMcPeakBurgeretal.2014, author = {Blome, Mark and McPeak, Kevin and Burger, Sven and Schmidt, Frank and Norris, David}, title = {Back-reflector design in thin-film silicon solar cells by rigorous 3D light propagation modeling}, volume = {33}, journal = {COMPEL: Int. J. Comput. Mathem. Electr. Electron. Eng.}, number = {4}, doi = {10.1108/COMPEL-12-2012-0367}, pages = {1282 -- 1295}, year = {2014}, language = {en} } @inproceedings{BurgerZschiedrichSchmidtetal.2008, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank and Evanschitzky, Peter and Erdmann, Andreas}, title = {Benchmark of rigorous methods for electromagnetic field simulation}, volume = {7122}, booktitle = {Photomask Technology}, editor = {Kawahira, H. and Zurbrick, L. S.}, publisher = {Proc. SPIE}, doi = {10.1117/12.801248}, pages = {71221}, year = {2008}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2011, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {Rigorous simulations of 3D patterns on extreme ultraviolet lithography masks}, volume = {8083}, booktitle = {Modelling Aspects in Optical Metrology III}, editor = {Bodermann, Bernd}, publisher = {Proc. SPIE}, doi = {10.1117/12.889831}, pages = {80831B}, year = {2011}, language = {en} } @inproceedings{BurgerPomplunSchmidtetal.2011, author = {Burger, Sven and Pomplun, Jan and Schmidt, Frank and Zschiedrich, Lin}, title = {Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap}, volume = {7933}, booktitle = {Physics and Simulation of Optoelectronic Devices XIX}, publisher = {Proc. SPIE}, doi = {10.1117/12.875044}, pages = {79330T}, year = {2011}, language = {en} } @incollection{BurgerZschiedrichKettneretal.2008, author = {Burger, Sven and Zschiedrich, Lin and Kettner, Benjamin and Schmidt, Frank}, title = {FEM simulation of light scattering by nonspherical objects}, booktitle = {Mie Theory 1908 - 2008}, editor = {Hergert, W. and Wriedt, T.}, publisher = {Universit{\"a}t Bremen}, pages = {82 -- 83}, year = {2008}, language = {en} } @inproceedings{BurgerZschiedrichKloseetal.2005, author = {Burger, Sven and Zschiedrich, Lin and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank and Enkrich, Christian and Linden, S. and Wegener, M. and Soukoulis, C.}, title = {Numerical Investigation of Light Scattering off Split-Ring Resonators}, volume = {5955}, booktitle = {Metamaterials}, editor = {Szoplik, T. and {\"O}zbay, E. and Soukoulis, C. and Zheludev, N.}, publisher = {Proc. SPIE}, doi = {10.1117/12.622184}, pages = {18 -- 26}, year = {2005}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2009, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank and Kettner, Benjamin and Lockau, D.}, title = {3D Finite-Element Simulations of Enhanced Light Transmission Through Arrays of Holes in Metal Films}, volume = {7390}, booktitle = {Numerical Methods in Optical Metrology}, publisher = {Proc. SPIE}, doi = {10.1117/12.827543}, pages = {73900H}, year = {2009}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2010, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {Finite element method for accurate 3D simulation of plasmonic waveguides}, volume = {7604}, booktitle = {Integrated Optics: Devices, Materials, and Technologies XIV}, publisher = {Proc. SPIE}, doi = {10.1117/12.841995}, pages = {76040F}, year = {2010}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2008, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {JCMsuite: An Adaptive FEM Solver for Precise Simulations in Nano-Optics}, booktitle = {Integrated Photonics and Nanophotonics Research and Applications}, publisher = {Optical Society of America}, doi = {10.1364/IPNRA.2008.ITuE4}, pages = {ITuE4}, year = {2008}, language = {en} } @article{BurgerZschiedrichSchmidt2010, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank}, title = {FEM Simulation of Plasmon Laser Resonances}, volume = {1281}, journal = {AIP Conference Proceedings}, publisher = {AIP}, doi = {10.1063/1.3498131}, pages = {1613 -- 1616}, year = {2010}, language = {en} } @inproceedings{BurgerZschiedrichSchaedleetal.2006, author = {Burger, Sven and Zschiedrich, Lin and Sch{\"a}dle, Achim and Klose, Roland and Kettner, Benjamin and Pomplun, Jan and Pollok, T. and Schmidt, Frank}, title = {Advanced FEM Analysis of Nano-Optical Devices}, booktitle = {Proc. Symposium on Photonics Technologies for the 7th Framework Programme}, year = {2006}, language = {en} } @inproceedings{BurgerZschiedrichSchmidtetal.2007, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank and K{\"o}hle, Roderick and Henkel, Thomas and K{\"u}chler, Bernd and N{\"o}lscher, Christoph}, title = {3D simulations of electromagnetic fields in nanostructures using the time-harmonic finite-element method}, volume = {6617}, booktitle = {Modeling Aspects in Optical Metrology}, editor = {Bosse, Harald}, publisher = {Proc. SPIE}, doi = {10.1117/12.726236}, pages = {66170V}, year = {2007}, language = {en} } @inproceedings{BurgerZschiedrichSchmidtetal.2007, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank and K{\"o}hle, Roderick and K{\"u}chler, Bernd and N{\"o}lscher, Christoph}, title = {EMF Simulations of Isolated and Periodic 3D Photomask Patterns}, volume = {6730}, booktitle = {Photomask Technology}, publisher = {Proc. SPIE}, pages = {6630}, year = {2007}, language = {en} } @inproceedings{BurgerKoehleZschiedrichetal.2005, author = {Burger, Sven and K{\"o}hle, Roderick and Zschiedrich, Lin and Gao, W. and Schmidt, Frank and M{\"a}rz, Reinhard and N{\"o}lscher, Christoph}, title = {Benchmark of FEM, Waveguide and FDTD Algorithms for Rigorous Mask Simulation}, volume = {5992}, booktitle = {Photomask Technology}, editor = {Weed, J. and Martin, P.}, publisher = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/physics/0601143}, doi = {10.1117/12.631696}, pages = {378 -- 389}, year = {2005}, language = {en} } @inproceedings{BurgerLockauZschiedrichetal.2009, author = {Burger, Sven and Lockau, D. and Zschiedrich, Lin and Schmidt, Frank}, title = {Finite-element simulations of light propagation through subwavelength apertures in metal films}, volume = {XVIII}, booktitle = {International Workshop on Optical Waveguide Theory and Numerical Modelling}, publisher = {Fraunhofer Institute for Applied Optics and Precision Engineering}, pages = {59}, year = {2009}, language = {en} } @incollection{BurgerPomplunSchmidt2012, author = {Burger, Sven and Pomplun, Jan and Schmidt, Frank}, title = {Finite Element Methods for Computational Nano-optics}, booktitle = {Encyclopedia of Nanotechnology}, editor = {Bhushan, B.}, publisher = {Springer Netherlands}, doi = {10.1007/978-90-481-9751-4_17}, pages = {837 -- 843}, year = {2012}, language = {en} }