@inproceedings{PomplunWenzelBurgeretal.2012, author = {Pomplun, Jan and Wenzel, Hans and Burger, Sven and Zschiedrich, Lin and Rozova, Maria and Schmidt, Frank and Crump, Paul and Ekhteraei, Hossein and Schultz, Christoph M. and Erbert, G{\"o}tz}, title = {Thermo-optical simulation of high-power diode lasers}, volume = {8255}, booktitle = {Proc. SPIE}, doi = {10.1117/12.909330}, pages = {825510}, year = {2012}, language = {en} } @article{SchmidtMaerz1996, author = {Schmidt, Frank and M{\"a}rz, Reinhard}, title = {On the Reference Wave Vector of Paraxial Helmholtz Equations}, volume = {14}, journal = {IEEE Journal of Lightwave Technology}, pages = {2395 -- 2400}, year = {1996}, language = {en} } @article{SchmidtNolting1992, author = {Schmidt, Frank and Nolting, Hans-Peter}, title = {Adaptive Multilevel Beam Propagation Method}, volume = {4}, journal = {IEEE Photonics Technology Letter}, pages = {1381 -- 1383}, year = {1992}, language = {en} } @inproceedings{SchmidtNolting1992, author = {Schmidt, Frank and Nolting, Hans-Peter}, title = {An Adaptive Approach to a Beam Propagation Method}, booktitle = {Integrated Photonics Research}, address = {New Orleans, Louisiana, USA}, pages = {302 -- 303}, year = {1992}, language = {en} } @inproceedings{SchaedleRuprechtSchmidt2007, author = {Sch{\"a}dle, Achim and Ruprecht, Daniel and Schmidt, Frank}, title = {Transparent boundary conditions - the pole condition approach}, booktitle = {Proceedings of Waves 2007}, editor = {et.al., N. Biggs}, pages = {301 -- 303}, year = {2007}, language = {en} } @article{SchmidtYevick1997, author = {Schmidt, Frank and Yevick, David}, title = {Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type Equations}, volume = {134}, journal = {J. Comput. Phys.}, number = {1}, doi = {10.1006/jcph.1997.5675}, pages = {96 -- 107}, year = {1997}, language = {en} } @inproceedings{SchmidtBurgerSchaedleetal.2005, author = {Schmidt, Frank and Burger, Sven and Sch{\"a}dle, Achim and Klose, Roland}, title = {Finite element methods for optical device design}, booktitle = {Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices}, doi = {10.1109/NUSOD.2005.1518133}, pages = {57 -- 58}, year = {2005}, language = {en} } @inproceedings{SchmidtDeuflhard1994, author = {Schmidt, Frank and Deuflhard, Peter}, title = {Discrete Transparent Boundary Conditions for Fresnel's Equation}, booktitle = {Integrated Photonics Research}, address = {San Francisco, California, USA}, pages = {45 -- 47}, year = {1994}, language = {en} } @article{SchmidtDeuflhard1995, author = {Schmidt, Frank and Deuflhard, Peter}, title = {Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.}, volume = {29}, journal = {Comput. Math. Appl.}, pages = {53 -- 76}, year = {1995}, language = {en} } @inproceedings{Schmidt2000, author = {Schmidt, Frank}, title = {Discrete Nonreflecting Boundary Conditions for the Helmholtz equation}, booktitle = {Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation}, editor = {Berm{\´u}dez, A. and G{\´o}mez, D. and Hazard, C. and Joly, P. and Roberts, J.}, address = {Waves 2000, Santiago de Compostella, Spain}, pages = {921 -- 925}, year = {2000}, language = {en} } @phdthesis{Schmidt2002, author = {Schmidt, Frank}, title = {Solution of Interior-Exterior Helmholtz-Type Problems Based on the Pole Condition Concept}, year = {2002}, language = {en} } @article{Schmidt2004, author = {Schmidt, Frank}, title = {Pole Condition: A new Approach to Solve Scattering Problems}, volume = {1}, journal = {Oberwolfach Report}, number = {1}, publisher = {Mathematisches Forschungsinstitut Oberwolfach}, pages = {615 -- 617}, year = {2004}, language = {en} } @phdthesis{Schmidt1989, author = {Schmidt, Frank}, title = {Ingenieurm{\"a}ßige Berechnung der Feldausbreitung in optischen Bauelementen der Lichtwellenleitertechnik}, year = {1989}, language = {en} } @article{Schmidt1990, author = {Schmidt, Frank}, title = {Simulation und Herstellung von Faserschleifkopplern}, volume = {39}, journal = {Wissenschaftliche Zeitschrift der Humboldt-Universit{\"a}t zu Berlin, R. Math./Naturwiss.}, number = {2}, pages = {115 -- 118}, year = {1990}, language = {en} } @article{Schmidt1993, author = {Schmidt, Frank}, title = {An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation.}, volume = {11}, journal = {IEEE Journal of Lightwave Technology}, number = {9}, pages = {1425 -- 1435}, year = {1993}, language = {en} } @inproceedings{ZschiedrichBurgerKettneretal.2006, author = {Zschiedrich, Lin and Burger, Sven and Kettner, Benjamin and Schmidt, Frank}, title = {Advanced Finite Element Method for Nano-Resonators}, volume = {6115}, booktitle = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/physics/0601025}, doi = {10.1117/12.646252}, pages = {611515}, year = {2006}, language = {en} } @inproceedings{ZschiedrichBurgerKloseetal.2005, author = {Zschiedrich, Lin and Burger, Sven and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {JCMmode: an adaptive finite element solver for the computation of leaky modes}, volume = {5728}, booktitle = {Integrated Optics: Devices, Materials, and Technologies IX}, editor = {Sidorin, Y. and W{\"a}chter, Christoph}, publisher = {Proc. SPIE}, doi = {10.1117/12.590372}, pages = {192 -- 202}, year = {2005}, language = {en} } @inproceedings{ZschiedrichBurgerPomplunetal.2007, author = {Zschiedrich, Lin and Burger, Sven and Pomplun, Jan and Schmidt, Frank}, title = {Goal oriented adaptive finite element method for precise simulation of optical components}, volume = {6475}, booktitle = {Proc. SPIE, Integrated Optics}, editor = {Sidorin, Y. and Waechter, Ch.}, pages = {64750H}, year = {2007}, language = {en} } @inproceedings{ZschiedrichBurgerSchaedleetal.2008, author = {Zschiedrich, Lin and Burger, Sven and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {A rigorous finite-element domain decomposition method for electromagnetic near field simulations}, volume = {6924}, booktitle = {Optical Microlithography XXI}, editor = {Levinson, Harry and Dusa, Mircea}, publisher = {SPIE}, doi = {10.1117/12.771989}, year = {2008}, language = {en} } @inproceedings{ZschiedrichBurgerSchaedleetal.2005, author = {Zschiedrich, Lin and Burger, Sven and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {Domain decomposition method for electromagnetic scattering problems: application to EUV lithography}, booktitle = {Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices}, doi = {10.1109/NUSOD.2005.1518132}, pages = {55 -- 56}, year = {2005}, language = {en} } @inproceedings{ZschiedrichGreinerPomplunetal.2012, author = {Zschiedrich, Lin and Greiner, Horst and Pomplun, Jan and Hammerschmidt, Martin and Burger, Sven and Schmidt, Frank}, title = {FEM simulations of light extraction from nanostructured organic light-emitting diodes}, booktitle = {Renewable Energy and the Environment Optics and Photonics Congress}, publisher = {Optical Society of America}, doi = {10.1364/SOLED.2012.LT2B.5}, pages = {LT2B.5}, year = {2012}, language = {en} } @article{ZschiedrichKloseSchaedleetal.2006, author = {Zschiedrich, Lin and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {A new finite element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D}, volume = {188}, journal = {J. Comput. Appl. Math.}, doi = {10.1016/j.cam.2005.03.047}, pages = {12 -- 32}, year = {2006}, language = {en} } @inproceedings{ZschiedrichSchmidt2008, author = {Zschiedrich, Lin and Schmidt, Frank}, title = {Finite element simulation of light propagation in non-periodic mask patterns}, volume = {7028}, booktitle = {Photomask and Next-Generation Lithography Mask Technology XV}, editor = {Horiuchi, Toshiyuki}, publisher = {SPIE}, year = {2008}, language = {en} } @article{YevickFrieseSchmidt2001, author = {Yevick, David and Friese, T. and Schmidt, Frank}, title = {A Comparison of Transparent Boundary Conditions for the Fresnel Equation}, volume = {168}, journal = {J. Comput. Phys.}, number = {2}, pages = {433 -- 444}, year = {2001}, language = {en} } @article{YevickYuSchmidt1997, author = {Yevick, David and Yu, J. and Schmidt, Frank}, title = {Analytic Studies of Absorbing and Impedance-Matched Boundary Layers}, volume = {9}, journal = {IEEE Photonics Technology Letters}, doi = {10.1109/68.554499}, pages = {73 -- 75}, year = {1997}, language = {en} } @article{ArellanoMingaleevKoltchanovetal.2013, author = {Arellano, Cristina and Mingaleev, Sergei F. and Koltchanov, Igor and Richter, Andre and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Efficient design of photonic integrated circuits (PICs) by combining device- and circuit- level simulation tools}, volume = {8627}, journal = {Proc. SPIE}, doi = {10.1117/12.2004378}, pages = {862711}, year = {2013}, language = {en} } @article{BurgerZschiedrichPomplunetal.2013, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Blome, Mark and Schmidt, Frank}, title = {Advanced finite-element methods for design and analysis of nano-optical structures: Applications}, volume = {8642}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1304.4356}, doi = {10.1117/12.2001094}, pages = {864205}, year = {2013}, language = {en} } @article{HammerschmidtLockauBurgeretal.2013, author = {Hammerschmidt, Martin and Lockau, Daniel and Burger, Sven and Schmidt, Frank and Schwanke, Christoph and Kirner, Simon and Calnan, Sonya and Stannowski, Bernd and Rech, Bernd}, title = {FEM-based optical modeling of silicon thin-film tandem solar cells with randomly textured interfaces in 3D}, volume = {8620}, journal = {Proc. SPIE}, doi = {10.1117/12.2001789}, pages = {86201H}, year = {2013}, language = {en} } @article{BurgerZschiedrichPomplunetal.2013, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank and Bodermann, Bernd}, title = {Fast simulation method for parameter reconstruction in optical metrology}, volume = {8681}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1304.4367}, doi = {10.1117/12.2011154}, pages = {868119}, year = {2013}, language = {en} } @article{ZschiedrichGreinerBurgeretal.2013, author = {Zschiedrich, Lin and Greiner, Horst and Burger, Sven and Schmidt, Frank}, title = {Numerical analysis of nanostructures for enhanced light extraction from OLEDs}, volume = {8641}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1304.4380}, doi = {10.1117/12.2001132}, pages = {86410B}, year = {2013}, language = {en} } @article{BeckerLockauSontheimeretal.2012, author = {Becker, Christiane and Lockau, Daniel and Sontheimer, Tobias and Schubert-Bischoff, Peter and Rudigier-Voigt, Eveline and Bockmeyer, Matthias and Schmidt, Frank and Rech, Bernd}, title = {Large-area 2D periodic crystalline silicon nanodome arrays on nanoimprinted glass exhibiting photonic band structure effects}, volume = {23}, journal = {Nanotechnology}, number = {13}, doi = {10.1088/0957-4484/23/13/135302}, pages = {135302}, year = {2012}, language = {en} } @article{LockauSontheimerBeckeretal.2013, author = {Lockau, Daniel and Sontheimer, Tobias and Becker, Christiane and Rudigier-Voigt, Eveline and Schmidt, Frank and Rech, Bernd}, title = {Nanophotonic light trapping in 3-dimensional thin-film silicon architectures}, volume = {21}, journal = {Opt. Express}, doi = {10.1364/OE.21.000A42}, pages = {A42}, year = {2013}, language = {en} } @article{LockauSontheimerPreideletal.2013, author = {Lockau, Daniel and Sontheimer, Tobias and Preidel, Veit and Becker, Christiane and Ruske, Florian and Schmidt, Frank and Rech, Bernd}, title = {Optical properties and Limits of a Large-Area Periodic Nanophotonic Light Trapping Design for Polycrystalline Silicon Thin Film Solar Cells}, volume = {1493}, journal = {MRS Proceedings}, doi = {10.1557/opl.2013.28}, pages = {59 -- 64}, year = {2013}, language = {en} } @inproceedings{WohlfeilBurgerStamatiadisetal.2014, author = {Wohlfeil, Benjamin and Burger, Sven and Stamatiadis, Christos and Pomplun, Jan and Schmidt, Frank and Zimmermann, Lars and Petermann, Klaus}, title = {Numerical Simulation of Grating Couplers for Mode Multiplexed Systems}, volume = {8988}, booktitle = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1403.2288}, doi = {10.1117/12.2044461}, pages = {89880K}, year = {2014}, language = {en} } @inproceedings{ZschiedrichMaerzBurgeretal.2006, author = {Zschiedrich, Lin and M{\"a}rz, Reinhard and Burger, Sven and Schmidt, Frank}, title = {Efficient 3D Finite Element Simulation of Fiber-Chip Coupling}, booktitle = {Integrated Photonics Research and Applications/Nanophotonics}, doi = {10.1364/IPRA.2006.ITuF1}, pages = {ITuF1}, year = {2006}, language = {en} } @incollection{PomplunZschiedrichKloseetal.2008, author = {Pomplun, Jan and Zschiedrich, Lin and Klose, Roland and Schmidt, Frank and Burger, Sven}, title = {Finite Element Simulation of Radiation Losses in Photonic Crystal Fibers}, booktitle = {Nanophotonic Materials: Photonic Crystals, Plasmonics, and Metamaterials}, publisher = {Wiley-VCH}, doi = {10.1002/9783527621880.ch17}, pages = {313 -- 331}, year = {2008}, language = {en} } @inproceedings{WenzelCrumpEkhteraeietal.2011, author = {Wenzel, Hans and Crump, Paul and Ekhteraei, Hossein and Schultz, Christoph M. and Pomplun, Jan and Burger, Sven and Zschiedrich, Lin and Schmidt, Frank and Erbert, G{\"o}tz}, title = {Theoretical and experimental analysis of the lateral modes of high-power broad-area lasers}, booktitle = {Numerical Simulation of Optoelectronic Devices}, doi = {10.1109/NUSOD.2011.6041183}, pages = {143 -- 144}, year = {2011}, language = {en} } @article{SontheimerPreidelLockauetal.2013, author = {Sontheimer, Tobias and Preidel, Veit and Lockau, Daniel and Back, Franziska and Rudigier-Voigt, Eveline and L{\"o}chel, Bernd and Erko, Alexei and Schmidt, Frank and Schnegg, Alexander and Lips, Klaus and Becker, Christiane and Rech, Bernd}, title = {Correlation between structural and opto-electronic characteristics of crystalline Si microhole arrays for photonic light management}, volume = {114}, journal = {Journal of Applied Physics}, number = {17}, publisher = {AIP Publishing}, doi = {10.1063/1.4829008}, pages = {173513}, year = {2013}, language = {en} } @article{LockauSontheimerPreideletal.2014, author = {Lockau, Daniel and Sontheimer, Tobias and Preidel, Veit and Ruske, Florian and Hammerschmidt, Martin and Becker, Christiane and Schmidt, Frank and Rech, Bernd}, title = {Advanced microhole arrays for light trapping in thin film silicon solar cells}, volume = {125}, journal = {Solar Energy Materials and Solar Cells}, doi = {10.1016/j.solmat.2013.11.024}, pages = {298 -- 304}, year = {2014}, language = {en} } @article{KirnerHammerschmidtSchwankeetal.2014, author = {Kirner, Simon and Hammerschmidt, Martin and Schwanke, Christoph and Lockau, Daniel and Calnan, Sonya and Frijnts, Tim and Neubert, Sebastian and Sch{\"o}pke, Andreas and Schmidt, Frank and Zollondz, Jens-Hendrik and Heidelberg, Andreas and Stannowski, Bernd and Rech, Bernd and Schlatmann, Rutger}, title = {Implications of TCO Topography on Intermediate Reflector Design for a-Si/μc-Si Tandem Solar Cells — Experiments and Rigorous Optical Simulations}, volume = {4}, journal = {IEEE Journal of Photovoltaics}, number = {1}, doi = {10.1109/JPHOTOV.2013.2279204}, pages = {10 -- 15}, year = {2014}, language = {en} } @inproceedings{HammerschmidtPomplunBurgeretal.2014, author = {Hammerschmidt, Martin and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Adaptive sampling strategies for effcient parameter scans in nano-photonic device simulations}, volume = {8980}, booktitle = {Proc. SPIE}, publisher = {SPIE}, doi = {10.1117/12.2036363}, pages = {89801O}, year = {2014}, language = {en} } @inproceedings{HammerschmidtLockauZschiedrichetal.2014, author = {Hammerschmidt, Martin and Lockau, Daniel and Zschiedrich, Lin and Schmidt, Frank}, title = {Optical modelling of incoherent substrate light-trapping in silicon thin film multi-junction solar cells with finite elements and domain decomposition}, volume = {8980}, booktitle = {Proc. SPIE: Physics and Simulation of Optoelectronic Devices XXII}, publisher = {SPIE}, doi = {10.1117/12.2036346}, pages = {898007}, year = {2014}, language = {en} } @inproceedings{JaegerBarthHammerschmidtetal.2016, author = {J{\"a}ger, Klaus and Barth, Carlo and Hammerschmidt, Martin and Herrmann, Sven and Burger, Sven and Schmidt, Frank and Becker, Christiane}, title = {Sinusoidal Nanotextures for Enhanced Light Management in Thin-Film Solar Cells}, booktitle = {28th Workshop on Quantum Solar Energy Conversion - (QUANTSOL)}, editor = {European Society for Quantum Solar Energy Conversion,}, year = {2016}, language = {en} } @article{JaegerKoeppelBarthetal.2016, author = {J{\"a}ger, Klaus and K{\"o}ppel, Grit and Barth, Carlo and Hammerschmidt, Martin and Herrmann, Sven and Burger, Sven and Schmidt, Frank and Becker, Christiane}, title = {Sinusoidal gratings for optimized light management in c-Si thin-film solar cells}, volume = {9898}, journal = {Proc. SPIE}, doi = {10.1117/12.2225459}, pages = {989808}, year = {2016}, language = {en} } @incollection{KantnerHoehneKopruckietal.2020, author = {Kantner, Markus and H{\"o}hne, Theresa and Koprucki, Thomas and Burger, Sven and W{\"u}nsche, Hans-J{\"u}rgen and Schmidt, Frank and Mielke, Alexander and Bandelow, Uwe}, title = {Multi-dimensional modeling and simulation of semiconductor nanophotonic devices}, volume = {194}, booktitle = {Semiconductor Nanophotonics}, editor = {Kneissl, Michael and Knorr, Andreas and Reitzenstein, Stephan and Hoffmann, Axel}, publisher = {Springer}, address = {Cham}, doi = {10.1007/978-3-030-35656-9_7}, pages = {241 -- 283}, year = {2020}, language = {en} } @inproceedings{HiremathZschiedrichBurgeretal.2014, author = {Hiremath, Kirankumar and Zschiedrich, Lin and Burger, Sven and Schmidt, Frank}, title = {Finite elements based numerical solution of nonlocal hydrodynamic Drude model of nano-plasmonic scatterers}, booktitle = {12th International Conference on Fiber Optics and Photonics}, doi = {10.1364/PHOTONICS.2014.M3D.4}, pages = {M3D.4}, year = {2014}, language = {en} } @misc{DeuflhardFrieseSchmidtetal.1996, author = {Deuflhard, Peter and Friese, Tilmann and Schmidt, Frank and M{\"a}rz, Reinhard and Nolting, Hans-Peter}, title = {Effiziente Eigenmodenberechnung f{\"u}r den Entwurf integriert-optischer Chips}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2131}, number = {SC-96-02}, year = {1996}, abstract = {{\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.}, language = {de} } @misc{SchmidtYevick1996, author = {Schmidt, Frank and Yevick, David}, title = {Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2289}, number = {SC-96-17}, year = {1996}, abstract = {We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schr{\"o}dinger-type equations. Our method supplies boundary conditions for the \$\theta\$-family of implicit one-step discretizations of Schr{\"o}dinger'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.}, language = {en} } @misc{SchmidtMaerz1995, author = {Schmidt, Frank and M{\"a}rz, Reinhard}, title = {On the Reference Wave Vector pf Paraxial Helmholtz Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1660}, number = {SC-94-38}, year = {1995}, abstract = {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.}, language = {en} } @misc{DeuflhardSchmidt1993, author = {Deuflhard, Peter and Schmidt, Frank}, title = {Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1205}, number = {SC-93-24}, year = {1993}, abstract = {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 Schr{\"o}dinger'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.}, language = {en} } @misc{Schmidt1991, author = {Schmidt, Frank}, title = {An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-628}, number = {SC-91-12}, year = {1991}, abstract = {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.}, language = {en} } @misc{Schmidt1997, author = {Schmidt, Frank}, title = {Computation of Discrete Transparent Boundary Conditions for the 2D Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3330}, number = {SC-97-64}, year = {1997}, abstract = {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.}, language = {en} }