TY - CHAP A1 - Burger, Sven A1 - Lockau, D. A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Finite-element simulations of light propagation through subwavelength apertures in metal films T2 - International Workshop on Optical Waveguide Theory and Numerical Modelling Y1 - 2009 VL - XVIII SP - 59 PB - Fraunhofer Institute for Applied Optics and Precision Engineering ER - TY - CHAP A1 - Burger, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank ED - Bhushan, B. T1 - Finite Element Methods for Computational Nano-optics T2 - Encyclopedia of Nanotechnology Y1 - 2012 U6 - https://doi.org/10.1007/978-90-481-9751-4_17 SP - 837 EP - 843 PB - Springer Netherlands ER - TY - CHAP A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - A fast and efficient Finite-Element Solver for 2D and 3D Photonic Band-Gap Problems T2 - Dig. LEOS/IEEE 2003 Summer Topicals Y1 - 2003 U6 - https://doi.org/10.1109/LEOSST.2003.1224282 SP - 75 ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - 3D FEM Simulations of High-Q Resonances in Photonic Crystal Microcavities T2 - Integrated Photonics Research, Silicon and Nanophotonics Y1 - 2010 U6 - https://doi.org/10.1364/IPRSN.2010.IWB7 SP - IWB7 PB - OSA ER - TY - CHAP A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin ED - Jena, Friedrich-Schiller-Universität T1 - FEM simulation of resonances in low-Q cavities for plasmon lasers T2 - International Workshop on Photonic Nanomaterials Y1 - 2010 SN - 978-3-00-031358-5 SP - 36 ER - TY - CHAP A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Numerical investigation of optical resonances in circular grating resonators T2 - Silicon Photonics V Y1 - 2010 U6 - https://doi.org/10.1117/12.842061 VL - 7606 SP - 760610 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Numerical Investigation of Photonic Crystal Microcavities in Silicon-on-Insulator Waveguides T2 - Photonic and Phononic Crystal Materials and Devices X Y1 - 2010 U6 - https://doi.org/10.1117/12.841867 VL - 7609 SP - 76091Q PB - Proc. SPIE ER - TY - CHAP A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schmidt, Frank A1 - Tyminski, Jacek A1 - Flagello, Donis A1 - Toshiharu, N. T1 - Reduced basis method for source mask optimization T2 - Photomask Technology Y1 - 2010 U6 - https://doi.org/10.1117/12.866101 VL - 7823 SP - 78230E PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Schädle, Achim A1 - Zschiedrich, Lin A1 - Schmidt, Frank ED - Andrews, David L. ED - Nunzi, Jean-Michel ED - Ostendorf, Andreas T1 - Advanced FEM Analysis of Nano-Optical Devices T2 - Nanophotonics Y1 - 2006 U6 - https://doi.org/10.1117/12.662942 VL - 6195 SP - 72 EP - 82 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Klose, Roland A1 - März, Reinhard A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Efficient Finite Element Methods for the Design of Microoptical Components T2 - Proc. Microoptics Conf. 2004 Y1 - 2004 ER - TY - CHAP A1 - Burger, Sven A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin ED - Sidorin, Y. ED - Wächter, Christoph T1 - FEM modelling of 3D photonic crystals and photonic crystal waveguides T2 - Integrated Optics : Devices, Materials and Technologies IX Y1 - 2005 U6 - https://doi.org/10.1117/12.585895 VL - 5728 SP - 164 EP - 173 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3D photonic crystal structures T2 - Scientific Computing in Electrical Engineering Y1 - 2006 U6 - https://doi.org/10.1007/978-3-540-32862-9_24 SP - 169 EP - 175 PB - Springer Verlag ER - TY - CHAP A1 - Burger, Sven A1 - Kleemann, B. A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Finite-Element Simulations of Light Propagation through Circular Subwavelength Apertures T2 - Microtechnologies for the New Millenium Y1 - 2009 U6 - https://doi.org/10.1117/12.822828 VL - 7366 SP - 736621 PB - Proc. SPIE ER - TY - CHAP A1 - Burger, Sven A1 - Köhle, Roderick A1 - Zschiedrich, Lin A1 - Nguyen, H. A1 - Schmidt, Frank A1 - März, Reinhard A1 - Nölscher, Christoph ED - Martin, P. ED - Naber, R. T1 - Rigorous Simulation of 3D Masks T2 - Photomask Technology Y1 - 2006 UR - http://arxiv.org/pdf/physics/0610218 VL - 6349 SP - 63494Z PB - Proc. SPIE ER - TY - CHAP A1 - Deuflhard, Peter A1 - Friese, T. A1 - Schmidt, Frank A1 - März, Reinhard A1 - Nolting, Hans-Peter ED - et al. Hoffmann, K.-H. T1 - Effiziente Eigenmodenberechnung für den Entwurf integriert-optischer Chips T2 - Mathematik - Schlüsseltechnologie für die Zukunft Y1 - 1996 SP - 267 EP - 279 PB - Springer Verlag ER - TY - GEN A1 - Gutsche, Philipp A1 - Judd, Thomas A1 - Schmidt, Frank T1 - A convergence study of different Rigorous Coupled Wave Analysis (RCWA) approaches to time-harmonic electromagnetic scattering problems with applications to nanooptical structures T2 - Verhandlungen der Deutschen Physikalischen Gesellschaft (DPG-Frühjahrstagung Berlin 2014) N2 - Reliable numerical simulations of nano-optical structures are the key for design and pre-fabrication processes in diverse disciplines such as lithography in semiconductor industries, spectroscopy of biological molecules, optimization of quantum dot cavities for single-photon sources, and computation of atomic forces like the Casimir Effect. For these purposes a variety of different methods, e.g. FDTD, FEM and RCWA, are in use. On the one hand, FDTD and FEM are investigated intensively - both in mathematics and numerical experiments - and their approximations and convergence properties are well known. On the other hand, there is a lack of these insights in RCWA. In spite of this, RCWA is commonly used to simulate a wide range of systems. We review historical and modern contributions to convergence improvements with respect to RCWA from the early sugesstions to modern developments. We study the convergence rates of the open-source software S4 and analyze the algorithmic properties in detail. Furthermore, we compare RCWA and FEM simulations for different classes of problems including 1D-binary gratings and 2D-periodic photonic crystals. Y1 - 2014 ER - TY - CHAP A1 - Burger, Sven A1 - Gutsche, Philipp A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank A1 - Wohlfeil, Benjamin A1 - Zschiedrich, Lin T1 - Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures T2 - Proc. SPIE Y1 - 2015 U6 - https://doi.org/10.1117/12.2190119 VL - 9630 SP - 96300S ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schmidt, Frank T1 - Reduced basis method for Maxwell's equations with resonance phenomena T2 - Proc. SPIE N2 - Rigorous optical simulations of 3-dimensional nano-photonic structures are an important tool in the analysis and optimization of scattering properties of nano-photonic devices or parameter reconstruction. To construct geometrically accurate models of complex structured nano-photonic devices the finite element method (FEM) is ideally suited due to its flexibility in the geometrical modeling and superior convergence properties. Reduced order models such as the reduced basis method (RBM) allow to construct self-adaptive, error-controlled, very low dimensional approximations for input-output relationships which can be evaluated orders of magnitude faster than the full model. This is advantageous in applications requiring the solution of Maxwell's equations for multiple parameters or a single parameter but in real time. We present a reduced basis method for 3D Maxwell's equations based on the finite element method which allows variations of geometric as well as material and frequency parameters. We demonstrate accuracy and efficiency of the method for a light scattering problem exhibiting a resonance in the electric field. T3 - ZIB-Report - 15-37 KW - reduced basis method KW - finite element method KW - maxwell equation KW - photonic crystal KW - nano-photonics Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55687 SN - 1438-0064 VL - 9630 SP - 96300R ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Pomplun, Jan A1 - Herrmann, Sven A1 - Schmidt, Frank T1 - hp-finite element method for simulating light scattering from complex 3D structures T2 - Proc. SPIE Y1 - 2015 U6 - https://doi.org/10.1117/12.2085795 VL - 9424 SP - 94240Z ER - TY - JOUR A1 - Shchukin, Vitaly A1 - Ledentsov, Jr., Nikolay A1 - Kropp, Jörg-R. A1 - Steinle, Gunther A1 - Ledentsov, Jr., Nikolay A1 - Burger, Sven A1 - Schmidt, Frank T1 - Single-Mode Vertical Cavity Surface Emitting Laser via Oxide-Aperture-Engineering of Leakage of High Order Transverse Modes JF - IEEE J. Quant. Electron. Y1 - 2014 U6 - https://doi.org/10.1109/JQE.2014.2364544 VL - 50 IS - 12 SP - 990 EP - 995 ER - TY - BOOK A1 - Lavrinenko, Andrei A1 - Laegsgaard, Jesper A1 - Gregersen, Niels A1 - Schmidt, Frank A1 - Soendergaard, Thomas ED - Wyant, James C. T1 - Numerical Methods in Photonics Y1 - 2014 SN - 9781466563889 PB - CRC Press ER - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 -