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 - 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 - GEN A1 - Hammerschmidt, Martin A1 - Weiser, Martin A1 - Santiago, Xavier Garcia A1 - Zschiedrich, Lin A1 - Bodermann, Bernd A1 - Burger, Sven T1 - Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion N2 - We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement uncertainties using a Bayesian approach. Further, we discuss the influence of numerical accuracy on the reconstruction result. T3 - ZIB-Report - 17-37 KW - computational metrology KW - optical metrology KW - computational lithography KW - nanolithography KW - finite- element methods KW - nanooptics Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64704 SN - 1438-0064 ER - TY - JOUR A1 - Hammerschmidt, Martin A1 - Weiser, Martin A1 - Santiago, Xavier Garcia A1 - Zschiedrich, Lin A1 - Bodermann, Bernd A1 - Burger, Sven T1 - Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion JF - Proc. SPIE Y1 - 2017 U6 - https://doi.org/10.1117/12.2270596 VL - 10330 SP - 1033004 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 - 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 - Zschiedrich, Lin A1 - Blome, Therese A1 - Greiner, Horst T1 - Simulation of advanced OLED light extraction structures with novel FEM methods T2 - Organic Photonics VI Y1 - 2014 U6 - https://doi.org/10.1117/12.2054146 VL - 9137 SP - 91370O 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 - Abebe, Muluneh G. A1 - Gomard, Guillaume A1 - Zschiedrich, Lin A1 - Rockstuhl, Carsten A1 - Paetzold, Ulrich W. A1 - Abass, Aimi T1 - Thermodynamics of Photon Recycling in Four Terminal Perovskite/si Tandem Solar Cells T2 - Optical Nanostructures and Advanced Materials for Photovoltaics Y1 - 2017 U6 - https://doi.org/10.1364/PV.2017.PM4A.2 SP - PM4A.2 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 - 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 - CHAP A1 - Musial, Anna A1 - Zolnacz, Kinga A1 - Srocka, Nicole A1 - Kravets, Oleh A1 - Große, Jan A1 - Schneider, Philipp-Immanuel A1 - Olszewski, Jacek A1 - Poturaj, Krzystof A1 - Wojcik, Grzegorz A1 - Mergo, Pawel A1 - Dybka, Kamil A1 - Dyrkacz, Mariusz A1 - Dlubek, Michal A1 - Rodt, Sven A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Urbanczyk, Waclaw A1 - Sek, Grzegorz A1 - Reitzenstein, Stephan T1 - Stand-alone quantum dot-based single-photon source operating at telecommunication wavelengths T2 - 10th International Conference on Spontaneous Coherence in Excitonic Systems ICSCE10 Y1 - 2020 SP - 39 ER - TY - CHAP A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Siaudinyté, Lauryna A1 - Manley, Phillip A1 - Schneider, Philipp-Immanuel A1 - Burger, Sven T1 - Forward simulation of coherent beams on grating structures for coherent scatterometry T2 - Proc. SPIE Y1 - 2023 U6 - https://doi.org/10.1117/12.2673231 VL - PC12619 SP - PC1261907 ER -