@incollection{BurgerKloseSchaedleetal.2006, author = {Burger, Sven and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3D photonic crystal structures}, booktitle = {Scientific Computing in Electrical Engineering}, publisher = {Springer Verlag}, doi = {10.1007/978-3-540-32862-9_24}, pages = {169 -- 175}, year = {2006}, language = {en} } @inproceedings{BurgerKleemannZschiedrichetal.2009, author = {Burger, Sven and Kleemann, B. and Zschiedrich, Lin and Schmidt, Frank}, title = {Finite-Element Simulations of Light Propagation through Circular Subwavelength Apertures}, volume = {7366}, booktitle = {Microtechnologies for the New Millenium}, publisher = {Proc. SPIE}, doi = {10.1117/12.822828}, pages = {736621}, year = {2009}, language = {en} } @inproceedings{BurgerKoehleZschiedrichetal.2006, author = {Burger, Sven and K{\"o}hle, Roderick and Zschiedrich, Lin and Nguyen, H. and Schmidt, Frank and M{\"a}rz, Reinhard and N{\"o}lscher, Christoph}, title = {Rigorous Simulation of 3D Masks}, volume = {6349}, booktitle = {Photomask Technology}, editor = {Martin, P. and Naber, R.}, publisher = {Proc. SPIE}, pages = {63494Z}, year = {2006}, language = {en} } @inproceedings{BurgerGutscheHammerschmidtetal.2015, author = {Burger, Sven and Gutsche, Philipp and Hammerschmidt, Martin and Herrmann, Sven and Pomplun, Jan and Schmidt, Frank and Wohlfeil, Benjamin and Zschiedrich, Lin}, title = {Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures}, volume = {9630}, booktitle = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1510.02607}, doi = {10.1117/12.2190119}, pages = {96300S}, year = {2015}, language = {en} } @misc{HammerschmidtHerrmannPomplunetal.2015, author = {Hammerschmidt, Martin and Herrmann, Sven and Pomplun, Jan and Zschiedrich, Lin and Burger, Sven and Schmidt, Frank}, title = {Reduced basis method for Maxwell's equations with resonance phenomena}, volume = {9630}, journal = {Proc. SPIE}, issn = {1438-0064}, doi = {10.1117/12.2190425}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55687}, pages = {96300R}, year = {2015}, abstract = {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.}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2015, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Herrmann, Sven and Schmidt, Frank}, title = {hp-finite element method for simulating light scattering from complex 3D structures}, volume = {9424}, booktitle = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1503.06617}, doi = {10.1117/12.2085795}, pages = {94240Z}, year = {2015}, language = {en} } @misc{HammerschmidtWeiserSantiagoetal.2017, author = {Hammerschmidt, Martin and Weiser, Martin and Santiago, Xavier Garcia and Zschiedrich, Lin and Bodermann, Bernd and Burger, Sven}, title = {Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64704}, year = {2017}, abstract = {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.}, language = {en} } @article{HammerschmidtWeiserSantiagoetal.2017, author = {Hammerschmidt, Martin and Weiser, Martin and Santiago, Xavier Garcia and Zschiedrich, Lin and Bodermann, Bernd and Burger, Sven}, title = {Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion}, volume = {10330}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1707.08467}, doi = {10.1117/12.2270596}, pages = {1033004}, year = {2017}, language = {en} } @misc{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}, issn = {1438-0064}, doi = {10.1117/12.2036346}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50410}, year = {2014}, abstract = {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.}, language = {en} } @misc{AmiranashviliBandelowBlomeetal.2014, author = {Amiranashvili, Shalva and Bandelow, Uwe and Blome, Mark and Burger, Sven and Schmidt, Frank and Schmidt, Kersten and Zschiedrich, Lin}, title = {Nanophotonics and nonlinear fiber optics}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and et al.,}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {257 -- 275}, year = {2014}, language = {en} } @inproceedings{ZschiedrichBlomeGreiner2014, author = {Zschiedrich, Lin and Blome, Therese and Greiner, Horst}, title = {Simulation of advanced OLED light extraction structures with novel FEM methods}, volume = {9137}, booktitle = {Organic Photonics VI}, doi = {10.1117/12.2054146}, pages = {91370O}, year = {2014}, language = {en} } @article{PomplunBurgerZschiedrichetal.2016, author = {Pomplun, Jan and Burger, Sven and Zschiedrich, Lin and Gutsche, Philipp and Schmidt, Frank}, title = {Method for fast computation of angular light scattering spectra from 2D periodic arrays}, volume = {9778}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1603.04169}, doi = {10.1117/12.2219666}, pages = {977839}, year = {2016}, language = {en} } @inproceedings{AbebeGomardZschiedrichetal.2017, author = {Abebe, Muluneh G. and Gomard, Guillaume and Zschiedrich, Lin and Rockstuhl, Carsten and Paetzold, Ulrich W. and Abass, Aimi}, title = {Thermodynamics of Photon Recycling in Four Terminal Perovskite/si Tandem Solar Cells}, booktitle = {Optical Nanostructures and Advanced Materials for Photovoltaics}, doi = {10.1364/PV.2017.PM4A.2}, pages = {PM4A.2}, year = {2017}, language = {en} } @misc{SchmidtFrieseZschiedrichetal.2000, author = {Schmidt, Frank and Friese, Tilmann and Zschiedrich, Lin and Deuflhard, Peter}, title = {Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6228}, number = {00-54}, year = {2000}, abstract = {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.}, language = {en} } @misc{HohageSchmidtZschiedrich2001, author = {Hohage, Thorsten and Schmidt, Frank and Zschiedrich, Lin}, title = {Solving time-harmonic scattering problems based on the condition: Theory}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6279}, number = {01-01}, year = {2001}, abstract = {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.}, language = {en} } @misc{HohageSchmidtZschiedrich2001, author = {Hohage, Thorsten and Schmidt, Frank and Zschiedrich, Lin}, title = {Solving time-harmonic scattering problems based on the pole condition: Convergence of the PML method}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6494}, number = {01-23}, year = {2001}, abstract = {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.}, language = {en} } @misc{HohageSchmidtZschiedrich2002, author = {Hohage, Thorsten and Schmidt, Frank and Zschiedrich, Lin}, title = {A new method for the solution of scattering problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6683}, number = {02-01}, year = {2002}, abstract = {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.}, language = {en} } @misc{RuprechtSchaedleSchmidtetal.2007, author = {Ruprecht, Daniel and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {Transparent boundary conditons for time-dependent problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9558}, number = {07-12}, year = {2007}, abstract = {A new approach to derive transparent boundary conditions (TBCs) for wave, Schr{\"o}dinger, 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 M{\"o}bius 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.}, language = {en} } @inproceedings{MusialZolnaczSrockaetal.2020, author = {Musial, Anna and Zolnacz, Kinga and Srocka, Nicole and Kravets, Oleh and Große, Jan and Schneider, Philipp-Immanuel and Olszewski, Jacek and Poturaj, Krzystof and Wojcik, Grzegorz and Mergo, Pawel and Dybka, Kamil and Dyrkacz, Mariusz and Dlubek, Michal and Rodt, Sven and Burger, Sven and Zschiedrich, Lin and Urbanczyk, Waclaw and Sek, Grzegorz and Reitzenstein, Stephan}, title = {Stand-alone quantum dot-based single-photon source operating at telecommunication wavelengths}, booktitle = {10th International Conference on Spontaneous Coherence in Excitonic Systems ICSCE10}, pages = {39}, year = {2020}, language = {en} } @inproceedings{HammerschmidtZschiedrichSiaudinyteetal.2023, author = {Hammerschmidt, Martin and Zschiedrich, Lin and Siaudinyt{\´e}, Lauryna and Manley, Phillip and Schneider, Philipp-Immanuel and Burger, Sven}, title = {Forward simulation of coherent beams on grating structures for coherent scatterometry}, volume = {PC12619}, booktitle = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/2309.06109}, doi = {10.1117/12.2673231}, pages = {PC1261907}, year = {2023}, language = {en} }