Finite Element simulation of radiation losses in photonic crystal fibers

In our work we focus on the accurate computation of light propagation in finite size photonic crystal structures with the finite element method (FEM). We discuss how we utilize numerical concepts like high-order finite elements, transparent boundary conditions and goal-oriented error estimators for adaptive grid refinement in order to compute radiation leakage in photonic crystal fibers and waveguides. Due to the fast convergence of our method we can use it e.g. to optimize the design of photonic crystal structures with respect to geometrical parameters, to minimize radiation losses and to compute attenutation spectra for different geometries

Efficient optimization of hollow-core photonic crystal fiber design using the finite-element method

We employ a finite-element (FE) solver with adaptive grid refinement to model hollow-core photonic crystal fibers (HC-PCFs) whose core is formed from 19 omitted cladding unit cells. We optimize the complete fiber geometry for minimal field intensity at material/air interfaces, which indicates low loss and high damage threshold, using multidimensional optimization. The optimal design shows a 99.8 % power fraction within the air and an overlap with a Gaussian mode of 96.9 %

Route planning with transportation network maps: an eye-tracking study.

Planning routes using transportation network maps is a common task that has received little attention in the literature. Here, we present a novel eye-tracking paradigm to investigate psychological processes and mechanisms involved in such a route planning. In the experiment, participants were first presented with an origin and destination pair before we presented them with fictitious public transportation maps. Their task was to find the connecting route that required the minimum number of transfers. Based on participants' gaze behaviour, each trial was split into two phases: (1) the search for origin and destination phase, i.e., the initial phase of the trial until participants gazed at both origin and destination at least once and (2) the route planning and selection phase. Comparisons of other eye-tracking measures between these phases and the time to complete them, which depended on the complexity of the planning task, suggest that these two phases are indeed distinct and supported by different cognitive processes. For example, participants spent more time attending the centre of the map during the initial search phase, before directing their attention to connecting stations, where transitions between lines were possible. Our results provide novel insights into the psychological processes involved in route planning from maps. The findings are discussed in relation to the current theories of route planning

Multi-dimensional modeling and simulation of semiconductor nanophotonic devices

Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources

Reduzierte Basis Methode für elektromagnetische Streuprobleme

A main objective of numerical analysis and modeling is the simulation of complex technological problems, arising in engineering and natural sciences. Numerical simulations help to understand, design and optimize, or control and characterize systems or components. Usually the behaviour of a system is described by physical quantities like temperature, stress, or electromagnetic fields. These fields are solutions to partial differential equations (PDEs), which are stated on the domain of interest with appropriate boundary conditions. Since in general the analytical solution to a PDE is unavailable, a discretization procedure such as finite element, finite, discontinuous Galerkin, or finite volume method has to be applied. The discretized system is then solved numerically. For real world problems the numerical solution is usually expensive, regarding computational resources and time. Computational times can be of the order of seconds, up to hours and days, and even many problems can not be solved at all with reasonable effort due to their complexity. In engineering applications like optimization or parameter estimation the discretized models have to be solved multiply for different configurations of the system under consideration, for example, regarding geometrical or material parameters. Hence, a large number of solutions for different parameters are required in reasonable time (many-query context), or a single solution has to be computed very fast (real-time context). Even for moderate problems these requirements can often not be met with above discretization methods. In applications usually the output of interest is not the solution of the PDE itself, but some derived quantities. Hence, a method for fast and reliable evaluation of input-output relationships is desirable. The input are, for example, geometrical or material parameters of the system under consideration. The output is given implicitly as a functional of the field variable, which is the solution to the input parameter dependent PDE. The reduced basis method offers a way to construct approximations to such input-output relationships, which can be evaluated very fast. The key is an online-offline decomposition. In a so-called offline phase the reduced model is built self-adaptively. In an actual application (online phase) only the reduced model is solved. Rigorous error estimation techniques allow to control and quantify the accuracy of the approximative reduced model, such that reduced basis solutions are reliable. In the present work we developed efficient techniques for the reduced basis method for electromagnetic scattering problems, with a focus on application to real world nano-optical problems. Especially in the field of a posteriori error estimation and multiple sources, established techniques were found to be infeasible and had to be further developed, in order to treat complex geometries in 2D and 3D and complex sources. Savings of computational costs of several orders of magnitude, could be demonstrated, compared to state-of-the-art methods. In application examples our results showed that the reduced basis method is very well suited for complex engineering tasks like real-time inverse scatterometry, parameter estimation, and design optimization of optical systems.Eine Hauptaufgabe von numerischer Analysis und Modellierung ist die Simulation komplexer technologischer Probleme im ingenieur- und naturwissenschaftlichen Bereich. Simulationen helfen, Systeme oder Komponenten besser zu verstehen, zu designen, zu optimieren oder zu charakterisieren. In vielen Anwendungsfeldern, wie numerischem Design, Parameterrekonstruktion oder bei inversen Problemen werden im Allgemeinen eine Vielzahl von Simulationen eines gegebenen Systems in Abhängigkeit von z.B. Geometrie- oder Materialparametern durchgeführt. Oft besteht dabei Echtzeitanforderung, so dass kurze Rechenzeiten des Vorwärtsproblems unverzichtbar sind. Vor allem für 3D-Probleme sind die Zeiten für die Berechnung einer einzigen Vorwärtslösung dafür jedoch oft zu lang. Thema der vorliegenden Arbeit ist die Reduzierte Basis Methode, die zum Ziel hat, parametrisierte Probleme in obigen Anwendungsfeldern in Echtzeit zu lösen. Die Grundidee besteht darin, den Lösungsprozess in eine langsame Offline- und einen schnelle Online-Phase aufzuspalten. In der Offline-Phase wird das zu Grunde liegende Problem mehrmals rigoros gelöst, wobei längere Rechenzeiten in Kauf genommen werden. Diese Lösungen bilden die Basis eines reduzierten niedrigdimensionalen Systems, das man durch Projektion aus dem ursprünglichen Problem erhält. Im Online-Schritt wird lediglich das reduzierte Problem gelöst. Da die Reduzierte Basis Methode Näherungslösungen liefert, ist es für die Qualität und Verlässlichkeit der Rechnungen von großer Bedeutung, rigorose Fehlerschätzer zu konstruieren. Anwendungsfeld dieser Arbeit ist das Gebiet "Computational Nano-Optics'', das sich mit der Lösung der Maxwellgleichungen in nanostrukturierten Systemen beschäftigt. Speziell werden Streuprobleme auf unbeschränkten, geometrisch parametrisierten 3D-Gebieten betrachtet. Vor allem auf dem Gebiet der a posteriori Fehlerschätzung sind bisherige ``State-of-the-Art'' Reduzierte Basis Methoden aufgrund extrem hohen Aufwands praktisch nicht durchführbar, um komplexe geometrisch parametrisierte Systeme in 2D und 3D zu behandeln. Daher wurde in der vorliegenden Arbeit ein neuer Fehlerschätzer entwickelt, der den Rechen- und Speicheraufwand um mehrere Größenordnungen reduziert. Dieser basiert auf Gebietszerlegungsmethoden, die auch für Fehlerschätzung von Finite Elemente Lösungen verwendet werden. Desweiteren wurde eine neue Technik für die Reduzierte Basis Methode entwickelt, die es erlaubt, die Reaktion von Systemen unter dem Einfluß einer Vielzahl von Quellen extrem effizient zu berechnen. Dies ist eine typische Situation in vielen nanooptischen Anwendungen, z.B. in der Lithographie. Als numerische Beispiele wurde die Optimierung von Photomasken und die inverse Scatterometrie von EUV (extrem ultraviolett) Masken untersucht. Die Arbeiten zur inversen Scatterometrie wurden in Kollaboration mit der Physikalisch-Technischen Bundesanstalt (PTB) am Berliner Elektronensynchrotron BESSY II (experimentelle Messungen) und dem Advanced Mask Technology Center (Herstellung einer EUV Testmaske und Mikroskopie) durchgeführt. Aufgrund der vielversprechenden Ergebnisse wird eine Prototypimplementierung der in dieser Arbeit entwickelten Methoden für die Auswertung von Streuexperimenten an der PTB eingesetzt

Paramilitaarne vägivald kui poliitilise radikaliseerumise toitepinnas? [Paramilitary violence as fodder for political radicalisation?]

I maailmasõja järel Baltikumis võidelnud Saksa vabakorpuste näideThe example of the German Freikorpswhich fought in the Baltic region after WWIThe article discusses the history of the Freikorps (“Free Corps”) formed in Germany after WWI, in a comparative analysis of two Freikorps which were recruited in Germany and fought in the Baltic region, and two Freikorps which only fought in Germany. The article compares the members of those Freikorps – the Baden assault battalion Kurland and the Von Medem Freikorps which fought in the Baltic region and the Würzburg Freikorps and the Haas battalion which operated only in Germany – on the basis of their generational affiliation as well as their subsequent involvement in national socialist organisations. It is concluded that the claims that the Freikorps members who fought in the Baltic region mostly belonged to the “war youth” generation who did not fight in WWI and whose fighting in the Baltic region caused their radicalisation manifested by their higher than average membership in the NSDAP, SS and SA, cannot be corroborated on the basis of the analysed units.KeywordsWWI, Weimar Republic, Freikorps, wars of independence in the Baltic countries, war youth and WWI veterans, national socialist organisations