Das Thema dieser Arbeit ist eine mögliche Steuerung eines optischen Solitons in nichtlinearen optischen Fasern. Es gelang, die interessierenden Solitonparameter wie Intensität, Dauer und Zeitverschiebung durch die Wechselwirkung mit einer dispersiven Welle geringer Intensität kontrollierbar zu modifizieren. Es wird eine neue analytische Theorie vorgestellt für die Wechselwirkung zwischen Solitonen und dispersiven Wellen, die auf der Kreuzphasenmodulation in nichtlinearen Fasern beruht. Das vorgestellte Modell kombiniert quantenmechnische Streutheorie und eine Erweiterung der Störungstheorie für Solitonen aus der nichtlinearen Optik. Damit wurden folgende neue Ergebnisse erzielt: (1) Die Entwicklung aller Solitonparameter wird korrekt vorhergesagt. Insbesondere wird die mögliche Verstärkung der Solitonamplitude erfolgreich bestimmt. (2) Passende Intervalle der Kontrollparameter, die eine effektive Solitonmanipulation garantieren, können quantitativ bestimmt werden. (3) Der Raman-Effekt wurde in die Modellbeschreibung eingebunden. Die klassische Abschätzung der Eigenfrequenzverschiebung des Solitons durch den Raman-Effekt wurde verbessert und erweitert durch eine neue Relation für den einhergehenden Amplitudenverlust. Weiterhin wurden solche Kontrollpulse bestimmt, die dieser Schwächung des Solitons entgegenwirken. Im Unterschied zu früheren Versuchen liefert die hier entwickelte Modellbeschreibung die passenden Parameterbereiche für eine stabile Auslöschung des Raman-Effektes. (4) Obwohl die Wechselwirkung selbst auf der Kreuzphasenmodulation basiert, spielt der ”self-steepening“- Effekt, der die Bildung von optischen Schocks beschreibt, eine entscheidende Rolle für eine effiziente Veränderung der Solitonparameter. / This work discusses the problem how to control an optical soliton propagating along a non- linear fiber. The approach chosen here is to change soliton delay, duration and intensity in a simple, predictable manner by applying low-intensity velocity-matched dispersive light waves. A new analytic theory of cross-phase modulation interactions of solitons with dispersive control waves is presented which combines quantum mechanical scattering theory, a modified soliton perturbation theory and a multi-scale approach. This led to the following new results: (1) The evolution of all soliton parameters is correctly predicted. In particular the possible amplitude enhancement of solitons is successfully quantified, which could not be obtained by the standard formulation of the soliton perturbation theory. (2) General ranges for control parameters are quantitatively determined, which ensure an effective interaction. (3) The Raman effect is incorporated into the theory. The classical estimation of the Raman self-frequency shift is refined and expanded by a new relation for the amplitude loss arising with the Raman self-frequency shift. Furthermore, control pulses are identified which cancel soliton degradation due to Raman effect. In contrast to previously reported attempts with the interaction scheme under consideration, even parameter ranges are found which lead to a stable cancellation of the Raman effect. (4) New qualitative insights into the underlying process emerged. The prominent role of the self-steepening effect could be isolated. Though the pulse interaction is mediated by cross-phase modulation, the self-steepening effect causes an essential enhancement leading to much stronger changes in soliton parameters.

Recently, a lot of research work has been dedicated toward enhancing performance, reliability and integrity of distributed energy resources that are integrated into distribution networks. The problem of islanding detection and islanding prevention (i.e. anti-islanding) has stimulated a lot of research due to its role in severely compromising the safety of working personnel and resulting in equipment damages. Various Islanding Detection Methods (IDMs) have been developed within the last ten years in anticipation of the tremendous increase in the penetration of Distributed Generation (DG) in distribution system. This work proposes new IDMs that rely on transient and distributed behaviors to improve integrity and performance of DGs while maintaining multi-DG islanding detection capability. In this thesis, the following questions have been addressed: How to utilize the transient behavior arising from an islanding condition to improve detectability and robust performance of IDMs in a distributive manner? How to reduce the negative stability impact of the well-known Sandia Frequency Shift (SFS) IDM while maintaining its islanding detection capability? How to incorporate the perturbations provided by each of DGs in such a way that the negative interference of different IDMs is minimized without the need of any type of communication among the different DGs? It is shown that the proposed techniques are local, scalable and robust against different loading conditions and topology changes. Also, the proposed techniques can successfully distinguish an islanding condition from other disturbances that may occur in power system networks. This work improves the efficiency, reliability and safety of integrated DGs, which presents a necessary advance toward making electric power grids a smart grid.

Since the last few years, the unprecedented growth of communication systems involving the propagation of electromagnetic waves is particularly due to developments in mobile phone technology. The reverberation chamber is a reliable bench-test, enabling the study of the effects of electromagnetic waves on a specific electronic appliance. However, the operating of a reverberation chamber being rather complicated, development of numerical models are of utmost importance to determine the crucial parameters to be considered.This thesis consists in the modelling and the simulation of the operating principles of a reverberation chamber by means of the Finite-Difference Time-Domain method. After a brief study based on field and power measurements performed in a reverberation chamber, the second chapter deals with the different problems encountered during the modelling. The consideration of losses being a very important factor in the operating of the chamber, two methods of implementation of these losses are set out in this chapter. Chapter~3 consists in the analysis of the influence of the stirrer on the first eigenmodes of the chamber; the latter modes can undergo a frequency shift of several MHz. Chapter~4 shows a comparison of results issued from high frequency simulations and theoretical statistical results. The problem of an object placed in the chamber, resulting in a field disturbance is also tackled. Finally, in the fifth chapter, a comparison of statistical results for stirrers having different shapes is set out.

Im Zuge der Miniaturisierung werden mechanische Nichtlinearitäten immer wichtiger für die Auslegung und Optimierung von mikromechanischen Drehratensensoren. Die vorliegende Arbeit beschäftigt sich mit neuen Simulationsmethoden zur Beschreibung dieser mechanischen Nichtlinearitäten. Die Methoden werden mit Benchmark-Simulationen und Messergebnissen validiert. Die Genauigkeit der neuen Simulationsmethoden erlaubt den Einsatz in der Designoptimierung von kommerziellen MEMS Drehratensensoren. / In this thesis, new simulation methods for the mechanical nonlinearities in microelectromechanical gyroscopes are developed and validated with benchmark simulations and experimental results. The benchmark simulations use transient finite element analysis that consider geometric nonlinear effects. Experimental results are from Laser Doppler Vibrometry and electrical measurements on wafer level. Two different simulation methods, the energy- and stiffness-based approach, are compared with respect to numerical performance and accuracy. In order to evaluate these methods, four different mechanical structures are taken into account: a doubly-clamped beam, a gyroscope test structure and two state-of-the-art gyroscopes with 1 and 2 axes. For the accuracy measurement, the simulated frequency shifts of modes are compared to the true frequency shifts that are developed from either benchmark simulation, Laser Doppler Vibrometry or electrical measurement. The presented methods allow to predict the frequency shift of modes accurately and with a minimum of computational cost. Furthermore, the methodologies allow to generate modal reduced order models which are compatible with common model order reduction in the field. This makes it possible to incorporate mechanical nonlinearity in already established reduced order models of gyroscopes. The simulation and modeling strategies are applicable for generic actuated structures that can be also in different fields of study such as the aerospace and earthquake engineering.