Efficient wave-optical simulations for the modeling of micro-optical elements

Modern optical fabrication technologies enable the realization of optical components in between very nanoscopic- and macroscopic scales without symmetries and with extraordinary accuracies. This opens up novel possibilities in the design of modern optical system. Nevertheless, the ability to take direct advantage out of these developments is intrinsically linked to profound numerical simulation tools to analyze, model and design these systems. Consequently, these demands trigger the steady development and improvement of algorithms, which advances the optical design process and therewith the functionality of related devices. It is one aim of this thesis to introduce and to discuss improved numerical techniques to model micro-optical systems. Moreover, it is a second aim of this thesis to also investigate the potential of these improved simulation methodologies to design micro-optical systems. In particular, an illumination concept is introduced, which allows to realize tailored illumination distributions in a highly integrated approach. Finally, it is a third aim of this thesis to use the improved simulation methodologies to solve inverse problems for the characterization of micro-optical components. In particular, the ability to resolve the origin of glass matrix distortions during fiber Bragg grating inscriptions will be discussed. Moreover, a computational sensing concept to characterize optical fibers will be introduced.