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Based on the reciprocity theorem, we present a formalism to calculate the power emitted by a dipole source into a particular propagating mode leaving an open optical system. The open system is completely arbitrary and the approach can be used in analytical calculations but may also be combined with numerical electromagnetic solvers to describe the emission of light sources into complex systems. We exemplify the use of the formalism in numerical simulations by analyzing the emission of a dipole that is placed inside a cavity with connected single mode exit waveguide. Additionally, we show at the example of a practical ring resonator system how the approach can be applied to systems that offer multiple electromagnetic energy decay channels. As a consequence of its inherent simplicity and broad applicability, the approach may serve as a powerful and practical tool for engineering light-matter-interaction in a variety of active optical systems.

We consider emitting nanoparticles in dielectric nanocomposites with varying refractive index contrast and geometry. For that we develop a simple and universal method to calculate the emission enhancement in nanocomposites that employs solely the calculation of the effective refractive index and electric field distributions from three quasistatic calculations with orthogonal polarizations. The method is exemplified for dilute nanocomposites without electromagnetic interaction between emitting particles as well as for dense nanocomposites with strong particle interaction. We show that the radiative decay in dielectric nanocomposites is greatly affected by the shape and arrangement of its constituents and give guidelines for larger enhancement.

Good OCR results for historical printings rely on the availability of recognition models trained on diplomatic transcriptions as ground truth, which is both a scarce resource and time-consuming to generate. Instead of having to train a separate model for each historical typeface, we propose a strategy to start from models trained on a combined set of available transcriptions in a variety of fonts. These \emph{mixed models} result in character accuracy rates over 90\% on a test set of printings from the same period of time, but without any representation in the training data, demonstrating the possibility to overcome the typography barrier by generalizing from a few typefaces to a larger set of (similar) fonts in use over a period of time. The output of these mixed models is then used as a baseline to be further improved by both fully automatic methods and semi-automatic methods involving a minimal amount of manual transcriptions. In order to evaluate the recognition quality of each model in a series of models generated during the training process in the absence of any ground truth, we introduce two readily observable quantities that correlate well with true accuracy. These quantities are \emph{mean character confidence C} (as given by the OCR engine OCRopus) and \emph{mean token lexicality L} (a distance measure of OCR tokens from modern wordforms taking historical spelling patterns into account, which can be calculated for any OCR engine). Whereas the fully automatic method is able to improve upon the result of a mixed model by only 1-2 percentage points, already 100-200 hand-corrected lines lead to much better OCR results with character error rates of only a few percent. This procedure minimizes the amount of ground truth production and does not depend on the previous construction of a specific typographic model.