This thesis investigates passively mode-locked semiconductor lasers by numerical methods. The understanding and optimization of such devices is crucial to the advancement of technologies such as optical data communication and dual comb spectroscopy. The focus of the thesis is therefore on the development of efficient numerical models, which are able both to perform larger parameter studies and to provide quantitative predictions. Along with that, visualization and evaluation techniques for the rich spatio-temporal laser dynamics are developed; these facilitate the physical interpretation of the observed features.
The investigations in this thesis revolve around two specific semiconductor devices, namely a monolithically integrated three-section tapered quantum-dot laser and a V-shaped external cavity laser. In both cases, the simulations closely tie in with experimental results, which have been obtained in collaboration with the TU Darmstadt and the ETH Zurich. Based on the successful numerical reproduction of the experimental findings, the emission dynamics of both lasers can be understood in terms of the cavity geometry and the active medium dynamics. The latter, in particular, highlights the value of the developed simulation tools, since the fast charge-carrier dynamics are generally not experimentally accessible during mode-locking operation. Lastly, the numerical models are used to perform laser design explorations and thus to derive recommendations for further optimizations.