  Passively mode-locked semiconductor disk lasers have received tremendous
attention from both science and industry. Their relatively inexpensive
production combined with excellent pulse performance and great emission
wavelength flexibility make them suitable laser candidates for applications
ranging from frequency comb tomography to spectroscopy. However, due to the
interaction of the active medium dynamics and the device geometry, emission
instabilities occur at high pump powers and thereby limit their performance
potential. Hence, understanding those instabilities becomes critical for an
optimal laser design. Using a delay-differential equation model, we are able to
detect, understand, and classify three distinct instabilities that limit the
maximum achievable pump power for the fundamental mode-locking state and link
them to characteristic positive net-gain windows. We furthermore derive a
simple analytic approximation in order to quantitatively describe the stability
boundary. Our results enable us to predict the optimal laser cavity
configuration with respect to positive net-gain instabilities and are therefore
of great relevance for the future development of passively mode-locking
semiconductor disk lasers.
