Q-switching and harmonic modelocking pulse instabilities of solid-state lasers

Passively modelocked solid-state lasers can exhibit two types of instabilities with very different origins. Near threshold, pulses are prone to the Q-switching instability, where pulse energy shows strong periodic modulation over successive roundtrips. This behaviour disappears as the pump power increases, giving way to the fundamental modelocked state-characterized by a single stable pulse circulating in the cavity. At higher pump levels, this state can become unstable again, leading to the generation of multiple equidistant pulses per roundtrip, forming harmonic modelocking states with 2, 3, …, n pulses. These instabilities critically affect laser performance, especially in systems using slow saturable absorbers, where accurate modelling becomes particularly challenging. Despite their practical relevance, analytical expressions for the boundaries of these instability regimes are scarce. In this work, we derive such expressions from a recently proposed generalization of the Haus master equation, providing a compact framework to describe the onset of both Q-switching (QML) and harmonic modelocking (HML) in passively modelocked solid-state lasers. These results contribute to a deeper understanding of the dynamics involved and offer valuable guidance for experimental design and optimization.