Q -switching stability limits of Kerr-lens mode locking

$Q$-switching instability restricts pulse shortening in Kerr-lens mode-locked lasers (KLMLs). However, $Q$-switching suppression in KLMLs has not been discussed to date because of the difficulty of treating the Kerr-lens effect theoretically. We investigated parameter ranges for stable Kerr-lens mode locking (KLM) against $Q$ switching theoretically and experimentally. We found the parameters and ranges required to suppress $Q$ switching in hard- and soft-aperture KLMLs. In soft-aperture KLMLs, both intracavity power and spatial mode matching between a pump beam and a cavity mode were found to be critical. These findings were verified experimentally using an Yb:${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ KLML. Our results provide cavity design criteria for stable KLMLs against $Q$ switching.