Q is the quality factor. It is 2pi times the ratio of the stored energy to the dissipated energy per time period. Essentially a measure of gain versus loss. Destroying the Q means creating losses higher than the gain which in our case will not allow the resonator to oscillate. So you have all heard of Q-switching. The AoM or EoM or rotating mirror for a mechanical Q-switch destroys the Q of the cavity not allowing the cavity to oscillate. The medium is pumped and allowed to create a maximum inversion then the Q is restored unleashing all the stored energy in a massive pulse. For our needs we prevent the 1064nm line from oscillating by creating losses higher than the gain.