 Laser relaxation oscillation

Small perturbations of a class-B laser exchange excitation between the upper-state population and cavity photon number. Linearization about a four-level lasing state gives $\ddot{w}+(r/{\tau }_2)\dot{w}+(r-1)w/({\tau }_c{\tau }_2)=0$. Its damped oscillation frequency is $(2\pi {)}^{-1}\sqrt{(r-1)/({\tau }_c{\tau }_2)-r^2/(4{\tau }_2^2)}$. Long population lifetime compared with photon lifetime permits underdamped relaxation.