 Laser rate equation

A laser rate equation approximates coupled evolution of population inversion and intracavity photon number, including pumping, spontaneous emission, stimulated emission and optical cavity losses. A simple model is $\dot{S}=[g(N)-1/{\tau }_c]S$, $\dot{N}=R_p-N/{\tau }_u-g(N)S$, where compatible normalizations absorb mode-volume factors. Large excess optical gain drives rapid field growth until inversion depletion reduces it below threshold.