where n RCP (t) and n LCP (t) are the time-dependent photon populations for RCP and LCP states, respectively, and n sp represents the background photon population, mainly contributed by spontaneous emission. In the stimulated emission regime, the lasing photon population is much greater than n sp . These populations are determined by the population inversion N (t) and cavity losses, with the former driven by the pump pulse energy, which we assume follows a Gaussian profile (with a pulse width 5 ns) in the time domain. The rate equations satisfy: