Coherent instabilities in random lasers

A numerical study is presented of random lasers as a function of the pumping rate above the threshold for lasing. Depending on the leakiness of the system resonances, which is typically larger in random lasers compared to conventional lasers, we observe that the stationary lasing regime becomes unstable above a second threshold. Coherent instabilities are observed as self pulsation at a single frequency of the output intensity, population inversion, as well as the atomic polarization. We find these Rabi oscillations have the same frequency everywhere in the random laser despite the fact that the field intensity strongly depends on the spatial location.