optical instabilities in a media with quantum inference effects in a micro-ring resonator

We present optical instabilities in a micro-ring resonator filled with media that includes quantum inference effects. the quantum interference effects we consider is a three-level atomic media whose levels are coupled by two laser beams under the λ-type configuration. under fast response conditions, we obtain optical instabilities in an alloptical bistable system and study the dynamics of the instability in the regime gain without inversion, which is due to the existence of the hopf instability in the lower branch of homogeneous stationary state solutions. we also investigated the dynamics of the system under the scan of the control parameter adiabatically, where the temporal oscillations of the intensity are period one, and the phase space of the field is a limit cycle.