Instabilities for a coherently driven absorber in a ring cavity

The transient behaviour of an absorber coherently driven by an external constant field and placed in a ring cavity, which exhibits a bistable steady state behaviour, is discussed. Propagation effects are fully taken into account in the limit of small transmittivity of the mirrors. Via a linear stability analysis it is proved that a part of the hysteresis cycle which represents the steady state solution is unstable. This fact demonstrates the possibility of self-pulsing behaviour for the transmitted light with a constant incident field