Instability of Stimulated Brillouin Scattering in a Fiber Ring Resonator

We investigate theoretically the instability of transient stimulated Brillouin scattering (SBS) in a high- finesse fiber ring resonator consisting of a fiber ring and directional coupler. Unlike many reports to date, the linear phase detuning of the cavity is taken into account. It is found that SBS instabilities including the self-pulsing and chaotic behavior can occur even if the length of the fiber resonator is very short. SBS instabilities depend strongly on the linear phase detuning, the input power, and the coupling coefficient of the coupler.