Self-pulsation threshold of Raman amplified Brillouin fiber cavities

An implicit equation for the oscillation threshold of stimulated Brillouin scattering from Raman amplified signals in fibers with external feedback is derived under the assumption of no depletion. This is compared to numerical investigations of Raman amplification schemes showing good agreement for high reflectivities. For low reflectivities and high attenuation or long fibers, the assumption of no depletion is shown not to be valid. In these cases the effects of the depletion on the self-pulsation is examined.