Linewidth narrowing in Brillouin lasers: Theoretical analysis

The linewidth narrowing observed in Brillouin fiber ring lasers is studied within the framework of the usual three-wave model of stimulated Brillouin scattering. We show that the phase noise of the pump laser is transferred to the emitted Stokes wave after being strongly reduced and smoothed under the combined influence of the acoustic damping and the cavity feedback. We then derive a simple analytical relation connecting the full width at half maximum of the Stokes linewidth to that of the pump laser.