  Stimulated Brillouin scattering (SBS) and Kerr-nonlinear four wave-mixing
(FWM) are among the most important and widely studied nonlinear effects in
optical fibres. At high powers SBS can be cascaded producing multiple Stokes
waves spaced by the Brillouin frequency shift. Here, we investigate the complex
nonlinear interaction of the cascade of Stokes waves, generated in a
Fabry-Perot chalcogenide fibre resonator through the combined action of SBS and
FWM. We demonstrate the existence of parameter regimes, in which pump and
Stokes waves attain a phase-locked steady state. Real-time measurements of 40ps
pulses with 8GHz repetition rate are presented, confirming short-and long-term
stability. Numerical simulations qualitatively agree with experiments and show
the significance of FWM in phase-locking of pump and Stokes waves. Our findings
can be applied for the design of novel picosecond pulse sources with GHz
repetition rate for optical communication systems.
