Interplay between cascaded stimulated Brillouin scattering and four-wave mixing in a fiber Fabry–Perot resonator

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Abstract
I theoretically investigate the simultaneous generation of cascaded stimulated Brillouin scattering (CSBS) and four-wave mixing (FWM) in a fiber Fabry–Perot resonator with reflection mirrors. The coupled-wave equations for a pump, Stokes, and anti-Stokes waves are derived. To discuss the stationary interplay between the two nonlinear processes, I further deduce the coupled-power equations by introducing some approximations into them. I investigate the effect of FWM on CSBS for asymmetric and symmetric resonators by numerically solving the coupled-power equations under the boundary conditions at the two mirrors. Compared with the case without FWM, the FWM process leads to the gradual generation of higher-order Stokes waves, splitting of the intersection of two transmitted or reflected optical powers, and the generation of anti-Stokes waves. The present analysis can well explain an earlier experiment [Opt. Commun. 32, 385 (1980)].