We develop a theoretical approach to describe stimulated Brillouin scattering (SBS) in Raman-pumped optical fibers. We derive the condition for the SBS threshold as a function of fiber parameters and the input power of forward and/or backward pump. A particular emphasis is given to the effect of the fiber length and unequal absorption coefficients for pump and signal wavelengths on the SBS threshold. Simple, yet accurate, analytical expressions for the SBS threshold in pumped fibers are also obtained. We show that in pumped fibers, the SBS threshold power is inversely proportional to the path-average integral of Raman gain. Validity ranges of derived formulas are considered in detail. The theoretical predictions are verified experimentally. The calculated values of the SBS threshold powers are in a good agreement with the measured threshold power in Raman-pumped dispersion-compensated fibers.
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