Threshold of stimulated Brillouin scattering pumped by a multi-longitudinal mode laser

On the basis of the multi-longitude theory of stimulated Brillouin scattering (SBS), a group of coupling wave equations without limitation to the mode separation of a laser was deduced while the random initial phases of the multi-longitudinal modes were introduced for SBS pumped by a free-operating laser. The dependences of broadband SBS threshold on the bandwidth of the laser, the number of the laser modes, the mode separation of the laser, the linewidth of Brillouin, and the ratio of the SBS interaction length to the laser coherence length were discussed in detail. And the theoretical results were consistent with the experimental results reported.