Stimulated Brillouin Scattering Model in Multi-Mode Fiber Lasers

A complete theoretical model on the stimulated Brillouin scattering (SBS) for multi-mode fibers (MMF) is developed by solving the optical-acoustic coupling wave equations. It shows that all optical modes of the signal and of SBS are coupling each other through proper acoustic waves. The Brillouin gain spectrum of each optical mode pair is obtained by certain three-wave couplings (optical-acoustic-optical). The model is further coupled with an optical amplification model on the fiber lasers to take the mode competition into account. By applying the model to a large mode-area double cladding fiber, it is found that the multi-acoustic mode combination plays an important role in the SBS coupling between optical higher order modes (HOM). While for double-mode (fundamental mode +HOM) performance, the SBS threshold increases gradually along with the increase of HOM content. It is also found that the SBS process in the fiber amplifiers can be completely different comparing with that of the passive fiber, because the mode competition not only changes the mode contents of the signal power but also influences the initial growth rate of SBS noise. The Al/Ge co-doped MMF is investigated theoretically as well, and is shown to be able to suppress SBS significantly. Finally we compare our model with a SBS experiment for a MMF, main theoretical predictions agree with the experiment well.