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Stimulated Brillouin scattering (SBS) is an important nonlinear opticaleffect which can both enable and impede optical processes in guided wavesystems. Highly multi-mode excitation of fibers has been proposed as a novelroute towards efficient suppression of SBS in both active and passive fibers.To study the effects of multimode excitation generally, we develop a theory ofSBS for arbitrary input excitations, fiber cross section geometries andrefractive index profiles. We derive appropriate nonlinear coupled modeequations for the signal and Stokes modal amplitudes starting from vectoroptical and tensor acoustic equations. Using applicable approximations, we findan analytical formula for the SBS (Stokes) gain susceptibility, which takesinto account the vector nature of both optical and acoustic modes exactly. Weshow that upon multimode excitation, the SBS power in each Stokes mode growsexponentially with a growth rate that depends parametrically on thedistribution of power in the signal modes. Specializing to isotropic fibers weare able to define and calculate an effective SBS gain spectrum for any choiceof multimode excitation. The peak value of this gain spectrum determines theSBS threshold, the maximum SBS-limited power that can be sent through thefiber. We show theoretically that peak SBS gain is greatly reduced by highlymultimode excitation due to gain broadening and relatively weaker intermodalSBS gain. We demonstrate that equal excitation of the 160 modes of acommercially available, highly multimode circular step index fiber raises theSBS threshold by a factor of 6.5, and find comparable suppression of SBS insimilar fibers with a D-shaped cross-section.

Theory of Stimulated Brillouin Scattering in Fibers for Highly Multimode Excitations