Theory of Stimulated Brillouin Scattering in Fibers for Highly Multimode Excitations

Stimulated Brillouin scattering (SBS) is an important nonlinear optical effect which can both enable and impede optical processes in guided wave systems. Highly multi-mode excitation of fibers has been proposed as a novel route towards efficient suppression of SBS in both active and passive fibers. To study the effects of multimode excitation generally, we develop a theory of SBS for arbitrary input excitations, fiber cross section geometries and refractive index profiles. We derive appropriate nonlinear coupled mode equations for the signal and Stokes modal amplitudes starting from vector optical and tensor acoustic equations. Using applicable approximations, we find an analytical formula for the SBS (Stokes) gain susceptibility, which takes into account the vector nature of both optical and acoustic modes exactly. We show that upon multimode excitation, the SBS power in each Stokes mode grows exponentially with a growth rate that depends parametrically on the distribution of power in the signal modes. Specializing to isotropic fibers we are able to define and calculate an effective SBS gain spectrum for any choice of multimode excitation. The peak value of this gain spectrum determines the SBS threshold, the maximum SBS-limited power that can be sent through the fiber. We show theoretically that peak SBS gain is greatly reduced by highly multimode excitation due to gain broadening and relatively weaker intermodal SBS gain. We demonstrate that equal excitation of the 160 modes of a commercially available, highly multimode circular step index fiber raises the SBS threshold by a factor of 6.5, and find comparable suppression of SBS in similar fibers with a D-shaped cross-section.