SBS suppression in fiber amplifiers with a broadband seed

We present a scalar, time-dependent, plane-wave model for stimulated Brillouin scattering (SBS) within a fiber amplifier having a seed linewidth comparable to, or greater than, the Brillouin frequency shift. The broadband model introduces the existence of a backward anti-Stokes wave, in addition to the Stokes wave present in the narrowband model. The model also incorporates a Fresnel reflection within the fiber or at the exit face. In the absence of Fresnel reflections, the SBS threshold increases linearly with seed linewidth, up to linewidths of at least three times the Brillouin frequency shift. In the presence of Fresnel reflections that seed the Stokes wave, the threshold increases sub-linearly, which agrees with previously reported experimental results. For non-zero reflections and modulation formats with very compact spectra, the threshold can decrease with bandwidth in the region 16-24 GHz due to seeding of the Stokes wave.