Optimization of phase modulation formats for suppression of stimulated Brillouin scattering in optical fibers

We theoretically investigate nonlinear optimization of periodic phase modulation for suppression of stimulated Brillouin scattering (SBS) in single-mode optical fibers. We use nonlinear multi-parameter Pareto optimization to find modulations that represent the best trade-off between SBS and optical linewidth, as measured by its RMS value. The optimization uses a temporal-amplitude-domain finite-difference Brillouin solver with noise initiation to find the best phase modulation patterns in the presence of coherent so-called cross-interactions. These can be important in short fibers, when the period is large enough to make the frequency-domain separation of the modulated signal comparable to, or smaller than, the Brillouin gain linewidth. We calculate the SBS threshold for the optimized modulation patterns and find that smaller spectral line-spacing improves the SBS threshold for the same linewidth. By contrast, whereas the maximum modulation depth and modulation frequency influences the range of accessible linewidths, they do not significantly alter the threshold for a given linewidth. We investigate the dependence on fiber length and find that while shorter fibers have a higher threshold, the increase is smaller than the often-assumed inverse dependence on length. Furthermore, we find that optimized formats are superior in terms of SBS threshold as well as in terms of linewidth control, compared to random modulation