Equations describing the direct relation between laser phase and Stokes light for SBS pumped by phase-modulated laser in optical fibers

Phase modulation is one of the most important methods to increase the threshold of the stimulated Brillouin scattering (SBS) in optical fibers. The mainstream theoretical model used to predict the SBS threshold is the transient three-wave coupling model. However, it is a general model and does not establish a straight relation between the laser phase and the Stokes light. In this paper, undepleted pump approximation is applied to the transient three-wave coupling model. Equations describing the evolution of the Stokes light in both time domain and frequency domain are derived. They establish a direct relation between the laser phase and Stokes light. All terms in the equations have clear physical interpretations. The equations are validated numerically by comparing with the original coupling model as well. It is found that the results match well when the Stokes average reflectivity is not greater than 1% which is usually used to define the SBS threshold.