Analytical approach of Brillouin Amplification over threshold

We report on an accurate closed form analytical model for the gain of a Brillouin fiber amplifier that accounts for material loss in the depleted pump regime. We determined the operational model limits with respect to its relevant parameters and pump regimes through both numerical and experimental validation. As such, our results enable accurate performance prediction of Brillouin fiber amplifiers operating in the weak pump, high gain, and saturation regimes alike.