The Brillouin fiber amplifier (BFA) has been used in Brillouin optical time and frequency domain analyzer based sensors. For BFA based distributed sensor the optimized working condition is to have the highest Brillouin gain, i.e., highest SNR, which avoids high pump depletion induced gain saturation. We have found that the optimum working condition for distributed sensor system is associated with the stimulated Brillouin scattering (SBS) threshold for BFA, which can be experimentally determined with Stokes power inflexion and/or Stokes spectrum linewidth minimum methods. This threshold depends on both pump and probe power instead of just the pump power as in Brillouin fiber generator (BFG), as well as on sensing length as confirmed by our experimental results and theoretical simulation. This was achieved by introducing the concept of absorption coefficient of the sensing medium defined as the ratio of the total output power to the total input power. We find that the medium absorption is minimized when input Stokes power is an order of magnitude lower than BFA threshold. This minimum is a signature of the balance between maximum Stokes gain and pump depletion which is also the reason why Stokes spectrum linewidth goes through a minimum.
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