“…In these equations, optical fibers are seeded with phase-modulated light, and the three-wave interaction among the pump (A L ), the Stokes (A S ), and acoustic (ρ) fields is described as following: www.nature.com/scientificreports www.nature.com/scientificreports/ here γ e is the electrostrictive constant, Г B is the Brillouin bandwidth, Ω B is the resonant acoustic frequency, c is the speed of light, n is the refractive index of fiber, ω is the optical frequency (ω ≈ ω L ≈ ω S ), ω L is the frequency of the pump light, which is the signal light of amplifier, ω S is the frequency of the Stokes light, ρ 0 is the mean density of the fiber medium, ε 0 is the vacuum permittivity, and f is a Gaussian random variable which initiates SBS. These equations can be solved via the initial conditions of the phase modulated pump wave 7,11,12 . When the optical spectrum of the pump laser is modulated to generate a series of equidistant spectral lines, the effective Brillouin gain G eff is expressed as 17 where L eff is the effective length of the fiber; g 0 = γ e 2 ω 2 /ρ 0 nc 3 ν S Г B ; ω L,j = ω L,0 + jΔυ, ω S,j = ω S,0 + jΔυ; ω L,0 is the central frequency of the pump light, Ω a is the frequency of the acoustic wave resonant with the laser mode oscillating at ω L,0 ; I L,m is the intensity of the pump light.…”