Theoretical evaluation of the Brillouin threshold and the steady-state Brillouin equations in standard single-mode optical fibers.

We first use the nonlocalized, fluctuating source model for the stimulated Brillouin scattering to get the exact spectrum of the Stokes wave in optical fibers with attenuation loss. A new relation for the evaluation of the critical pump power (or Brillouin threshold) depending on the fiber length is then introduced, which should be more precise than the well-known Smith formula. Furthermore, we give for the first time, to the best of our knowledge, an approximate solution for standard steady-state Brillouin equations, which consists of two simple relations.