An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient

The analysis of steady state Brillouin scattering in a long single mode optical fiber is presented. Meanwhile, an approximate analytical functions of distributed Brillouin scattering and pump wave along the fiber with the fiber attenuation coefficient are obtained for the first time. A comparison is made among the analytical solutions with the attenuation coefficient, the analytical solutions without the attenuation coefficient and the exact numerical solutions. The results show that the analytical solutions with fiber attenuation coefficient are more close to the numerical solutions, which can be used to describe the power distribution of the pump wave and the Stokes wave along the long distance single mode optical fiber accurately.