Optical wave splitting due to transient energy convection between the pump and Stokes waves in stimulated Brillouin scattering

In this paper, we prove theoretically that both the stimulated Stokes scattering and its reverse process can occur simultaneously for the light and acoustic waves at different points of the medium, resulting in transient and alternate energy flow between the pump and Stokes waves in the stimulated Brillouin scattering. Furthermore, it is found that stimulated Stokes scattering and its reverse process will dominate alternately on the whole during the three-wave coupling, but the eventual net energy flow must be from the pump wave to the Stokes wave as a result of the finite lifetime of acoustical phonons. It is also deduced that direction of energy flow between the pump and Stokes waves will turn to the opposite side once any one of the three waves experiences a ${\pi}$-phase shift. Consequently, we present that transient energy convection between the pump and Stokes waves can give rise to optical wave splitting for the output pump and Stokes pulses, and is also responsible for the generation of Brillouin solitons because energy reflux can provide additional dissipation for the Stokes and acoustic waves to achieve the gain-loss balance.