The simultaneous forward and backward stimulated Brillouin scattering (SBS)
of crossed laser beams is studied in detail. Analytical solutions are obta
ined for the linearized equations governing the transient phase of the inst
ability and the nonlinear equations governing the steady state. These solut
ions show that backward SBS dominates the initial evolution of the instabil
ity, whereas forward SBS dominates the steady state. The analysis of this p
aper is verified by numerical simulation [S1063-651X(99)02711-7].