The nature of stimulated Brillouin scattering (SBS) temporal modulatio
ns for a focused beam in a finite-length cell with homogeneous medium
is examined numerically. The finite phonon lifetime produces determini
stic oscillations at the threshold while the inclusion of the random n
oise as an initiation source of SBS leads to stochastic fluctuations i
n Stokes intensity and phase. A unified study of both modulations unde
r different parameters is presented. The results indicate a large usef
ul parameter space for excellent Stokes beam quality.