  In this paper, we explore the spatio-temporal dynamics of spontaneous and
stimulated forward Brillouin scattering. This general treatment incorporates
the optomechanical coupling produced by boundary-induced radiation pressures
(boundary motion) and material-induced electrostrictive forces (photo-elastic
effects), permitting straightforward application to a range of emerging micro-
and nano-scale optomechanical systems. Through a self-consistent fully coupled
nonlinear treatment, developed within a general Hamiltonian framework, we
establish the connection between the power spectral density of spontaneously
scattered light in forward Brillouin interactions and the nonlinear coupling
strength. We show that, in sharp contrast to backward Brillouin scattering,
noise-initiated stimulated forward Brillouin scattering is forbidden in the
majority of experimental systems. In fact, the single-pass gain, which
characterizes the threshold for energy transfer in back-scattering processes,
is negative for a large class of forward Brillouin devices. Beyond this
frequent experimental case, we explore mechanisms for dispersive symmetry
breaking that lead to amplification and dynamics reminiscent of backward
Brillouin scattering.
