  We examine the effect of acoustic mode confinement on Stimulated Brillouin
Scattering in optical waveguides that consist of a guiding core embedded in a
solid substrate. We find that SBS can arise due to coupling to acoustic modes
in three different regimes. First, the acoustic modes may be guided by total
internal reflection; in this case the SBS gain depends directly on the degree
of confinement of the acoustic mode in the core, which is in turn determined by
the acoustic V-parameter. Second, the acoustic modes may be leaky, but may
nevertheless have a sufficiently long lifetime to have a large effect on the
SBS gain; the lifetime of acoustic modes in this regime depends not only on the
contrast in acoustic properties between the core and the cladding, but is also
highly dependent on the waveguide dimensions. Finally SBS may occur due to
coupling to free modes, which exist even in the absence of acoustic
confinement; we find that the cumulative effect of coupling to these
non-confined modes results in significant SBS gain. We show how the different
acoustic properties of core and cladding lead to these different regimes, and
discuss the feasibility of SBS experiments using different material systems.
