  We develop a general framework of evaluating the gain coefficient of
Stimulated Brillouin Scattering (SBS) in optical waveguides via the overlap
integral between optical and elastic eigen-modes. We show that spatial symmetry
of the optical force dictates the selection rules of the excitable elastic
modes. By applying this method to a rectangular silicon waveguide, we
demonstrate the spatial distributions of optical force and elastic eigen-modes
jointly determine the magnitude and scaling of SBS gain coefficient in both
forward and backward SBS processes. We further apply this method to inter-modal
SBS process, and demonstrate that the coupling between distinct optical modes
are necessary to excite elastic modes with all possible symmetries.
