Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain

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.