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Silicon-based stimulated Brillouin scattering (SBS) promotes the on-chip all-optical signal processing network by interfacing silicon photonic and phononic technologies. Controllable and strong Brillouin coupling in silicon is a key requirement for this purpose. Here, we demonstrate traveling-wave forward SBS and Brillouin gain through a class of hybrid photonic-phononic silicon waveguides on the silicon-on-insulator (SOI) platform. This design combines the advantages of a silicon ridge waveguide and phononic crystal slab, allowing the independent control on the confined optical and acoustic modes. The strong and tailorable Brillouin nonlinearity is demonstrated via the heterodyne four-wave mixing spectroscopy. Three-tone gain experiment reveals a small-signal Stokes gain of 0.9 dB in a 1.085 cm length straight waveguide device at moderate pump power. The limiting factors and further improvements of net …