  Flexible control of photons and phonons in silicon nanophotonic waveguides is
a key feature for emerging applications in communications, sensing and quantum
technologies. Strong phonon leakage towards the silica under-cladding hampers
optomechanical interactions in silicon-on-insulator. This limitation has been
circumvented by totally or partially removing the silica under-cladding to form
pedestal or silicon membrane waveguides. Remarkable optomechanical interactions
have been demonstrated in silicon using pedestal strips, membrane ribs, and
photonic/phononic crystal membrane waveguides. Still, the mechanical
frequencies are limited to the 1-5 GHz range. Here, we exploit the periodic
nanostructuration in Si membrane gratings to shape GHz phononic modes and
near-infrared photonic modes, achieving ultrahigh mechanical frequency (10 GHz)
and strong photon-phonon overlap (61.5%) simultaneously. Based on this concept,
we experimentally demonstrate a one-dimension optomechanical micro-resonator
with a high mechanical frequency of 10 GHz and a quality factor of 1000. These
results were obtained at room temperature and ambient conditions with an
intracavity optical power below 1 mW, illustrating the efficient optical
driving of the mechanical mode enabled by the proposed approach.
