  Cavity optomechanics has become a powerful tool to manipulate mechanical
motion via optical fields. When driving an optomechanical cavity with
blue-detuned laser the mechanical motion is amplified, ultimately resulting in
phonon lasing. In this work, we show that a silicon optomechanical crystal
cavity can be used as an optoelectronic oscillator when driven to the phonon
lasing condition. To this end, we use an optomechanical cavity designed to have
a breathing-like mechanical mode vibrating at $\Omega_{m}/2\pi=$3.897 GHz in a
full phononic bandgap. Our measurements show that the first harmonic displays a
phase noise of -100 dBc/Hz at 100 kHz, which is a considerable value for a free
running oscillator. Stronger blue-detuned driving leads eventually to the
formation of an optomechanical frequency comb, with lines spaced by the
mechanical frequency. We also measure the phase noise for higher-order
harmonics and show that, unlike in Brillouin oscillators, the noise is
increased as corresponding to classical harmonic mixing. Finally, we present
real-time measurements of the comb waveform and show that it can be adjusted to
a theoretical model recently presented. Our results suggest that silicon
optomechanical cavities could be relevant elements in microwave photonics and
optical RF processing, in particular in disciplines requiring low-weight,
compactness and fiber interconnection.
