Microwave generation and frequency comb in a silicon optomechanical cavity with a full phononic bandgap

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.