  Optomechanical oscillators stand out as high-performance and versatile
candidates for serving as reference clocks in sequential photonic integrated
circuits. Indeed, they have the unique capability of simultaneously generating
mechanical tones and optical signal modulations at frequencies determined by
their geometrical design. In this context, the concept of synchronization
introduces a powerful means to precisely coordinate the dynamics of multiple
oscillators in a controlled manner, thus increasing efficiency and preventing
errors in signal processing photonic systems or communication interfaces. In
this work, we demonstrate the cascaded injection locking of a pair of
silicon-based optomechanical crystal cavities to an external reference signal
that subtly modulates the laser driving one of the oscillators. Both cavities
interact solely through a weak mechanical link, making the extension of this
synchronization mechanism to an increased number of optomechanical oscillators
within a common chip more feasible than relying solely on optical interactions.
Thus, the combination of the obtained results, supported by a numerical model,
with remote optical injection locking schemes discussed in the literature, lays
the groundwork for the distribution of reference signals within large networks
of processing elements in future phonon-photon hybrid circuits.
