  Lasers differ from other light sources in that they are coherent, and their
coherence makes them indispensable to both fundamental research and practical
application. In optomechanical cavities, phonon and photon lasing is
facilitated by the ability of photons and phonons to interact intensively and
excite one another coherently. The lasing linewidths of both phonons and
photons are critical for practical application. However, thus far, these
linewidths have not been explored in detail in cavity optomechanical systems.
This study investigates the underlying dynamics of lasing in optomechanical
cavities and experimentally demonstrates simultaneous photon and phonon lasing
with narrow linewidths in a silicon optomechanical crystal cavity. We find that
the linewidths can be accounted for by two distinct physical mechanisms in two
regimes, namely the normal regime and the reversed regime, where the intrinsic
optical decay rate is either larger or smaller than the intrinsic mechanical
decay rate. In the normal regime, an ultra-narrow spectral linewidth of 5.4 kHz
for phonon lasing at 6.22 GHz can be achieved regardless of the linewidth of
the pump light, while these results are counterintuitively unattainable for
photon lasing in the reversed regime. These results pave the way towards
harnessing the coherence of both photons and phonons in silicon photonic
devices and reshaping their spectra, potentially opening up new technologies in
sensing, metrology, spectroscopy, and signal processing, as well as in
applications requiring sources that offer an ultra-high degree of coherence.
