  Numerous modern technologies are reliant on the low-phase noise and exquisite
timing stability of microwave signals. Substantial progress has been made in
the field of microwave photonics, whereby low noise microwave signals are
generated by the down-conversion of ultra-stable optical references using a
frequency comb. Such systems, however, are constructed with bulk or fiber
optics and are difficult to further reduce in size and power consumption. Our
work addresses this challenge by leveraging advances in integrated photonics to
demonstrate low-noise microwave generation via two-point optical frequency
division. Narrow linewidth self-injection locked integrated lasers are
stabilized to a miniature Fabry-P\'{e}rot cavity, and the frequency gap between
the lasers is divided with an efficient dark-soliton frequency comb. The
stabilized output of the microcomb is photodetected to produce a microwave
signal at 20 GHz with phase noise of -96 dBc/Hz at 100 Hz offset frequency that
decreases to -135 dBc/Hz at 10 kHz offset--values which are unprecedented for
an integrated photonic system. All photonic components can be heterogeneously
integrated on a single chip, providing a significant advance for the
application of photonics to high-precision navigation, communication and timing
systems.
