  Integrated-photonics microchips now enable a range of advanced
functionalities for high-coherence applications such as data transmission,
highly optimized physical sensors, and harnessing quantum states, but with
cost, efficiency, and portability much beyond tabletop experiments. Through
high-volume semiconductor processing built around advanced materials there
exists an opportunity for integrated devices to impact applications cutting
across disciplines of basic science and technology. Here we show how to
synthesize the absolute frequency of a lightwave signal, using integrated
photonics to implement lasers, system interconnects, and nonlinear frequency
comb generation. The laser frequency output of our synthesizer is programmed by
a microwave clock across 4 THz near 1550 nm with 1 Hz resolution and
traceability to the SI second. This is accomplished with a heterogeneously
integrated III/V-Si tunable laser, which is guided by dual
dissipative-Kerr-soliton frequency combs fabricated on silicon chips. Through
out-of-loop measurements of the phase-coherent, microwave-to-optical link, we
verify that the fractional-frequency instability of the integrated photonics
synthesizer matches the $7.0*10^{-13}$ reference-clock instability for a 1
second acquisition, and constrain any synthesis error to $7.7*10^{-15}$ while
stepping the synthesizer across the telecommunication C band. Any application
of an optical frequency source would be enabled by the precision optical
synthesis presented here. Building on the ubiquitous capability in the
microwave domain, our results demonstrate a first path to synthesis with
integrated photonics, leveraging low-cost, low-power, and compact features that
will be critical for its widespread use.
