  Optical-frequency synthesizers are lasers stabilized and programmed from a
microwave clock for applications, especially in fundamental measurements and
spectroscopy, optical-communication links, and precision sensing of numerous
physical effects. In a synthesizer, a frequency comb provides a reference grid
across a broad spectrum and a frequency-tunable laser accomplishes synthesis by
phase-lock to the comb. Optical synthesizers have matured to chip-scale with
integrated photonics, however, the tunable laser and frequency comb
fundamentally constrain the tuning range. Here, we present an optical
synthesizer based on four-wave mixing (FWM) spectral translation of a tunable
laser and a frequency comb. We implement both the spectral translation and the
frequency comb by use of advanced microresonators. The intrinsic energy
conservation of FWM ensures deterministic optical synthesis, and it allows a
nearly arbitrary frequency tuning range by the dependence of resonant FWM on
group-velocity dispersion, temperature, and tunable laser frequency. Moreover,
we take advantage of highly efficient parametric amplification associated with
spectral translation. We operate spectral translation across output ranges up
to 200 THz, and we characterize it through ultraprecise optical-frequency
metrology, demonstrating <0.1 Hz absolute accuracy and a fractional frequency
precision of 4.7x10^(-13) in 1 s measurements. Our experiments introduce
integrated-nonlinear-photonic circuits that enable complex intrinsic
functionalities, such as our approach to optical-frequency synthesis with
nearly limitless bandwidth.
