Optical-frequency synthesizers, which generate frequency-stable light from a single microwave-frequency reference, are revolutionizing ultrafast science and metrology, but their size, power requirement and cost need to be reduced if they are to be more widely used. Integrated-photonics microchips can be used in high-coherence applications, such as data transmission , highly optimized physical sensors and harnessing quantum states , to lower cost and increase efficiency and portability. Here we describe a method for synthesizing the absolute frequency of a lightwave signal, using integrated photonics to create a phase-coherent microwave-to-optical link. We use a heterogeneously integrated III-V/silicon tunable laser, which is guided by nonlinear frequency combs fabricated on separate silicon chips and pumped by off-chip lasers. The laser frequency output of our optical-frequency synthesizer can be programmed by a microwave clock across 4 terahertz near 1,550 nanometres (the telecommunications C-band) with 1 hertz resolution. Our measurements verify that the output of the synthesizer is exceptionally stable across this region (synthesis error of 7.7 × 10 or below). Any application of an optical-frequency source could benefit from the high-precision optical synthesis presented here. Leveraging high-volume semiconductor processing built around advanced materials could allow such low-cost, low-power and compact integrated-photonics devices to be widely used.

The transfer of high-quality time-frequency signals between remote locations underpins a broad range of applications including precision navigation and timing, the new field of clock-based geodesy, long-baseline interferometry, coherent radar arrays, tests of general relativity and fundamental constants, and the future redefinition of the second [1-7]. However, present microwave-based time-frequency transfer [8-10] is inadequate for state-of-the-art optical clocks and oscillators [1,11-15] that have femtosecond-level timing jitter and accuracies below 1E-17; as such, commensurate optically-based transfer methods are needed. While fiber-based optical links have proven suitable [16,17], they are limited to comparisons between fixed sites connected by a specialized bidirectional fiber link. With the exception of tests of the fundamental constants, most applications instead require more flexible connections between remote and possibly portable optical clocks and oscillators. Here we demonstrate optical time-frequency transfer over free-space via a two-way exchange between coherent frequency combs, each phase-locked to the local optical clock or oscillator. We achieve femtosecond-scale timing deviation, a residual instability below 1E-18 at 1000 s and systematic offsets below 4E-19, despite frequent signal fading due to atmospheric turbulence or obstructions across the 2-km link. This free-space transfer would already enable terrestrial links to support clock-based geodesy. If combined with satellite-based free-space optical communications, it provides a path toward global-scale geodesy, high-accuracy time-frequency distribution, satellite-based relativity experiments, and "optical GPS" for precision navigation

We demonstrate coherent dual frequency-comb spectroscopy for detecting variations in greenhouse gases. High signal-to-noise spectra are acquired spanning 5990 to 6260 cm -1 (1600 to 1670 nm) covering ~700 absorption features from CO 2 , CH 4 , H 2 O, HDO, and 13 CO 2 , across a 2-km open-air path. The transmission of each frequency comb tooth is resolved, leading to spectra with <1 kHz frequency accuracy, no instrument lineshape, and a 0.0033-cm -1 point spacing. The fitted path-averaged concentrations and temperature yield dry-air mole fractions. These are compared with a point sensor under well-mixed conditions to evaluate current absorption models for real atmospheres. In heterogeneous conditions, timeresolved data demonstrate tracking of strong variations in mole fractions. A precision of <1 ppm for CO 2 and <3 ppb for CH 4 is achieved in 5 minutes in this initial demonstration. Future portable systems could support regional emissions monitoring and validation of the spectral databases critical to global satellitebased trace gas monitoring.

We describe the design, fabrication, and performance of a self-referenced, optically coherent frequency comb. The system robustness is derived from a combination of an optics package based on polarization-maintaining fiber, saturable absorbers for mode-locking, high signal-to-noise ratio (SNR) detection of the control signals, and digital feedback control for frequency stabilization. The output is phase-coherent over a 1-2 μm octave-spanning spectrum with a pulse repetition rate of ∼200 MHz and a residual pulse-to-pulse timing jitter <3 fs well within the requirements of most frequency-comb applications. Digital control enables phase coherent operation for over 90 h, critical for phase-sensitive applications such as timekeeping. We show that this phase-slip free operation follows the fundamental limit set by the SNR of the control signals. Performance metrics from three nearly identical combs are presented. This laptop-sized comb should enable a wide-range of applications beyond the laboratory.

The use of optical clocks or oscillators in future ultraprecise navigation, gravitational sensing, coherent arrays, and relativity experiments will require time comparison and synchronization over terrestrial or satellite free-space links. Here, we demonstrate full unambiguous synchronization of two optical time scales across a free-space link. The time deviation between synchronized time scales is below 1 fs over durations from 0.1 to 6500 s, despite atmospheric turbulence and kilometer-scale path length variations. Over 2 days, the time wander is 40 fs peak to peak. Our approach relies on the two-way reciprocity of a single-spatial-mode optical link, valid to below 225 attoseconds across a turbulent 4-km path. This femtosecond level of time-frequency transfer should enable optical networks using state-of-the-art optical clocks or oscillators.