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.

Laboratory optical atomic clocks achieve remarkable accuracy (now counted to 18 digits or more), opening possibilities to explore fundamental physics and enable new measurements. However, their size and use of bulk components prevent them from being more widely adopted in applications that require precision timing. By leveraging silicon-chip photonics for integration and to reduce component size and complexity, we demonstrate a compact optical-clock architecture. Here a semiconductor laser is stabilized to an optical transition in a microfabricated rubidium vapor cell, and a pair of interlocked Kerr-microresonator frequency combs provide fully coherent optical division of the clock laser to generate an electronic 22 GHz clock signal with a fractional frequency instability of one part in 10 13 . These results demonstrate key concepts of how to use silicon-chip devices in future portable and ultraprecise optical clocks. Main Text:Optical atomic clocks, which rely on high-frequency, narrow-linewidth optical transitions to stabilize a clock laser, outperform their microwave counterparts by several orders of magnitude due to their inherently large quality factors (1). Optical clocks based on laser-cooled and latticetrapped atoms have demonstrated fractional instabilities at the 10 -18 level (2), setting stringent new limits on tests of fundamental physics (3, 4) and may eventually replace microwave clocks in global timekeeping, navigation and the definition of the SI second (5). Despite their excellent performance, optical clocks are almost exclusively operated by metrological institutions and universities due to their large size and complexity.Although significant progress has been made in reducing the size of laser-cooled atomic clocks to fit inside a mobile trailer (6), applications of these clocks are still limited to metrological clock comparisons and precision geodesy (7). In contrast, optical oscillators referenced to thermal atomic or molecular vapors can be realized in small form factors and still reach instabilities below 10 -14 (8,9). A fully integrated optical clock would benefit many of the applications (10) that currently utilize compact or chip-scale (11) microwave atomic clocks but, until recently, techniques for on-chip laser stabilization to atoms (12) and optical frequency division (13) were not available. Here, we propose and demonstrate an architecture for an integrated optical clock, based on an atomic vapor cell implemented on a silicon chip and a

Microresonator frequency combs can be an enabling technology for optical frequency synthesis and timekeeping in low size, weight, and power architectures. Such systems require comb operation in low-noise, phase-coherent states such as solitons, with broad spectral bandwidths (e.g., octave-spanning) for self-referencing to detect the carrier-envelope offset frequency. However, accessing such states is complicated by thermo-optic dispersion. For example, in the Si3N4 platform, precisely dispersion-engineered structures can support broadband operation, but microsecond thermal time constants often require fast pump power or frequency control to stabilize the solitons. In contrast, here we consider how broadband soliton states can be accessed with simple pump laser frequency tuning, at a rate much slower than the thermal dynamics. We demonstrate octave-spanning soliton frequency combs in Si3N4 microresonators, including the generation of a multi-soliton state with a pump power near 40 mW and a single-soliton state with a pump power near 120 mW. We also develop a simplified two-step analysis to explain how these states are accessed without fast control of the pump laser, and outline the required thermal properties for such operation. Our model agrees with experimental results as well as numerical simulations based on a Lugiato-Lefever equation that incorporates thermo-optic dispersion. Moreover, it also explains an experimental observation that a member of an adjacent mode family on the red-detuned side of the pump mode can mitigate the thermal requirements for accessing soliton states.

We present a first implementation of optical-frequency-comb-based rapid trace gas detection in the molecular fingerprint region in the mid-infrared. Near-real-time acquisition of broadband absorption spectra with 0.0056 cm(-1) maximum resolution is demonstrated using a frequency comb Fourier transform spectrometer which operates in the 2100-to-3700-cm(-1) spectral region. We achieve part-per-billion detection limits in 30 seconds of integration time for several important molecules including methane, ethane, isoprene, and nitrous oxide. Our system enables precise concentration measurements even in gas mixtures that exhibit continuous absorption bands, and it allows detection of molecules at levels below the noise floor via simultaneous analysis of multiple spectral features.

We explore the dynamical response of dissipative Kerr solitons to changes in pump power and detuning and show how thermal and nonlinear processes couple these parameters to the frequency-comb degrees of freedom. Our experiments are enabled by a Pound-Drever-Hall (PDH) stabilization approach that provides on-demand, radio-frequency control of the frequency comb. PDH locking not only guides Kerr-soliton formation from a cold microresonator but opens a path to decouple the repetition and carrier-envelope-offset frequencies. In particular, we demonstrate phase stabilization of both Kerr-comb degrees of freedom to a fractional frequency precision below 10^{-16}, compatible with optical-time-keeping technology. Moreover, we investigate the fundamental role that residual laser-resonator detuning noise plays in the spectral purity of microwave generation with Kerr combs.

We present a high bandwidth piezoelectric-actuated mirror for length stabilization of an optical cavity. The actuator displays a transfer function with a flat amplitude response and greater than 135 • phase margin up to 200 kHz, allowing a 180 kHz unity gain frequency to be achieved in a closed servo loop. To the best of our knowledge, this actuator has achieved the largest servo bandwidth for a piezoelectric transducer (PZT). The actuator should be very useful in a wide variety of applications requiring precision control of optical lengths, including laser frequency stabilization, optical interferometers, and optical communications.

The ability to spectrally translate lightwave signals in a compact, low-power platform is at the heart of the promise of nonlinear nanophotonic technologies. For example, a device to link the telecommunications band with visible and short near-infrared wavelengths can enable a connection between high-performance chipintegrated lasers based on scalable nanofabrication technology with atomic systems used for time and frequency metrology. While second-order nonlinear (χ (2) ) systems are the natural approach for bridging such large spectral gaps, here we show that third-order nonlinear (χ (3) ) systems, despite their typically much weaker nonlinear response, can realize spectral translation with unprecedented performance. By combining resonant enhancement with nanophotonic mode engineering in a silicon nitride microring resonator, we demonstrate efficient spectral translation of a continuous-wave signal from the telecom band (≈ 1550 nm) to the visible band (≈ 650 nm) through cavity-enhanced four-wave mixing. We achieve such translation over a wide spectral range >250 THz with a translation efficiency of (30.1 ± 2.8) % and using an ultra-low pump power of (329 ± 13) µW. The translation efficiency projects to (274 ± 28) % at 1 mW and is more than an order of magnitude larger than what has been achieved in current nanophotonic devices.

The on-chip creation of coherent light at visible wavelengths is crucial to field-level deployment of spectroscopy and metrology systems. Although on-chip lasers have been implemented in specific cases, a general solution that is not restricted by limitations of specific gain media has not been reported. Here, we propose creating visible light from an infrared pump by widely-separated optical parametric oscillation (OPO) using silicon nanophotonics. The OPO creates signal and idler light in the 700 nm and 1300 nm bands, respectively, with a 900 nm pump. It operates at a threshold power of (0.9 ± 0.1) mW, over 50× smaller than other widely-separated microcavity OPO works, which have only been reported in the infrared. This low threshold enables direct pumping without need of an intermediate optical amplifier. We further show how the device design can be modified to generate 780 nm and 1500 nm light with a similar power efficiency. Our nanophotonic OPO shows distinct advantages in power efficiency, operation stability, and device scalability, and is a major advance towards flexible on-chip generation of coherent visible light. arXiv:1909.07248v1 [physics.optics]