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Disk-integrated observations of the Sun provide a unique vantage point to explore stellar activity and its effect on measured radial velocities. Here, we report a new approach for disk-integrated solar spectroscopy and evaluate its capabilities for solar radial velocity measurements. Our approach is based on a near-infrared laser heterodyne radiometer (LHR) combined with an optical frequency comb calibration, and we show that this combination enables precision, disk-integrated solar spectroscopy with high spectral resolution (~800,000), high signal-to-noise ratio (~2,600), and absolute frequency accuracy. We use the comb-calibrated LHR to record spectra of the solar Fe I 1565 nm transition over a six-week period. We show that our measurements reach sub-meter-per-second radial velocity precision over a single day, and we use daily measurements of the absolute line center to assess the long-term stability of the comb-calibrated LHR approach. We use this long-duration dataset to quantify the principal uncertainty sources that impact the measured radial velocities, and we discuss future modifications that can further improve this approach in studies of stellar variability and its impact on radial velocity measurements.

Compact photonic systems that offer high frequency stability and low noise are of increasing importance to applications in precision metrology, quantum computing, communication, and advanced sensing technologies. However, on-chip resonators comprised of dielectrics cannot match the frequency stability and noise characteristics of Fabry-Perot cavities, whose electromagnetic modes live almost entirely in vacuum. In this study, we present a novel strategy to interface micro-fabricated Fabry-Perot cavities with photonic integrated circuits to realize compact, high-performance integrated systems. Using this new integration approach, we demonstrate self-injection locking of an on-chip laser to a milimeter-scale vacuum-gap Fabry-Perot using a circuit interface that transforms the reflected cavity response to enable efficient feedback to the laser. This system achieves a phase noise of -97 dBc/Hz at 10 kHz offset frequency, a fractional frequency stability of 5*10-13 at 10 ms, a 150 Hz 1/pi integral linewidth, and a 35 mHz fundamental linewidth. We also present a complementary integration strategy that utilizes a vertical emission grating coupler and a back-reflection cancellation circuit to realize a fully co-integrated module that effectively redirects the reflected signals and isolates back-reflections with a 10 dB suppression ratio, readily adaptable for on-chip PDH locking. Together, these demonstrations significantly enhance the precision and functionality of RF photonic systems, paving the way for continued advancements in photonic applications.

We introduce a new parallelized approach to photothermal microscopy that utilizes mid-infrared dual-comb lasers, enabling simultaneous measurements at hundreds of wavelengths. This technology allows for high-speed, label-free chemical identification with super-resolution infrared imaging, overcoming the limitations of slow, single-wavelength-laser methods.

A resonant electro-optic (EO) frequency comb is generated through electro-optic modulation of laser light within an optical resonator. Compared to cavity-less EO combs generated in a single pass through a modulator, resonant EO combs can produce broader spectra with lower radio frequency (RF) power and offer a measure of noise filtering beyond the cavity's linewidth. Understanding, measuring, and suppressing the sources of phase noise in resonant EO combs is crucial for their applications in metrology, astrophotonics, optical clock generation, and fiber-optic communication. According to the standard phase noise model of frequency combs, only two variables - the common mode offset and repetition rate phase noise - are needed to fully describe the phase noise of comb lines. However, in this work we demonstrate analytically, numerically, and experimentally that this standard model breaks down for resonant EO combs at short timescales (high frequencies) and under certain comb parameters. Specifically, a third phase noise component emerges. Consequently, resonant EO combs feature qualitatively different phase noise from their cavity-less counterparts and may not exhibit the anticipated noise filtering. A more complete description of the deviations from the standard phase noise model is critical to accurately predict the performance of frequency combs. The description presented here paves the way for improved designs tailored to applications such as super-continuum generation and optical communication.

The search for earth-like exoplanets with the Doppler radial velocity technique is an extremely challenging and multifaceted precision spectroscopy problem. Currently, one of the limiting instrumental factors in reaching the required long-term $10^{-10}$ level of radial velocity precision is the defect-driven sub-pixel quantum efficiency variations in the large-format detector arrays used by precision echelle spectrographs. Tunable frequency comb calibration sources that can fully map the point spread function across a spectrograph's entire bandwidth are necessary for quantifying and correcting these detector artifacts. In this work, we demonstrate a combination of laser frequency and mode spacing control that allows full and deterministic tunability of a 30 GHz electro-optic comb together with its filter cavity. After supercontinuum generation, this gives access to any optical frequency across 700 - 1300 nm. Our specific implementation is intended for the comb deployed at the Habitable Zone Planet Finder spectrograph and its near-infrared Hawaii-2RG array, but the techniques apply to all laser frequency combs used for precision astronomical spectrograph calibration and other applications that require broadband tuning.

Mid-infrared microscopy is an important tool for biological analyses, allowing a direct probe of molecular bonds in their low energy landscape. In addition to the label-free extraction of spectroscopic information, the application of broadband sources can provide a third dimension of chemical specificity. However, to enable widespread deployment, mid-infrared microscopy platforms need to be compact and robust while offering high speed, broad bandwidth and high signal-to-noise ratio (SNR). In this study, we experimentally showcase the integration of a broadband, high-repetition-rate dual-comb spectrometer (DCS) in the mid-infrared range with a scanning microscope. We employ a set of 1-GHz mid-infrared frequency combs, demonstrating their capability for high-speed and broadband hyperspectral imaging of polymers and ovarian tissue. The system covers 1000 $\mathrm{cm^{-1}}$ at $\mathrm{\nu_c=2941 \; cm^{-1}}$ with 12.86 kHz spectra acquisition rate and 5 $\mathrm{\mu m}$ spatial resolution. Taken together, our experiments and analysis elucidate the trade-off between bandwidth and speed in DCS as it relates to microscopy. This provides a roadmap for the future advancement and application of high-repetition-rate DCS hyperspectral imaging.

We demonstrate a vacuum-gap ultrastable optical reference cavity that does not require a vacuum enclosure. Our simple method of optical contact bonding in a vacuum environment allows for cavity operation in air while maintaining vacuum between the cavity mirrors. Vacuum is maintained long term, with no observed degradation in cavity stability for over 1 year after bonding. For a 1550 nm laser stabilized to a 9.7 mL in-vacuum bonded cavity, the measured Allan deviation is $2.4\times 10^{-14}$ at 1 s and its phase noise is thermal-noise-limited from 0.1 Hz to 10 kHz, reaching about -105 dBc/Hz at 10 kHz offset frequency. This represents the highest stability of any oscillator operated without a vacuum enclosure. Furthermore, we demonstrate a 0.5 mL in-vacuum bonded cavity created using microfabricated mirrors and cavity dicing, with phase noise reaching -95 dBc/Hz at 10 kHz offset frequency. By relieving the need for high-vacuum enclosures, we greatly enhance the portability and utility of low noise, compact cavity-stabilized lasers, with applications ranging from environmental sensing to mobile optical clocks to ultralow noise microwave generation.

The detection of light of thermal origin is the principal means by which humanity has learned about our world and the cosmos. In optical astronomy, in particular, direct detection of thermal photons and the resolution of their spectra have enabled discoveries of the broadest scope and impact. Such measurements, however, do not capture the phase of the thermal fields--a parameter that has proven crucial to transformative techniques in radio astronomy such as synthetic aperture imaging. Over the last 25 years, tremendous progress has occurred in laser science, notably in the phase-sensitive, broad bandwidth, high resolution, and traceable spectroscopy enabled by the optical frequency comb. In this work, we directly connect the fields of frequency comb laser spectroscopy and passive optical sensing as applied to astronomy, remote sensing, and atmospheric science. We provide fundamental sensitivity analysis of dual-comb correlation spectroscopy (DCCS), whereby broadband thermal light is measured via interferometry with two optical frequency combs. We define and experimentally verify the sensitivity scaling of DCCS at black body temperatures relevant for astrophysical observations. Moreover, we provide comparison with direct detection techniques and more conventional laser heterodyne radiometry. Our work provides the foundation for future exploration of comb-based broadband synthetic aperture hyperspectral imaging across the infrared and optical spectrum.

Next-generation communications, radar and navigation systems will extend and exploit the higher bandwidth of the millimeter-wave domain for increased communication data rates as well as radar with higher sensitivity and increased spatial resolution. However, realizing these advantages will require the generation of millimeter-wave signals with low phase noise in simple and compact form-factors. The rapidly developing field of photonic integration addresses this challenge and provides a path toward simplified and portable, low-noise mm-wave generation for these applications. We leverage these advances by heterodyning two silicon photonic chip lasers, phase-locked to the same miniature Fabry-Perot (F-P) cavity to demonstrate a simple framework for generating low-noise millimeter-waves with phase noise below the thermal limit of the F-P cavity. Specifically, we generate 94.5 GHz and 118.1 GHz millimeter-wave signals with phase noise of -117 dBc/Hz at 10 kHz offset, decreasing to -120 dBc/Hz at 40 kHz offset, a record low value for such photonic devices. We achieve this with existing technologies that can be integrated into a platform less than $\approx$ 10 mL in volume. Our work illustrates the significant potential and advantages of low size, weight, and power (SWaP) photonic-sourced mm-waves for communications and sensing.

Modern communication, navigation, and radar systems rely on low noise and frequency-agile microwave sources. In this application space, photonic systems provide an attractive alternative to conventional microwave synthesis by leveraging high spectral purity lasers and optical frequency combs to generate microwaves with exceedingly low phase noise. However, these photonic techniques suffer from a lack of frequency tunability, and also have substantial size, weight, and power requirements that largely limit their use to laboratory settings. In this work, we address these shortcomings with a hybrid opto-electronic approach that combines simplified optical frequency division with direct digital synthesis to produce tunable low-phase-noise microwaves across the entire X-band. This results in exceptional phase noise at 10 GHz of -156 dBc/Hz at 10 kHz offset and fractional frequency instability of 1x10^-13 at 0.1 s. Spot tuning away from 10 GHz by 500 MHz, 1 GHz, and 2 GHz, yields phase noise at 10 kHz offset of -150 dBc/Hz, -146 dBc/Hz, and -140 dBc/Hz, respectively. The synthesizer architecture is fully compatible with integrated photonic implementations that will enable a versatile microwave source in a chip-scale package. Together, these advances illustrate an impactful and practical synthesis technique that shares the combined benefits of low timing noise provided by photonics and the frequency agility of established digital synthesis.

Dual-comb spectroscopy in the ultraviolet (UV) and visible would enable broad bandwidth electronic spectroscopy with unprecedented frequency resolution. However, there are significant challenges in generation, detection and processing of dual-comb data that have restricted its progress in this spectral region. In this work, we leverage robust 1550 nm few-cycle pulses to generate frequency combs in the UV-visible. We couple this source to a wavelength multiplexed dual-comb spectrometer and simultaneously retrieve 100 MHz comb-mode-resolved spectra over three distinct harmonics spanning 380-800 nm. The experiments highlight the path to continuous dual-comb coverage spanning 200-750 nm, offering extensive access to electronic transitions in atoms, molecules, and solids.

Photonics offer numerous functionalities that can be used to realize astrophotonic instruments. The most spectacular example to date is the ESO Gravity instrument at the Very Large Telescope in Chile. Integrated astrophotonic devices stand to offer critical advantages for instrument development, including extreme miniaturization, as well as integration, superior thermal and mechanical stabilization owing to the small footprint, and high replicability offering cost savings. Numerous astrophotonic technologies have been developed to address shortcomings of conventional instruments to date, including for example the development of photonic lanterns, complex aperiodic fiber Bragg gratings, complex beam combiners to enable long baseline interferometry, and laser frequency combs for high precision spectral calibration of spectrometers. Despite these successes, the facility implementation of photonic solutions in astronomical instrumentation is currently limited because of (1) low throughputs from coupling to fibers, coupling fibers to chips, propagation and bend losses, device losses, etc, (2) difficulties with scaling to large channel count devices needed for large bandwidths and high resolutions, and (3) efficient integration of photonics with detectors, to name a few. In this roadmap, we identify 24 areas that need further development. We outline the challenges and advances needed across those areas covering design tools, simulation capabilities, fabrication processes, the need for entirely new components, integration and hybridization and the characterization of devices. To realize these advances the astrophotonics community will have to work cooperatively with industrial partners who have more advanced manufacturing capabilities. With the advances described herein, multi-functional instruments will be realized leading to novel observing capabilities for both ground and space platforms.

The fields of precision timekeeping and spectroscopy increasingly rely on optical frequency comb interferometry. However, comb-based measurements are not described by existing quantum theory because they exhibit both large mode mismatch and finite strength local oscillators. To establish this quantum theory, we derive measurement operators for homodyne detection with arbitrary mode overlap. These operators are a combination of quadrature and intensity-like measurements, which inform a filter that maximizes the quadrature measurement signal-to-noise ratio. Furthermore, these operators establish a foundation to extend frequency-comb interferometry to a wide range of scenarios, including metrology with nonclassical states of light.

The unique benefits of Fabry-Pérot resonators as frequency-stable reference cavities and as an efficient interface between atoms and photons make them an indispensable resource for emerging photonic technologies. To bring these performance benefits to next-generation communications, computation, and timekeeping systems, it will be necessary to develop strategies to integrate compact Fabry-Pérot resonators with photonic integrated circuits. In this paper, we demonstrate a novel reflection cancellation circuit that utilizes a numerically optimized multi-port polarization-splitting grating coupler to efficiently interface high-finesse Fabry-Pérot resonators with a silicon photonic circuit. This circuit interface produces spatial separation of the incident and reflected waves, as required for on-chip Pound-Drever-Hall frequency locking, while also suppressing unwanted back reflections from the Fabry-Pérot resonator. Using inverse design principles, we design and fabricate a polarization-splitting grating coupler that achieves 55% coupling efficiency. This design realizes an insertion loss of 5.8 dB for the circuit interface and more than 9 dB of back reflection suppression, and we demonstrate the versatility of this system by using it to interface several reflective off-chip devices.

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-Pérot 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.

Molecular diagnostics are a primary tool of modern chemistry, enabling researchers to map chemical reaction pathways and rates to better design and control chemical systems. Many chemical reactions are complex and fast, and existing diagnostic approaches provide incomplete information. For example, mass spectrometry is optimized to gather snapshots of the presence of many chemical species, while conventional laser spectroscopy can quantify a single chemical species through time. Here we optimize for multiple objectives by introducing a high-speed and broadband, mid-infrared dual frequency comb absorption spectrometer. The optical bandwidth of >1000 cm-1 covers absorption fingerprints of many species with spectral resolution <0.03 cm-1 to accurately discern their absolute quantities. Key to this advance are 1 GHz pulse repetition rate frequency combs covering the 3-5 um region that enable microsecond tracking of fast chemical process dynamics. We demonstrate this system to quantify the abundances and temperatures of each species in the complete reactants-to-products breakdown of 1,3,5-trioxane, which exhibits a formaldehyde decomposition pathway that is critical to modern low temperature combustion systems. By maximizing the number of observed species and improving the accuracy of temperature and concentration measurements, this spectrometer advances understanding of chemical reaction pathways and rates and opens the door for novel developments such as combining high-speed chemistry with machine learning.

We report precision atmospheric spectroscopy of $CO_2$ using a laser heterodyne radiometer (LHR) calibrated with an optical frequency comb. Using the comb-calibrated LHR, we record spectra of atmospheric $CO_2$ near 1572.33 nm with a spectral resolution of 200 MHz using sunlight as a light source. The measured $CO_2$ spectra exhibit frequency shifts by approximately 11 MHz over the course of the five-hour measurement, and we show that these shifts are caused by Doppler effects due to wind along the spectrometer line of sight. The measured frequency shifts are in excellent agreement with an atmospheric model, and we show that our measurements track the wind-induced Doppler shifts with a relative frequency precision of 100 kHz (15 cm/s), equivalent to a fractional precision of a few parts in $10^{10}$. These results demonstrate that frequency-comb-calibrated LHR enables precision velocimetry that can be of use in applications ranging from climate science to astronomy.

We present an in-vacuum bonded, 9.7 mL-volume Fabry-Pérot ultrastable optical reference cavity that operates without a vacuum enclosure. A laser stabilized to the cavity demonstrates low, thermal noise-limited phase noise and 5x10^-14 Allan deviation at 1 second.

The introduction of nonlinear nanophotonic devices to the field of optical frequency comb metrology has enabled new opportunities for low-power and chip-integrated clocks, high-precision frequency synthesis, and broad bandwidth spectroscopy. However, most of these advances remain constrained to the near-infrared region of the spectrum, which has restricted the integration of frequency combs with numerous quantum and atomic systems in the ultraviolet and visible. Here, we overcome this shortcoming with the introduction of multi-segment nanophotonic thin-film lithium niobate (LN) waveguides that combine engineered dispersion and chirped quasi-phase matching for efficient supercontinuum generation via the combination of $\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities. With only 90 pJ of pulse energy at 1550 nm, we achieve gap-free frequency comb coverage spanning 330 to 2400 nm. The conversion efficiency from the near-infrared pump to the UV-Visible region of 350-550 nm is nearly 20%. Harmonic generation via the $\chi^{(2)}$ nonlinearity in the same waveguide directly yields the carrier-envelope offset frequency and a means to verify the comb coherence at wavelengths as short as 350 nm. Our results provide an integrated photonics approach to create visible and UV frequency combs that will impact precision spectroscopy, quantum information processing, and optical clock applications in this important spectral window.

Frequency combs with mode spacing in the range of 10 to 20 gigahertz (GHz) are critical for increasingly important applications such as astronomical spectrograph calibration, high-speed dual-comb spectroscopy, and low-noise microwave generation. While electro-optic modulators and microresonators can provide narrowband comb sources at this repetition rate, a significant remaining challenge is a means to produce pulses with sufficient peak power to initiate nonlinear supercontinuum generation spanning hundreds of terahertz (THz) as required for self-referencing in these applications. Here, we provide a simple, robust, and universal solution to this problem using off-the-shelf polarization-maintaining (PM) amplification and nonlinear fiber components. This fiber-integrated approach for nonlinear temporal compression and supercontinuum generation is demonstrated with a resonant electro-optic frequency comb at 1550 nm. We show how to readily achieve pulses shorter than 60 fs at a repetition rate of 20 GHz and with peak powers in excess of 2 kW. The same technique can be applied to picosecond pulses at 10 GHz to demonstrate temporal compression by a factor of 9x yielding 50 fs pulses with peak power of 5.5 kW. These compressed pulses enable flat supercontinuum generation spanning more than 600 nm after propagation through multi-segment dispersion-tailored anomalous-dispersion highly nonlinear fiber (HNLF) or tantala waveguides. The same 10 GHz source can readily achieve an octave-spanning spectrum for self-referencing in dispersion-engineered silicon nitride waveguides. This simple all-fiber approach to nonlinear spectral broadening fills a critical gap for transforming any narrowband 10 to 20 GHz frequency comb into a broadband spectrum for a wide range of applications that benefit from the high pulse rate and require access to the individual comb modes.

We develop and demonstrate a compact (less than $6$ mL) portable Fabry-Pérot optical reference cavity. A laser locked to the cavity is thermal noise limited at $2\times10^{-14}$ fractional frequency stability. Broadband feedback control with an electro-optic modulator enables near thermal-noise-limited phase noise performance from $1$ Hz to $10$ kHz offset frequencies. The additional low vibration, temperature, and holding force sensitivity of our design makes it well suited for out-of-the-lab applications such as optically derived low noise microwave generation, compact and mobile optical atomic clocks, and environmental sensing through deployed fiber networks.

The possibility of an Earth-Sun analog beyond our solar system is one of the most longstanding questions in science. At present, answering this question embodies an extremely difficult measurement problem that requires multiple coordinated advances in astronomical telescopes, fiber optics, precision spectrographs, large format detector arrays, and advanced data processing. Taken together, addressing this challenge will require the measurement and calibration of shifts in stellar spectra at the 10^-10 level over multi-year periods. The potential for such precision has recently been advanced by the introduction of laser frequency combs (LFCs) to the field of precision astronomical spectroscopy. However, the expense, complexity and lack of full spectral coverage of LFCs has limited their widespread use and ultimate impact. To address this issue, we explore simple and robust white-light-illuminated Fabry-Perot (FP) etalons as spectral calibrators for precise radial velocity measurements. We track the frequencies of up to 13,000 etalon modes of the installed FPs from two state-of-the-art astronomical spectrographs. Combining these measurements with modeling, we trace unexpected chromatic variations of the FP modes to sub-picometer changes in the dielectric layers of the broad bandwidth FP mirrors. This yields the determination of the frequencies of the FP modes with precision approaching 10^-11/day, equivalent to a radial velocity (RV) Doppler shift of 3 mm/s/day. These results represent critical progress in precision RV measurements on two fronts: first, they make FP etalons a more powerful stand-alone calibration tool, and second, they demonstrate the capability of LFCs to extend cm/s level RV measurement precision over periods approaching a year. Together, these advances highlight a path to achieving spectroscopic calibration at levels that will be critical for finding earths like our own.

Non-perturbative and phase-sensitive light-matter interactions have led to the generation of attosecond pulses of light and the control electrical currents on the same timescale. Traditionally, probing these effects via high harmonic generation has involved complicated lasers and apparatuses to generate the few-cycle and high peak power pulses needed to obtain and measure spectra that are sensitive to the phase of the light wave. Instead, we show that nonlinear effects dependent on the carrier-envelope phase can be accessed in solid state crystals with simple low-energy frequency combs that we combine with high-sensitivity demodulation techniques to measure harmonic spectral modulations. Central to this advance is the use of a scalable 100 MHz Erbium-fiber frequency comb at 1550 nm to produce 10 nJ, 20 fs pulses which are focused to the TW/cm2 level. In a single pass through a 500 \mum ZnO crystal this yields harmonic spectra as short as 200 nm. With this system, we introduce a technique of carrier-envelope amplitude modulation spectroscopy (CAMS) and use it to characterize the phase-sensitive modulation of the ultraviolet harmonics with 85 dB signal-to-noise ratio. We further verify the non-perturbative nature of the harmonic generation through polarization gating of the driving pulse to increase the effects of the carrier-envelope phase. Our work demonstrates robust and ultra-sensitive methods for generating and characterizing harmonic generation at 100 MHz rates that should provide advantages in the study of attosecond nonlinear processes in solid state systems. Additionally, as a simple and low-noise frequency comb, this broadband source will be useful for precision dual-comb spectroscopy of a range of physical systems across the ultraviolet and visible spectral regions (200 - 650 nm).

Lasers with hertz-level linewidths on timescales up to seconds are critical for precision metrology, timekeeping, and manipulation of quantum systems. Such frequency stability typically relies on bulk-optic lasers and reference cavities, where increased size is leveraged to improve noise performance, but with the trade-off of cost, hand assembly, and limited application environments. On the other hand, planar waveguide lasers and cavities exploit the benefits of CMOS scalability but are fundamentally limited from achieving hertz-level linewidths at longer times by stochastic noise and thermal sensitivity inherent to the waveguide medium. These physical limits have inhibited the development of compact laser systems with frequency noise required for portable optical clocks that have performance well beyond conventional microwave counterparts. In this work, we break this paradigm to demonstrate a compact, high-coherence laser system at 1548 nm with a 1 s integrated linewidth of 1.1 Hz and fractional frequency instability less than 10$^{-14}$ from 1 ms to 1 s. The frequency noise at 1 Hz offset is suppressed by 11 orders of magnitude from that of the free-running diode laser down to the cavity thermal noise limit near 1 Hz$^2$/Hz, decreasing to 10$^{-3}$ Hz$^2$/Hz at 4 kHz offset. This low noise performance leverages wafer-scale integrated lasers together with an 8 mL vacuum-gap cavity that employs micro-fabricated mirrors with sub-angstrom roughness to yield an optical $Q$ of 11.8 billion. Significantly, all the critical components are lithographically defined on planar substrates and hold the potential for parallel high-volume manufacturing. Consequently, this work provides an important advance towards compact lasers with hertz-level linewidths for applications such as portable optical clocks, low-noise RF photonic oscillators, and related communication and navigation systems.

The Fabry-Pérot resonator is one of the most widely used optical devices, enabling scientific and technological breakthroughs in diverse fields including cavity QED, optical clocks, precision length metrology and spectroscopy. Though resonator designs vary widely, all high-end applications benefit from mirrors with the lowest loss and highest finesse possible. Fabrication of the highest finesse mirrors relies on centuries-old mechanical polishing techniques, which offer losses at the part-per-million (ppm) level. However, no existing fabrication techniques are able to produce high finesse resonators with the large range of mirror geometries needed for scalable quantum devices and next-generation compact atomic clocks. In this paper, we introduce a new and scalable approach to fabricate mirrors with ultrahigh finesse ($\geq 10^{6}$) and user-defined radius of curvature spanning four orders of magnitude ($10^{-4}-10^{0}$ m). We employ photoresist reflow and reactive ion etching to shape and transfer mirror templates onto a substrate while maintaining sub-Angstrom roughness. This substrate is coated with a dielectric stack and used to create arrays of compact Fabry-Pérot resonators with finesse values as high as 1.3 million and measured excess loss $<$ 1 ppm. Optical ringdown measurements of 43 devices across 5 substrates reveal that the fabricated cavity mirrors -- with both small and large radii of curvature -- produce an average coating-limited finesse of 1.05 million. This versatile new approach opens the door to scalable fabrication of high-finesse miniaturized Fabry-Pérot cavities needed for emerging quantum optics and frequency metrology technologies.

Lasers stabilized to vacuum-gap Fabry-Pérot optical reference cavities display extraordinarily low noise and high stability, with linewidths much less than 1 Hz. These lasers can expand into new applications and ubiquitous use with the development of compact, portable cavities that are manufacturable at scale. Here we demonstrate an 8 mL volume Fabry-Pérot cavity constructed with mirrors that are fabricated lithographically with finesse near 1 million. A laser locked to the cavity exhibits phase noise limited by the cavity thermal noise for offset frequencies ranging from 1 Hz to $\approx$ 1 kHz, with a fractional frequency stability of 7$\times$10$^{-15}$ at 1 second. Furthermore, the use of microfabricated mirrors allows us to expand the design space of centimeter-scale cavities, and we explore the noise implications of pushing towards cavity volumes of 2 mL or less.

Mid-infrared (MIR) spectrometers are invaluable tools for molecular fingerprinting and hyper-spectral imaging. Among the available spectroscopic approaches, GHz MIR dual-comb absorption spectrometers have the potential to simultaneously combine the high-speed, high spectral resolution, and broad optical bandwidth needed to accurately study complex, transient events in chemistry, combustion, and microscopy. However, such a spectrometer has not yet been demonstrated due to the lack of GHz MIR frequency combs with broad and full spectral coverage. Here, we introduce the first broadband MIR frequency comb laser platform at 1 GHz repetition rate that achieves spectral coverage from 3 to 13 \mum. This frequency comb is based on a commercially available 1.56 \mum mode-locked laser, robust all-fiber Er amplifiers and intra-pulse difference frequency generation (IP-DFG) of few-cycle pulses in ḩi(2) nonlinear crystals. When used in a dual comb spectroscopy (DCS) configuration, this source will simultaneously enable measurements with \mus time resolution, 1 GHz (0.03 cm-1) spectral point spacing and a full bandwidth of >5 THz (>166 cm-1) anywhere within the MIR atmospheric windows. This represents a unique spectroscopic resource for characterizing fast and non-repetitive events that are currently inaccessible with other sources.

Precision laser spectroscopy is key to many developments in atomic and molecular physics and the advancement of related technologies such as atomic clocks and sensors. However, in important spectroscopic scenarios, such as astronomy and remote sensing, the light is of thermal origin and interferometric or diffractive spectrometers typically replace laser spectroscopy. In this work, we employ laser-based heterodyne radiometry to measure incoherent light sources in the near-infrared and introduce techniques for absolute frequency calibration with a laser frequency comb. Measuring the solar continuum, we obtain a signal-to-noise ratio that matches the fundamental quantum-limited prediction given by the thermal photon distribution and our system's efficiency, bandwidth, and averaging time. With resolving power R~1,000,000 we determine the center frequency of an iron line in the solar spectrum to sub-MHz absolute frequency uncertainty in under 10 minutes, a fractional precision 1/4000 the linewidth. Additionally, we propose concepts that take advantage of refractive beam shaping to decrease the effects of pointing instabilities by 100x, and of frequency comb multiplexing to increase data acquisition rates and spectral bandwidths by comparable factors. Taken together, our work brings the power of telecommunications photonics and the precision of frequency comb metrology to laser heterodyne radiometry, with implications for solar and astronomical spectroscopy, remote sensing, and precise Doppler velocimetry.

Single-cycle pulses with deterministic carrier-envelope phase enable the study and control of light-matter interactions at the sub-cycle timescale, as well as the efficient generation of low-noise multi-octave frequency combs. However, current single-cycle light sources are difficult to implement and operate, hindering their application and accessibility in a wider range of research. In this paper, we present a single-cycle 100 MHz frequency comb in a compact, turn-key, and reliable all-silica-fiber format. This is achieved by amplifying 2 $\mu$m seed pulses in heavily-doped Tm:fiber, followed by cascaded self-compression to yield 6.8 fs pulses with 215 kW peak power and 374 mW average power. The corresponding spectrum covers more than two octaves, from below 700 nm up to 3500 nm. Driven by this single-cycle pump, supercontinuum with 180 mW of integrated power and a smooth spectral amplitude between 2100 and 2700 nm is generated directly in silica fibers. To broaden applications,few-cycle pulses extending from 6 $\mu$m to beyond 22 $\mu$m with long-term stable carrier-envelope phase are created using intra-pulse difference frequency, and electro-optic sampling yields comb-tooth-resolved spectra. Our work demonstrates the first all-fiber configuration that generates single-cycle pulses, and provides a practical source to study nonlinear optics on the same timescale.

High-harmonic generation (HHG) provides short-wavelength light that is useful for precision spectroscopy and probing ultrafast dynamics. We report efficient, phase-coherent harmonic generation up to 9th-order (333 nm) in chirped periodically poled lithium niobate waveguides driven by phase-stable $\leq$12-nJ, 100 fs pulses at 3 $\mu$m with 100 MHz repetition rate. A mid-infrared to ultraviolet-visible conversion efficiency as high as 10% is observed, amongst an overall 23% conversion of the fundamental to all harmonics. We verify the coherence of the harmonic frequency combs despite the complex highly nonlinear process. Numerical simulations based on a single broadband envelope equation with quadratic nonlinearity give estimates for the conversion efficiency within approximately 1 order of magnitude over a wide range of experimental parameters. From this comparison we identify a dimensionless parameter capturing the competition between three-wave mixing and group-velocity walk-off of the harmonics that governs the cascaded HHG physics. These results can inform cascaded HHG in a range of different platforms.

We use frequency comb-based optical two-way time-frequency transfer (O-TWTFT) to measure the optical frequency ratio of state-of-the-art ytterbium and strontium optical atomic clocks separated by a 1.5 km open-air link. Our free-space measurement is compared to a simultaneous measurement acquired via a noise-cancelled fiber link. Despite non-stationary, ps-level time-of-flight variations in the free-space link, ratio measurements obtained from the two links, averaged over 30.5 hours across six days, agree to $6\times10^{-19}$, showing that O-TWTFT can support free-space atomic clock comparisons below the $10^{-18}$ level.

Atomic clocks occupy a unique position in measurement science, exhibiting higher accuracy than any other measurement standard and underpinning six out of seven base units in the SI system. By exploiting higher resonance frequencies, optical atomic clocks now achieve greater stability and lower frequency uncertainty than existing primary standards. Here, we report frequency ratios of the $^{27}$Al$^+$, $^{171}$Yb and $^{87}$Sr optical clocks in Boulder, Colorado, measured across an optical network spanned by both fiber and free-space links. These ratios have been evaluated with measurement uncertainties between $6\times10^{-18}$ and $8\times10^{-18}$, making them the most accurate reported measurements of frequency ratios to date. This represents a critical step towards redefinition of the SI second and future applications such as relativistic geodesy and tests of fundamental physics.

A compact and robust coherent laser light source that provides spectral coverage from the ultraviolet to infrared is desirable for numerous applications, including heterodyne super resolution imaging[1], broadband infrared microscopy[2], protein structure determination[3], and standoff atmospheric trace-gas detection[4]. Addressing these demanding measurement problems, laser frequency combs[5] combine user-defined spectral resolution with sub-femtosecond timing and waveform control to enable new modalities of high-resolution, high-speed, and broadband spectroscopy[6-9]. In this Letter we introduce a scalable source of near-single-cycle, 0.56 MW pulses generated from robust and low-noise erbium fiber (Er:fiber) technology, and we use it to generate a frequency comb that spans six octaves from the ultraviolet (350 nm) to mid-infrared (22500 nm). The high peak power allows us to exploit the second-order nonlinearities in infrared-transparent, nonlinear crystals (LiNbO$_3$, GaSe, and CSP) to provide a robust source of phase-stable infrared ultra-short pulses with simultaneous spectral brightness exceeding that of an infrared synchrotron[10]. Additional cascaded second-order nonlinearities in LiNbO$_3$ lead to comb generation with four octaves of simultaneous coverage (0.350 to 5.6 $\mu$m). With a comb-tooth linewidth of 10 kHz at 193 THz, we realize a notable spectral resolving power exceeding 10$^{10}$ across 0.86 PHz of bandwidth. We anticipate that this compact and accessible technology will open new opportunities for multi-band precision spectroscopy, coherent microscopy, ultra-high sensitivity nanoscopy, astronomical spectroscopy, and precision carrier-envelope phase (CEP) stable strong field phenomena.

We demonstrate mid-infrared (MIR) frequency combs at 10 GHz repetition rate via intra-pulse difference-frequency generation (DFG) in quasi-phase-matched nonlinear media. Few-cycle pump pulses ($\mathbf{\lesssim}$15 fs, 100 pJ) from a near-infrared (NIR) electro-optic frequency comb are provided via nonlinear soliton-like compression in photonic-chip silicon-nitride waveguides. Subsequent intra-pulse DFG in periodically-poled lithium niobate waveguides yields MIR frequency combs in the 3.1--4.1 $\mu$m region, while orientation-patterned gallium phosphide provides coverage across 7--11 $\mu$m. Cascaded second-order nonlinearities simultaneously provide access to the carrier-envelope-offset frequency of the pump source via in-line f-2f nonlinear interferometry. The high-repetition rate MIR frequency combs introduced here can be used for condensed phase spectroscopy and applications such as laser heterodyne radiometry.

Low noise and high repetition rate optical frequency combs are desirable for many applications from timekeeping to precision spectroscopy. For example, gigahertz repetition rate sources greatly increase the acquisition speed of spectra in a dual-comb modality when compared to lower repetition rate sources, while still maintaining sufficient instantaneous resolution to resolve ro-vibrational signatures from molecules in a variety of conditions. In this paper, we present the stabilization and characterization of a turnkey commercial 1~GHz mode-locked laser that operates at telecom wavelengths (1.56 $\mu$m). Fiber amplification and spectral broadening result in the high signal-to-noise ratio detection and stabilization of $\textit{f}_{\textit{ceo}}$ with 438 mrad of residual phase noise (integrated from 10$^2$ to 10$^7$ Hz). Simultaneously, we stabilize the beatnote between the nearest comb mode and a cavity stabilized continuous-wave laser at 1.55 $\mu$m with 41 mrad of residual phase noise (integrated from 10$^2$ to 10$^7$ Hz). This robust, self-referenced comb system is built with off-the-shelf polarization-maintaining fiber components and will be useful for a wide range of low noise frequency comb applications that benefit from the increased repetition rate.

When illuminated by a white light source, the discrete resonances of a Fabry-Perot interferometer (FP) provide a broad bandwidth, comb-like spectrum useful for frequency calibration. We report on the design, construction and laboratory characterization of two planar, passively stabilized, low finesse (~40) FPs spanning 380 nm to 930 nm and 780 nm to 1300 nm, with nominal free spectral ranges of 20 GHz and 30 GHz respectively. These instruments are intended to calibrate astronomical spectrographs in radial velocity searches for extrasolar planets. By tracking the frequency drift of three widely-separated resonances in each FP we measure fractional frequency drift rates as low as 1 x 10^(-10) / day. However we find that the fractional drift rate varies across the three sample wavelengths, such that the drift of two given resonance modes disagrees with the ratio of their mode numbers. We explore possible causes of this behavior, as well as quantify the temperature and optical power sensitivity of the FPs. Our results demonstrate the advancement of Fabry-Perot interferometers as robust and frequency-stable calibrators for astronomical and other broad bandwidth spectroscopy applications, but also highlight the need for chromatic characterization of these systems.

Optical atomic clocks are poised to redefine the SI second, thanks to stability and accuracy more than one hundred times better than the current microwave atomic clock standard. However, the best optical clocks have not seen their performance transferred to the electronic domain, where radar, navigation, communications, and fundamental research rely on less stable microwave sources. By comparing two independent optical-to-electronic signal generators, we demonstrate a 10 GHz microwave signal with phase that exactly tracks that of the optical clock phase from which it is derived, yielding an absolute fractional frequency instability of 1*10-18 in the electronic domain. Such faithful reproduction of the optical clock phase expands the opportunities for optical clocks both technologically and scientifically for time-dissemination, navigation, and long-baseline interferometric imaging.

We report an all-polarization-maintaining fiber optic approach to generating sub-2 cycle pulses at 2 \mum and a corresponding octave-spanning optical frequency comb. Our configuration leverages mature Er:fiber laser technology at 1.5 \mum to provide a seed pulse for a thulium-doped fiber amplifier that outputs 330 mW average power at 100 MHz repetition rate. Following amplification, nonlinear self-compression in fiber decreases the pulse duration to 9.5 fs, or 1.4 optical cycles. Approximately 32 % of the energy sits within the pulse peak, and the polarization extinction ratio is more than 15 dB. The spectrum of the ultrashort pulse spans from 1 \mum to beyond 2.4 \mum and enables direct measurement of the carrier-envelope offset frequency using only 12 mW, or ~3.5 % of the total power. Our approach employs only commercially-available fiber components, resulting in a turnkey amplifier design that is compact, and easy to reproduce in the larger community. Moreover, the overall design and self-compression mechanism are scalable in repetition rate and power. As such, this system should be useful as a robust frequency comb source in the near-infrared or as a pump source to generate mid-infrared frequency combs.

We report on the development of a high-power mid-infrared frequency comb with 100 MHz repetition rate and 100 fs pulse duration. Difference frequency generation is realized between two branches derived from an Er:fiber comb, amplified separately in Yb:fiber and Er:fiber amplifiers. Average powers of 6.7 W and 14.9 W are generated in the 2.9 $\mu$m idler and 1.6 $\mu$m signal, respectively. With high average power, excellent beam quality, and passive carrier-envelope phase stabilization, this light source is a promising platform for generating broadband frequency combs in the far infrared, visible, and deep ultraviolet.

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use generally applicable quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state non-destructively, leaving the molecule ready for further manipulation. We resolve rotational transitions to 11 significant digits and derive the rotational constant of CaH+ to be B_R = 142501777.9(1.7) kHz. Our approach suits a wide range of molecular ions, including polyatomics and species relevant for tests of fundamental physics, chemistry, and astrophysics.

We demonstrate the use of a flexible digital servo system for the optical stabilization of both the repetition rate and carrier-envelope offset frequency of a laser frequency comb. The servo system is based entirely on a low-cost field programmable gate array, simple electronic components, and existing open-source software. Utilizing both slow and fast feedback actuators of a commercial mode-locked laser frequency comb, we maintain cycle-slip free locking of optically-derived beatnotes over a 30 hour period, and measure residual phase noise at or below ~0.1 rad, corresponding to <100 attosecond timing jitter on the optical phase locks. This stability is sufficient for high-precision frequency comb applications, and indicates comparable performance to existing frequency control systems. The modularity of this system allows for it to be easily adapted to suit the servo actuators of a wide variety of laser frequency combs and continuous-wave lasers, reducing cost and complexity barriers, and enabling digital phase control in a wide range of settings.

The microscale integration of mid- and longwave-infrared photonics could enable the development of fieldable, robust chemical sensors, as well as highly efficient infrared frequency converters. However, such technology would be defined by the choice of material platform, which immediately determines the strength and types of optical nonlinearities available, the optical transparency window, modal confinement, and physical robustness. In this work, we demonstrate a new platform, suspended AlGaAs waveguides integrated on silicon, providing excellent performance in all of these metrics. We demonstrate low propagation losses within a span of nearly two octaves (1.26 to 4.6 $\mu$m) with exemplary performance of 0.45 dB/cm at $\lambda = 2.4$ $\mu$m. We exploit the high nonlinearity of this platform to demonstrate 1560 nm-pumped second-harmonic generation and octave-spanning supercontinuum reaching out to 2.3 $\mu$m with 3.4 pJ pump pulse energy. With mid-IR pumping, we generate supercontinuum spanning from 2.3 to 6.5 $\mu$m. Finally, we demonstrate the versatility of the platform with mid-infrared passive devices such as low-loss 10 $\mu$m-radius bends, compact power splitters with 96 $\pm$ 1% efficiency and edge couplers with 3.0 $\pm$ 0.1 dB loss. This platform has strong potential for multi-functional integrated photonic systems in the mid-IR.

We have measured the quadratic Zeeman coefficient for the ${^{1}S_{0} \leftrightarrow {^{3}P_{0}}}$ optical clock transition in $^{27}$Al$^{+}$, $C_{2}=-71.944(24)$~MHz/T$^{2}$, and the unperturbed hyperfine splitting of the $^{25}$Mg$^{+}$ $^{2}S_{1/2}$ ground electronic state, $\Delta W / h = 1~788~762~752.85(13)$~Hz, with improved uncertainties. Both constants are relevant to the evaluation of the $^{27}$Al$^{+}$ quantum-logic clock systematic uncertainty. The measurement of $C_{2}$ is in agreement with a previous measurement and a new calculation at the $1~\sigma$ level. The measurement of $\Delta W$ is in good agreement with a recent measurement and differs from a previously published result by approximately $2\sigma$. With the improved value for $\Delta W$, we deduce an improved value for the nuclear-to-electronic g-factor ratio $g_{I}/g_{J} = 9.299 ~308 ~313(60) \times 10^{-5}$ and the nuclear g-factor for the $^{25}$Mg nucleus $g_{I} = 1.861 ~957 ~82(28) \times 10^{-4}$. Using the values of $C_{2}$ and $\Delta W$ presented here, we derive a quadratic Zeeman shift of the $^{27}$Al$^{+}$ quantum-logic clock of $\Delta \nu / \nu = -(9241.8 \pm 3.7) \times 10^{-19}$, for a bias magnetic field of $B \approx 0.12$~mT.

We present an ultrahigh-$Q$, solid-silica microrod resonator operated under ambient conditions that supports laser-fractional-frequency stabilization to the thermal-noise limit of $3 \times 10^{-13}$ and a linewidth of 62 Hz. We characterize the technical-noise mechanisms for laser stabilization, which contribute significantly less than thermal noise. With fiber photonics, we generate optical and microwave reference signals provided by the microrod modes and the free-spectral range, respectively. Our results suggest the future physical considerations for a miniature, low noise, and robust optical-frequency source.

A time scale is a procedure for accurately and continuously marking the passage of time. It is exemplified by Coordinated Universal Time (UTC), and provides the backbone for critical navigation tools such as the Global Positioning System (GPS). Present time scales employ microwave atomic clocks, whose attributes can be combined and averaged in a manner such that the composite is more stable, accurate, and reliable than the output of any individual clock. Over the past decade, clocks operating at optical frequencies have been introduced which are orders of magnitude more stable than any microwave clock. However, in spite of their great potential, these optical clocks cannot be operated continuously, which makes their use in a time scale problematic. In this paper, we report the development of a hybrid microwave-optical time scale, which only requires the optical clock to run intermittently while relying upon the ensemble of microwave clocks to serve as the flywheel oscillator. The benefit of using clock ensemble as the flywheel oscillator, instead of a single clock, can be understood by the Dick-effect limit. This time scale demonstrates for the first time sub-nanosecond accuracy for a few months, attaining a fractional frequency uncertainty of 1.45*10-16 at 30 days and reaching the 10-17 decade at 50 days, with respect to UTC. This time scale significantly improves the accuracy in timekeeping and could change the existing time-scale architectures.

Beginning with a continuous wave laser at 1064 nm, we generate a 30 GHz electro-optic frequency comb which contains 100 lines spanning 3 THz. The initial comb is subsequently amplified, spectrally broadened in normal dispersion photonic crystal fiber, and then temporally compressed to provide 74 fs pulses with average power of up to 2.6 W. When launched into a second photonic crystal fiber with anomalous dispersion, a supercontinuum spanning 800-1350 nm is generated. Second harmonic generation allows for extension of the 30 GHz comb into the visible, yielding greater than 300 THz of total spectral bandwidth. Such a broad bandwidth, high repetition rate comb is a compelling source for astronomical spectrograph calibration.

The discovery and characterization of exoplanets around nearby stars is driven by profound scientific questions about the uniqueness of Earth and our Solar System, and the conditions under which life could exist elsewhere in our Galaxy. Doppler spectroscopy, or the radial velocity (RV) technique, has been used extensively to identify hundreds of exoplanets, but with notable challenges in detecting terrestrial mass planets orbiting within habitable zones. We describe infrared RV spectroscopy at the 10 m Hobby-Eberly telescope that leverages a 30 GHz electro-optic laser frequency comb with nanophotonic supercontinuum to calibrate the Habitable Zone Planet Finder spectrograph. Demonstrated instrument precision <10 cm/s and stellar RVs approaching 1 m/s open the path to discovery and confirmation of habitable zone planets around M-dwarfs, the most ubiquitous type of stars in our Galaxy.

Microresonator-based soliton frequency combs - microcombs - have recently emerged to offer low-noise, photonic-chip sources for optical measurements. Owing to nonlinear-optical physics, microcombs can be built with various materials and tuned or stabilized with a consistent framework. Some applications require phase stabilization, including optical-frequency synthesis and measurements, optical-frequency division, and optical clocks. Partially stabilized microcombs can also benefit applications, such as oscillators, ranging, dual-comb spectroscopy, wavelength calibration, and optical communications. Broad optical bandwidth, brightness, coherence, and frequency stability have made frequency-comb sources important for studying comb-matter interactions with atoms and molecules. Here, we explore direct microcomb atomic spectroscopy, utilizing a cascaded, two-photon 1529-nm atomic transition of rubidium. Both the microcomb and the atomic vapor are implemented with planar fabrication techniques to support integration. By fine and simultaneous control of the repetition rate and carrier-envelope-offset frequency of the soliton microcomb, we obtain direct sub-Doppler and hyperfine spectroscopy of the $4^2D_{5/2}$ manifold. Moreover, the entire set of microcomb modes are stabilized to this atomic transition, yielding absolute optical-frequency fluctuations of the microcomb at the kilohertz-level over a few seconds and < 1 MHz day-to-day accuracy. Our work demonstrates atomic spectroscopy with microcombs and provides a rubidium-stabilized microcomb laser source, operating across the 1550 nm band for sensing, dimensional metrology, and communication.

Mid-infrared laser frequency combs are compelling sources for precise and sensitive metrology with applications in molecular spectroscopy and spectro-imaging. The infrared atmospheric window between 3-5.5 $\mu$m in particular provides vital information regarding molecular composition. Using a robust, fiber-optic source of few-cycle pulses in the near-infrared, we experimentally demonstrate ultra-broad bandwidth nonlinear phenomena including harmonic and difference frequency generation in a single pass through periodically poled lithium niobate (PPLN). These $\chi^{(2)}$ nonlinear optical processes result in the generation of frequency combs across the mid-infrared atmospheric window which we employ for dual-comb spectroscopy of acetone and carbonyl sulfide with resolution as high as 0.003 cm$^{-1}$. Moreover, cascaded $\chi^{(2)}$ nonlinearities in the same PPLN directly provide the carrier-envelope offset frequency of the near-infrared driving pulse train in a compact geometry.

Kerr microresonators generate interesting and useful fundamental states of electromagnetic radiation through nonlinear interactions of continuous-wave (CW) laser light. Using photonic-integration techniques, functional devices with low noise, small size, low-power consumption, scalable fabrication, and heterogeneous combinations of photonics and electronics can be realized. Kerr solitons, which stably circulate in a Kerr microresonator, have emerged as a source of coherent, ultrafast pulse trains and ultra-broadband optical-frequency combs. Using the f-2f technique, Kerr combs support carrier-envelope-offset phase stabilization for optical synthesis and metrology. In this paper, we introduce a Kerr-microresonator optical clockwork based on optical-frequency division (OFD), which is a powerful technique to transfer the fractional-frequency stability of an optical clock to a lower frequency electronic clock signal. The clockwork presented here is based on a silicon-nitride (Si$_3$N$_4$) microresonator that supports an optical-frequency comb composed of soliton pulses at 1 THz repetition rate. By electro-optic phase modulation of the entire Si$_3$N$_4$ comb, we arbitrarily generate additional CW modes between the Si$_3$N$_4$ comb modes; operationally, this reduces the pulse train repetition frequency and can be used to implement OFD to the microwave domain. Our experiments characterize the residual frequency noise of this Kerr-microresonator clockwork to one part in $10^{17}$, which opens the possibility of using Kerr combs with high performance optical clocks. In addition, the photonic integration and 1 THz resolution of the Si$_3$N$_4$ frequency comb makes it appealing for broadband, low-resolution liquid-phase absorption spectroscopy, which we demonstrate with near infrared measurements of water, lipids, and organic solvents.

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.

Frequency combs based on nonlinear-optical phenomena in integrated photonics are a versatile light source that can explore new applications, including frequency metrology, optical communications, and sensing. We demonstrate robust frequency-control strategies for near-infrared, octave-bandwidth soliton frequency combs, created with nanofabricated silicon-nitride ring resonators. Group-velocity-dispersion engineering allows operation with a 1064 nm pump laser and generation of dual-dispersive-wave frequency combs linking wavelengths between approximately 767 nm and 1556 nm. To tune the mode frequencies of the comb, which are spaced by 1 THz, we design a photonic chip containing 75 ring resonators with systematically varying dimensions and we use 50 $^\circ$C of thermo-optic tuning. This single-chip frequency comb source provides access to every wavelength including those critical for near-infrared atomic spectroscopy of rubidium, potassium, and cesium. To make this possible, solitons are generated consistently from device-to-device across a single chip, using rapid pump frequency sweeps that are provided by an optical modulator.

Molecular spectroscopy in the mid-infrared portion of the electromagnetic spectrum (3--25 um) has been a cornerstone interdisciplinary analytical technique widely adapted across the biological, chemical, and physical sciences. Applications range from understanding mesoscale trends in climate science via atmospheric monitoring to microscopic investigations of cellular biological systems via protein characterization. Here, we present a compact and comprehensive approach to infrared spectroscopy incorporating the development of broadband laser frequency combs across 3--27 um, encompassing the entire mid-infrared, and direct electric-field measurement of the corresponding near single-cycle infrared pulses of light. Utilizing this unified apparatus for high-resolution and accurate frequency comb spectroscopy, we present the infrared spectra of important atmospheric compounds such as ammonia and carbon dioxide in the molecular fingerprint region. To further highlight the ability to study complex biological systems, we present a broadband spectrum of a monoclonal antibody reference material consisting of more than 20,000 atoms. The absorption signature resolves the amide I and II vibrations, providing a means to study secondary structures of proteins. The approach described here, operating at the boundary of ultrafast physics and precision spectroscopy, provides a table-top solution and a widely adaptable technique impacting both applied and fundamental scientific studies.

Analog photonic links require high-fidelity, high-speed optical-to-electrical conversion for applications such as radio-over-fiber, synchronization at kilometer-scale facilities, and low-noise electronic signal generation. Photodetector nonlinearity is a particularly vexing problem, causing signal distortion and excess noise, especially in systems utilizing ultrashort optical pulses. Here we show that photodetectors designed for high power handling and high linearity can perform optical-to-electrical conversion of ultrashort optical pulses with unprecedented linearity over a large photocurrent range. We also show that the broadband, complex impedance of the circuit following the photodiode modifies the linearity significantly. By externally manipulating the circuit impedance, we extend the detector's linear range to higher photocurrents, with over 50 dB rejection of amplitude-to-phase conversion for photocurrents up to 40 mA. This represents a 1000-fold improvement over state-of-the-art photodiodes and significantly extends the attainable microwave power by a factor of four. As such, we eliminate the long-standing requirement in ultrashort pulse detection of precise tuning of the photodiode's operating parameters (average photocurrent, bias voltage or temperature) to coincide with a nonlinearity minimum. These results should also apply more generally to reduce nonlinear distortion in a range of other microwave photonics applications.

We experimentally demonstrate wide-band (>100 THz) frequency down-conversion of near-infrared (NIR) femtosecond-scale pulses from an Er:fiber laser to the mid-infrared (MIR) using four-wave-mixing (FWM) in photonic-chip silicon-nitride waveguides. The engineered dispersion in the nanophotonic geometry, along with the wide transparency range of silicon nitride, enables large-detuning FWM phase-matching and results in tunable MIR from 2.6-3.6 um on a single chip with 100-pJ-scale pump-pulse energies. Additionally, we observe > 20 dB broadband parametric gain for the NIR pulses when the FWM process is operated in a frequency up-conversion configuration. Our results demonstrate how integrated photonic circuits could realize multiple nonlinear optical phenomena on the same chip and lead to engineered synthesis of broadband, tunable, and coherent light across the NIR and MIR wavelength bands from fiber-based pumps.

Modern nonlinear optical materials allow light of one wavelength be efficiently converted into light at another wavelength. However, designing nonlinear optical materials to operate with ultrashort pulses is difficult, because it is necessary to match both the phase velocities and group velocities of the light. Here we show that self-organized nonlinear gratings can be formed with femtosecond pulses propagating through nanophotonic waveguides, providing simultaneous group-velocity matching and quasi-phase-matching for second harmonic generation. We record the first direct microscopy images of photo-induced nonlinear gratings, and demonstrate how these waveguides enable simultaneous $\chi^{(2)}$ and $\chi^{(3)}$ nonlinear processes, which we utilize to stabilize a laser frequency comb. Finally, we derive the equations that govern self-organized grating formation for femtosecond pulses and explain the crucial role of group-velocity matching. In the future, such nanophotonic waveguides could enable scalable, reconfigurable nonlinear optical systems.

We experimentally demonstrate a versatile technique for performing dual-comb interferometry using a single frequency comb. By rapid switching of the repetition rate, the output pulse train can be delayed and heterodyned with itself to produce interferograms. The full speed and resolution of standard dual-comb interferometry is preserved while simultaneously offering a significant experimental simplification and cost savings. We show that this approach is particularly suited for absolute distance metrology due to an extension of the non-ambiguity range as a result of the continuous repetition-rate switching.

Tremendous scientific progress has been achieved through the development of nonlinear integrated photonics. Prominent examples are Kerr-frequency-comb generation in micro-resonators, and supercontinuum generation and frequency conversion in nonlinear photonic waveguides. High conversion efficiency is enabling for applications of nonlinear optics, including such broad directions as high-speed optical signal processing, metrology, and quantum communication and computation. In this work, we demonstrate a gallium-arsenide-on-insulator (GaAs) platform for nonlinear photonics. GaAs has among the highest second- and third-order nonlinear optical coefficients, and use of a silica cladding results in waveguides with a large refractive index contrast and low propagation loss for expanded design of nonlinear processes. By harnessing these properties and developing nanofabrication with GaAs, we report a record normalized second-harmonic efficiency of 13,000% W-1cm-2 at a fundamental wavelength of 2 um. This work paves the way for high performance nonlinear photonic integrated circuits (PICs), which not only can transition advanced functionalities outside the lab through fundamentally reduced power consumption and footprint, but also enables future optical sources and detectors.

We present a hybrid fiber/waveguide design for a 100-MHz frequency comb that is fully self-referenced and temperature controlled with less than 5 W of electrical power. Self-referencing is achieved by supercontinuum generation in a silicon nitride waveguide, which requires much lower pulse energies (~200 pJ) than with highly nonlinear fiber. These low-energy pulses are achieved with an erbium fiber oscillator/amplifier pumped by two 250-mW passively-cooled pump diodes that consume less than 5 W of electrical power. The temperature tuning of the oscillator, necessary to stabilize the repetition rate in the presence of environmental temperature changes, is achieved by resistive heating of a section of gold-palladium-coated fiber within the laser cavity. By heating only the small thermal mass of the fiber, the repetition rate is tuned over 4.2 kHz (corresponding to an effective temperature change of 4.2 \degC) with a fast time constant of 0.5 s, at a low power consumption of 0.077 W/\degC, compared to 2.5 W/\degC in the conventional 200-MHz comb design.

We report and characterize low-temperature, plasma-deposited deuterated silicon nitride thin films for nonlinear integrated photonics. With a peak processing temperature less than 300$^\circ$C, it is back-end compatible with pre-processed CMOS substrates. We achieve microresonators with a quality factor of up to $1.6\times 10^6 $ at 1552 nm, and $>1.2\times 10^6$ throughout $\lambda$ = 1510 -- 1600 nm, without annealing or stress management. We then demonstrate the immediate utility of this platform in nonlinear photonics by generating a 1 THz free spectral range, 900-nm-bandwidth modulation-instability microresonator Kerr comb and octave-spanning, supercontinuum-broadened spectra.

We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-$\chi^{(2)}$ nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive-wave generation in the 2.5--3 $\text{\mu}$m region and intra-pulse difference-frequency generation in the 4--5 $\text{\mu}$m region. By engineering the quasi-phase-matched grating profiles, tunable, narrow-band MIR and broadband MIR spectra are both observed in this geometry. Finally, we perform numerical modeling using a nonlinear envelope equation, which shows good quantitative agreement with the experiment---and can be used to inform waveguide designs to tailor the MIR frequency combs. Our results identify a path to a simple single-branch approach to mid-infrared frequency comb generation in a compact platform using commercial Er:fiber technology.

Detection of weak radial velocity shifts of host stars induced by orbiting planets is an important technique for discovering and characterizing planets beyond our solar system. Optical frequency combs enable calibration of stellar radial velocity shifts at levels required for detection of Earth analogs. A new chip-based device, the Kerr soliton microcomb, has properties ideal for ubiquitous application outside the lab and even in future space-borne instruments. Moreover, microcomb spectra are ideally suited for astronomical spectrograph calibration and eliminate filtering steps required by conventional mode-locked-laser frequency combs. Here, for the calibration of astronomical spectrographs, we demonstrate an atomic/molecular line-referenced, near-infrared soliton microcomb. Efforts to search for the known exoplanet HD 187123b were conducted at the Keck-II telescope as a first in-the-field demonstration of microcombs.

Spectroscopy in the molecular fingerprint spectral region (6.5-20 $\mu$m) yields critical information on material structure for physical, chemical and biological sciences. Despite decades of interest and effort, this portion of the electromagnetic spectrum remains challenging to cover with conventional laser technologies. In this report, we present a simple and robust method for generating super-octave, optical frequency combs in the fingerprint region through intra-pulse difference frequency generation in an orientation-patterned gallium phosphide crystal. We demonstrate the utility of this unique coherent light source for high-precision, dual-comb spectroscopy in methanol and ethanol vapor. These results highlight the potential of laser frequency combs for a wide range of molecular sensing applications, from basic molecular spectroscopy to nanoscopic imaging.

Controlling femtosecond optical pulses with temporal precision better than one cycle of the carrier field has a profound impact on measuring and manipulating interactions between light and matter. We explore pulses that are carved from a continuous-wave laser via electro-optic modulation and realize the regime of sub-cycle optical control without a mode-locked resonator. Our ultrafast source, with a repetition rate of 10 GHz, is derived from an optical-cavity-stabilized laser and a microwave-cavity-stabilized electronic oscillator. Sub-cycle timing jitter of the pulse train is achieved by coherently linking the laser and oscillator through carrier-envelope phase stabilization enabled by a photonic-chip supercontinuum that spans up to 1.9 octaves across the near infrared. Moreover, the techniques we report are relevant for other ultrafast lasers with repetition rates up to 30 GHz and may allow stable few-cycle pulses to be produced by a wider range of sources.

Carrier-envelope phase stabilization of optical pulses enables exquisitely precise measurements by way of direct optical-frequency synthesis, absolute optical-to-microwave phase conversion, and control of ultrafast waveforms. We report such phase stabilization for Kerr-microresonator frequency combs integrated on silicon chips, and verify their fractional-frequency inaccuracy at <3x10-16. Our work introduces an interlocked Kerr-comb configuration comprised of one silicon-nitride and one silica microresonator, which feature nearly harmonic repetition frequencies and can be generated with one laser. These frequency combs support an ultrafast-laser regime with few-optical-cycle, 1-picosecond-period soliton pulses and a total dispersive-wave-enhanced bandwidth of 170 THz, while providing a stable phase-link between the optical and microwave domains. To accommodate low-power and mobile application platforms, our phase-locked frequency-comb system operates with <250 mW of chip-coupled power. Our work establishes Kerr-microresonator combs as a viable technology for applications like optical-atomic timekeeping, optical synthesis, and related directions.

Supercontinuum generation in integrated photonic waveguides is a versatile source of broadband light, and the generated spectrum is largely determined by the phase-matching conditions. Here we show that quasi-phase-matching via periodic modulations of the waveguide structure provides a useful mechanism to control the evolution of ultrafast pulses and the supercontinuum spectrum. We experimentally demonstrate quasi-phase-matched supercontinuum to the TE20 and TE00 waveguide modes, which enhances the intensity of the SCG in specific spectral regions by as much as 20 dB. We utilize higher-order quasi-phase-matching (up to the 16th order) to enhance the intensity in numerous locations across the spectrum. Quasi-phase-matching adds a unique dimension to the design-space for SCG waveguides, allowing the spectrum to be engineered for specific applications.