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Optical parametric oscillation in a Kerr nonlinear microresonator can generate coherent laser light with frequencies that are widely separated from the pump frequency, allowing, for example, visible light to be generated using a near-infrared pump. To be practically useful, the pump-to-signal conversion efficiency must be far higher than what has been demonstrated in microresonator-based oscillators with widely-separated output frequencies. To address this challenge, here we theoretically and numerically study parametric oscillations in Kerr nonlinear microresonators, revealing an intricate solution space that arises from an interplay of nonlinear processes. As a start, we use a three-mode approximation to derive an efficiency-maximizing relation between pump power and frequency mismatch. However, realistic devices, such as integrated microring resonators, support far more than three modes. Hence, a more accurate model that includes the entire modal landscape is necessary to determine potential inefficiencies arising from unwanted competing nonlinear processes. To this end, we numerically simulate the Lugiato-Lefever Equation that accounts for the full spectrum of nonlinearly-coupled resonator modes. We observe and characterize two nonlinear phenomena linked to parametric oscillations in multi-mode resonators: Mode competition and cross phase modulation-induced modulation instability. Both processes may impact conversion efficiency. Finally, we show how to increase the conversion efficiency to ≈ 25 % by tuning the microresonator loss rates. Our analysis will guide microresonator designs that aim for high conversion efficiency and output power.

Optical parametric oscillators are widely used to generate coherent light at frequencies not accessible by conventional laser gain. However, chip-based parametric oscillators operating in the visible spectrum have suffered from pump-to-signal conversion efficiencies typically less than 0.1%. Here, we demonstrate efficient optical parametric oscillators based on silicon nitride photonics that address frequencies between 260 (1150 nm) and 510 THz (590 nm). Pumping silicon nitride microrings near 385 THz (780 nm) yields monochromatic signal and idler waves with unprecedented output powers in this wavelength range. We estimate on-chip output powers (separately for the signal and idler) between 1 and 5 mW and conversion efficiencies reaching [Formula: see text]. Underlying this improved performance is our development of pulley waveguides for broadband near-critical coupling, which exploits a fundamental connection between the waveguide-resonator coupling rate and conversion efficiency. Finally, we find that mode competition reduces conversion efficiency at high pump powers, thereby constraining the maximum realizable output power. Our work proves that optical parametric oscillators built with integrated photonics can produce useful amounts of visible laser light with high efficiency.

Thermal noise is ubiquitous in microscopic systems and high-precision measurements. The control of thermal noise would reveal quantum regimes1 and enable fundamental physics searches2. Recently, nonlinearity in microresonators has enabled laser devices such as Kerr microresonator soliton frequency combs3. Soliton microcombs explore nonlinear dynamics and enable optical synthesizers4, optical clockwork5 and data communications systems6. Here, we explore how thermal noise leads to the fundamental decoherence of microcombs. We show that a particle-like soliton, which is an ensemble of comb modes, is closely coupled to the thermal fluctuations of its silicon-chip-based resonator. The microcomb modal linewidth is thus thermally broadened, and we characterize these thermal-noise correlations through a soliton effective temperature. Moreover, we demonstrate that passive laser cooling reduces soliton thermal decoherence to far below the ambient-temperature limit. We implement laser cooling by photothermal forcing, and we observe cooling of the frequency comb modes to 84 K. Our work illuminates inherent connections between nonlinear photonics and microscopic fluctuations. Observations of decoherence from thermodynamic noise in microresonator soliton frequency combs and laser cooling that reduces soliton thermal decoherence to far below the ambient-temperature limit are described, linking nonlinear photonics and microscopic fluctuations.

We numerically and theoretically explore the pump-to-signal conversion efficiency of Kerr microresonator optical parametric oscillators. We identify mode competition and cross-phase modulation-induced modulation instability as parasitic nonlinear processes that curb efficiency.

A 305 GHz dissipative Kerr soliton is synchronized to a chip-scale 10GHz mode-locked laser through regenerative harmonic injection locking, the repetition rate stability of the mode-locked laser after synchronization is shown to be 10−9 at 100 ms.

We show how soliton microcomb breathing oscillations synchronize to either the soliton repetition rate or to applied pump-laser phase modulation. In experiments, we observe locking ratios up to N = 8.

We present an optical frequency division technique to transfer the timing stability of a stabilized Kerr Microresonator Soliton Frequency Comb (~305 GHz repetition rate) to a chip-scaled mode-locked laser (~10 GHz repetition rate).

We explore intrinsic thermal noise in soliton microcombs, revealing thermodynamic correlations induced by nonlinearity and group-velocity dispersion. A suitable dispersion design gives rise to control over thermal-noise transduction from the environment to a soliton microcomb. We present simulations with the Lugiato-Lefever equation (LLE), including temperature as a stochastic variable. By systematically tuning the dispersion, we suppress repetition-rate frequency fluctuations by up to 50 decibels for different LLE soliton solutions. In an experiment, we observe a measurement-system-limited 15-decibel reduction in the repetition-rate phase noise for various settings of the pump-laser frequency, and our measurements agree with a thermal-noise model. Finally, we compare two octave-spanning soliton microcombs with similar optical spectra and offset frequencies, but with designed differences in dispersion. Remarkably, their thermal-noise-limited carrier-envelope-offset frequency linewidths are 1 MHz and 100 Hz, which demonstrates an unprecedented potential to mitigate thermal noise. Our results guide future soliton-microcomb design for low-noise applications, and, more generally, they illuminate emergent properties of nonlinear, multi-mode optical systems subject to intrinsic fluctuations.

The fundamental thermally-driven fluctuations of matter, present in all finite temperature systems and described by the fluctuation-dissipation theorem, are responsible for the precision-limiting noise processes of many measurement devices, including Johnson noise in resistors and thermo-mechanical noise in Fabry-Perot cavities. The LIGO interferometer’s noise floor was famously limited by thermo-elastic fluctuations on its mirror coatings. I will present measurements and analysis of thermo-refractive noise in photonic microresonators, examine how this noise sets a fundamental limit for the coherence of Kerr-microresonator optical frequency combs, and present a novel technique for beating this limit using laser cooling.

Orthogonal control of both degrees of freedom of a Kerr comb soliton allows high-precision atomic spectroscopy and stabilization., Microresonator-based soliton frequency combs, microcombs, have recently emerged to offer low-noise, photonic-chip sources for applications, spanning from timekeeping to optical-frequency synthesis and ranging. Broad optical bandwidth, brightness, coherence, and frequency stability have made frequency combs important to directly probe atoms and molecules, especially in trace gas detection, multiphoton light-atom interactions, and spectroscopy in the extreme ultraviolet. Here, we explore direct microcomb atomic spectroscopy, using a cascaded, two-photon 1529-nm atomic transition in a rubidium micromachined cell. Fine and simultaneous repetition rate and carrier-envelope offset frequency control of the soliton enables direct sub-Doppler and hyperfine spectroscopy. Moreover, the entire set of microcomb modes are stabilized to this atomic transition, yielding absolute optical-frequency fluctuations at the kilohertz level over a few seconds and

We report a comprehensive study of low-power, octave-bandwidth, single-soliton microresonator frequency combs in both the 1550 nm and 1064 nm bands. Our experiments utilize fully integrated silicon-nitride Kerr microresonators, and we demonstrate direct soliton generation with widely available distributed-Bragg-reflector lasers that provide less than 40 mW of chip-coupled laser power. We report measurements of soliton thermal dynamics and demonstrate how rapid laser-frequency control, consistent with the thermal timescale of a microresonator, facilitates stabilization of octave-bandwidth soliton combs. Moreover, since soliton combs are completely described by fundamental linear and nonlinear dynamics of the intraresonator field, we demonstrate the close connection between modeling and generation of octave-bandwidth combs. Our experiments advance the development of self-referenced frequency combs with integrated-photonics technology, and comb-laser sources with tens of terahertz pulse bandwidth across the near-infrared., 9 pages, 5 figures. Section IV supersedes unpublished supplementary material found in an earlier manuscript from the authors (arXiv:1711.06251v2)

We present a technique for optical-frequency synthesis by four-wave-mixing spectral translation of a soliton microcomb in a second microresonator. We demonstrate broadly tunable translation by over 600 nm and explore parametric amplification of the microcomb.

An ultra-low linewidth WDM comb is realized using an integrated SiN SBS laser to pump a 128 GHz channel spacing SiN Kerr soliton microring resonator. We measure the frequency noise of each of 25 C-band individual comb lines yielding ultra-low ~10Hz fundamental and ~4.0kHz integral linewidths for high-capacity coherent WDM.

We report octave spanning frequency combs generated by self-injection locking a distributed feedback laser to a Kerr microresonator. This method benefits from mitigated thermal transients and eliminates an optical isolator which simplifies photonic integration. ©2020 The Author(s)

This essay explores a historical fiction that attempts to present a “historically accurate rendition” of the Haitian revolution after postmodernism deconstructed both narrative and history, leaving an intellectual climate skeptical of narrative’s ability to depict the historically real. In Bell’s All Souls’ Rising , characters and plot blend not just with history and not only through historicity, but balance on acceptance or rejection of the narrators’ distinctly diverse historiographic consciousnesses. Bell establishes the contemporary historical novel by productively querying narrative’s production and embracing its myriad possibilities to create a narrative that rejects unity but aspires to comprehensiveness.

We report the first demonstration of octave spanning frequency combs generated by self-injection locking a distributed feedback laser to a Kerr microresonator. This method benefits from mitigated thermal transients and eliminates an optical isolator which simplifies photonic integration.

Kerr microresonators generate interesting and useful fundamental states of electromagnetic radiation through nonlinear interactions of continuous-wave (CW) laser light. With 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 can support carrier-envelope-offset phase stabilization to enable optical synthesis and metrology. Here, we introduce a Kerr-microresonator optical clockwork, which is a foundational device that distributes optical-clock signals to the mode-difference frequency of a comb. Our clockwork is based on a silicon-nitride (Si_{3}N_{4}) microresonator that generates a Kerr-soliton frequency comb with a repetition frequency of 1 THz. We measure our terahertz clockwork by electro-optic modulation with a microwave signal, enabling optical-based timing experiments in this wideband and high-speed frequency range. Moreover, by EO phase modulation of our entire Kerr-soliton comb, we arbitrarily generate additional CW modes between the 1-THz modes to reduce the repetition frequency and increase the resolution of the comb. Our experiments characterize the absolute frequency noise of this Kerr-microresonator clockwork to one part in 10^{17}, which is the highest accuracy and precision ever reported with this technology and opens the possibility of measuring high-performance optical clocks with Kerr combs.

We explore the regime of strong thermal-noise correlations between a Kerr soliton and its environment, including a thermal-noise-limited carrier-envelope phase. By passive photothermal backaction, we effectively laser cool the soliton to 84 K.

We report octave-spanning, single-soliton frequency combs at both 1550 nm and 1064 nm with less than 40 mW of on-chip power. We also demonstrate soliton generation at 1064 nm with a standard DBR laser.

We report accurate phase stabilization of an interlocking pair of Kerr-microresonator frequency combs. The two combs, one based on silicon nitride and one on silica, feature nearly harmonic repetition frequencies and can be generated with one laser. The silicon-nitride comb supports an ultrafast-laser regime with three-optical-cycle, 1-picosecond-period soliton pulses and a total dispersive-wave-enhanced bandwidth of 170 THz, while providing a stable phase-link between optical and microwave frequencies. We demonstrate nanofabrication control of the silicon-nitride comb’s carrier-envelope offset frequency and spectral profile. The phase-locked combs coherently reproduce their clock with a fractional precision of

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

We present measurements of the carrier-envelope-offset frequency noise spectrum of a silicon nitride Kerr-microresonator comb. Our preliminary observations suggest that thermal decoherence, which is enhanced by the small mode volume in microresonators, is an important contribution.

We demonstrate direct generation of Kerr-microresonator solitons with measured 100 percent success rate using an increasing-frequency scan of a phase-modulated pump laser. A reversed soliton step is observed. The phase modulation controls the solitons' properties.

We explore frequency-stable Kerr-soliton systems, one using a dual-microcomb architecture for self-referencing and another using atomic spectroscopy. We demonstrate an integrated-photonics frequency synthesizer and rubidium-referenced soliton pulses.

We show how microresonators driven by optical pulses enable the efficient, low-power generation of Kerr solitons and potentially open the door to new nonlinear regimes. We observe two new kinds of low-noise Kerr frequency combs.

Dissipative solitons formed in Kerr microresonators may enable chip-scale frequency combs for precision optical metrology. Here we explore the creation of an octave-spanning, 15-GHz repetition-rate microcomb suitable for both f-2f self-referencing and optical-frequency comparisons across the near infrared. This is achieved through a simple and reliable approach to deterministically generate, and subsequently frequency stabilize, soliton pulse trains in a silica-disk resonator. Efficient silicon-nitride waveguides provide a supercontinuum spanning 700 to 2100 nm, enabling both offset-frequency stabilization and optical-frequency measurements with >100 nW per mode. We demonstrate the stabilized comb by performing a microcomb-mediated comparison of two ultrastable optical-reference cavities.

We demonstrate a frequency-stabilized, dual-Kerr microcomb that guides an integrated Vernier-laser optical frequency synthesizer, all derived from an RF clock. The synthesizer's stability is

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, radiofrequency 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-timekeeping technology. Moreover, we investigate the fundamental role that residual laser-resonator detuning noise plays in the spectral purity of microwave generation with Kerr combs., 6 pages, 4 figures

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, stably 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 have necessitated 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 in a thermally stable way 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 report a photonic-chip optical-frequency synthesizer using interlocking 1 THz and 22 GHz Kerr microcombs, which provide f-2f self-referencing and a dense comb spanning the C-band, respectively. We demonstrate the optical synthesizer with Hz resolution.

We generate single Kerr-cavity solitons from a 15 GHz silica resonator. These pulses are compressed in normal dispersion fiber and used to generate a coherent octave-spanning supercontinuum.

We report the demonstration of octave-spanning soliton microcomb states in high-Q Si 3 N 4 microresonators. These states are shown to be thermally stable and therefore can be accessed with slow frequency tuning of the pump laser.

We implement an optical single-sideband, suppressed-carrier modulator with a Kerr microcomb pump laser. Rapid frequency scanning enables exploration of Kerr-comb physics, and practically reduces its sensitivity to challenging resonator thermal bistability and mode-structure imperfection effects.

Laboratory optical atomic clocks achieve remarkable accuracy (now counted to 18 digits or more), opening possibilities for exploring fundamental physics and enabling new measurements. However, their size and the 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 1013. These results demonstrate key concepts of how to use silicon-chip devices in future portable and ultraprecise optical clocks.

We demonstrate an octave-span Kerr frequency comb with 1 THz mode spacing based on a silicon-nitride microring. The dispersion-engineered microring allows for low-pump-power operation and dispersive-wave emission at 1 μm and 2 μm wavelengths to facilitate self-referencing. We report measurements of the comb's frequency noise properties.

Optical frequency combs based on solitons in nonlinear microresonators open up new regimes for optical metrology and signal processing across a range of expanding and emerging applications. In this work, we advance these combs toward applications by demonstrating protected single-soliton formation and operation in a Kerr-nonlinear microresonator using a phase-modulated pump laser. Phase modulation gives rise to spatially/temporally varying effective loss and detuning parameters, leading to an operation regime in which multi-soliton degeneracy is lifted and a single soliton is the only observable behavior. We achieve direct, on-demand excitation of single solitons as indicated by reversal of the characteristic “soliton step.” Phase modulation also enables precise, high bandwidth control of the soliton pulse train’s properties, and we measure dynamics that agree closely with simulations. We show that the technique can be extended to high-repetition-frequency Kerr solitons through subharmonic phase modulation. These results will facilitate straightforward generation and control of Kerr-soliton microcombs for integrated photonics systems.

We engineer dispersion and coupling of a Si3N4 microresonator to achieve an octave-spanning comb with a 200mW pump. Our microcomb features dispersive-wave spectral peaks at 1 μm and 2 μm, which potentially enable on-chip self-referencing.

We experimentally demonstrate direct Kerr-microresonator frequency-comb atomic spectroscopy, utilizing a cascaded two-photon 1529-nm transition in a rubidium micro-machined vapor cell. The demonstration is a path for compact atomic frequency references and multiphoton comb-atom interactions.

We introduce an architecture for optical-frequency synthesis using photonic-chip frequency combs and a heterogeneously integrated CW laser. The Kerr dual-comb that we describe offers a microwave-optical link to discipline the laser to an RF clock.