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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.

The remarkable frequency stability of resonant systems in the optical domain (optical cavities and atomic transitions) can be harnessed at frequency scales accessible by electronics using optical frequency division. This capability is revolutionizing technologies spanning time keeping to high-performance electrical signal sources. A version of the technique called 2-point optical frequency division (2P-OFD) is proving advantageous for application to high-performance signal sources. In 2P-OFD, an optical cavity anchors two spectral endpoints defined by lines of a frequency comb. The comb need not be self-referenced, which greatly simplifies the system architecture and reduces power requirements. Here, a 2P-OFD microwave signal source is demonstrated with record-low phase noise using a microcomb. Key to this advance is a spectral endpoint defined by a frequency agile single-mode dispersive wave that is emitted by the microcomb soliton. Moreover, the system frequency reference is a compact all-solid-state optical cavity with a record Q-factor. The results advance integrable microcomb-based signal sources into the performance realm of much larger microwave sources.

Optical frequency division based on bulk or fiber optics provides unprecedented spectral purity for microwave oscillators. To extend the applications of this approach, the big challenges are to develop miniaturized optical frequency division oscillators without trading off phase noise performance. In this paper, we report a chip-scale electro-optical frequency division microwave oscillator with ultra-low phase noise performance. Dual laser sources are co-self-injection-locked to a single silicon nitride spiral resonator to provide a record high-stability, fully on-chip optical reference. An integrated electro-optical frequency comb based on a novel thin-film lithium niobate phase modulator chip is incorporated for the first time to perform optical-to-microwave frequency division. The resulting chip-scale photonic microwave oscillator achieves a phase noise level of -129 dBc/Hz at 10 kHz offset for 37.7 GHz carrier. The results represent a major advance in high performance, integrated photonic microwave oscillators for applications including signal processing, radar, timing, and coherent communications.

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-P\'{e}rot 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.

A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then developed perturbatively to solve this representation of Maxwell equations. QLA consists of an interleaved unitary sequence of collision operators (that entangle on lattice-site qubits) and streaming operators (that move this entanglement throughout the lattice). External potential operators are introduced to handle gradients in the refractive indices, and these operators are typically non-unitary, but sparse matrices. By also interleaving the external potential operators with the unitary collide-stream operators one achieves a QLA which conserves energy to high accuracy. Some two dimensional simulations results are presented for the scattering of a one-dimensional (1D) pulse off a localized anisotropic dielectric object., Comment: 16 pages, 22 figures

By self-injection-locking a 1560 nm distributed feedback semiconductor laser to a high-$Q$ silicon nitride resonator, a high-coherence 780 nm second harmonic signal is generated via the photogalvanic-induced second-order nonlinearity. A record-low frequency noise floor of 4 Hz$^2$/Hz is achieved for the 780 nm emission. The approach can be generalized for signal generation over a wide range of visible and near-visible bands.

Thermal silica is a common dielectric used in all silicon-photonic circuits. And bound hydroxyl ions (Si-OH) can provide a significant component of optical loss in this material on account of the wet nature of the thermal oxidation process. A convenient way to quantify this loss relative to other mechanisms is through OH-absorption at 1380 nm. Here, using ultra-high-Q thermal-silica wedge microresonators, the OH absorption loss peak is measured and distinguished from the scattering loss base line over a wavelength range from 680 nm to 1550 nm. Record-high on-chip resonator Q factors are observed for near-visible and visible wavelengths, and the absorption limited Q factor is as high as 8 billion in the telecom band. OH ion content level around 2.4 ppm (weight) is inferred from both Q measurements and by Secondary Ion Mass Spectroscopy (SIMS) depth profiling., Comment: 4 pages, 3 figures

Soliton microcombs are helping to advance the miniaturization of a range of comb systems. These combs mode lock through the formation of short temporal pulses in anomalous dispersion resonators. Here, a new microcomb is demonstrated that mode locks through the formation of pulse pairs in normal-dispersion coupled-ring resonators. Unlike conventional microcombs, pulses in this system cannot exist alone, and instead must phase lock in pairs to form a bright soliton comb. Also, the pulses can form at recurring spectral windows and the pulses in each pair feature different optical spectra. This pairwise mode-locking modality extends to higher dimensions and we demonstrate 3-ring systems in which 3 pulses mode lock through alternating pairwise pulse coupling. The results are demonstrated using the new CMOS-foundry platform that has not previously produced bright solitons on account of its inherent normal dispersion. The ability to generate multi-color pulse pairs over multiple rings is an important new feature for microcombs. It can extend the concept of all-optical soliton buffers and memories to multiple storage rings that multiplex pulses with respect to soliton color and that are spatially addressable. The results also suggest a new platform for the study of quantum combs and topological photonics.

Normal group velocity dispersion (GVD) microcombs offer high comb line power and high pumping efficiency compared to bright pulse microcombs. The recent demonstration of normal GVD microcombs using CMOS-foundry-produced microresonators is an important step towards scalable production. However, the chromatic dispersion of CMOS devices is large and impairs generation of broadband microcombs. Here, we report the development of a microresonator in which GVD is reduced due to a couple-ring resonator configuration. Operating in the turnkey self-injection-locking mode, the resonator is hybridly integrated with a semiconductor laser pump to produce high-power-efficiency combs spanning a bandwidth of 9.9 nm (1.22 THz) centered at 1560 nm, corresponding to 62 comb lines. Fast, linear optical sampling of the comb waveform is used to observe the rich set of near-zero GVD comb behaviors, including soliton molecules, switching waves (platicons) and their hybrids. Tuning of the 20 GHz repetition rate by electrical actuation enables servo locking to a microwave reference, which simultaneously stabilizes the comb repetition rate, offset frequency and temporal waveform. This hybridly integrated system could be used in coherent communications or for ultra-stable microwave signal generation by two-point optical frequency division., Comment: 8 pages, 4 figures

While photonic integrated circuits (PICs) are being widely used in applications such as telecommunications and datacenter interconnects, PICs capable of replacing bulk optics and fibers in high-precision, highly-coherent applications will require ultra-low-noise laser sources to be integrated with other photonic components in a compact and robustly aligned format -- that is, on a single chip. Such PICs could offer superior scalability for complex functionalities and volume production, as well as improved stability and reliability over time. However, there are two major issues preventing the realization of such envisioned PICs: the high phase noise of semiconductor lasers, and the difficulty of integrating optical isolators directly on chip. PICs are still considered as inferior solutions in optical systems such as microwave synthesizers, optical gyroscopes and atomic clocks, despite their advantages in size, weight, power consumption and cost (SWaPC). Here, we challenge this convention by introducing three-dimensional (3D) integration in silicon photonics that results in ultra-low-noise, isolator-free PICs. Through multiple monolithic and heterogeneous processing sequences, direct on-chip integration of III-V gain and ultra-low-loss (ULL) silicon nitride (SiN) waveguides with optical loss around 0.5 dB/m are demonstrated. Consequently, the demonstrated PIC enters a new regime, such that an integrated ultra-high-Q cavity reduces the laser noise close to that of fiber lasers. Moreover, the cavity acts as an effective block for any downstream on-chip or off-chip reflection-induced destabilization, thus eliminating the need for optical isolators. We further showcase isolator-free, widely-tunable, low-noise, heterodyne microwave generation using two ultra-low-noise lasers on the same silicon chip.

Chip-integrated optical frequency combs are attractive optical sources in comb applications requiring high-repetition-rate, low power consumption, or compact size. Spontaneous soliton formation via Kerr parametric oscillation is a promising generation principle in these frequency combs, and has been demonstrated in several material platforms over the past decade. Of these materials, AlGaAs has one of the largest Kerr nonlinearity coefficients allowing low pump threshold comb generation. However, bright soliton generation using this material has only been possible at cryogenic temperature because of the large thermo-optic effect at room temperature, which hinders stable access to the soliton regime. Here, we report self-stabilized single soliton generation in AlGaAs microresonators at room temperature by utilizing a rising soliton step in large free-spectral-range resonators. With sub-milliWatt optical pump power, 1 THz repetition-rate soliton generation is demonstrated. Perfect soliton crystal formation and soliton breather states are also observed. Besides the advantages of large optical nonlinearity, the devices are natural candidates for integration with III-V pump lasers., Comment: 7 pages, 3 figure

The effect of the thickness of the dielectric boundary layer that connects a material of refractive index $n_1$ to another of index $n_2$ is considered for the propagation of an electromagnetic pulse. For very thin boundary layer the scattering properties of the pulse mimics that found from the Fresnel jump conditions for a plane wave - except that the transmission to incident amplitudes are augmented by a factor of $\sqrt{n_2/n_1}$. As the boundary layer becomes thicker one finds deviations away from the Fresnel conditions and eventually one approaches WKB propagation. However there is found a small but unusual dip in part of the transmitted pulse that persists in time. The quantum lattice algorithm (QLA) used recovers the Maxwell equations to second order in a small parameter -- but QLA still recovers Maxwell equations when this parameter is unity. The expansion parameter is the speed of the pulse in medium $n_1$., Comment: 14 pages, 10 figures

Microwave signal generation with fast frequency tuning underlies many applications including sensing, imaging, ranging, time keeping, wireless communication, and high-speed electronics. Soliton microcombs are a promising new approach for photonic-based microwave signal synthesis. To date, however, tuning rate has been limited in microcombs (and in frequency combs generally). Here, we demonstrate the first microwave-rate soliton microcomb whose repetition rate can be tuned at a high speed. By integrating an electro-optic tuning/modulation element into a lithium niobate comb microresonator, a modulation bandwidth up to 75 MHz and a continuous frequency modulation rate up to 5.0 * 10^14 Hz/s are achieved, several orders-of-magnitude faster than existing microcomb technology. These features are especially useful for disciplining an optical VCO to a long-term reference such as an optical clock or for tight phase lock in dual-microcomb clocks or synthesizers. Moreover, the microwave signal rate can be set to any X - W band rate. Besides its positive impact on microwave photonics, fast repetition rate control is generally important in all applications of frequency combs.

High coherence visible and near-visible laser sources are centrally important to the operation of advanced position/navigation/timing systems as well as classical/quantum sensing systems. However, the complexity and size of these bench-top lasers is an impediment to their transitioning beyond the laboratory. Here, a system-on-a-chip that emits high-coherence visible and near-visible lightwaves is demonstrated. The devices rely upon a new approach wherein wavelength conversion and coherence increase by self-injection-locking are combined within in a single nonlinear resonator. This simplified approach is demonstrated in a hybridly-integrated device and provides a short-term linewidth around 10-30 kHz. On-chip, converted optical power over 2 mW is also obtained. Moreover, measurements show that heterogeneous integration can result in conversion efficiency higher than 25% with output power over 11 mW. Because the approach uses mature III-V pump lasers in combination with thin-film lithium niobate, it can be scaled for low-cost manufacturing of high-coherence visible emitters. Also, the coherence generation process can be transferred to other frequency conversion processes including optical parametric oscillation, sum/difference frequency generation, and third-harmonic generation.

A qubit lattice algorithm (QLA) is developed for Maxwell equations in a two-dimensional Cartesian geometry. In particular, the initial value problem of electromagnetic pulse scattering off a localized 2D dielectric object is considered. A matrix formulation of the Maxwell equations, using the Riemann-Silberstein-Weber vectors, forms a basis for the QLA and a possible unitary representation. The electromagnetic fields are discretized using a 16-qubit representation at each grid point. The discretized QLA equations reproduce Maxwell equations to second order in an appropriate expansion parameter $\epsilon$. The properties of scattered waves depend on the scale length of the transition layer separating the vacuum from the core of the dielectric. The time evolution of the fields gives interesting physical insight into scattering when propagating fields are excited within the dielectric medium. Furthermore, simulations show that the QLA recovers Maxwell equations even when $\epsilon \sim 1$., Comment: 22 pages, 32 figures

Stimulated Brillouin scattering provides optical gain for efficient and narrow-linewidth lasers in high-Q microresonator systems. However, the thermal dependence of the Brillouin process, as well as the microresonator, impose strict temperature control requirements for long-term frequency-stable operation. Here, we study Brillouin back action and use it to both measure and phase-sensitively lock modal temperature to a reference temperature defined by the Brillouin phase-matching condition. At a specific lasing wavelength, the reference temperature can be precisely set by adjusting resonator free spectral range. This backaction control method is demonstrated in a chip-based Brillouin laser, but can be applied in all Brillouin laser platforms. It offers a new approach for frequency-stable operation of Brillouin lasers in atomic clock, frequency metrology, and gyroscope applications.

The development of integrated semiconductor lasers has miniaturized traditional bulky laser systems, enabling a wide range of photonic applications. A progression from pure III-V based lasers to III-V/external cavity structures has harnessed low-loss waveguides in different material systems, leading to significant improvements in laser coherence and stability. Despite these successes, however, key functions remain absent. In this work, we address a critical missing function by integrating the Pockels effect into a semiconductor laser. Using a hybrid integrated III-V/Lithium Niobate structure, we demonstrate several essential capabilities that have not existed in previous integrated lasers. These include a record-high frequency modulation speed of 2 exahertz/s (2.0$\times$10$^{18}$ Hz/s) and fast switching at 50 MHz, both of which are made possible by integration of the electro-optic effect. Moreover, the device co-lases at infrared and visible frequencies via the second-harmonic frequency conversion process, the first such integrated multi-color laser. Combined with its narrow linewidth and wide tunability, this new type of integrated laser holds promise for many applications including LiDAR, microwave photonics, atomic physics, and AR/VR.

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.

Integrated photonics has profoundly impacted a wide range of technologies underpinning modern society. The ability to fabricate a complete optical system on a chip offers unrivalled scalability, weight, cost and power efficiency. Over the last decade, the progression from pure III-V materials platforms to silicon photonics has significantly broadened the scope of integrated photonics by combining integrated lasers with the high-volume, advanced fabrication capabilities of the commercial electronics industry. Yet, despite remarkable manufacturing advantages, reliance on silicon-based waveguides currently limits the spectral window available to photonic integrated circuits (PICs). Here, we present a new generation of integrated photonics by directly uniting III-V materials with silicon nitride (SiN) waveguides on Si wafers. Using this technology, we present the first fully integrated PICs at wavelengths shorter than silicon's bandgap, demonstrating essential photonic building blocks including lasers, photodetectors, modulators and passives, all operating at sub-um wavelengths. Using this platform, we achieve unprecedented coherence and tunability in an integrated laser at short wavelength. Furthermore, by making use of this higher photon energy, we demonstrate superb high temperature performance and, for the first time, kHz-level fundamental linewidths at elevated temperatures. Given the many potential applications at short wavelengths, the success of this integration strategy unlocks a broad range of new integrated photonics applications.

Optical microresonators with high quality ($Q$) factors are essential to a wide range of integrated photonic devices. Steady efforts have been directed towards increasing microresonator $Q$ factors across a variety of platforms. With success in reducing microfabrication process-related optical loss as a limitation of $Q$, the ultimate attainable $Q$, as determined solely by the constituent microresonator material absorption, has come into focus. Here, we report measurements of the material-limited $Q$ factors in several photonic material platforms. High-$Q$ microresonators are fabricated from thin films of SiO$_2$, Si$_3$N$_4$, Al$_{0.2}$Ga$_{0.8}$As and Ta$_2$O$_5$. By using cavity-enhanced photothermal spectroscopy, the material-limited $Q$ is determined. The method simultaneously measures the Kerr nonlinearity in each material and reveals how material nonlinearity and ultimate $Q$ vary in a complementary fashion across photonic materials. Besides guiding microresonator design and material development in four material platforms, the results help establish performance limits in future photonic integrated systems., Comment: Maodong Gao, Qi-Fan Yang and Qing-Xin Ji contributed equally to this work. 9 pages, 4 figures, 1 table

Silicon nitride (SiN) waveguides with ultra-low optical loss enable integrated photonic applications including low noise, narrow linewidth lasers, chip-scale nonlinear photonics, and microwave photonics. Lasers are key components to SiN photonic integrated circuits (PICs), but are difficult to fully integrate with low-index SiN waveguides due to their large mismatch with the high-index III-V gain materials. The recent demonstration of multilayer heterogeneous integration provides a practical solution and enabled the first-generation of lasers fully integrated with SiN waveguides. However a laser with high device yield and high output power at telecommunication wavelengths, where photonics applications are clustered, is still missing, hindered by large mode transition loss, nonoptimized cavity design, and a complicated fabrication process. Here, we report high-performance lasers on SiN with tens of milliwatts output through the SiN waveguide and sub-kHz fundamental linewidth, addressing all of the aforementioned issues. We also show Hertz-level linewidth lasers are achievable with the developed integration techniques. These lasers, together with high-$Q$ SiN resonators, mark a milestone towards a fully-integrated low-noise silicon nitride photonics platform. This laser should find potential applications in LIDAR, microwave photonics and coherent optical communications., Comment: 8 pages, 3 figures

Dissipative soliton Kerr frequency combs in microresonators have recently been demonstrated with the self-injection locking process. They have the advantage of turnkey deterministic comb generation and simplifying dark soliton generation in the normal dispersion regime. Here, the formation process of dark pulses triggered by self-injection locking is studied by regarding them as a pair of domain walls that connect domains having different intracavity powers. The self-injection locking mechanism allows the domain walls to self-regulate their position so that a wide range of dark comb states can be accessed, and the duty cycle is controlled by the feedback phase. Direct imaging of the dark pulse shape using the electro-optic sampling technique is used to verify the theory. The results provide new physical insights as well as a new operational modality for this important class of nonlinear waves., Comment: 20 pages, 10 figures

Narrow-linewidth lasers are important to many applications spanning precision metrology to sensing systems. Characterization of these lasers requires precise measurements of their frequency noise spectra. Here we demonstrate a correlated self-heterodyne (COSH) method capable of measuring frequency noise as low as 0.01 Hz$^2$/Hz at 1 MHz offset frequency. The measurement setup is characterized by both commercial and lab-built lasers, and features low optical power requirements, fast acquisition time and high intensity noise rejection., Comment: 10 pages, 6 figures

Driven by narrow-linewidth bench-top lasers, coherent optical systems spanning optical communications, metrology and sensing provide unrivalled performance. To transfer these capabilities from the laboratory to the real world, a key missing ingredient is a mass-produced integrated laser with superior coherence. Here, we bridge conventional semiconductor lasers and coherent optical systems using CMOS-foundry-fabricated microresonators with record high $Q$ factor over 260 million and finesse over 42,000. Five orders-of-magnitude noise reduction in the pump laser is demonstrated, and for the first time, fundamental noise below 1 Hz$^2$ Hz$^{-1}$ is achieved in an electrically-pumped integrated laser. Moreover, the same configuration is shown to relieve dispersion requirements for microcomb generation that have handicapped certain nonlinear platforms. The simultaneous realization of record-high $Q$ factor, highly coherent lasers and frequency combs using foundry-based technologies paves the way for volume manufacturing of a wide range of coherent optical systems., Comment: 19 pages, 11 figures

Coherently-pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of soliton microcombs. Here, this diffusive motion and its impact on Kerr soliton timing jitter is studied experimentally. Typically hidden below technical noise contributions, the quantum limit is discerned by measuring counter-propagating solitons. Their relative motion features only weak interactions and also presents excellent common mode suppression of technical noise. This is in strong contrast to co-propagating solitons which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong mutual motion correlation. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multi-soliton physics

Both the group velocity and phase velocity of two solitons can be synchronized by a Kerr-effect mediated interaction, causing what is known as soliton trapping. Trapping can occur when solitons travel through single-pass optical fibers or when circulating in optical resonators. Here, we demonstrate and theoretically explain a new manifestation of soliton trapping that occurs between counter-propagating solitons in microresonators. When counter-pumping a microresonator using slightly detuned pump frequencies and in the presence of backscattering, the group velocities of clockwise and counter-clockwise solitons undergo periodic modulation instead of being locked to a constant velocity. Upon emission from the microcavity, the solitons feature a relative oscillatory motion having an amplitude that can be larger than the soliton pulse width. This relative motion introduces a sideband fine structure into the optical spectrum of the counter-propagating solitons. Our results highlight the significance of coherent pumping in determining soliton dynamics within microresonators and add a new dimension to the physics of soliton trapping.

Non-Hermitian Hamiltonians describing open systems can feature singularities called exceptional points (EPs). Resonant frequencies become strongly dependent on externally applied perturbations near an EP which has given rise to the concept of EP-enhanced sensing in photonics. However, while increased sensor responsivity has been demonstrated, it is not known if this class of sensor results in improved signal-to-noise performance. Here, enhanced responsivity of a laser gyroscope caused by operation near an EP is shown to be exactly compensated by increasing sensor noise in the form of linewidth broadening. The noise, of fundamental origin, increases according to the Petermann factor, because the mode spectrum loses the oft-assumed property of orthogonality. This occurs as system eigenvectors coalesce near the EP and a biorthogonal analysis confirms experimental observations. Besides its importance to the physics of microcavities and non-Hermitian photonics, this is the first time that fundamental sensitivity limits have been quantified in an EP sensor.

While soliton microcombs offer the potential for integration of powerful frequency metrology and precision spectroscopy systems, their operation requires complex startup and feedback protocols that necessitate difficult-to-integrate optical and electrical components. Moreover, CMOS-rate microcombs, required in nearly all comb systems, have resisted integration because of their power requirements. Here, a regime for turnkey operation of soliton microcombs co-integrated with a pump laser is demonstrated and theoretically explained. Significantly, a new operating point is shown to appear from which solitons are generated through binary turn-on and turn-off of the pump laser, thereby eliminating all photonic/electronic control circuitry. These features are combined with high-Q $Si_3N_4$ resonators to fully integrate into a butterfly package microcombs with CMOS frequencies as low as 15 GHz, offering compelling advantages for high-volume production., Comment: Boqiang Shen, Lin Chang, Junqiu Liu, Heming Wang and Qi-Fan Yang contributed equally to this work

Recent advances in nonlinear optics have revolutionized the area of integrated photonics, providing on-chip solutions to a wide range of new applications. Currently, the state of the art integrated nonlinear photonic devices are mainly based on dielectric material platforms, such as Si3N4 and SiO2. While semiconductor materials hold much higher nonlinear coefficients and convenience in active integration, they suffered in the past from high waveguide losses that prevented the realization of highly efficient nonlinear processes on-chip. Here we challenge this status quo and demonstrate an ultra-low loss AlGaAs-on-insulator (AlGaAsOI) platform with anomalous dispersion and quality (Q) factors beyond 1.5*10^6. Such a high quality factor, combined with the high nonlinear coefficient and the small mode volume, enabled us to demonstrate a record low Kerr frequency comb generation threshold of ~36 uW for a resonator with a 1 THz free spectral range (FSR), ~100 times lower compared to that in previous semiconductor platform. Combs with >250 nm broad span have been generated under a pump power lower than the threshold power of state of the art dielectric micro combs. A soliton-step transition has also been observed for the first time from an AlGaAs resonator. This work is an important step towards ultra-efficient semiconductor-based nonlinear photonics and will lead to fully integrated nonlinear photonic integrated circuits (PICs) in near future.

Soliton microcombs offer the prospect of advanced optical metrology and timing systems in compact form factors. In these applications, pumping of microcombs directly from a semiconductor laser without amplification or triggering components is desirable for reduced power operation and to simplify system design. At the same time, low repetition rate microcombs are required in many comb applications for interface to detectors and electronics, but their increased mode volume makes them challenging to pump at low power. Here, 10 GHz repetition rate soliton microcombs are directly pumped by low-power (< 20 mW) diode lasers. High-Q silica microresonators are used for this low power operation and are packaged into fiber-connectorized modules that feature temperature control for improved long-term frequency stability.

Exceptional points (EPs) are special spectral degeneracies of non-Hermitian Hamiltonians governing the dynamics of open systems. At the EP two or more eigenvalues and the corresponding eigenstates coalesce. Recently, it has been proposed that EPs can enhance the sensitivity of optical gyroscopes. Here we report measurement of rotation sensitivity boost by over 4X resulting from operation of a chip-based stimulated Brillouin gyroscope near an exceptional point. A second-order EP is identified in the gyroscope and originates from the dissipative coupling between the clockwise and counterclockwise lasing modes. The modes experience opposing Sagnac shifts under application of a rotation, but near the exceptional point new modal admixtures dramatically increase the Sagnac shift. Modeling confirms the measured enhancement. Besides the ability to operate an optical gyroscope with enhanced sensitivity, this result provides a new platform for study of non-Hermitian physics and nonlinear optics with precise control.

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., Comment: 5 pages, 3 figures

For its many useful properties, including second and third-order optical nonlinearity as well as electro-optic control, lithium niobate is considered an important potential microcomb material. Here, a soliton microcomb is demonstrated in a monolithic high-Q lithium niobate resonator. Besides the demonstration of soliton mode locking, the photorefractive effect enables mode locking to self-start and soliton switching to occur bi-directionally. Second-harmonic generation of the soliton spectrum is also observed, an essential step for comb self-referencing. The Raman shock time constant of lithium niobate is also determined by measurement of soliton self-frequency-shift. Besides the considerable technical simplification provided by a self-starting soliton system, these demonstrations, together with the electro-optic and piezoelectric properties of lithium niobate, open the door to a multi-functional microcomb providing f-2f generation and fast electrical control of optical frequency and repetition rate, all of which are critical in applications including time keeping, frequency synthesis/division, spectroscopy and signal generation.

Optical communication systems have come through five orders of magnitude improvement in data rate over the last three decades. The increased demand in data traffic and the limited optoelectronic component bandwidths have led to state-of-the-art systems employing hundreds of separate lasers in each transmitter. Given the limited optical amplifier bandwidths, focus is now shifting to maximize the spectral efficiency, SE. However, the frequency jitter from neighbouring lasers results in uncertainties of the exact channel wavelength, requiring large guardbands to avoid catastrophic channel overlap. Optical frequency combs with optimal line spacings (typically around 10-50 GHz) can overcome these limitations and maximize the SE. Recent developments in microresonator-based soliton frequency combs (hereafter microcombs) promise a compact, power efficient multi-wavelength and phase-locked light source for optical communications. Here we demonstrate a microcomb-based communication link achieving state-of-the-art spectral efficiency that has previously only been possible with bulk-optics systems. Compared to previous microcomb works in optical communications, our microcomb features a narrow line spacing of 22.1 GHz. In addition, it provides a four order-of-magnitude more stable line spacing compared to free-running lasers. The optical signal-to-noise ratio (OSNR) is sufficient for information encoding using state-of-the-art high-order modulation formats. This enables us to demonstrate transmission of a 12 Tb/s superchannel over distances ranging from a single 82 km span with an SE exceeding 10 bits/s/Hz, to 2000 km with an SE higher than 6 bits/s/Hz. These results demonstrate that microcombs can attain the SE that will spearhead future optical networks.

Acquisition of laser frequency with high resolution under continuous and abrupt tuning conditions is important for sensing, spectroscopy and communications. Here, a single microresonator provides rapid and broad-band measurement of frequencies across the optical C-band with a relative frequency precision comparable to conventional dual frequency comb systems. Dual-locked counter-propagating solitons having slightly different repetition rates are used to implement a Vernier spectrometer. Laser tuning rates as high as 10 THz/s, broadly step-tuned lasers, multi-line laser spectra and also molecular absorption lines are characterized using the device. Besides providing a considerable technical simplification through the dual-locked solitons and enhanced capability for measurement of arbitrarily tuned sources, this work reveals possibilities for chip-scale spectrometers that greatly exceed the performance of table-top grating and interferometer-based devices.

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., Comment: 11 pages, 4 figures

Fast-responding detector arrays are commonly used for imaging rapidly-changing scenes. Besides array detectors, a single-pixel detector combined with a broadband optical spectrum can also be used for rapid imaging by mapping the spectrum into a spatial coordinate grid and then rapidly measuring the spectrum. Here, optical frequency combs generated from high-$Q$ silica microresonators are used to implement this method. The microcomb is dispersed in two spatial dimensions to measure a test target. The target-encoded spectrum is then measured by multi-heterodyne beating with another microcomb having a slightly different repetition rate, enabling an imaging frame rate up to 200 kHz and fillrates as high as 48 MegaPixels/s. The system is used to monitor the flow of microparticles in a fluid cell. Microcombs in combination with a monolithic waveguide grating array imager could greatly magnify these results by combining the spatial parallelism of detector arrays with spectral parallelism of optics., Comment: Chengying Bao and Myoung-Gyun Suh contribute equally

We demonstrate protected single-soliton formation and operation in a Kerr microresonator using a phase-modulated pump laser. Phase modulation gives rise to spatially varying effective loss and detuning parameters, which in turn lead to an operation regime in which multi-soliton degeneracy is lifted and a single soliton is the only observable behavior. Direct excitation of single solitons is indicated by observed reversal of the characteristic 'soliton step.' Phase modulation also enables precise control of the soliton pulse train's properties, and measured dynamics agree closely with simulations. We show that the technique can be extended to high repetition-frequency Kerr solitons through subharmonic phase modulation. These results facilitate straightforward generation and control of Kerr-soliton microcombs for integrated photonics systems.

Solitons are self-sustained wavepackets that occur in many physical systems. Their recent demonstration in optical microresonators has provided a new platform for study of nonlinear optical physics with practical implications for miniaturization of time standards, spectroscopy tools and frequency metrology systems. However, despite its importance to understanding of soliton physics as well as development of new applications, imaging the rich dynamical behaviour of solitons in microcavities has not been possible. These phenomena require a difficult combination of high-temporal-resolution and long-record-length in order to capture the evolving trajectories of closely-spaced microcavity solitons. Here, an imaging method is demonstrated that visualizes soliton motion with sub-picosecond resolution over arbitrary time spans. A wide range of complex soliton transient behaviors are characterized in the temporal or spectral domain, including soliton formation, collisions, spectral breathing and soliton decay. This method can serve as a universal visualization tool for understanding complex soliton physics in microcavities., Comment: Xu Yi and Qi-Fan Yang contributed equally to this work

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.

An external-cavity diode laser is reported with ultralow noise, high power coupled to a fiber, and fast tunability. These characteristics enable the generation of an optical frequency comb in a silica micro-resonator with a single-soliton state. Neither an optical modulator nor an amplifier was used in the experiment. This demonstration greatly simplifies the soliton generation setup and represents a significant step forward to a fully integrated soliton comb system., Comment: 7 pages, 5 figures

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., Comment: 10 pages, 6 figures

Laser linewidth is of central importance in spectroscopy, frequency metrology and all applications of lasers requiring high coherence. It is also of fundamental importance, because the Schawlow-Townes laser linewidth limit is of quantum origin. Recently, a theory of stimulated Brillouin laser (SBL) linewidth has been reported. While the SBL linewidth formula exhibits power and optical Q factor dependences that are identical to the Schawlow-Townes formula, a source of noise not present in two-level lasers, phonon occupancy of the Brillouin mechanical mode, is predicted to be the dominant SBL linewidth contribution. Moreover, the quantum-limit of the SBL linewidth is predicted to be twice the Schawlow-Townes limit on account of phonon participation. To help confirm this theory the SBL fundamental linewidth is measured at cryogenic temperatures in a silica microresonator. Its temperature dependence and the SBL linewidth theory are combined to predict the number of thermo-mechanical quanta at three temperatures. The result agrees with the Bose-Einstein phonon occupancy of the microwave-rate Brillouin mode in support of the SBL linewidth theory prediction.

Frequency combs have applications that extend from the ultra-violet into the mid-infrared bands. Microcombs, a miniature and often semiconductor-chip-based device, can potentially access most of these applications, but are currently more limited in spectral reach. Here, we demonstrate mode-locked silica microcombs with emission near the edge of the visible spectrum. By using both geometrical and mode-hybridization dispersion control, devices are engineered for soliton generation while also maintaining optical $Q$ factors as high as 80 million. Electronics-bandwidth-compatible (20 GHz) soliton mode locking is achieved with low pumping powers (parametric oscillation threshold powers as low as 5.4 mW). These are the shortest wavelength soliton microcombs demonstrated to date and could be used in miniature optical clocks. The results should also extend to visible and potentially ultra-violet bands., Comment: Seung Hoon Lee, Dong Yoon Oh, Qi-Fan Yang, Boqiang Shen and Heming Wang contributed equally to this work

Laser-based range measurement systems (LIDAR) are important in many application areas including autonomous vehicles, robotics, manufacturing, formation-flying of satellites, and basic science. Coherent laser ranging systems using dual frequency combs provide an unprecedented combination of long range, high precision and fast update rate. Here, dual-comb distance measurement using chip-based soliton microcombs is demonstrated. Moreover, the dual frequency combs are generated within a single microresonator as counter-propating solitons using a single pump laser. Time-of-flight measurement with 200 nm precision at 500 ms averaging time is demonstrated. Also, the dual comb method extends the ambiguity distance to 26 km despite a soliton spatial period of only 16 mm. This chip-based source is an important step towards miniature dual-comb laser ranging systems that are suitable for photonic integration.

Solitons occur in many physical systems when a nonlinearity compensates wave dispersion. Their recent formation in microresonators opens a new research direction for nonlinear optical physics and provides a platform for miniaturization of spectroscopy and frequency metrology systems. These microresonator solitons orbit around a closed waveguide path and produce a repetitive output pulse stream at a rate set by the round-trip time. In this work counter-propagating solitons that simultaneously orbit in an opposing sense (clockwise/counter-clockwise) are studied. Despite sharing the same spatial mode family, their round-trip times can be precisely and independently controlled. Furthermore, a state is possible in which both the relative optical phase and relative repetition rates of the distinct soliton streams are locked. This state allows a single resonator to produce dual-soliton frequency-comb streams having different repetition rates, but with high relative coherence useful in both spectroscopy and laser ranging systems., Comment: Qi-Fan Yang and Xu Yi contributed equally to this work

Optical microcavities are essential in numerous technologies and scientific disciplines. However, their application in many areas relies exclusively upon discrete microcavities in order to satisfy challenging combinations of ultra-low-loss performance (high cavity-Q-factor) and cavity design requirements. Indeed, finding a microfabrication bridge connecting ultra-high-Q device functions with micro and nanophotonic circuits has been a long-term priority of the microcavity field. Here, an integrated ridge resonator having a record Q factor over 200 million is presented. Its ultra-low-loss and flexible cavity design brings performance that has been the exclusive domain of discrete silica and crytalline microcavity devices to integrated systems. Two distinctly different devices are demonstrated: soliton sources with electronic repetition rates and high-coherence Brillouin lasers. This multi-device capability and performance from a single integrated cavity platform represents a critical advance for future nanophotonic circuits and systems., Comment: (1) Added Fig.4 to show high-coherence Brillouin lasing using the integrated resonator; (2) Added system illustrations (Fig. 1a); (3) Changed title of paper to reflect demonstrations of both low-repetition-rate soliton mode locking and Brillouin laser using the integrated resonator; (4) Fig. 6 added in Methods to describe resonator-to-waveguide phase-matching control; (5) Other minor changes

Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and to offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power in the form of a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. A limiting case is demonstrated in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton is shown to induce bistable behavior in the spectral and temporal properties of the soliton. Also, an operating point of enhanced repetition-rate stability is predicted and observed. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications., Comment: Xu Yi, Qi-Fan Yang and Xueyue Zhang contributed equally to this work

Rapid characterization of optical and vibrational spectra with high resolution can identify species in cluttered environments and is important for assays and early alerts. In this regard, dual-comb spectroscopy has emerged as a powerful approach to acquire nearly instantaneous Raman and optical spectra with unprecedented resolution. Spectra are generated directly in the electrical domain and avoid bulky mechanical spectrometers. Recently, a miniature soliton-based comb has emerged that can potentially transfer the dual-comb method to a chip platform. Unlike earlier microcombs, these new devices achieve high-coherence, pulsed mode locking. They generate broad, reproducible spectral envelopes, which is essential for dual-comb spectroscopy. Here, dual-comb spectroscopy is demonstrated using these devices. This work shows the potential for integrated, high signal-to-noise spectroscopy with fast acquisition rates., Comment: 7 pages, 4 figures

Solitons are wavepackets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fiber waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical-potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The discovery of a new optical soliton can impact work in other areas of photonics including nonlinear optics and spectroscopy., Comment: Qi-Fan Yang and Xu Yi contributed equally to this work