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Second-harmonic generation allows for coherently bridging distant regions of the optical spectrum, with applications ranging from laser technology to self-referencing of frequency combs. However, accessing the nonlinear response of a medium typically requires high-power bulk sources, specific nonlinear crystals, and complex optical setups, hindering the path toward large-scale integration. Here we address all of these issues by engineering a chip-scale second-harmonic (SH) source based on the frequency doubling of a semiconductor laser self-injection-locked to a silicon nitride microresonator. The injection-locking mechanism, combined with a high-Q microresonator, results in an ultra-narrow intrinsic linewidth at the fundamental harmonic frequency as small as 57 Hz. Owing to the extreme resonant field enhancement, quasi-phase-matched second-order nonlinearity is photoinduced through the coherent photogalvanic effect and the high coherence is mapped on the generated SH field. We show how such optical poling technique can be engineered to provide efficient SH generation across the whole C and L telecom bands, in a reconfigurable fashion, overcoming the need for poling electrodes. Our device operates with milliwatt-level pumping and outputs SH power exceeding 2 mW, for an efficiency as high as 280%/W under electrical driving. Our findings suggest that standalone, highly-coherent, and efficient SH sources can be integrated in current silicon nitride photonics, unlocking the potential of $\chi^{(2)}$ processes in the next generation of integrated photonic devices., Comment: 8 pages, 4 figures

Photonic integrated circuits based on Lithium Niobate have demonstrated the vast capabilities afforded by material with a high Pockels coefficient, allowing linear and high-speed modulators operating at CMOS voltage levels for applications ranging from data-center communications and photonic accelerators for AI. However despite major progress, the industrial adoption of this technology is compounded by the high cost per wafer. Here we overcome this challenge and demonstrate a photonic platform that satisfies the dichotomy of allowing scalable manufacturing at low cost, while at the same time exhibiting equal, and superior properties to those of Lithium Niobate. We demonstrate that it is possible to manufacture low loss photonic integrated circuits using Lithium Tantalate, a material that is already commercially adopted for acoustic filters in 5G and 6G. We show that LiTaO3 posses equally attractive optical properties and can be etched with high precision and negligible residues using DUV lithography, diamond like carbon (DLC) as a hard mask and alkaline wet etching. Using this approach we demonstrate microresonators with an intrinsic cavity linewidth of 26.8 MHz, corresponding to a linear loss of 5.6 dB/m and demonstrate a Mach Zehnder modulator with Vpi L = 4.2 V cm half-wave voltage length product. In comparison to Lithium Niobate, the photonic integrated circuits based on LiTaO3 exhibit a much lower birefringence, allowing high-density circuits and broadband operation over all telecommunication bands (O to L band), exhibit higher photorefractive damage threshold, and lower microwave loss tangent. Moreover, we show that the platform supports generation of soliton microcombs in X-Cut LiTaO3 racetrack microresonator with electronically detectable repetition rate, i.e. 30.1 GHz., 8 pages, 4 figures

Low-noise microwave signals can be efficiently generated with microresonator-based dissipative Kerr solitons ('microcombs'). However, the achieved phase noise in integrated microcombs is presently several orders of magnitude above the limit imposed by fundamental thermorefractive noise. One of the major contributors to this additional noise is the pump laser frequency noise transduction to the soliton pulse repetition rate via the Raman self-frequency shift. Quiet points (QPs) allow minimizing the transduction of laser frequency noise to soliton group velocity. While this method has allowed partial reduction of phase noise towards the fundamental thermodynamical limit, it relies on accidental mode crossings and only leads to very narrow regions of laser detuning where cancellation occurs, significantly narrower than the cavity linewidth. Here we present a method to deterministically engineer the QP, both in terms of its spectral width, and position, showing an increased phase noise suppression. This is achieved using coupled high-Q resonators arranged in the Vernier configuration. Investigating a generalized Lugiato-Lefever equation that accounts for the hybridized mode spectral displacement, we discover a continuum of possible QPs within the soliton existence region, characterized by ultra-low noise performance. Furthermore, we discover that by using two controlled optical mode crossings, it is possible to achieve regions where the QPs interact with each other enabling a substantial increase of the noise suppression range. Our work demonstrates a promising way to reach the fundamental limit of low-noise microwave generation in integrated microcombs., 5 figures

Erbium-doped fiber lasers exhibit high coherence and low noise as required for applications in fiber optic sensing, gyroscopes, LiDAR, and optical frequency metrology. Endowing Erbium-based gain in photonic integrated circuits can provide a basis for miniaturizing low-noise fiber lasers to chip-scale form factor, and enable large-volume applications. Yet, while major progress has been made in the last decade on integrated lasers based on silicon photonics with III-V gain media, the integration of Erbium lasers on chip has been compounded by large laser linewidth. Recent advances in photonic integrated circuit-based high-power Erbium-doped amplifiers, make a new class of rare-earth-ion-based lasers possible. Here, we demonstrate a fully integrated chip-scale Erbium laser that achieves high power, narrow linewidth, frequency agility, and the integration of a III-V pump laser. The laser circuit is based on an Erbium-implanted ultralow-loss silicon nitride Si$_3$N$4$ photonic integrated circuit. This device achieves single-mode lasing with a free-running intrinsic linewidth of 50 Hz, a relative intensity noise of $$10 MHz offset, and output power up to 17 mW, approaching the performance of fiber lasers and state-of-the-art semiconductor extended cavity lasers. An intra-cavity microring-based Vernier filter enables wavelength tunability of $>$ 40 nm within the C- and L-bands while attaining side mode suppression ratio (SMSR) of $>$ 70 dB, surpassing legacy fiber lasers in tuning and SMRS performance. This new class of low-noise, tuneable Erbium waveguide laser could find applications in LiDAR, microwave photonics, optical frequency synthesis, and free-space communications. Our approach is extendable to other wavelengths, and more broadly, constitutes a novel way to photonic integrated circuit-based rare-earth-ion-doped lasers.

Photonic crystals, material structures in which the dielectric function varies periodically in one, two, or three dimensions, can provide exquisite control over the propagation and confinement of light. By tailoring their band structure, exceptional optical effects can be achieved, such as slow light propagation or, through the creation of photonic bandgaps, optical cavities with both a high quality factor and a small mode volume. Photonic crystal cavities have been used to realize compact nano-lasers and achieve strong coupling to quantum emitters, such as semiconductor quantum dots, color centers, or cold atoms. A useful attribute of photonic crystals is the ability to create chirped mirrors. Chirping has underpinned advances in ultra-fast lasers based on bulk mirrors, but has yet to be fully exploited in integrated photonics, where it could provide a means to engineer otherwise unattainable dispersion profiles for a range of nonlinear optical applications, including soliton frequency comb generation. The vast majority of integrated resonators for frequency combs make use of microring geometries, where only waveguide width and height are varied to engineer dispersion. Generation of frequency combs has been demonstrated with one-dimensional photonic crystal cavities made of silicon nitride, but the low index contrast prevents formation of broad soliton combs. We overcome these challenges by using a photonic-crystal Fabry-P\'erot resonator made of gallium phosphide, a material with a high refractive index and a Kerr nonlinearity 200 times larger than that of silicon nitride. We employ chirped photonic crystal mirrors to provide anomalous dispersion. With subharmonic pulsed pumping at an average power of 23.6 mW, we are able to access stable dissipative Kerr frequency combs. We demonstrate soliton formation with a 3-dB bandwidth of 3.0 THz, corresponding to a pulse duration of 60 fs., Comment: 22 pages, 16 figures

Microelectronic integration is a key enabler for the ubiquitous deployment of devices in large volumes ranging from MEMS and imaging sensors to consumer electronics. Such integration has also been achieved in photonics, where compact optical transceivers for data centers employ co-integrated photonic and electronic components. Chip-scale integration is of particular interest to coherent laser ranging i.e. frequency modulated continuous wave (FMCW LiDAR), a perception technology that benefits from instantaneous velocity and distance detection, eye-safe operation, long-range and immunity to interference. Full wafer-scale integration of this technology has been compounded by the stringent requirements on the lasers, requiring high optical coherence, low chirp nonlinearity and requiring optical amplifiers. Here, we overcome this challenge and demonstrate a photonic-electronic integrated circuit-based coherent LiDAR engine, that combined all functionalities using fully foundry-compatible wafer scale manufacturing. It is comprised of a micro-electronic based high voltage arbitrary waveform generator, a hybrid photonic circuit based tunable Vernier laser with piezoelectric actuators, and an erbium-doped waveguide optical amplifier - all realized in a wafer scale manufacturing compatible process that comprises III-V semiconductors, SiN silicon nitride photonic integrated circuits as well as 130nm SiGe BiCMOS technology. The source is a turnkey, linearization-free, and can serve as a 'drop-in' solution in any FMCW LiDAR, that can be seamlessly integrated with an existing focal plane and optical phased array LiDAR approaches, constituting a missing step towards a fully chip-scale integrated LiDAR system.

Recent advances in the development of ultra-low loss silicon nitride integrated photonic circuits have heralded a new generation of integrated lasers capable of reaching fiber laser coherence. However, these devices presently are based on self-injection locking of distributed feedback (DFB) laser diodes, increasing both the cost and requiring tuning of laser setpoints for their operation. In contrast, turn-key legacy laser systems use reflective semiconductor optical amplifiers (RSOA). While this scheme has been utilized for integrated photonics-based lasers, so far, no cost-effective RSOA-based integrated lasers exist that are low noise and simultaneously feature fast, mode-hop-free and linear frequency tuning as required for frequency modulated continuous wave (FMCW) LiDAR or for laser locking in frequency metrology. Here we overcome this challenge and demonstrate a RSOA-based, frequency agile integrated laser, that can be tuned with high speed, with high linearity at low power. This is achieved using monolithic integration of piezoelectrical actuators on ultra-low loss silicon nitride photonic integrated circuits in a Vernier filter-based laser scheme. The laser operates at 1550 nm, features 6 mW output power, 400 Hz intrinsic laser linewidth, and allows ultrafast wavelength switching within 7 ns rise time and 75 nW power consumption. In addition, we demonstrate the suitability for FMCW LiDAR by showing laser frequency tuning over 1.5 GHz at 100 kHz triangular chirp rate with nonlinearity of 0.25% after linearization, and use the source for measuring a target scene 10 m away with a 8.5 cm distance resolution.

Silicon nitride (Si 3 N 4 ) is an ever-maturing integrated platform for nonlinear optics but mostly considered for third-order [χ (3) ] nonlinear interactions. Recently, second-order [χ (2) ] nonlinearity was introduced into Si 3 N 4 via the photogalvanic effect, resulting in the inscription of quasi-phase–matched χ (2) gratings. However, the full potential of the photogalvanic effect in microresonators remains largely unexplored for cascaded effects. Here, we report combined χ (2) and χ (3) nonlinear effects in a normal dispersion Si 3 N 4 microresonator. We demonstrate that the photo-induced χ (2) grating also provides phase-matching for the sum-frequency generation process, enabling the initiation and successive switching of primary combs. In addition, the doubly resonant pump and second-harmonic fields allow for effective third-harmonic generation, where a secondary optically written χ (2) grating is identified. Last, we reach a broadband microcomb state evolved from the sum-frequency–coupled primary comb. These results expand the scope of cascaded effects in microresonators.

Photonic integrated circuits are indispensible for data transmission within modern datacenters and pervade into multiple application spheres traditionally limited for bulk optics, such as LiDAR and biosensing. Of particular interest are ferroelectrics such as Lithium Niobate, which exhibit a large electro-optical Pockels effect enabling ultrafast and efficient modulation, but are difficult to process via dry etching . For this reason, etching tightly confining waveguides - routinely achieved in silicon or silicon nitride - has not been possible. Diamond-like carbon (DLC) was discovered in the 1950s and is a material that exhibits an amorphous phase, excellent hardness, and the ability to be deposited in nano-metric thin films. It has excellent thermal, mechanical, and electrical properties, making it an ideal protective coating. Here we demonstrate that DLC is also a superior material for the manufacturing of next-generation photonic integrated circuits based on ferroelectrics, specifically Lithium Niobate on insulator (LNOI). Using DLC as a hard mask, we demonstrate the fabrication of deeply etched, tightly confining, low loss photonic integrated circuits with losses as low as 5.6 dB/m. In contrast to widely employed ridge waveguides, this approach benefits from a more than 1 order of magnitude higher area integration density while maintaining efficient electro-optical modulation, low loss, and offering a route for efficient optical fiber interfaces. As a proof of concept, we demonstrate a frequency agile hybrid integrated III-V Lithium Niobate based laser with kHz linewidth and tuning rate of 0.7 Peta-Hertz per second with excellent linearity and CMOS-compatible driving voltage. Our approach can herald a new generation of tightly confining ferroelectric photonic integrated circuits., 10 pages, 5 figures

An enduring challenge in constructing mechanical oscillator-based hybrid quantum systems is to ensure engineered coupling to an auxiliary degree of freedom while maintaining good mechanical isolation from the environment, that is, low quantum decoherence, consisting of thermal decoherence and dephasing. Here, we overcome this challenge by introducing a superconducting circuit optomechanical platform which exhibits a low quantum decoherence while having a large optomechanical coupling, which allows us to prepare the quantum ground and squeezed states of motion with high fidelity. We directly measure a thermal decoherence rate of 20.5 Hz (corresponding to T_1 = 7.7 ms) as well as a pure dephasing rate of 0.09 Hz, resulted in a 100-fold improvement of quantum-state lifetime compared to the prior optomechanical systems. This enables us to reach to 0.07 quanta motional ground state occupation (93% fidelity) and realize mechanical squeezing of -2.7 dB below zero-point-fluctuation. Furthermore, we observe the free evolution of mechanical squeezed state, preserving its non-classical nature over milli-second timescales. Such ultra-low quantum decoherence not only increases the fidelity of quantum control and measurement of macroscopic mechanical systems, but may also benefit interfacing with qubits, and places the system in a parameter regime suitable for tests of quantum gravity. (Keywords: Quantum optomechanics, Superconducting circuit electromechanics, Quantum squeezing, Quantum memory, Quantum coherence)

We theoretically and experimentally investigate the formation of dissipative coherent structures in Kerr nonlinear optical microresonators, whose integrated dispersion exceeds the free-spectral range. We demonstrate that the presence of any periodic modulation along the resonator's circumference, such as periodically varying dispersion, can excite higher-order comb structures. We explore the outcomes of coherent microcomb generation in both cases of anomalous and normal dispersion. We are able to access this regime in microresonators via the high peak power of synchronous pulse-driving. For solitons in anomalous dispersion, we observe the formation of higher-order phase-matched dispersive waves (`Kelly-like' sidebands), where the folded dispersion crosses the frequency comb grid. In normal dispersion, we see the coexistence of switching wave fronts with Faraday instability-induced period-doubling patterns, manifesting as powerful satellite microcombs highly separated either side of the core microcomb while sharing the same repetition rate. This regime of dispersion-modulated phase matching opens a dimension of Kerr cavity physics and microcomb generation, particularly for the spectral extension and tuneability of microcombs in normal dispersion., Comment: Supplementary information will be added to posting in coming days

Recently, integrated photonic circuits have brought new capabilities to electron microscopy and been used to demonstrate efficient electron phase modulation and electron-photon correlations. Here, we quantitatively analyze the feasibility of high fidelity and high purity quantum state heralding using a free electron and a photonic integrated circuit with parametric coupling, and propose schemes to shape useful electron and photonic states in different application scenarios. Adopting a dissipative quantum electrodynamics treatment, we formulate a framework for the coupling of free electrons to waveguide spatial-temporal modes. To avoid multimode-coupling induced state decoherence, we show that with proper waveguide design, the interaction can be reduced to a single-mode coupling to a quasi-TM00 mode. In the single-mode coupling limit, we go beyond the conventional state ladder treatment, and show that the electron-photon energy correlations within the ladder subspace can still lead to a fundamental purity and fidelity limit on complex optical and electron state preparations through heralding schemes. We propose applications that use this underlying correlation to their advantage, but also show that the imposed limitations for general applications can be overcome by using photonic integrated circuits with an experimentally feasible interaction length, showing its promise as a platform for free-electron quantum optics.

The availability of thin-film lithium niobate on insulator (LNOI) and advances in processing have led to the emergence of fully integrated LiNbO3 electro-optic devices, including low-voltage, high-speed modulators, electro-optic frequency combs, and microwave-optical transducers. Yet to date, LiNbO3 photonic integrated circuits (PICs) have mostly been fabricated using non-standard etching techniques that lack the reproducibility routinely achieved in silicon photonics. Widespread future application of thin-film LiNbO3 requires a reliable and scalable solution using standard processing and precise lithographic control. Here we demonstrate a heterogeneously integrated LiNbO3 photonic platform that overcomes the abovementioned challenges by employing wafer-scale bonding of thin-film LiNbO3 to planarized low-loss silicon nitride (Si3N4) photonic integrated circuits, a mature foundry-grade integrated photonic platform. The resulting devices combine the substantial Pockels effect of LiNbO3 with the scalability, high-yield, and complexity of the underlying Si3N4 PICs. Importantly, the platform maintains the low propagation loss (

The ability to amplify optical signals is of pivotal importance across science and technology. The development of optical amplifiers has revolutionized optical communications, which are today pervasively used in virtually all sensing and communication applications of coherent laser sources. In the telecommunication bands, optical amplifiers typically utilize gain media based on III-V semiconductors or rare-earth-doped fibers. Another way to amplify optical signals is to utilize the Kerr nonlinearity of optical fibers or waveguides via parametric processes. Such parametric amplifiers of travelling continuous wave have been originally developed in the microwave domain, and enable quantum-limited signal amplification with high peak gain, broadband gain spectrum tailored via dispersion control, and ability to enable phase sensitive amplification. Despite these advantages, optical amplifiers based on parametric gain have proven impractical in silica fibers due to the low Kerr nonlinearity. Recent advances in photonic integrated circuits have revived interest in parametric amplifiers due to the significantly increased nonlinearity in various integrated platforms. Yet, despite major progress, continuous-wave-pumped parametric amplifiers built on photonic chips have to date remained out of reach. Here we demonstrate a chip-based travelling-wave optical parametric amplifier with net signal gain in the continuous-wave regime. Using ultralow-loss, dispersion-engineered, meter-long, silicon nitride photonic integrated circuits that are tightly coiled on a photonic chip, we achieve a continuous parametric gain of 12 dB that exceeds both the on-chip optical propagation loss and fiber-chip-fiber coupling losses in the optical C-band.

We theoretically study the dynamics and spatio-temporal pattern formation of driven lattices of nonlinear optical microresonators and analyze the formation of dissipative structures, in particular dissipative Kerr solitons. We consider both equally coupled one-dimensional chains, as well as the topological Su-Schrieffer-Heeger model. We show the complexity of the four-wave mixing pathways arising in these systems with the increasing dimensionality due to the combined spatial and synthetic frequency dimension of each resonator, and show that it can be modeled using a two-dimensional variant of the Lugiato-Lefever equation. We demonstrate the existence of two fundamentally different dynamical regimes in one-dimensional chains - elliptic and hyperbolic - inherent to the system. In the elliptic regime, we generate hexagonal patterns and a two-dimensional dissipative Kerr soliton corresponding to the global spatio-temporal mode-locking and discuss its similarity to edge-state solitons in the two-dimensional Haldane topological lattice. We find that the presence of the second dimension leads to the observation of regularized wave collapse. Furthermore, we study similarities and differences between a one-dimensional topological lattice and a single cavity and analyze nonlinearly induced edge-to-bulk scattering in the Su-Schrieffer-Heeger model. Moreover, we show that soliton formation can both be impaired in trivial but, importantly, also topologically protected bands due to nonlinear bulk edge scattering., 11 pages, 6 figures

Low-noise lasers are of central importance in a wide variety of applications, including high spectral-efficiency coherent communication protocols, distributed fibre sensing, and long distance coherent LiDAR. In addition to low phase noise, frequency agility, that is, the ability to achieve high-bandwidth actuation of the laser frequency, is imperative for triangular chirping in frequency-modulated continuous-wave (FMCW) based ranging or any optical phase locking as routinely used in metrology. While integrated silicon-based lasers have experienced major advances and are now employed on a commercial scale in data centers, integrated lasers with sub-100 Hz-level intrinsic linewidth are based on optical feedback from photonic circuits that lack frequency agility. Here, we demonstrate a wafer-scale-manufacturing-compatible hybrid photonic integrated laser that exhibits ultralow intrinsic linewidth of 25 Hz while offering unsurpassed megahertz actuation bandwidth, with a tuning range larger than 1 GHz. Our approach uses ultralow-loss (1 dB/m) Si$_3$N$_4$ photonic microresonators, combined with aluminium nitride (AlN) or lead zirconium titanate (PZT) microelectromechanical systems (MEMS) based stress-optic actuation. Electrically driven low-phase noise lasing is attained by self-injection locking of an Indium Phosphide (InP) laser chip and only limited by fundamental thermo-refractive noise. By utilizing difference drive and apodization of the photonic chip, a flat actuation response up to 10 MHz is achieved. We leverage this capability to demonstrate a compact coherent LiDAR engine that can generate up to 800 kHz FMCW triangular optical chirp signals, requiring neither any active linearization nor predistortion compensation, and perform a 10 m optical ranging experiment, with a resolution of 12.5 cm.

Multi-mode waveguides are ubiquitously used in integrated photonics. Although interaction among different spatial waveguide eigenmodes can induce novel nonlinear phenomena, spatial mode interaction is typically undesired. Adiabatic bends, such as Euler bends, have been favoured to suppress spatial mode interaction. Here, we adapt and optimize Euler bends to build compact racetrack microresonators based on ultralow-loss, multi-mode, silicon nitride photonic integrated circuits. The racetrack microresonators feature a footprint of only 0.21 mm(2) for 19.8 GHz free spectral range, suitable for tight photonic integration. We quantitatively investigate the suppression of spatial mode interaction in the racetrack microresonators with Euler bends. We show that the low optical loss rate (15.5 MHz) is preserved, on par with the mode interaction strength (25 MHz). This results in an unperturbed microresonator dispersion profile. We further generate a single dissipative Kerr soliton of 19.8 GHz repetition rate without complex laser tuning schemes or auxiliary lasers. The optimized Euler bends and racetrack microresonators can be building blocks for integrated nonlinear photonic systems, as well as linear circuits for programmable processors or photonic quantum computing., Adiabatic bends are used to reduce the optical loss of waveguides for integrated optics, but quantitative analysis of their adiabaticity have not been reported. Here, racetrack microresonators with circular and Euler bends are compared quantitatively, showing that the adiabatic Euler bends can preserve low optical loss and avoid spatial mode interaction in multimode waveguides.

The past decade has witnessed major advances in the development of microresonator-based frequency combs (microcombs) that are broadband optical frequency combs with repetition rates in the millimeter-wave to microwave domain. Integrated microcombs can be manufactured using wafer-scale process and have been applied in numerous applications. Most of these advances are based on the harnessing of dissipative Kerr solitons (DKS) in optical microresonators with anomalous group velocity dispersion (GVD). However, microcombs can also be generated with normal GVD using dissipative localized structures that are referred to as "dark pulse", "switching wave" or "platicon". Importantly, as most materials feature intrinsic normal GVD, the requirement of dispersion engineering is significantly relaxed for platicon generation. Therefore while DKS microcombs require particular designs and fabrication processes, platicon microcombs can be readily built using standard CMOS-compatible platforms such as thin-film (i.e. typically below 300 nm) Si3N4. Yet laser self-injection locking that has been recently used to create highly compact integrated DKS microcomb modules has not been demonstrated for platicons. Here we report the first fully integrated platicon microcomb operating at a microwave-K-band repetition rate. Using laser self-injection locking of a DFB laser edge-coupled to a Si3N4 microresonator, platicons are electrically initiated and stably maintained, enabling a compact microcomb module without any complex control. We further characterize the phase noise of the platicon repetition rate and the pumping laser. The observation of self-injection-locked platicons facilitates future wide adoption of microcombs as a build-in block in standard photonic integrated architectures via commercial foundry service.

Silicon photonics enables wafer-scale integration of optical functionalities on chip. A silicon-based laser frequency combs could significantly expand the applications of silicon photonics, by providing integrated sources of mutually coherent laser lines for terabit-per-second transceivers, parallel coherent LiDAR, or photonics-assisted signal processing. Here, we report on heterogeneously integrated laser soliton microcombs combining both InP/Si semiconductor lasers and ultralow-loss silicon nitride microresonators on monolithic silicon substrate. Thousands of devices are produced from a single wafer using standard CMOS techniques. Using on-chip electrical control of the microcomb-laser relative optical phase, these devices can output single-soliton microcombs with 100 GHz repetition rate. Our approach paves the way for large-volume, low-cost manufacturing of chip-based frequency combs for next-generation high-capacity transceivers, datacenters, space and mobile platforms.

Solitons are shape preserving waveforms that are ubiquitous across nonlinear dynamical systems and fall into two separate classes, that of bright solitons, formed in the anomalous group velocity dispersion regime, and `dark solitons' in the normal dispersion regime. Both types of soliton have been observed in BEC, hydrodynamics, polaritons, and mode locked lasers, but have been particularly relevant to the generation of chipscale microresonator-based frequency combs (microcombs), used in numerous system level applications in timing, spectroscopy, and communications. For microcombs, both bright solitons, and alternatively dark pulses based on interlocking switching waves, have been studied. Yet, the existence of localized dissipative structures that fit between this dichotomy has been theoretically predicted, but proven experimentally elusive. Here we report the discovery of dissipative structures that embody a hybrid between switching waves and dissipative solitons, existing in the regime of (nearly) vanishing group velocity dispersion where third-order dispersion is dominant, hence termed as `zero-dispersion solitons'. These dissipative structures are formed via collapsing switching wave fronts, forming clusters of quantized solitonic sub-structures. The switching waves are formed directly via synchronous pulse-driving of a photonic chip-based Si3N4 microresonator. The resulting frequency comb spectrum is extremely broad in both the switching wave and zero-dispersion soliton regime, reaching 136 THz or 97% of an octave. Fourth-order dispersion engineering results in dual-dispersive wave formation, and a novel quasi-phase matched wave related to Faraday instability. This exotic unanticipated dissipative structure expands the domain of Kerr cavity physics to the regime near zero-dispersion and could present a superior alternative to conventional solitons for broadband comb generation., Comment: 11 pages, 6 figures. 1 video as supplementary information. 1 Supplementary Information Document

The driven-dissipative photonic dimer comprised of two evanescently coupled high-Q microresonators is a fundamental element of multimode soliton lattices. It has demonstrated a variety of emergent nonlinear phenomena including supermode soliton generation, symmetry breaking, and soliton hopping. In this article, we present another aspect of dissipative soliton generation in coupled resonators, revealing the advantages of this system over conventional single resonator platforms. Namely, we show that the accessibility of solitons drastically varies for symmetric and antisymmetric supermode families of the dimer. Linear measurements reveal that the coupling between transverse modes, which gives rise to avoided mode crossings, can be almost completely suppressed. We explain the origin of this phenomenon and show its crucial influence on the dissipative Kerr soliton formation process in lattices of coupled high-Q resonators of any type. Choosing a particular example of the topological Su-Schrieffer-Heeger model, we demonstrate how the edge state can be protected from the interaction with higher-order modes, allowing for the formation of topological Kerr solitons.

Soliton microcombs constitute chip-scale optical frequency combs, and have the potential to impact a myriad of applications from frequency synthesis and telecommunications to astronomy. The requirement on external driving lasers has been significantly relaxed with the demonstration of soliton formation via self-injection locking of the pump laser to the microresonator. Yet to date, the dynamics of this process has not been fully understood. Prior models of self-injection locking were not able to explain sufficiently large detunings, crucial for soliton formation. Here we develop a theoretical model of self-injection locking to a nonlinear microresonator (nonlinear self-injection locking) for the first time and show that self- and cross-phase modulation of the clockwise and counter-clockwise light enables soliton formation. Using an integrated soliton microcomb of directly detectable 30 GHz repetition rate, consisting of a DFB laser self-injection-locked to a Si3N4 microresonator chip, we study the soliton formation dynamics via self-injection locking, as well as the repetition rate evolution, experimentally. We reveal that Kerr nonlinearity in microresonator significantly modifies locking dynamics, making laser emission frequency red detuned. We propose and implement a novel technique for measurements of the nonlinear frequency tuning curve and concurrent observation of microcomb states switching in real time.

Photonic chip-based soliton microcombs have shown rapid progress and have already been used in many system-level applications, including coherent communications, astrophysical spectrometer calibration and ultrafast ranging. While there has been substantial progress in realizing soliton microcombs that rely on compact laser diodes, culminating in devices that only utilize a semiconductor amplifier or a self-injection-locked laser as a pump source, accessing and generating single soliton states with electronically detectable line rates from a compact laser module has remained challenging. Here we demonstrate a current-initiated, $\mathrm{Si_3N_4}$ chip-based, 99-GHz soliton microcomb driven directly by an ultra-compact, low-noise laser. This approach does not require any fast laser tuning mechanism, and single soliton states can be accessed by changing the current of the laser diode. A simple, yet reliable, packaging technique has been developed to demonstrate the viability of such a microcomb system in field-deployable applications., 5 Pages, 3 figures

Integrated photonics is increasing in importance for compact, robust, and scalable enabling quantum technologies. This is particularly interesting for developing quantum communication networks, where resources need to be deployed in the field. We exploit photonic chip-based $ \rm Si_3 N_4$ ring microresonators for the generation of photon pairs with low-loss, high-noise suppression and coincidence rates of $80\times 10^3\,$s$^{-1}$. A simple photonic noise characterisation technique is presented that distinguishes linear and nonlinear contributions that is useful for system design and optimisation. We then demonstrate an all-fibre $750\,$MHz clock-rate sequential Time-Bin entanglement scheme with raw interference visibilities $>\,98\,\%$.

Microwave photonic technologies, which upshift the carrier into the optical domain to facilitate the generation and processing of ultrawide-band electronic signals at vastly reduced fractional bandwidths, have the potential to achieve superior performance compared to conventional electronics for targeted functions. For microwave photonic applications such as filters, coherent radars, subnoise detection, optical communications and low-noise microwave generation, frequency combs are key building blocks. By virtue of soliton microcombs, frequency combs can now be built using CMOS compatible photonic integrated circuits, operated with low power and noise, and have already been employed in system-level demonstrations. Yet, currently developed photonic integrated microcombs all operate with repetition rates significantly beyond those that conventional electronics can detect and process, compounding their use in microwave photonics. Here we demonstrate integrated soliton microcombs operating in two widely employed microwave bands, X- and K-band. These devices can produce more than 300 comb lines within the 3-dB-bandwidth, and generate microwave signals featuring phase noise levels below 105 dBc/Hz (140 dBc/Hz) at 10 kHz (1 MHz) offset frequency, comparable to modern electronic microwave synthesizers. In addition, the soliton pulse stream can be injection-locked to a microwave signal, enabling actuator-free repetition rate stabilization, tuning and microwave spectral purification, at power levels compatible with silicon-based lasers (

Supercontinuum generation in optical fibers is one of the most dramatic nonlinear effects discovered, allowing short pulses to be converted into multi-octave spanning coherent spectra. However, generating supercontinua that are both coherent and broadband requires pulses that are simultaneously ultrashort with high peak power. This results in a reducing efficiency with increasing pulse repetition rate, that has hindered supercontinua at microwave line spacing, i.e. 10s of GHz. Soliton microcombs by contrast, can generate octave-spanning spectra, but with good conversion efficiency only at vastly higher repetition rates in the 100s of GHz. Here, we bridge this efficiency gap with resonant supercontinuum, allowing supercontinuum generation using input pulses with an ultra-low 6 picojoule energy, and duration of 1 picosecond, 10-fold longer than what is typical. By applying synchronous pulse-driving to a dispersion-engineered, low-loss Si$_3$N$_4$ photonic chip microresonator, we generate dissipative Kerr solitons with a strong dispersive wave, both bound to the input pulse. This creates a smooth, flattened 2,200 line frequency comb, with an electronically detectable repetition rate of 28 GHz, constituting the largest bandwidth-line-count product for any microcomb generated to date. Strikingly, we observe that solitons exist in a weakly bound state with the input pulse, stabilizing their repetition rate, but simultaneously allowing noise transfer from one to the other to be suppressed even for offset frequencies 100 times lower than the linear cavity decay rate. We demonstrate that this nonlinear filtering can be enhanced by pulse-driving asynchronously, in order to preserve the coherence of the comb. Taken together, our work establishes resonant supercontinuum as a promising route to broadband and coherent spectra.

On-chip optical waveguides with low propagation losses and precisely engineered group velocity dispersion (GVD) are important to nonlinear photonic devices such as soliton microcombs. Yet, despite intensive research efforts, nonlinear integrated photonic platforms still feature propagation losses orders of magnitude higher than in standard optical fiber. The tight confinement and high index contrast of integrated waveguides make them highly susceptible to fabrication induced surface roughness. Therefore, microresonators with ultra-high Q factors are, to date, only attainable in polished bulk crystalline, or chemically etched silica based devices, that pose however challenges for full photonic integration. Here, we demonstrate the fabrication of silicon nitride ($\mathrm{Si_3N_4}$) waveguides with unprecedentedly smooth sidewalls and tight confinement with record low propagation losses. This is achieved by combining the photonic Damascene process with a novel reflow process, which reduces etching roughness, while sufficiently preserving dimensional accuracy. This leads to previously unattainable \emph{mean} microresonator Q factors larger than $5\times10^6$ for tightly confining waveguides with anomalous dispersion. Via systematic process step variation and two independent characterization techniques we differentiate the scattering and absorption loss contributions, and reveal metal impurity related absorption to be an important loss origin. Although such impurities are known to limit optical fibers, this is the first time they are identified, and play a tangible role, in absorption of integrated microresonators. Taken together, our work provides new insights in the origins of propagation losses in $\mathrm{Si_3N_4}$ waveguides and provides the technological basis for integrated nonlinear photonics in the ultra-high Q regime.

Directly accessing the middle infrared, the molecular functional group spectral region, via supercontinuum generation processes based on turn-key fiber lasers offers the undeniable advantage of simplicity and robustness. Recently, the assessment of the coherence of the mid-IR dispersive wave in silicon nitride waveguides, pumped at telecom wavelength, established an important first step towards mid-IR frequency comb generation based on such compact systems. Yet, the spectral reach and efficiency still fall short for practical implementation. Here, we experimentally demonstrate for the first time to our knowledge, that fs-fiber laser driven systems based on large-cross section silicon nitride waveguides can reach, with powers sufficient to drive dual-comb spectroscopy, the important greenhouse gases spectral region near 4 micron, typically accessed through different frequency generation or more complex approaches. We show, from a 2 micron femtosecond fiber laser, up to 30% power conversion and milliwatt-level output powers, proving that such sources are suitable candidate for compact, chip-integrated spectroscopic and sensing applications.

Elastic strain engineering utilizes stress to realize unusual material properties. For instance, strain can be used to enhance the electron mobility of a semiconductor, enabling more efficient solar cells and smaller, faster transistors. In the context of nanomechanics, the pursuit of resonators with ultra-high coherence has led to intense study of a complementary strain engineering technique, "dissipation dilution", whereby the stiffness of a material is effectively increased without added loss. Dissipation dilution is known to underlie the anomalously high Q factor of Si$_3$N$_4$ nanomechanical resonators, including recently-developed "soft-clamped" resonators; however, the paradigm has to date relied on weak strain produced during material synthesis. By contrast, the use of geometric strain engineering techniques -- capable of producing local stresses near the material yield strength -- remains largely unexplored. Here we show that geometric strain combined with soft-clamping can produce unprecedentedly high Q nanomechanical resonators. Specifically, using a spatially non-uniform phononic crystal pattern, we colocalize the strain and flexural motion of a Si$_3$N$_4$ nanobeam, while increasing the former to near the yield strength. This combined strategy produces string-like modes with room-temperature Q$\times$frequency products approaching $10^{15}$ Hz, an unprecedented value for a mechanical oscillator of any size. The devices we study can have force sensitivities of aN/rtHz, perform hundreds of quantum coherent oscillations at room temperature, and attain Q > 400 million at radio frequencies. These results signal a paradigm shift in the control of nanomechanical dissipation, with impact ranging from precision force microscopy to tests of quantum gravity. Combining the reported approach with crystalline or 2D materials may lead to further improvement, of as yet unknown limitation., 9 pages, 8 figures

Kerr optical frequency combs with multi-gigahertz spacing have previously been demonstrated in chip-scale microresonators, with potential applications in coherent communication, spectroscopy, arbitrary waveform generation, and radio frequency photonic oscillators. In general, the harmonics of a frequency comb are identically polarized in a single microresonator. In this work, we report that one comb in one polarization is generated by an orthogonally polarized soliton comb and two low-noise, orthogonally polarized combs interact with each other and exist simultaneously in a single microresonator. The second comb generation is attributed to the strong cross-phase modulation with the orthogonally polarized soliton comb and the high peak power of the intracavity soliton pulse. Experimental results show that a second frequency comb is excited even when a continuous wave light as a "seed"-with power as low as 0.1 mW-is input, while its own power level is below the threshold of comb generation. Moreover, the second comb has a concave envelope, which is different from the sech2 envelope of the soliton comb. This is due to the frequency mismatch between the harmonics and the resonant frequency. We also find that the repetition rates of these two combs coincide, although two orthogonal resonant modes are characterized by different free spectral ranges.

Mid-infrared optical frequency combs are of significant interest for molecular spectroscopy due to the large absorption of molecular vibrational modes on one hand, and the ability to implement superior comb-based spectroscopic modalities with increased speed, sensitivity and precision on the other hand. Substantial advances in mid-infrared frequency comb generation have been made in recent years based on nonlinear frequency conversion, microresonator Kerr frequency combs, quantum cascade lasers and mode locking regimes. Here we demonstrate a simple, yet effective method for the direct generation of mid-infrared optical frequency combs in the region from ${2.5-4~\mu{\rm m}}$, i.e. ${2500-4000~{\rm cm}^{-1}}$ covering a large fraction of the functional group region, directly from a conventional and compact erbium-fiber-based femtosecond laser in the telecommunication band (i.e. ${1.55~\mu{\rm m}}$). The wavelength conversion is based on dispersive wave generation within the supercontinuum process in large-cross-section and dispersion-engineered silicon nitride (${\rm Si_3N_4}$) waveguides. The long-wavelength dispersive wave, with its position lithographically determined, performs as a mid-infrared frequency comb, whose coherence is demonstrated via optical heterodyne measurements. Such a simple and versatile approach to mid-infrared frequency comb generation is suitable for spectroscopic applications in the first mid-infrared atmospheric window. Moreover, the compactness and simplicity of the approach have the potential to realize compact dual-comb spectrometers. The generated combs have a fine teeth-spacing, making them also suitable for gas phase analysis.

Integrated waveguides exhibiting efficient second-order nonlinearities are crucial to obtain compact and low power optical signal processing devices. Silicon nitride (SiN) has shown second harmonic generation (SHG) capabilities in resonant structures and single-pass devices leveraging intermodal phase matching, which is defined by waveguide design. Lithium niobate allows compensating for the phase mismatch using periodically poled waveguides, however the latter are not reconfigurable and remain difficult to integrate with SiN or silicon (Si) circuits. Here we show the all-optical enhancement of SHG in SiN waveguides by more than 30 dB. We demonstrate that a Watt-level laser causes a periodic modification of the waveguide second-order susceptibility. The resulting second order nonlinear grating has a periodicity allowing for quasi phase matching (QPM) between the pump and SH mode. Moreover, changing the pump wavelength or polarization updates the period, relaxing phase matching constraints imposed by the waveguide geometry. We show that the grating is long term inscribed in the waveguides, and we estimate a second order nonlinearity of the order of 0.3 pm/V, while a maximum conversion efficiency (CE) of 1.8x10-6 W-1 cm-2 is reached.

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

Self-referencing turns pulsed laser systems into self-referenced frequency combs. Such frequency combs allow counting of optical frequencies and have a wide range of applications. The required optical bandwidth to implement self-referencing is typically obtained via nonlinear broadening in optical fibers. Recent advances in the field of Kerr frequency combs have provided a path towards the development of compact frequency comb sources that provide broadband frequency combs, exhibit microwave repetition rates and that are compatible with on-chip photonic integration. These devices have the potential to significantly expand the use of frequency combs. Yet to date self-referencing of such Kerr frequency combs has only been attained by applying conventional, fiber based broadening techniques. Here we demonstrate external broadening-free self-referencing of a Kerr frequency comb. An optical spectrum that spans two-thirds of an octave is directly synthesized from a continuous wave laser-driven silicon nitride microresonator using temporal dissipative Kerr soliton formation and soliton Cherenkov radiation. Using this coherent bandwidth and two continuous wave transfer lasers in a 2f-3f self-referencing scheme, we are able to detect the offset frequency of the soliton Kerr frequency comb. By stabilizing the repetition rate to a radio frequency reference the self-referenced frequency comb is used to count and track the continuous wave pump laser's frequency. This work demonstrates the principal ability of soliton Kerr frequency combs to provide microwave-to-optical clockworks on a chip., 6 pages, 4 figures

The coupling of laser light to a mechanical oscillator via radiation pressure leads to the emergence of quantum mechanical correlations between the amplitude and phase quadrature of the laser beam. These correlations form a generic non-classical resource which can be employed for quantum-enhanced force metrology, and give rise to ponderomotive squeezing in the limit of strong correlations. To date, this resource has only been observed in a handful of cryogenic cavity optomechanical experiments. Here, we demonstrate the ability to efficiently resolve optomechanical quantum correlations imprinted on an optical laser field interacting with a room temperature nanomechanical oscillator. Direct measurement of the optical field in a detuned homodyne detector ("variational measurement") at frequencies far from the resonance frequency of the oscillator reveal quantum correlations at the few percent level. We demonstrate how the absolute visibility of these correlations can be used for a quantum-enhanced estimation of the quantum back-action force acting on the oscillator, and provides for an enhancement in the relative signal-to-noise ratio for the estimation of an off-resonant external force, even at room temperature.

High confinement, integrated silicon nitride (SiN) waveguides have recently emerged as attractive platform for on-chip nonlinear optical devices. The fabrication of high-Q SiN microresonators with anomalous group velocity dispersion (GVD) has enabled broadband nonlinear optical frequency comb generation. Such frequency combs have been successfully applied in coherent communication and ultrashort pulse generation. However, the reliable fabrication of high confinement waveguides from stoichiometric, high stress SiN remains challenging. Here we present a novel photonic Damascene fabrication process enabling the use of substrate topography for stress control and thin film crack prevention. With close to unity sample yield we fabricate microresonators with $1.35\,\mu\mathrm{m}$ thick waveguides and optical Q factors of $3.7\times10^{6}$ and demonstrate single temporal dissipative Kerr soliton (DKS) based coherent optical frequency comb generation. Our newly developed process is interesting also for other material platforms, photonic integration and mid infrared Kerr comb generation., Comment: Accepted for publication in Optica

The formation of temporal dissipative solitons in continuous wave laser driven microresonators enables the generation of coherent, broadband and spectrally smooth optical frequency combs as well as femtosecond pulses with compact form factor. Here we report for the first time on the observation of a Raman-induced soliton self-frequency shift for a microresonator soliton. The Raman effect manifests itself in amorphous SiN microresonator based single soliton states by a spectrum that is hyperbolic secant in shape, but whose center is spectrally red-shifted (i.e. offset) from the continuous wave pump laser. The Raman induced spectral red-shift is found to be tunable via the pump laser detuning and grows linearly with peak power. The shift is theoretically described by the first order shock term of the material's Raman response, and we infer a Raman shock time of 20 fs for amorphous SiN. Moreover, we observe that the Raman induced frequency shift can lead to a cancellation or overcompensation of the soliton recoil caused by the formation of a (coherent) dispersive wave. The observations are in excellent agreement with numerical simulations based on the Lugiato-Lefever equation (LLE) with a Raman shock term. Our results contribute to the understanding of Kerr frequency combs in the soliton regime, enable to substantially improve the accuracy of modeling and are relevant to the fundamental timing jitter of microresonator solitons.

This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb generation where they are of particular importance. Here, one example is spectral broadening and self-referencing enabled by the ultra-short pulsed nature of the solitons. Another example is dissipative Kerr soliton formation in integrated on-chip microresonators where the emission of a dispersive wave allows for the direct generation of unprecedentedly broadband and coherent soliton spectra with smooth spectral envelope., Comment: To appear in "Nonlinear optical cavity dynamics", ed. Ph. Grelu

We demonstrate dispersion engineering of integrated silicon nitride based ring resonators through conformal coating with hafnium dioxide deposited on top of the structures via atomic layer deposition (ALD). Both, magnitude and bandwidth of anomalous dispersion can be significantly increased. All results are confirmed by high resolution frequency-comb-assisted-diode-laser spectroscopy and are in very good agreement with the simulated modification of the mode spectrum., Comment: 4 pages, 4 figures

Stimulated Raman scattering (SRS) in ultra-high-Q surface-tension-induced spherical and chip-based toroid microcavities is considered both theoretically and experimentally. These microcavities are fabricated from silica, exhibit small mode volume (typically 1000 $\mu m^{3}$) and possess whispering-gallery type modes with long photon storage times (in the range of 100 ns), significantly reducing the threshold for stimulated nonlinear optical phenomena. Oscillation threshold levels of less than 100 $\mu $% -Watts of launched fiber pump power, in microcavities with quality factors of 100 million are observed. Using a steady state analysis of the coupled-mode equations for the pump and Raman whispering-gallery modes, the threshold, efficiencies and cascading properties of SRS in UHQ devices are derived. The results are experimentally confirmed in the telecommunication band (1550nm) using tapered optical fibers as highly efficient waveguide coupling elements for both pumping and signal extraction. The device performance dependence on coupling, quality factor and modal volume are measured and found to be in good agreement with theory. This includes analysis of the threshold and efficiency for cascaded Raman scattering. The side-by-side study of nonlinear oscillation in both spherical microcavities and toroid microcavities on-a-chip also allows for comparison of their properties. In addition to the benefits of a wafer-scale geometry, including integration with optical, electrical or mechanical functionality, microtoroids on-a-chip exhibit single mode Raman oscillation over a wide range of pump powers., Comment: 12 pages, 15 figures

Low phase noise lasers based on the combination of III-V semiconductors and silicon photonics are well established in the near-infrared spectral regime. Recent advances in the development of low-loss silicon nitride-based photonic integrated resonators have allowed to outperform bulk external diode and fiber lasers in both phase noise and frequency agility in the 1550 nm-telecommunication window. Here, we demonstrate for the first time a hybrid integrated laser composed of a gallium nitride (GaN) based laser diode and a silicon nitride photonic chip-based microresonator operating at record low wavelengths as low as 410 nm in the near-ultraviolet wavelength region suitable for addressing atomic transitions of atoms and ions used in atomic clocks, quantum computing, or for underwater LiDAR. Using self-injection locking to a high Q (0.4 $\times$ 10$^6$) photonic integrated microresonator we observe a phase noise reduction of the Fabry-P\'erot laser at 461 nm by a factor greater than 100$\times$, limited by the device quality factor and back-reflection., Comment: 10 pages, 8 figures