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Narrow-linewidth yet tunable laser oscillators are one of the most important tools for precision metrology, optical atomic clocks, sensing and quantum computing. Commonly used tunable coherent oscillators are based on stimulated emission or stimulated Brillouin scattering; as a result, the operating wavelength band is limited by the gain media. Based on nonlinear optical gain, optical parametric oscillators (OPOs) enable coherent signal generation within the whole transparency window of the medium used. However, the demonstration of OPO-based Hertz-level linewidth and tunable oscillators has remained elusive. Here, we present a tunable coherent oscillator based on a multimode coherent OPO in a high-Q microresonator, i.e., a microcomb. Single-mode coherent oscillation is realized through self-injection locking (SIL) of one selected comb line. We achieve coarse tuning up to 20 nm, and an intrinsic linewidth down to sub-Hertz level, which is three orders of magnitude lower than the pump. Furthermore, we demonstrate that this scheme results into repetition rate stabilization of the microcomb. These results open exciting possibilities for generating tunable coherent radiation where stimulated emission materials are difficult to obtain, and the stabilization of microcomb sources beyond the limits imposed by the thermorefractive noise in the cavity.

CMOS-compatible Kerr microcombs have drawn substantial interest as mass-manufacturable, compact alternatives to bulk frequency combs. This could enable deployment of many comb-reliant applications previously confined to laboratories. Particularly enticing is the prospect of microcombs performing optical frequency division in compact optical atomic clocks. Unfortunately, it is difficult to meet the self-referencing requirement of microcombs in these systems due to the $\sim$THz repetition rates typically required for octave-spanning comb generation. Additionally, it is challenging to spectrally engineer a microcomb system to align a comb mode with an atomic clock transition with sufficient signal-to-noise ratio. Here, we adopt a Vernier dual-microcomb scheme for optical frequency division of a stabilized ultranarrow-linewidth continuous-wave laser at 871 nm to a $\sim$235 MHz output frequency. In addition to enabling measurement of the comb repetition rates, this scheme brings the freedom to pick comb lines from either or both of the combs. We exploit this flexibility to shift an ultra-high-frequency ($\sim$100 GHz) carrier-envelope offset beat down to frequencies where detection is possible and to place a comb line close to the 871 nm laser - tuned so that if frequency-doubled it would fall close to the clock transition in $^{171}$Yb$^+$. Moreover, we introduce a novel scheme which suppresses frequency noise arising from interferometric phase fluctuations in our dual-comb system and reduces the frequency instability down to our measurement limit. Our dual-comb system can potentially combine with an integrated ion trap toward future chip-scale optical atomic clocks.

Astronomical precision spectroscopy underpins searches for life beyond Earth, direct observation of the expanding Universe and constraining the potential variability of physical constants across cosmological scales. Laser frequency combs can provide the critically required accurate and precise calibration to the astronomical spectrographs. For cosmological studies, extending the calibration with such astrocombs to the ultraviolet spectral range is highly desirable, however, strong material dispersion and large spectral separation from the established infrared laser oscillators have made this exceedingly challenging. Here, we demonstrate for the first time astronomical spectrograph calibrations with an astrocomb in the ultraviolet spectral range below 400 nm. This is accomplished via chip-integrated highly nonlinear photonics in periodically-poled, nano-fabricated lithium niobate waveguides in conjunction with a robust infrared electro-optic comb generator, as well as a chip-integrated microresonator comb. These results demonstrate a viable route towards astronomical precision spectroscopy in the ultraviolet and may contribute to unlocking the full potential of next generation ground- and future space-based astronomical instruments.

The analysis of optical spectra - emission or absorption -- has been arguably the most powerful approach for discovering and understanding matters. The invention and development of many kinds of spectrometers have equipped us with versatile yet ultra-sensitive diagnostic tools for trace gas detection, isotope analysis, and resolving hyperfine structures of atoms and molecules. With proliferating data and information, urgent and demanding requirements have been placed today on spectrum analysis with ever-increasing spectral bandwidth and frequency resolution. These requirements are especially stringent for broadband laser sources that carry massive information, and for dispersive devices used in information processing systems. In addition, spectrum analyzers are expected to probe the device's phase response where extra information is encoded. Here we demonstrate a novel vector spectrum analyzer (VSA) that is capable of characterizing passive devices and active laser sources in one setup. Such a dual-mode VSA can measure loss, phase response and dispersion properties of passive devices. It also can coherently map a broadband laser spectrum into the RF domain. The VSA features a bandwidth of 55.1 THz (1260 to 1640 nm), frequency resolution of 471 kHz, and dynamic range of 56 dB. Meanwhile, our fiber-based VSA is compact and robust. It requires neither high-speed modulators and photodetectors, nor any active feedback control. Finally, we successfully employ our VSA for applications including characterization of integrated dispersive waveguides, mapping frequency comb spectra, and coherent light detection and ranging (LiDAR). Our VSA presents an innovative approach for device analysis and laser spectroscopy, and can play a critical role in future photonic systems and applications for sensing, communication, imaging, and quantum information processing.

The foundry development of integrated photonics has revolutionized today's optical interconnect and datacenters. Over the last decade, we have witnessed the rising of silicon nitride (Si$_3$N$_4$) integrated photonics, which is currently transferring from laboratory research to foundry manufacturing. The development and transition are triggered by the ultimate need of low optical loss offered by Si$_3$N$_4$, which is beyond the reach of silicon and III-V semiconductors. Combined with modest Kerr nonlinearity, tight optical confinement and dispersion engineering, Si$_3$N$_4$ has today become the leading platform for linear and Kerr nonlinear photonics, and has enabled chip-scale lasers featuring ultralow noise on par with table-top fiber lasers. However, so far all the reported fabrication processes of tight-confinement, dispersion-engineered Si$_3$N$_4$ photonic integrated circuit (PIC) with optical loss down to few dB/m have only been developed on 4-inch or smaller wafers. Yet, to transfer these processes to established CMOS foundries that typically operate 6-inch or even larger wafers, challenges remain. In this work, we demonstrate the first foundry-standard fabrication process of Si$_3$N$_4$ PIC with only 2.6 dB/m loss, thickness above 800 nm, and near 100% fabrication yield on 6-inch wafers. Such thick and ultralow-loss Si$_3$N$_4$ PIC enables low-threshold generation of soliton frequency combs. Merging with advanced heterogeneous integration, active ultralow-loss Si$_3$N$_4$ integrated photonics could pave an avenue to addressing future demands in our increasingly information-driven society.

Lithium niobate (LN) is a promising material for future complex photonic-electronic circuits, with wide applications in fields like communications, sensing, quantum optics, and computation. LN took a great stride toward compact photonic integrated circuits (PICs) with the development of partially-etched LN on insulator (LNOI) waveguides. However, integration density is still limited for future high-compact PICs due to the partial edge nature of their waveguides. Here, we demonstrate a fully-etched LN PIC platform which, for the first time, simultaneously achieves ultra-low propagation loss and compact circuit size. The tightly-confined fully-etched LN waveguides with smooth sidewalls allow us to bring the bending radius down to 20 $\mu$m (corresponds to 1 THz FSR). We have achieved compact high-$Q$ microring resonators with $Q/V$ of 7.1 $\times$ 10$^{4}$ $\mu$m$^{-3}$, almost one order of magnitude larger than previous demonstrations. The statistical mean propagation losses of our LN waveguides is 8.5 dB/m (corresponds to mean $Q$-factor of 4.9 $\times$ 10$^{6}$) even with a small bending radius of 40 $\mu$m. Our compact and ultra-low-loss LN platform shows great potential in future miniaturized multifunctional integration systems. As complementary evidence to show the utility of our platform, we demonstrate soliton microcombs with an ultra-high repetition rate of 500 GHz in LN.

Structure-from-Motion is a technology used to obtain scene structure through image collection, which is a fundamental problem in computer vision. For unordered Internet images, SfM is very slow due to the lack of prior knowledge about image overlap. For sequential images, knowing the large overlap between adjacent frames, SfM can adopt a variety of acceleration strategies, which are only applicable to sequential data. To further improve the reconstruction efficiency and break the gap of strategies between these two kinds of data, this paper presents an efficient covisibility-based incremental SfM. Different from previous methods, we exploit covisibility and registration dependency to describe the image connection which is suitable to any kind of data. Based on this general image connection, we propose a unified framework to efficiently reconstruct sequential images, unordered images, and the mixture of these two. Experiments on the unordered images and mixed data verify the effectiveness of the proposed method, which is three times faster than the state of the art on feature matching, and an order of magnitude faster on reconstruction without sacrificing the accuracy. The source code is publicly available at https://github.com/openxrlab/xrsfm, Comment: Accepted 27 May 2023 (TCSVT)

Empowering autonomous agents with 3D understanding for daily objects is a grand challenge in robotics applications. When exploring in an unknown environment, existing methods for object pose estimation are still not satisfactory due to the diversity of object shapes. In this paper, we propose a novel framework for category-level object shape and pose estimation from a single RGB-D image. To handle the intra-category variation, we adopt a semantic primitive representation that encodes diverse shapes into a unified latent space, which is the key to establish reliable correspondences between observed point clouds and estimated shapes. Then, by using a SIM(3)-invariant shape descriptor, we gracefully decouple the shape and pose of an object, thus supporting latent shape optimization of target objects in arbitrary poses. Extensive experiments show that the proposed method achieves SOTA pose estimation performance and better generalization in the real-world dataset. Code and video are available at https://zju3dv.github.io/gCasp., Comment: CoRL 2022, 18 pages, 13 figures, typos corrected, references added

Measuring microcombs in amplitude and phase provides unique insight into the nonlinear cavity dynamics but spectral phase measurements are experimentally challenging. Here, we report a linear heterodyne technique assisted by electro-optic downconversion that enables differential phase measurement of such spectra with unprecedented sensitivity (-50 dBm) and bandwidth coverage (> 110 nm in the telecommunications range). We validate the technique with a series of measurements, including single cavity and photonic molecule microcombs.

Optical hyperparametric oscillation based on the third-order nonlinearity is one of the most significant mechanisms to generate coherent electromagnetic radiation and produce quantum states of light. Advances in dispersion-engineered high-$Q$ microresonators allow for generating signal waves far from the pump and decrease the oscillation power threshold to submilliwatt levels. However, the pump-to-signal conversion efficiency and absolute signal power are low, fundamentally limited by parasitic mode competition and attainable cavity intrinsic $Q$ to coupling $Q$ ratio, i.e., $Q_{\rm i}/Q_{\rm c}$. Here, we use Friedrich-Wintgen bound states in the continuum (BICs) to overcome the physical challenges in an integrated microresonator-waveguide system. As a result, on-chip coherent hyperparametric oscillation is generated in BICs with unprecedented conversion efficiency and absolute signal power. This work not only opens a path to generate high-power and efficient continuous-wave electromagnetic radiation in Kerr nonlinear media but also enhances the understanding of microresonator-waveguide system - an elementary unit of modern photonics.

Laser frequency combs are enabling some of the most exciting scientific endeavours in the 21st century, ranging from the development of optical clocks to the calibration of the astronomical spectrographs used for searching Earth-like exoplanets. Today, dissipative Kerr solitons generated in microresonators offer the prospect of attaining frequency combs in miniaturized systems by capitalizing on advances in photonic integration. Most of the applications based on soliton microcombs rely on tuning a continuous-wave laser into a longitudinal mode of a microresonator whose dimensions are engineered to display anomalous dispersion at the pump laser frequency. In this configuration, however, nonlinear physics precludes from attaining dissipative Kerr solitons with high power conversion efficiency, with typical comb powers amounting to ~1% of the available laser power. Here, we demonstrate that this fundamental limitation can be overcome by inducing a controllable frequency shift to a selected cavity resonance. Experimentally, we realize this shift using two linearly coupled anomalous-dispersion microresonators (a photonic molecule), resulting in a coherent dissipative Kerr soliton with a conversion efficiency exceeding 50% and excellent line spacing stability. We describe the physical soliton dynamics in this configuration, and discover the system displays unusual characteristics, such as the possibility to backwards initiate solitons and stable operation with a blue detuned pump laser. By optimizing the microcomb power available on chip, these results facilitate the practical implementation of a scalable integrated photonic architecture for energy-efficient applications.

Thermal noise usually dominates the low-frequency region of the optical phase noise of soliton microcombs, leading to decoherence and limiting many aspects of applications. In this work, we demonstrate a simple and reliable way to mitigate this noise by laser cooling with the pump laser. The key is rendering the pump laser to simultaneously excite two neighboring cavity modes from different families that are respectively red and blue detuned, one for soliton generation and the other one for laser cooling.

Multiple applications of relevance in photonics, such as spectrally efficient coherent communications, microwave synthesis or the calibration of astronomical spectrographs, would benefit from soliton microcombs operating at repetition rates <50GHz. However, attaining soliton microcombs with low repetition rates using photonic integration technologies represents a formidable challenge. Expanding the cavity volume results in a drop of intracavity intensity that can only be offset by an encompassing rise in quality factor. In addition, reducing the footprint of the microresonator on a planar integrated circuit requires race-track designs that typically result into extra modal coupling losses and disruptions into the dispersion, preventing the generation of the dissipative single soliton state. Here, we report the generation of sub-50GHz soliton microcombs in dispersion-engineered silicon nitride microresonators. In contrast to other approaches, our devices feature an optimized racetrack design that minimizes the coupling to higher-order modes and reduces the footprint size by an order of magnitude to ~1mm2. The statistical intrinsic Q reaches 19 million, and soliton microcombs at 20.5GHz and 14.0GHz repetition rates are successfully generated. Importantly, the fabrication process is entirely subtractive, meaning that the devices can be directly patterned on the Si3N4 film. This standard approach facilitates integration with further components and devices.

Optical amplifiers are essential in numerous photonic applications. Parametric amplifiers, relying on a nonlinear material to create amplification, are uniquely promising as they can amplify without generating excess noise. Here, we demonstrate amplification based on the 3rd order nonlinearity in a single chip, while in addition reporting a noise figure significantly below the conventional quantum limit when operated in phase-sensitive mode. Our results show the potential of nanophotonics for realizing continuous-wave parametric amplification that can enable applications in optical communications, signal processing and quantum optics across a wide range of frequencies., Comment: Parts of this works were presented at CLEO-PDP and OFC-PDP

Soliton microcombs provide a versatile platform for realizing fundamental studies and technological applications. To be utilized as frequency rulers for precision metrology, soliton microcombs must display broadband phase coherence, a parameter characterized by the optical phase or frequency noise of the comb lines and their corresponding optical linewidths. Here, we analyse the optical phase-noise dynamics in soliton microcombs generated in silicon nitride high-Q microresonators and show that, because of the Raman self-frequency shift or dispersive-wave recoil, the Lorentzian linewidth of some of the comb lines can, surprisingly, be narrower than that of the pump laser. This work elucidates information about the physical limits in phase coherence of soliton microcombs and illustrates a new strategy for the generation of spectrally coherent light on chip., Comment: 14 pages, 10 figures

Many physical systems display quantized energy states. In optics, interacting resonant cavities show a transmission spectrum with split eigenfrequencies, similar to the split energy levels that result from interacting states in bonded multi-atomic, i.e. molecular, systems. Here, we study the nonlinear dynamics of photonic diatomic molecules in linearly coupled microresonators and demonstrate that the system supports the formation of self-enforcing solitary waves when a laser is tuned across a split energy level. The output corresponds to a frequency comb (microcomb) whose characteristics in terms of power spectral distribution are unattainable in single-mode (atomic) systems. Photonic molecule microcombs are coherent, reproducible, and reach high conversion efficiency and spectral flatness whilst operated with a laser power of a few milliwatts. These properties can favor the heterogeneous integration of microcombs with semiconductor laser technology and facilitate applications in optical communications, spectroscopy and astronomy.

Microresonator frequency combs (microcombs) are enabling new applications in frequency synthesis and metrology from high-speed laser ranging to coherent optical communications. One critical parameter that dictates the performance of the microcomb is the optical quality factor (Q) of the microresonator. Microresonators fabricated in planar structures such as silicon nitride (Si3N4) allow for dispersion engineering and the possibility to monolithically integrate the microcomb with other photonic devices. However, the relatively large refractive index contrast and the tight optical confinement required for dispersion engineering make it challenging to attain Si3N4 microresonators with Qs > 10 000 000 using standard subtractive processing methods. In this work, we achieve ultra-smooth Si3N4 microresonators featuring mean intrinsic Qs around 11 million. The cross-section geometry can be precisely engineered in the telecommunications band to achieve either normal or anomalous dispersion, and we demonstrate the generation of mode-locked dark-pulse Kerr combs as well as soliton microcombs. Such high-Qs allow us to generate soliton microcombs with photodetectable repetition rates, demonstrated here for the first time in Si3N4 microresonators fabricated using a subtractive processing method. These results enhance the possibilities for co-integration of microcombs with high-performance photonic devices, such as narrow-linewidth external-cavity diode lasers, ultra-narrow filters and demultiplexers., Comment: 9pages, 4 figures

Silicon nitride is awell-established material for photonic devices and integrated circuits. It displays a broad transparency window spanning from the visible to the mid-IR and waveguides can be manufactured with low losses. An absence of nonlinear multi-photon absorption in the erbium lightwave communications band has enabled various nonlinear optic applications in the past decade. Silicon nitride is a dielectric material whose optical and mechanical properties strongly depend on the deposition conditions. In particular, the optical bandgap can be modified with the gas flow ratio during low-pressure chemical vapor deposition (LPCVD). Here we show that this parameter can be controlled in a highly reproducible manner, providing an approach to synthesize the nonlinear Kerr coefficient of the material. This holistic empirical study provides relevant guidelines to optimize the properties of LPCVD silicon nitride waveguides for nonlinear optics applications that rely on the Kerr effect.