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χ (2) -translated microcomb generation in microresonators that possess both χ (2) and χ (3) nonlinear responses opens the door for ultra-broadband integrated comb sources. The interplay between the second- and third-order nonlinearities within a fixed coupling coefficient fertilizes complicated cavity dynamics which is of paramount scientific and technological potential. However, this coupling coefficient can be drastically wavelength-dependent, which is lack of consideration in previous studies. Here, we extend the range of coupling strengths to a full description and propose a new approach to delineate the spectral response of the interactions between the χ (2) and χ (3) nonlinearities. Critically, the underpinned physics is enabled by avoided mode crossing (AMX) in concentric double-ring microresonators. We demonstrate that the evolution of the anti-symmetric mode at fundamental wavelengths disrupts spectral symmetry, leading to asymmetric χ (2) -translated optical frequency combs at second-harmonic wavelengths. Simultaneous generation of skewed two-color optical frequency combs is numerically realized in an exemplary gallium phosphide-on-insulator platform with a coupling constant from 133.3 m -1 W -1/2 to 7.4 m -1 W -1/2 , showing reasonable agreement with our theoretical model. Our findings provide a novel approach to shaping the optical frequency comb, which may facilitate potential applications in self-referencing and frequency metrology with desired comb spectral shapes.

Introduction: In order to explore the correlation between discharge readiness and Harris score or self-care ability of patients undergoing total hip arthroplasty (THA) based on the enhanced recovery after surgery (ERAS) concept. We carried out this single center retrospective study., Methods: We enrolled 331 patients who underwent THA. These patients were divided into the higher score group and the lower score group according to median discharge readiness score. After the baseline data of these patients were compared, the effect factors of discharge readiness of these patients was analyzed through univariate and multivariate logistic regression analyses and mixed effects models., Results: The results demonstrated that there was a correlation between discharge readiness and changes in Harris score 30 days after discharge (compared with that before surgery) in these patients. Besides, the Harris score and self-care ability 30 days after discharge were higher than those at the time of discharge. In addition, patients in the higher score group exhibited a higher Harris score compared with those in the lower score group. From the evaluation at different time points after discharge, there was a significant difference in the Harris score between both groups., Discussion: It can be inferred that the discharge readiness of patients undergoing THA was correlated with the Harris score but not with the self-care ability. These results are expected to provide guidance for the physical and mental recovery of patients undergoing total hip replacement under the ERAS concept. Furthermore, these findings may contribute to higher diagnosis, treatment, and nursing levels of orthopedic medical staff., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Liu, Chen, Shan, Dai, Qin, Yang, Ji, Tan and Yu.)

We measured the covariance matrix of the fields generated in an integrated third-order optical parametric oscillator operating above threshold. We observed up to (2.3 ± 0.3) dB of squeezing in amplitude difference and inferred (4.9 ± 0.7) dB of on-chip squeezing, while an excess of noise for the sum of conjugated quadratures hinders the entanglement. The degradation of amplitude correlations and state purity for increasing the pump power is consistent with the observed growth of the phase noise of the fields, showing the necessity of strategies for phase noise control aiming at entanglement generation in these systems.

The generation of spectrally pure microwave signals is a critical functionality in fundamental and applied sciences, including metrology and communications. Optical frequency combs enable the powerful technique of optical frequency division (OFD) to produce microwave oscillations of the highest quality 1,2 . Current implementations of OFD require multiple lasers, with space- and energy-consuming optical stabilization and electronic feedback components, resulting in device footprints incompatible with integration into a compact and robust photonic platform 3-5 . Here we demonstrate all-optical OFD on a photonic chip by synchronizing two distinct dynamical states of Kerr microresonators pumped by a single continuous-wave laser. The inherent stability of the terahertz beat frequency between the signal and idler fields of an optical parametric oscillator is transferred to a microwave frequency of a Kerr soliton comb, and synchronization is achieved via a coupling waveguide without the need for electronic locking. OFD factors of N = 34 and 468 are achieved for 227 GHz and 16 GHz soliton combs, respectively. In particular, OFD enables a 46 dB phase-noise reduction for the 16 GHz soliton comb, resulting in the lowest microwave noise observed in an integrated photonics platform. Our work represents a simple, effective approach for performing OFD and provides a pathway towards chip-scale devices that can generate microwave frequencies comparable to the purest tones produced in metrological laboratories., (© 2024. The Author(s), under exclusive licence to Springer Nature Limited.)

Visible-light photonic integrated circuits (PICs) promise scalability for technologies such as quantum information, biosensing, and scanning displays, yet extending large-scale silicon photonics to shorter wavelengths has been challenging due to the higher losses. Silicon nitride (SiN) has stood out as the leading platform for visible photonics, but the propagation losses strongly depend on the film's deposition and fabrication processes. Current loss measurement techniques cannot accurately distinguish between absorption and surface scattering, making it difficult to identify the dominant loss source and reach the platform's fundamental limit. Here we demonstrate an ultra-low loss, high-confinement SiN platform that approaches the limits of absorption and scattering across the visible spectrum. Leveraging the sensitivity of microresonators to loss, we probe and discriminate each loss contribution with unparalleled sensitivity, and derive their fundamental limits and scaling laws as a function of wavelength, film properties and waveguide parameters. Through the design of the waveguide cross-section, we show how to approach the absorption limit of the platform, and demonstrate the lowest propagation losses in high-confinement SiN to date across the visible spectrum. We envision that our techniques for loss characterization and minimization will contribute to the development of large-scale, dense PICs that redefine the loss limits of integrated platforms across the electromagnetic spectrum.

Total internal reflection (TIR) governs the guiding mechanisms of almost all dielectric waveguides and therefore constrains most of the light in the material with the highest refractive index. The few options available to access the properties of lower-index materials include designs that are either lossy, periodic, exhibit limited optical bandwidth or are restricted to subwavelength modal volumes. Here, we propose and demonstrate a guiding mechanism that leverages symmetry in multilayer dielectric waveguides as well as evanescent fields to strongly confine light in low-index materials. The proposed waveguide structures exhibit unusual light properties, such as uniform field distribution with a non-Gaussian spatial profile and scale invariance of the optical mode. This guiding mechanism is general and can be further extended to various optical structures, employed for different polarizations, and in different spectral regions. Therefore, our results can have huge implications for integrated photonics and related technologies., (© 2023. Springer Nature Limited.)

Silicon photonics has gained great success mainly due to the promise of realizing compact devices in high volume through the low-cost foundry model. It is burgeoning from laboratory research into commercial production endeavors such as datacom and telecom. However, it is unsuitable for some emerging applications which require coverage across the visible or mid infrared (mid-IR) wavelength bands. It is desirable to introduce other wideband materials through heterogeneous integration, while keeping the integration compatible with wafer-scale fabrication processes on silicon substrates. We discuss the properties of silicon-family materials including silicon, silicon nitride, and silica, and other non-group IV materials such as metal oxide, tantalum pentoxide, lithium niobate, aluminum nitride, gallium nitride, barium titanate, piezoelectric lead zirconate titanate, and 2D materials. Typical examples of devices using these materials on silicon platform are provided. We then introduce a general fabrication method and low-loss process treatment for photonic devices on the silicon platform. From an applications viewpoint, we focus on three new areas requiring integration: sensing, optical comb generation, and quantum information processing. Finally, we conclude with perspectives on how new materials and integration methods can address previously unattainable wavelength bands while maintaining the advantages of silicon, thus showing great potential for future widespread applications., (© 2023 the author(s), published by De Gruyter, Berlin/Boston.)

Kerr soliton combs operate in the anomalous group-velocity dispersion regime through the excitation of dissipative solitons. The generated bandwidth is largely dependent on the cavity dispersion, with higher-order dispersion contributing to dispersive-wave (DW) generation that allows for power enhancement of the comb lines at the wings of the spectrum. However, the spectral position of the DW is highly sensitive to the overall cavity dispersion, and the inevitable dimension variations that occur during the fabrication process result in deviations in the DW emission wavelength. Here, we demonstrate active tuning of the DW wavelength, enabling post-fabrication spectral shaping of the soliton spectrum. We control the DW position by introducing a wavelength-controllable avoided mode crossing through actively tuning the resonances of a silicon nitride coupled microresonator via integrated heaters. We demonstrate DW tuning over 113 nm with a spectral power that can exceed the peak soliton spectral power. In addition, our modeling reveals buildup and enhancement of the DW in the auxiliary resonator, indicating that the mode hybridization arising from the strong coupling between the two resonators is critical for DW formation.

Synchronization is a ubiquitous phenomenon in nature that manifests as the spectral or temporal locking of coupled nonlinear oscillators. In the field of photonics, synchronization has been implemented in various laser and oscillator systems, enabling applications including coherent beam combining and high-precision pump-probe measurements. Recent experiments have also shown time-domain synchronization of Kerr frequency combs via coupling of two separate oscillators operating in the dissipative soliton [i.e., anomalous group velocity dispersion (GVD)] regime. Here, we demonstrate all-optical synchronization of Kerr combs in the nonsolitonic, normal GVD regime in which phase-locked combs with high pump-to-comb conversion efficiencies and relatively flat spectral profiles are generated. Our results reveal the universality of Kerr comb synchronization and extend its scope beyond the soliton regime, opening a promising path toward coherently combined normal GVD Kerr combs with spectrally flat profiles and high comb-line powers in an efficient microresonator platform.

Supercontinuum sources for optical coherence tomography (OCT) have raised great interest as they provide broad bandwidth to enable high resolution and high power to improve imaging sensitivity. Commercial fiber-based supercontinuum systems require high pump powers to generate broad bandwidth and customized optical filters to shape/attenuate the spectra. They also have limited sensitivity and depth performance. We introduce a supercontinuum platform based on a 1-mm 2 Si 3 N 4 photonic chip for OCT. We directly pump and efficiently generate supercontinuum near 1300 nm without any postfiltering. With a 25-pJ pump pulse, we generate a broadband spectrum with a flat 3-dB bandwidth of 105 nm. Integrating the chip into a spectral domain OCT system, we achieve 105-dB sensitivity and 1.81-mm 6-dB sensitivity roll-off with 300-μW optical power on sample. We image breast tissue to demonstrate strong imaging performance. Our chip will pave the way toward portable OCT and incorporating integrated photonics into optical imaging technologies.

We report soliton-effect pulse compression of low energy (∼25 p J ), picosecond pulses on a photonic chip. An ultra-low-loss, dispersion-engineered 40-cm-long waveguide is used to compress 1.2-ps pulses by a factor of 18, which represents, to our knowledge, the largest compression factor yet experimentally demonstrated on-chip. Our scheme allows for interfacing with an on-chip picosecond source and offers a path towards a fully integrated stabilized frequency comb source.

We investigate the conversion efficiency (CE) of soliton modelocked Kerr frequency combs. Our analysis reveals three distinct scaling regimes of CE with the cavity free spectral range (FSR), which depends on the relative contributions of the coupling and propagation loss to the total cavity loss. Our measurements, for the case of critical coupling, verify our theoretical prediction over a range of FSRs and pump powers. Our numerical simulations also indicate that mode crossings have an adverse effect on the achievable CE. Our results indicate that microresonator combs operating with spacings in the electronically detectable regime are highly inefficient, which could have implications for integrated Kerr comb devices.

The need for solving optimization problems is prevalent in various physical applications, including neuroscience, network design, biological systems, socio-economics, and chemical reactions. Many of these are classified as non-deterministic polynomial-time hard and thus become intractable to solve as the system scales to a large number of elements. Recent research advances in photonics have sparked interest in using a network of coupled degenerate optical parametric oscillators (DOPOs) to effectively find the ground state of the Ising Hamiltonian, which can be used to solve other combinatorial optimization problems through polynomial-time mapping. Here, using the nanophotonic silicon-nitride platform, we demonstrate a spatial-multiplexed DOPO system using continuous-wave pumping. We experimentally demonstrate the generation and coupling of two microresonator-based DOPOs on a single chip. Through a reconfigurable phase link, we achieve both in-phase and out-of-phase operation, which can be deterministically achieved at a fast regeneration speed of 400 kHz with a large phase tolerance.

Squeezed states are a primary resource for continuous-variable (CV) quantum information processing. To implement CV protocols in a scalable and robust way, it is desirable to generate and manipulate squeezed states using an integrated photonics platform. In this Letter, we demonstrate the generation of quadrature-phase squeezed states in the radio-frequency carrier sideband using a small-footprint silicon-nitride microresonator with a dual-pumped four-wave-mixing process. We record a squeezed noise level of 1.34 dB (±0.16  dB) below the photocurrent shot noise, which corresponds to 3.09 dB (±0.49  dB) of quadrature squeezing on chip. We also show that it is critical to account for the nonlinear behavior of the pump fields to properly predict the squeezing that can be generated in this system. This technology represents a significant step toward creating and manipulating large-scale CV cluster states that can be used for quantum information applications, including universal quantum computing.

A simple and compact straight-cavity laser oscillator incorporating a cascaded quadratic nonlinear crystal and a semiconductor saturable absorber mirror (SESAM) can deliver stable femtosecond modelocking at high pulse repetition rates >10 GHz. In this paper, we experimentally investigate the influence of intracavity dispersion, pump brightness, and cavity design on modelocking with high repetition rates, and use the resulting insights to demonstrate a 10.4-GHz straight-cavity SESAM-modelocked Yb:CALGO laser delivering 108-fs pulses with 812 mW of average output power. This result represents a record-level performance for diode-pumped femtosecond oscillators with repetition rates above 10 GHz. Using the oscillator output without any optical amplification, we demonstrate coherent octave-spanning supercontinuum generation (SCG) in a silicon nitride waveguide. Subsequent f-to-2f interferometry with a periodically poled lithium niobate waveguide enables the detection of a strong carrier-envelope offset (CEO) beat note with a 33-dB signal-to-noise ratio.

Frequency encoding of quantum information together with fiber and integrated photonic technologies can significantly reduce the complexity and resource requirements for realizing all-photonic quantum networks. The key challenge for such frequency domain processing of single photons is to realize coherent and selective interactions between quantum optical fields of different frequencies over a range of bandwidths. Here, we report frequency-domain Hong-Ou-Mandel interference with spectrally distinct photons generated from a chip-based microresonator. We use four-wave mixing to implement an active "frequency beam splitter" and achieve interference visibilities of 0.95±0.02. Our work establishes four-wave mixing as a tool for selective high-fidelity two-photon operations in the frequency domain which, combined with integrated single-photon sources, provides a building block for frequency-multiplexed photonic quantum networks.

Compact beam steering in the visible spectral range is required for a wide range of emerging applications, such as augmented and virtual reality displays, optical traps for quantum information processing, biological sensing, and stimulation. Optical phased arrays (OPAs) can shape and steer light to enable these applications with no moving parts on a compact chip. However, OPA demonstrations have been mainly limited to the near-infrared spectral range due to the fabrication and material challenges imposed by the shorter wavelengths. Here, we demonstrate the first chip-scale phased array operating at blue wavelengths (488 nm) using a high-confinement silicon nitride platform. We use a sparse aperiodic emitter layout to mitigate fabrication constraints at this short wavelength and achieve wide-angle beam steering over a 50° field of view with a full width at half-maximum beam size of 0.17°. Large-scale integration of this platform paves the way for fully reconfigurable chip-scale three-dimensional volumetric light projection across the entire visible range.

The use of nanophotonics to rapidly and precisely reconfigure light beams for the optical stimulation of neurons in vivo has remained elusive. Here we report the design and fabrication of an implantable silicon-based probe that can switch and route multiple optical beams to stimulate identified sets of neurons across cortical layers and simultaneously record the produced spike patterns. Each switch in the device consists of a silicon nitride waveguide structure that can be rapidly (<20 μs) reconfigured by electrically tuning the phase of light. By using an eight-beam probe, we show in anaesthetized mice that small groups of single neurons can be independently stimulated to produce multineuron spike patterns at sub-millisecond precision. We also show that a probe integrating co-fabricated electrical recording sites can simultaneously optically stimulate and electrically measure deep-brain neural activity. The technology is scalable, and it allows for beam focusing and steering and for structured illumination via beam shaping. The high-bandwidth optical-stimulation capacity of the device might facilitate the probing of the spatiotemporal neural codes underlying behaviour.

We demonstrate various regimes of synchronization in systems of two coupled cavity soliton-based Kerr frequency combs. We show subharmonic, harmonic, and harmonic-ratio synchronization of coupled microresonators, and reveal their dynamics in the form of Arnold tongues, structures that are ubiquitous in nonlinear dynamical systems. Our experimental results are well corroborated by numerical simulations based on coupled Lugiato-Lefever equations. This Letter illustrates the newfound degree of flexibility in synchronizing Kerr combs across a wide range of comb spacings and could find applications in time and frequency metrology, spectroscopy, microwave photonics, optical communications, and astronomy.

We demonstrate an approach for automated Kerr comb generation in the normal group-velocity dispersion (GVD) regime. Using a coupled-ring geometry in silicon nitride, we precisely control the wavelength location and splitting strength of avoided mode crossings to generate low-noise frequency combs with pump-to-comb conversion efficiencies of up to 41%, which is the highest reported to date for normal-GVD Kerr combs. Our technique enables on-demand generation of a high-power comb source for applications such as wavelength-division multiplexing in optical communications.

Optical coherence tomography (OCT) is a powerful interferometric imaging technique widely used in medical fields such as ophthalmology, cardiology and dermatology. Superluminescent diodes (SLDs) are widely used as light sources in OCT. Recently integrated chip-based frequency combs have been demonstrated in numerous platforms and the possibility of using these broadband chip-scale combs for OCT has been raised extensively over the past few years. However, the use of these chip-based frequency combs as light sources for OCT requires bandwidth and power compatibility with current OCT systems and have not been shown to date. Here we generate frequency combs based on chip-scale lithographically-defined microresonators and demonstrate its capability as a novel light source for OCT. The combs are designed with a small spectral line spacing of 0.21 nm which ensure imaging range comparable to commercial system and operated at non-phase locked regime which provide conversion efficiency of 30%. The comb source is shown to be compatible with a standard commercial spectral domain (SD) OCT system and enables imaging of human tissue with image quality comparable to the one achieved with tabletop commercial sources. The comb source also provides a path towards fully integrated OCT systems.

We demonstrate that nondegenerate four-wave mixing in a Si&#95;{3}N&#95;{4} microring resonator can result in a nonlinear coupling rate between two optical fields exceeding their energy dissipation rate in the resonator, corresponding to strong nonlinear coupling. We demonstrate that this leads to a Rabi-like splitting, for which we provide a theoretical description in agreement with our experimental results. This yields new insight into the dynamics of nonlinear optical interactions in microresonators and access to novel phenomena.

We demonstrate a chip-scale f-2f interferometer for carrier-envelope-offset frequency (f CEO ) detection. This is enabled by simultaneously producing octave-spanning coherent supercontinuum generation and second-harmonic generation in a single dispersion-engineered silicon nitride waveguide. We measure the f CEO beatnote of an 80 MHz modelocked pump source with a signal-to-noise ratio of 25 dB. Our simple approach for f-2f interferometry enables a straightforward route towards a chip-scale self-referenced frequency comb source that can operate at low pulse energies.

Optical frequency combs are broadband sources that offer mutually coherent, equidistant spectral lines with unprecedented precision in frequency and timing for an array of applications 1 . Frequency combs generated in microresonators through the Kerr nonlinearity require a single-frequency pump laser and have the potential to provide highly compact, scalable and power-efficient devices 2,3 . Here we demonstrate a device-a laser-integrated Kerr frequency comb generator-that fulfils this potential through use of extremely low-loss silicon nitride waveguides that form both the microresonator and an integrated laser cavity. Our device generates low-noise soliton-mode-locked combs with a repetition rate of 194 gigahertz at wavelengths near 1,550 nanometres using only 98 milliwatts of electrical pump power. The dual-cavity configuration that we use combines the laser and microresonator, demonstrating the flexibility afforded by close integration of these components, and together with the ultra low power consumption should enable production of highly portable and robust frequency and timing references, sensors and signal sources. This chip-based integration of microresonators and lasers should also provide tools with which to investigate the dynamics of comb and soliton generation.

Dual-comb spectroscopy is a powerful technique for real-time, broadband optical sampling of molecular spectra, which requires no moving components. Recent developments with microresonator-based platforms have enabled frequency combs at the chip scale. However, the need to precisely match the resonance wavelengths of distinct high quality-factor microcavities has hindered the development of on-chip dual combs. We report the simultaneous generation of two microresonator combs on the same chip from a single laser, drastically reducing experimental complexity. We demonstrate broadband optical spectra spanning 51 THz and low-noise operation of both combs by deterministically tuning into soliton mode-locked states using integrated microheaters, resulting in narrow (<10 kHz) microwave beat notes. We further use one comb as a reference to probe the formation dynamics of the other comb, thus introducing a technique to investigate comb evolution without auxiliary lasers or microwave oscillators. We demonstrate high signal-to-noise ratio absorption spectroscopy spanning 170 nm using the dual-comb source over a 20-μs acquisition time. Our device paves the way for compact and robust spectrometers at nanosecond time scales enabled by large beat-note spacings (>1 GHz).

We demonstrate the generation of counter-rotating cavity solitons in a silicon nitride microresonator using a fixed, single-frequency laser. We demonstrate a dual three-soliton state with a difference in the repetition rates of the soliton trains that can be tuned by varying the ratio of pump powers in the two directions. Such a system enables a highly compact, tunable dual comb source that can be used for applications such as spectroscopy and distance ranging.

We design and demonstrate a compact, narrow-linewidth integrated laser based on low-loss silicon nitride waveguides coupled to a III-V gain chip. By using a highly confined optical mode, we simultaneously achieve compact bends and ultra-low loss. We leverage the narrowband backreflection of a high-Q microring resonator to act as a cavity output mirror, a single-mode filter, and a propagation delay all in one. This configuration allows the ring to provide feedback and obtain a laser linewidth of 13 kHz with 1.7 mW output power around 1550 nm. This demonstration realizes a compact sub-millimeter silicon nitride laser cavity with a narrow linewidth.

We demonstrate a novel approach to producing coherent, directional supercontinuum and cascaded dispersive waves using dispersion engineering in waveguides. By pumping in the normal group-velocity dispersion (GVD) regime, with two zero-GVD points to one side of the pump, pulse compression of the first dispersive wave generated in the anomalous GVD region results in the generation of a second dispersive wave beyond the second zero-GVD point in the normal GVD regime. As a result, we achieve an octave-spanning supercontinuum generated primarily to one side of the pump spectrum. We theoretically investigate the dynamics and show that the generated spectrum is highly coherent. We experimentally confirm this dynamical behavior and the coherence properties in silicon nitride waveguides by performing direct detection of the carrier-envelope-offset frequency of our femtosecond pump source using an f-2f interferometer. Our technique offers a path towards a stabilized, high-power, integrated supercontinuum source with low noise and high coherence, with applications including direct comb spectroscopy.

The generation of temporal cavity solitons in microresonators results in coherent low-noise optical frequency combs that are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems, manifesting themselves as a localized temporal structure that exhibits oscillatory behaviour. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation. Our study constitutes a significant contribution to understanding the soliton dynamics within the larger context of nonlinear science.

We experimentally and theoretically investigate the dynamics of microresonator-based frequency comb generation assisted by mode coupling in the normal group-velocity dispersion (GVD) regime. We show that mode coupling can initiate intracavity modulation instability (MI) by directly perturbing the pump-resonance mode. We also observe the formation of a low-noise comb as the pump frequency is tuned further into resonance from the MI point. We determine the phase-matching conditions that accurately predict all the essential features of the MI and comb spectra, and extend the existing analogy between mode coupling and high-order dispersion to the normal GVD regime. We discuss the applicability of our analysis to the possibility of broadband comb generation in the normal GVD regime.

We report, to the best of our knowledge, the first demonstration of thermally controlled soliton mode-locked frequency comb generation in microresonators. By controlling the electric current through heaters integrated with silicon nitride microresonators, we demonstrate a systematic and repeatable pathway to single- and multi-soliton mode-locked states without adjusting the pump laser wavelength. Such an approach could greatly simplify the generation of mode-locked frequency combs and facilitate applications such as chip-based dual-comb spectroscopy.