Mode spectrum and temporal soliton formation in optical microresonators

A wideband, high-resolution vector spectrum analyzer for integrated photonics

The analysis of optical spectra-emission or absorption-has been arguably the most powerful approach for discovering and understanding matter. 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 (1260-1640 nm), a frequency resolution of 471 kHz, and a 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 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.

Electro-Optical Comb Envelope Engineering Based on Mode Crossing

Resonator-enhanced electro-optical (EO) combs could generate a series of comb lines with high coherence and stability. Recently, EO comb based on thin-film lithium niobate (TFLN) has begun to show great potential thanks to the high second-order nonlinearity coefficient of lithium niobate crystal. Here we demonstrate that EO comb envelope engineering based on mode crossing induced a quality factor reduction in the TFLN racetrack microcavity both in the numerical simulation and experiment. Our method paves the way for the generation of EO combs with an arbitrary envelope.

Integrated waveguide coupled ultralow-loss multimode waveguides based on silicon nitride resonators

On-chip micro-ring resonators (MRRs) with low loss and large free spectral ranges (FSRs) are important for photonic devices. So far, ultra-low-loss silicon-nitride (Si3N4) waveguides are primarily fabricated in laboratories, as they often demand special processes to reduce transmission losses. While, Si3N4 waveguides fabricated by the standard multi-project wafer (MPW)-based processes often suffer from significant sidewall scattering, resulting in high scattering losses. Here, we present an innovative approach to photonics by introducing a compact and multi-mode structure. This approach significantly reduces the contact between the optical field and the rough sidewalls in the high-confinement Si3N4 waveguide. By incorporating modified Euler bends, and a weakly tapered gap directional coupler, adiabatic transmission with simultaneous ultra-low loss and compact size is achieved even in 7-µm wide waveguide. Results show that the intrinsic quality factor Qi of MRR is (6.8 ± 0.4) × 106 at the wavelength of 1550 nm, which is approximately four times higher than the previously reported by the same fabrication process. An ultra-low loss of 0.051 ± 0.003 dB/cm is achieved based on the standard LIGENTEC-AN800 technology. This accomplishment addresses a critical challenge in high-confinement waveguides. Our work provides new insights into the low propagation loss in Si3N4 waveguides and provides a broader prospect for integrated photonics in the ultra-high-Q regime.

High-Q adiabatic micro-resonators on a wafer-scale ion-sliced 4H-silicon carbide-on-insulator platform

A 4H-silicon carbide-on-insulator (4H-SiCOI) has emerged as a prominent material contender for integrated photonics owing to its outstanding material properties such as CMOS compatibility, high refractive index, and high second- and third-order nonlinearities. Although various micro-resonators have been realized on the 4H-SiCOI platform, enabling numerous applications including frequency conversion and electro-optical modulators, they may suffer from a challenge associated with spatial mode interactions, primarily due to the widespread use of multimode waveguides. We study the suppression of spatial mode interaction with Euler bends, and demonstrate micro-resonators with improved Q values above 1 × 105 on ion-sliced 4H-SiCOI platform with a SiC thickness nonuniformity less than 1%. The spatial-mode-interaction-free micro-resonators reported on the CMOS-compatible wafer-scale 4H-SiCOI platform would constitute an important ingredient for the envisaged large-scale integrated nonlinear photonic circuits.

Investigating the thermal robustness of soliton crystal microcombs

Soliton crystals are a novel form of microcomb, with relatively high conversion efficiency, good thermal robustness, and simple initiation among the methods to generate them. Soliton crystals can be easily generated in microring resonators with an appropriate mode-crossing. However, fabrication defects can significantly affect the mode-crossing placement and strength in devices. To enable soliton crystal states to be harnessed for a broader range of microcomb applications, we need a better understanding of the link between mode-crossing properties and the desired soliton crystal properties. Here, we investigate how to generate the same soliton crystal state in two different microrings, how changes in microring temperature change the mode-crossing properties, and how mode-crossing properties affect the generation of our desired soliton crystal state. We find that temperature affects the mode-crossing position in these rings but without major changes in the mode-crossing strength. We find that our wanted state can be generated over a device temperature range of 25 ∘C, with different mode-crossing properties, and is insensitive to the precise mode-crossing position between resonances.

Binding dynamics of cavity solitons in a Kerr resonator with high order dispersion

Cavity solitons are persistent light pulses arising from the externally driven Kerr resonators. Thanks to the passive parametric gain, cavity soliton has been endowed with the natural advantage of the chip-scaled integration since it was first experimentally generated in the fiber-based platform. Deterministic single soliton with smooth spectrum is a preferred state for numerous applications. However, multiple solitons are more common in the resonators with anomalous dispersion. In this condition, adjacent solitons are easily perturbed to attract and collide with each other. Some experimental observations deviated from the aforementioned description have recorded the stable soliton intervals that can last for a long time scale. This phenomenon is known as soliton binding and is attributed to the presence of narrow resonant sidebands in the spectrum. While the stationary configuration of two binding solitons has been investigated, the dynamical evolution remains an area for further exploration. In this paper, we discuss the binding dynamics of the cavity solitons in the presence of high-order dispersion. The proposed theoretical predictions match well with the numerical results, encompassing both the stationary stable intervals and dynamic trajectories. Our research will provide a comprehensive insight into the soliton motion induced by the internal perturbations.

Massive and parallel 10 Tbit/s physical random bit generation with chaotic microcomb

Ultrafast physical random bit (PRB) generators and integrated schemes have proven to be valuable in a broad range of scientific and technological applications. In this study, we experimentally demonstrated a PRB scheme with a chaotic microcomb using a chip-scale integrated resonator. A microcomb contained hundreds of chaotic channels, and each comb tooth functioned as an entropy source for the PRB. First, a 12 Gbits/s PRB signal was obtained for each tooth channel with proper post-processing and passed the NIST Special Publication 800-22 statistical tests. The chaotic microcomb covered a wavelength range from 1430 to 1675 nm with a free spectral range (FSR) of 100 GHz. Consequently, the combined random bit sequence could achieve an ultra-high rate of about 4 Tbits/s (12 Gbits/s × 294 = 3.528 Tbits/s), with 294 teeth in the experimental microcomb. Additionally, denser microcombs were experimentally realized using an integrated resonator with 33.6 GHz FSR. A total of 805 chaotic comb teeth were observed and covered the wavelength range from 1430 to 1670 nm. In each tooth channel, 12 Gbits/s random sequences was generated, which passed the NIST test. Consequently, the total rate of the PRB was approximately 10 Tbits/s (12 Gbits/s × 805 = 9.66 Tbits/s). These results could offer potential chip solutions of Pbits/s PRB with the features of low cost and a high degree of parallelism.

Surpassing the nonlinear conversion efficiency of soliton microcombs

Laser frequency combs are enabling some of the most exciting scientific endeavours in the twenty-first century, ranging from the development of optical clocks to the calibration of the astronomical spectrographs used for discovering Earth-like exoplanets. Dissipative Kerr solitons generated in microresonators currently 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 engineered to display anomalous dispersion. In this configuration, however, nonlinear physics precludes one 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, resulting in a coherent dissipative Kerr soliton with a conversion efficiency exceeding 50% and excellent line spacing stability. We describe the soliton dynamics in this configuration and find vastly modified characteristics. By optimizing the microcomb power available on-chip, these results facilitate the practical implementation of a scalable integrated photonic architecture for energy-efficient applications.

Machine learning assisted inverse design of microresonators

The high demand for fabricating microresonators with desired optical properties has led to various techniques to optimize geometries, mode structures, nonlinearities, and dispersion. Depending on applications, the dispersion in such resonators counters their optical nonlinearities and influences the intracavity optical dynamics. In this paper, we demonstrate the use of a machine learning (ML) algorithm as a tool to determine the geometry of microresonators from their dispersion profiles. The training dataset with ∼460 samples is generated by finite element simulations and the model is experimentally verified using integrated silicon nitride microresonators. Two ML algorithms are compared along with suitable hyperparameter tuning, out of which Random Forest yields the best results. The average error on the simulated data is well below 15%.

Impact of stimulated Raman scattering on dark soliton generation in a silica microresonator

Generating a coherent optical frequency comb at an arbitrary wavelength is important for fields such as precision spectroscopy and optical communications. Dark solitons which are coherent states of optical frequency combs in normal dispersion microresonators can extend the operating wavelength range of these combs. While the existence and dynamics of dark solitons has been examined extensively, requirements for the modal interaction for accessing the soliton state in the presence of a strong Raman interaction at near visible wavelengths has been less explored. Here, analysis on the parametric and Raman gain in a silica microresonator is performed, revealing that four-wave mixing parametric gain which can be created by a modal-interaction-aided additional frequency shift is able to exceed the Raman gain. The existence range of the dark soliton is analyzed as a function of pump power and detuning for given modal coupling conditions. We anticipate these results will benefit fields requiring optical frequency combs with high efficiency and selectable wavelength such as biosensing applications using silica microcavities that have a strong Raman gain in the normal dispersion regime.

Soliton formation and spectral translation into visible on CMOS-compatible 4H-silicon-carbide-on-insulator platform

Recent advancements in integrated soliton microcombs open the route to a wide range of chip-based communication, sensing, and metrology applications. The technology translation from laboratory demonstrations to real-world applications requires the fabrication process of photonics chips to be fully CMOS-compatible, such that the manufacturing can take advantage of the ongoing evolution of semiconductor technology at reduced cost and with high volume. Silicon nitride has become the leading CMOS platform for integrated soliton devices, however, it is an insulator and lacks intrinsic second-order nonlinearity for electro-optic modulation. Other materials have emerged such as AlN, LiNbO₃, AlGaAs and GaP that exhibit simultaneous second- and third-order nonlinearities. Here, we show that silicon carbide (SiC) -- already commercially deployed in nearly ubiquitous electrical power devices such as RF electronics, MOSFET, and MEMS due to its wide bandgap properties, excellent mechanical properties, piezoelectricity and chemical inertia -- is a new competitive CMOS-compatible platform for nonlinear photonics. High-quality-factor microresonators (Q = 4 × 10⁶) are fabricated on 4H-SiC-on-insulator thin films, where a single soliton microcomb is generated. In addition, we observe wide spectral translation of chaotic microcombs from near-infrared to visible due to the second-order nonlinearity of SiC. Our work highlights the prospects of SiC for future low-loss integrated nonlinear and quantum photonics that could harness electro-opto-mechanical interactions on a monolithic platform.

Dissipative Kerr single soliton generation with extremely high probability via spectral mode depletion

Optical Kerr solitons generation based on microresonators is essential in nonlinear optics. Among various soliton generation processes, the single soliton generation plays a pivotal role since it ensures rigorous mode-locking on each comb line whose interval equals the free spectral range (FSR) of the microresonator. Current studies show that single soliton generation is challenging due to cavity instability. Here, we propose a new method to greatly improve single soliton generation probalility in the anomalous group velocity dispersion (GVD) regime in a micro-ring resonator based on silicon nitride. The improvement is realized by introducing mode depletion through an integrated coupled filter. It is convenient to introduce controllable single mode depletion in a micro-ring resonator by adjusting the response function of a coupled filter. We show that spectral mode depletion (SMD) can significantly boost the single soliton generation probability. The effect of SMD on the dynamics of optical Kerr solitons generation are also discussed. The proposed method offers a straightforward and simple way to facilitate robust single soliton generation, and will have an impact on the research development in optical Kerr soliton generation and on-chip optical frequency mode manipulation.

Active tuning of dispersive waves in Kerr soliton combs

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.

Thermal tuning of mode crossing and the perfect soliton crystal in a Si3N4 microresonator

Dissipative Kerr solitons in high quality microresonators have attracted much attention in the past few years. They provide ideal platforms for a number of applications. Here, we fabricate the Si₃N₄ microring resonator with anomalous dispersion for the generation of single soliton and soliton crystal. Based on the strong thermal effect in the high-Q microresonator, the location and strength of the avoided mode crossing in the device can be changed by the intracavity power. Because the existence of the avoided mode crossing can induce the perfect soliton crystal with specific soliton number, we could choose the appropriate pumped resonance mode and appropriate pump power to obtain the perfect soliton crystals on demand.

Protected generation of dissipative Kerr solitons in supermodes of coupled optical microresonators

A photonic dimer composed 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 and soliton hopping. Here, 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 markedly varies for symmetric and antisymmetric supermode families. Linear measurements reveal that the coupling between transverse modes, giving rise to avoided mode crossings, can be substantially suppressed. We explain the origin of this phenomenon and show its influence on the dissipative Kerr soliton generation in lattices of coupled resonators of any type. Choosing an 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.

Optical frequency combs in aqueous and air environments at visible to near-IR wavelengths

The ability to detect and identify molecules at high sensitivity without the use of labels or capture agents is important for medical diagnostics, threat identification, environmental monitoring, and basic science. Microtoroid optical resonators, when combined with noise reduction techniques, have been shown capable of label-free single molecule detection; however, they still require a capture agent and prior knowledge of the target molecule. Optical frequency combs can potentially provide high precision spectroscopic information on molecules within the evanescent field of the microresonator; however, this has not yet been demonstrated in air or aqueous biological sensing. For aqueous solutions in particular, impediments include coupling and thermal instabilities, reduced Q factor, and changes to the mode spectrum. Here we overcome a key challenge toward single-molecule spectroscopy using optical microresonators: the generation of a frequency comb at visible to near-IR wavelengths when immersed in either air or aqueous solution. The required dispersion is achieved via intermodal coupling, which we show is attainable using larger microtoroids, but with the same shape and material that has previously been shown ideal for ultra-high sensitivity biosensing. We believe that the continuous evolution of this platform will allow us in the future to simultaneously detect and identify single molecules in both gas and liquid at any wavelength without the use of labels.

Mid-infrared optical parametric oscillation spanning 3.4-8.2μm in a MgF2microresonator

Mid-infrared optical parametric oscillators (OPOs) offer a compelling route for accessing the 'molecular fingerprint' region and, thus, can find intensive applications such as precision spectroscopy and trace gas detection. Yet it still remains rather a challenge to realize broadband mid-infrared OPOs within a single cavity, usually limited by strict phase-matching conditions for wide spectral coverage and available pump power for adequate frequency generation. Here, we report the mid-infrared parametric oscillation spanning from 3.4 to 8.2μm, based on four-wave mixing in a high-QMgF₂microresonator with optimized dispersion. The center wavelength at 4.78μm is determined by the continuous tunable quantum cascade laser source, which contributes to effective expansion towards longer wavelength, as well as systemic miniaturization with smaller pump module. Such results could not only shed light on new ultimates of crystal and other microresonators, but also inspire explorations on their growing potentials in near future.

Quadratic strong coupling in AlN Kerr cavity solitons

Photonic platforms with χ⁽²⁾ nonlinearity offer new degrees of freedom for Kerr frequency comb development. Here, we demonstrate Kerr soliton generation at 1550 nm with phase-matched quadratic coupling to the 775 nm harmonic band in a single AlN microring and thus the formation of dual-band mode-locked combs. In the strong quadratic coupling regime where the χ⁽²⁾ phase-matching window overlaps the pump mode, the pump-to-harmonic-comb conversion efficiency is optimized. However, the strong quadratic coupling also drastically modifies the Kerr comb generation dynamics and decreases the probability of soliton generation. By engineering the χ⁽²⁾ phase-matching wavelength, we are able to achieve a balance between high conversion efficiency and high soliton formation rate under the available pump power and microring quality factors. Our numerical simulations confirm the experimental observations. These findings provide guidance on tailoring single-cavity dual-band coherent comb sources.

Dark-Bright Soliton Bound States in a Microresonator

Dissipative Kerr solitons in microresonators have facilitated the development of fully coherent, chip-scale frequency combs. In addition, dark soliton pulses have been observed in microresonators in the normal dispersion regime. Here, we report bound states of mutually trapped dark-bright soliton pairs in a microresonator. The soliton pairs are generated seeding two modes with opposite dispersion but with similar group velocities. One laser operating in the anomalous dispersion regime generates a bright soliton microcomb, while the other laser in the normal dispersion regime creates a dark soliton via Kerr-induced cross-phase modulation with the bright soliton. Numerical simulations agree well with experimental results and reveal a novel mechanism to generate dark soliton pulses. The trapping of dark and bright solitons can lead to light states with the intriguing property of constant output power while spectrally resembling a frequency comb. These results can be of interest for telecommunication systems, frequency comb applications, and ultrafast optics.

Efficient chip-based optical parametric oscillators from 590 nm to 1150 nm

Optical parametric oscillators are widely used to generate coherent light at frequencies not accessible by conventional laser gain. However, chip-based parametric oscillators operating in the visible spectrum have suffered from pump-to-signal conversion efficiencies typically less than 0.1 %. Here, we demonstrate efficient optical parametric oscillators based on silicon nitride photonics that address frequencies between 260 THz (1150 nm) and 510 THz (590 nm). Pumping silicon nitride microrings near 385 THz (780 nm) yields monochromatic signal and idler waves with unprecedented output powers in this wavelength range. We estimate on-chip output powers (separately for the signal and idler) between 1 mW and 5 mW and conversion efficiencies reaching ≈15 %. Underlying this improved performance is our development of pulley waveguides for broadband near-critical coupling, which exploits a fundamental connection between the waveguide-resonator coupling rate and conversion efficiency. Finally, we find that mode competition reduces conversion efficiency at high pump powers, thereby constraining the maximum realizable output power. Our work proves that optical parametric oscillators built with integrated photonics can produce useful amounts of visible laser light with high efficiency.

A squeezed quantum microcomb on a chip

The optical microresonator-based frequency comb (microcomb) provides a versatile platform for nonlinear physics studies and has wide applications ranging from metrology to spectroscopy. The deterministic quantum regime is an unexplored aspect of microcombs, in which unconditional entanglements among hundreds of equidistant frequency modes can serve as critical ingredients to scalable universal quantum computing and quantum networking. Here, we demonstrate a deterministic quantum microcomb in a silica microresonator on a silicon chip. 40 continuous-variable quantum modes, in the form of 20 simultaneously two-mode squeezed comb pairs, are observed within 1 THz optical span at telecommunication wavelengths. A maximum raw squeezing of 1.6 dB is attained. A high-resolution spectroscopy measurement is developed to characterize the frequency equidistance of quantum microcombs. Our demonstration offers the possibility to leverage deterministically generated, frequency multiplexed quantum states and integrated photonics to open up new avenues in fields of spectroscopy, quantum metrology, and scalable, continuous-variable-based quantum information processing.

Suppression of avoided resonance crossing in microresonators

Kerr frequency comb generation in microresonators is enabled by notable developments in fabrication technology and novel nonlinear material platforms. However, even in a low loss and highly nonlinear microresonator, the avoided resonance crossing may hamper reliable frequency comb generation. We present a method to suppress the avoided resonance crossing induced by polarization mode coupling. Our approach employs a filter waveguide coupled to a microring resonator for selective filtering of the TM₀₀ mode while keeping the operational TE₀₀ mode with low loss. We experimentally demonstrate an avoided-crossing-suppressed microresonator in the AlGaAs-on-insulator platform.

Conversion efficiency of soliton Kerr combs

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.

Low-Loss Integrated Nanophotonic Circuits with Layered Semiconductor Materials

Monolayer transition-metal dichalcogenides with direct bandgaps are emerging candidates for optoelectronic devices, such as photodetectors, light-emitting diodes, and electro-optic modulators. Here we report a low-loss integrated platform incorporating molybdenum ditelluride monolayers with silicon nitride photonic microresonators. We achieve microresonator quality factors >3 × 10⁶ in the telecommunication O- to E-bands. This paves the way for low-loss, hybrid photonic integrated circuits with layered semiconductors, not requiring heterogeneous wafer bonding.

Dispersive-wave induced noise limits in miniature soliton microwave sources

Compact, low-noise microwave sources are required throughout a wide range of application areas including frequency metrology, wireless-communications and airborne radar systems. And the photonic generation of microwaves using soliton microcombs offers a path towards integrated, low noise microwave signal sources. In these devices, a so called quiet-point of operation has been shown to reduce microwave frequency noise. Such operation decouples pump frequency noise from the soliton's motion by balancing the Raman self-frequency shift with dispersive-wave recoil. Here, we explore the limit of this noise suppression approach and reveal a fundamental noise mechanism associated with fluctuations of the dispersive wave frequency. At the same time, pump noise reduction by as much as 36 dB is demonstrated. This fundamental noise mechanism is expected to impact microwave noise (and pulse timing jitter) whenever solitons radiate into dispersive waves belonging to different spatial mode families.

Dirac solitons in optical microresonators

Mode-coupling-induced dispersion has been used to engineer microresonators for soliton generation at the edge of the visible band. Here, we show that the optical soliton formed in this way is analogous to optical Bragg solitons and, more generally, to the Dirac soliton in quantum field theory. This optical Dirac soliton is studied theoretically, and a closed-form solution is derived in the corresponding conservative system. Both analytical and numerical solutions show unusual properties, such as polarization twisting and asymmetrical optical spectra. The closed-form solution is also used to study the repetition rate shift in the soliton. An observation of the asymmetrical spectrum is analysed using theory. The properties of Dirac optical solitons in microresonators are important at a fundamental level and provide a road map for soliton microcomb generation in the visible band.

Spectral extension and synchronization of microcombs in a single microresonator

Broadband optical frequency combs are extremely versatile tools for precision spectroscopy, ultrafast ranging, as channel generators for telecom networks, and for many other metrology applications. Here, we demonstrate that the optical spectrum of a soliton microcomb generated in a microresonator can be extended by bichromatic pumping: one laser with a wavelength in the anomalous dispersion regime of the microresonator generates a bright soliton microcomb while another laser in the normal dispersion regime both compensates the thermal effect of the microresonator and generates a repetition-rate-synchronized second frequency comb. Numerical simulations agree well with experimental results and reveal that a bright optical pulse from the second pump is passively formed in the normal dispersion regime and trapped by the primary soliton. In addition, we demonstrate that a dispersive wave can be generated and influenced by cross-phase-modulation-mediated repetition-rate synchronization of the two combs. The demonstrated technique provides an alternative way to generate broadband microcombs and enables the selective enhancement of optical power in specific parts of a comb spectrum.

Photonic Dissipation Control for Kerr Soliton Generation in Strongly Raman-Active Media

Microcavity solitons enable miniaturized coherent frequency comb sources. However, the formation of microcavity solitons can be disrupted by stimulated Raman scattering, particularly in the emerging crystalline microcomb materials with high Raman gain. Here, we propose and implement dissipation control-tailoring the energy dissipation of selected cavity modes-to purposely raise or lower the threshold of Raman lasing in a strongly Raman-active lithium niobate microring resonator and realize on-demand soliton mode locking or Raman lasing. Numerical simulations are carried out to confirm our analyses and agree well with experiment results. Our work demonstrates an effective approach to address strong stimulated Raman scattering for microcavity soliton generation.

Deterministic single-soliton generation in a graphene-FP microresonator

Dissipative Kerr solitons (DKS) in high-Q microresonators have attracted considerable attention for their broadband optical frequency combs and ultra-short pulse generation. Owing to thermal effects, complicated tuning strategies are required to generate and sustain the single-soliton state in microresonators. In this paper, we propose a novel microresonator scheme based on the Fabry-Pérot fiber resonator and single-layer graphene saturable absorber (SA) and demonstrate that this design allows deterministic single-soliton generation without frequency tuning and has strong robustness against pump perturbation. The soliton range and thermal instability of the proposed device are also discussed. This work facilitates a novel nonlinear platform connecting high-Q microresonators and conventional SA-assisted mode-locking operations.

Quadratic soliton mode-locked degenerate optical parametric oscillator

We examine the existence condition of the quadratic soliton mode-locked degenerate optical parametric oscillator in the previously unexplored parameter space. We study the nature of the quadratic solitons and divide their dynamics into two distinctive branches, depending on the system parameters. Origin of the quadratic soliton perturbation is identified, and strategy to mitigate its detrimental effect is developed. Frequency comb with terahertz bandwidth and femtosecond pulse duration are attainable in an example periodically poled lithium niobate waveguide resonator. Design rules of the quadratic soliton mode-locking are summarized. The principle can be further extended to other material platforms, making it a competitive ultrashort pulse and broadband comb source architecture at the mid-infrared.

Polychromatic Cherenkov Radiation Induced Group Velocity Symmetry Breaking in Counterpropagating Dissipative Kerr Solitons

High-order-dispersion-induced dispersive waves emitted by dissipative Kerr solitons are frequently observed in microresonator frequency comb generation. Also known as soliton Cherenkov radiation, this type of dispersive wave plays a critical role in comb spectrum broadening as well as the formation of soliton bound states. Here, we report the experimental observation of symmetry breaking in the group velocity of counterpropagating solitons in a crystalline microresonator. Induced by the polychromatic Cherenkov radiation, soliton bound states are formed, showing different group velocities with different spatiotemporal separations between constituent solitons. By bidirectionally pumping the microresonator with laser fields of equal power and frequency, we demonstrate the degeneracy lifting of repetition rates of the counterpropagating solitons. Our work not only shines new light on the impact of dispersive waves in nonlinear cavities, but also introduces a novel approach to develop compact dual-comb spectrometers.

High-Q Si3N4 microresonators based on a subtractive processing for Kerr nonlinear optics

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 > 10⁷ using standard subtractive processing methods - i.e. photonic devices are patterned directly on the as-deposited Si₃N₄ film. 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 100 GHz soliton microcombs, 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.

Subharmonic Entrainment of Kerr Breather Solitons

We predict subharmonic entrainment of breather-soliton oscillations to a periodic perturbation at the round-trip time T_{R} in Kerr-nonlinear optical resonators; an integer ratio T_{b}/T_{R}=N≫1 results for breathing period T_{b}. Rigid entrainment is observed with intermediate finesse (F∼30-40) for N up to 20, and we propose a way to realize higher entrainment ratios at higher finesse. This nontrivial synchronization across the widely separated timescales of the photon lifetime and round-trip time points to a new direction for research in this field and may find application, for example, in the measurement of a pulse train repetition rate that is electronically inaccessible.

Modal analysis for noise characterization and propagation in a femtosecond oscillator

We study noise propagation dynamics in a femtosecond oscillator by injecting external noise on the pump intensity. We utilize a spectrally resolved homodyne detection technique that enables simultaneous measurement of amplitude and phase quadrature noises of different spectral bands of the oscillator. We perform a modal analysis of the oscillator noise in which each mode corresponds to a particular temporal/spectral shape of the pulsed light. We compare this modal approach with the conventional noise detection methods and find the superiority of our method, in particular unveiling a complete physical picture of noise distribution in the femtosecond oscillator.

High-quality factor, high-confinement microring resonators in 4H-silicon carbide-on-insulator

Silicon carbide (SiC) exhibits promising material properties for nonlinear integrated optics. We report on a SiC-on-insulator platform based on crystalline 4H-SiC and demonstrate high-confinement SiC microring resonators with sub-micron waveguide cross-sectional dimensions. The Q factor of SiC microring resonators in such a sub-micron waveguide dimension is improved by a factor of six after surface roughness reduction by applying a wet oxidation process. We achieve a high Q factor (73,000) for such devices and show engineerable dispersion from normal to anomalous dispersion by controlling the waveguide cross-sectional dimension, which paves the way toward nonlinear applications in SiC microring resonators.

Soliton bursts and deterministic dissipative Kerr soliton generation in auxiliary-assisted microcavities

Dissipative Kerr solitons in resonant frequency combs offer a promising route for ultrafast mode-locking, precision spectroscopy and time-frequency standards. The dynamics for the dissipative soliton generation, however, are intrinsically intertwined with thermal nonlinearities, limiting the soliton generation parameter map and statistical success probabilities of the solitary state. Here, via use of an auxiliary laser heating approach to suppress thermal dragging dynamics in dissipative soliton comb formation, we demonstrate stable Kerr soliton singlet formation and soliton bursts. First, we access a new soliton existence range with an inverse-sloped Kerr soliton evolution-diminishing soliton energy with increasing pump detuning. Second, we achieve deterministic transitions from Turing-like comb patterns directly into the dissipative Kerr soliton singlet pulse bypassing the chaotic states. This is achieved by avoiding subcomb overlaps at lower pump power, with near-identical singlet soliton comb generation over twenty instances. Third, with the red-detuned pump entrance route enabled, we uncover unique spontaneous soliton bursts in the direct formation of low-noise optical frequency combs from continuum background noise. The burst dynamics are due to the rapid entry and mutual attraction of the pump laser into the cavity mode, aided by the auxiliary laser and matching well with our numerical simulations. Enabled by the auxiliary-assisted frequency comb dynamics, we demonstrate an application of automatic soliton comb recovery and long-term stabilization against strong external perturbations. Our findings hold potential to expand the parameter space for ultrafast nonlinear dynamics and precision optical frequency comb stabilization.

Light Concentration by Metal-Dielectric Micro-Resonators for SERS Sensing

Metal-dielectric micro/nano-composites have surface plasmon resonances in visible and near-infrared domains. Excitation of coupled metal-dielectric resonances is also important. These different resonances can allow enhancement of the electromagnetic field at a subwavelength scale. Hybrid plasmonic structures act as optical antennae by concentrating large electromagnetic energy in micro- and nano-scales. Plasmonic structures are proposed for various applications such as optical filters, investigation of quantum electrodynamics effects, solar energy concentration, magnetic recording, nanolasing, medical imaging and biodetection, surface-enhanced Raman scattering (SERS), and optical super-resolution microscopy. We present the review of recent achievements in experimental and theoretical studies of metal-dielectric micro and nano antennae that are important for fundamental and applied research. The main impact is application of metal-dielectric optical antennae for the efficient SERS sensing.

From the Lugiato-Lefever equation to microresonator-based soliton Kerr frequency combs

The model, that is usually called the Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a perfect and exact description of Kerr frequency combs-first observed in 2007, i.e. 20 years after the original formulation of the LLE-and in particular describe soliton states. Observed to spontaneously form in Kerr frequency combs in crystalline microresonators in 2013, such DKS are preferred state of operation, offering coherent and broadband optical frequency combs, whose bandwidth can be extended exploiting soliton-induced broadening phenomena. Combined with the ability to miniaturize and integrate on-chip, microresonator-based soliton Kerr frequency combs have already found applications in self-referenced frequency combs, dual-comb spectroscopy, frequency synthesis, low noise microwave generation, laser frequency ranging, and astrophysical spectrometer calibration, and have the potential to make comb technology ubiquitous. As such, pattern formation in driven, dissipative nonlinear optical systems is becoming the central Physics of soliton micro-comb technology.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Imaging soliton dynamics in optical microcavities

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

Thermal and Nonlinear Dissipative-Soliton Dynamics in Kerr-Microresonator Frequency Combs

We explore the dynamical response of dissipative Kerr solitons to changes in pump power and detuning and show how thermal and nonlinear processes couple these parameters to the frequency-comb degrees of freedom. Our experiments are enabled by a Pound-Drever-Hall (PDH) stabilization approach that provides on-demand, radio-frequency control of the frequency comb. PDH locking not only guides Kerr-soliton formation from a cold microresonator but opens a path to decouple the repetition and carrier-envelope-offset frequencies. In particular, we demonstrate phase stabilization of both Kerr-comb degrees of freedom to a fractional frequency precision below 10^{-16}, compatible with optical-time-keeping technology. Moreover, we investigate the fundamental role that residual laser-resonator detuning noise plays in the spectral purity of microwave generation with Kerr combs.

Dispersion engineered high quality lithium niobate microring resonators

Lithium niobate (LN) exhibits outstanding material properties with great potential for many applications. Recent advance in LN integrated photonics on chip-scale platforms has shown significant advantages in device engineering and functionality innovation. Precise engineering of group-velocity dispersion (GVD) is crucial for many important nonlinear photonic applications. In this paper, we demonstrate high-Q LN microring resonators, with optical Q above 1 million, whose GVD can be flexibly controlled in both normal and anomalous dispersion regimes, with a value between -0.128 ps²/m and 0.043 ps²/m in the telecom band, by controlling the device cross section and by utilizing the birefringence. We are able to achieve a small anomalous GVD of -0.015 ps²/m that is even smaller than that of a silica optical fiber. The flexible engineering of GVD paves a critical step towards broad nonlinear photonic applications in high-Q LN microring resonators.

Two-dimensional nonlinear modes and frequency combs in bottle microresonators

We theoretically investigate frequency comb generation in a bottle microresonator accounting for the azimuthal and axial degrees of freedom. We first identify a discrete set of the axial nonlinear modes of a bottle microresonator that appear as tilted resonances bifurcating from the spectrum of linear axial modes. We then study azimuthal modulational instability of these modes and show that families of two-dimensional (2D) soliton states localized both azimuthally and axially bifurcate from them at critical pump frequencies. Depending on detuning, 2D solitons can be stable, form persistent breathers or chaotic spatio-temporal patterns, or exhibit collapse-like evolution.

Stimulated Raman Scattering Imposes Fundamental Limits to the Duration and Bandwidth of Temporal Cavity Solitons

Temporal cavity solitons (CS) are optical pulses that can persist in passive resonators, and they play a key role in the generation of coherent microresonator frequency combs. In resonators made of amorphous materials, such as fused silica, they can exhibit a spectral redshift due to stimulated Raman scattering. Here we show that this Raman-induced self-frequency-shift imposes a fundamental limit on the duration and bandwidth of temporal CSs. Specifically, we theoretically predict that stimulated Raman scattering introduces a previously unidentified Hopf bifurcation that leads to destabilization of CSs at large pump-cavity detunings, limiting the range of detunings over which they can exist. We have confirmed our theoretical predictions by performing extensive experiments in synchronously driven fiber ring resonators, obtaining results in excellent agreement with numerical simulations. Our results could have significant implications for the future design of Kerr frequency comb systems based on amorphous microresonators.

Raman-Kerr frequency combs in microresonators with normal dispersion

We generalize the coupled mode formalism to study the generation of frequency combs in microresonators with simultaneous Raman and Kerr nonlinearities and investigate an impact of the former on the formation of frequency combs and dynamics of platicons in the regime of the normal group velocity dispersion. We demonstrate that the Raman effect initiates generation of sidebands, which cascade further in four-wave mixing and reshape into the Raman-Kerr frequency combs. We reveal that the Raman scattering induces a strong instability of the platicon pulses associated with the Kerr effect and normal dispersion. This instability results in branching of platicons and complex spatiotemporal dynamics.

Towards visible soliton microcomb generation

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

Breathing dissipative solitons in optical microresonators

Dissipative solitons are self-localised structures resulting from the double balance of dispersion by nonlinearity and dissipation by a driving force arising in numerous systems. In Kerr-nonlinear optical resonators, temporal solitons permit the formation of light pulses in the cavity and the generation of coherent optical frequency combs. Apart from shape-invariant stationary solitons, these systems can support breathing dissipative solitons exhibiting a periodic oscillatory behaviour. Here, we generate and study single and multiple breathing solitons in coherently driven microresonators. We present a deterministic route to induce soliton breathing, allowing a detailed exploration of the breathing dynamics in two microresonator platforms. We measure the relation between the breathing frequency and two control parameters—pump laser power and effective-detuning—and observe transitions to higher periodicity, irregular oscillations and switching, in agreement with numerical predictions. Using a fast detection, we directly observe the spatiotemporal dynamics of individual solitons, which provides evidence of breather synchronisation.

Dissipative Kerr solitons enable optical frequency comb generation in microresonators, but these solitons can undergo a breathing transition which impacts the stability of such microcombs. Here, Lucas et al. deterministically induce soliton breathing and directly observe the spatiotemporal dynamics.

Light localization and SERS in tip-shaped silicon metasurface

Optical properties of two dimensional periodic system of the silicon micro-cones are investigated. The metasurface, composed of the silicon tips, shows enhancement of the local optical field. Finite element computer simulations as well as real experiment reveal anomalous optical response of the dielectric metasurface due to excitation of the dielectric resonances. Various electromagnetic resonances are considered in the dielectric cone. The metal-dielectric resonances, which are excited between metal nanoparticles and dielectric cones, are also considered. The resonance local electric field can be much larger than the field in the usual surface plasmon resonances. To investigate local electric field the signal molecules are deposited on the metal nanoparticles. We demonstrate enhancement of the electromagnetic field and Raman signal from the complex of DTNB acid molecules and gold nanoparticles, which are distributed over the metasurface. The metasurfaces composed from the dielectric resonators can have quasi-continuous spectrum and serve as an efficient SERS substrates.

Frequency stability characterization of a broadband fiber Fabry-Pérot interferometer

An optical etalon illuminated by a white light source provides a broadband comb-like spectrum that can be employed as a calibration source for astronomical spectrographs in radial velocity (RV) surveys for extrasolar planets. For this application the frequency stability of the etalon is critical, as its transmission spectrum is susceptible to frequency fluctuations due to changes in cavity temperature, optical power and input polarization. In this paper we present a laser frequency comb measurement technique to characterize the frequency stability of a custom-designed fiber Fabry-Pérot interferometer (FFP). Simultaneously probing the stability of two etalon resonance modes, we assess both the absolute stability of the etalon and the long-term stability of the cavity dispersion. We measure mode positions with MHz precision, which corresponds to splitting the FFP resonances by a part in 500 and to RV precision of ≈ 1 m s^-1. We address limiting systematic effects, including the presence of parasitic etalons, that need to be overcome to push the metrology of this system to the equivalent RV precision of 10 cm s^-1. Our results demonstrate a means to characterize environmentally-driven perturbations of etalon resonance modes across broad spectral bandwidths, as well as motivate the benefits and challenges of FFPs as spectrograph calibrators.

Investigation of the local dispersion change in anomalous dispersion microcavity and quantitative analysis of the phase-matching in Kerr comb generation

We numerically simulate Kerr comb generation in an anomalous dispersion microcavity by modal expansion method and demonstrate that the initiation of comb generation is affected by the change of local dispersion possibly caused by avoided mode crossings. We also quantitatively analyze the instantaneous phase matching of different modes and reveal the characteristics of energy distribution in different modes in the dynamics of comb generation. We demonstrate that the local dispersion change can control the Kerr comb to transform between Type I and Type II combs. We also find that local dispersion is closely related to the stability of the power of Kerr comb lines, something that can change the dynamical state of the system near the Hamiltonian-Hopf bifurcation under an anomalous dispersion regime from a quasi-periodic oscillation state to a periodic state (Turing patterns).