Dispersive-wave induced noise limits in miniature soliton microwave sources

Self-Suppressed Quantum-Limited Timing Jitter and Fundamental Noise Limit of Soliton Microcombs

Quantum-limited timing jitter of soliton microcombs has long been recognized as their fundamental noise limit. Here, we surpass such limit by utilizing dispersive wave dynamics in multimode microresonators. Through the viscous force provided by these dispersive waves, the quantum-limited timing jitter can be suppressed to a much lower level that forms the ultimate fundamental noise limit of soliton microcombs. Our findings enable coherence engineering of soliton microcombs in the quantum regime, providing critical guidelines for using soliton microcombs to synthesize ultralow-noise microwave and optical signals.

All-optical frequency division on-chip using a single laser

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 quality1,2. 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 platform3-5. 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.

Photonic chip-based low-noise microwave oscillator

Numerous modern technologies are reliant on the low-phase noise and exquisite timing stability of microwave signals. Substantial progress has been made in the field of microwave photonics, whereby low-noise microwave signals are generated by the down-conversion of ultrastable optical references using a frequency comb1-3. Such systems, however, are constructed with bulk or fibre optics and are difficult to further reduce in size and power consumption. In this work we address this challenge by leveraging advances in integrated photonics to demonstrate low-noise microwave generation via two-point optical frequency division4,5. Narrow-linewidth self-injection-locked integrated lasers6,7 are stabilized to a miniature Fabry-Pérot cavity8, and the frequency gap between the lasers is divided with an efficient dark soliton frequency comb9. The stabilized output of the microcomb is photodetected to produce a microwave signal at 20 GHz with phase noise of -96 dBc Hz-1 at 100 Hz offset frequency that decreases to -135 dBc Hz-1 at 10 kHz offset-values that are unprecedented for an integrated photonic system. All photonic components can be heterogeneously integrated on a single chip, providing a significant advance for the application of photonics to high-precision navigation, communication and timing systems.

Strong interactions between solitons and background light in Brillouin-Kerr microcombs

Dissipative Kerr-soliton combs are laser pulses regularly sustained by a localized solitary wave on top of a continuous-wave background inside a nonlinear resonator. Usually, the intrinsic interactions between the background light and solitons are weak and localized. Here, we demonstrate a strong interaction between the generated soliton comb and the background light in a Brillouin-Kerr microcomb system. This strong interaction enables the generation of a monostable single-soliton microcomb on a silicon chip. Also, new phenomena related to soliton physics including solitons hopping between different states as well as controlling the formations of the soliton states by the pump power, are observed owing to such strong interaction. Utilizing this monostable single-soliton microcomb, we achieve the 100% deterministic turnkey operation successfully without any feedback controls. Importantly, it allows to output turnkey ultra-low-noise microwave signals using a free-running pump.

Low-phase-noise microwave generation with a free-running dual-pumped Si3N4 soliton microcomb

Microwave signals can be generated by photodetecting the repetition frequencies of the soliton microcombs. In comparison to other methods, the dual-pumped method allows for the stable generation of the soliton microcombs even with resonators having lower Q-factors. However, introducing an additional pump laser may affect the phase noise of the generated microwave signals when using these dual-pumped soliton microcombs. Here, we investigate the factors that could influence the phase noise of microwave signals generated with dual-pumped soliton microcombs, including the polarization, amplitude noise, and phase noise of the two pumps. We demonstrate a 25.25 (12.63) GHz microwave with phase noise reaching -112(-118) dBc/Hz at a 10 kHz offset frequency, surpassing the performance of previous reports on microwave generation using free-running Si3N4 soliton microcombs, even those generated with higher Q microresonators. We analyze the noise floor of the generated microwave signals and establish a phase noise simulation model to study the limiting factors in our system. Our work highlights the potential of generating low-phase-noise microwave signals using free-running dual-pumped soliton microcombs.

Theory of soliton self-frequency shift in silica optical microresonators with a modified Raman response by the Boson peak

We theoretically study the Raman-induced self-frequency shift of dissipative Kerr soliton in silica optical resonators by taking into consideration the Boson peak. We find that the Boson peak will greatly increase the soliton self-frequency shift and contribute even more than the shift induced by the Lorentzian response for certain pulse durations. We also show that the revised Raman shock time is associated with the pulse width even for a relatively long pulse. Moreover, we demonstrate that the background continuous wave decreases the self-frequency shift of the soliton via the interference with the soliton. Our theoretical and simulated results display excellent agreement with the previous experimental values in the silica-based Kerr-soliton microcomb.

Ultra-low time jitter transform-limited dissipative Kerr soliton microcomb

Microresonator soliton frequency combs offer unique flexibility in synthesizing microwaves over a wide range of frequencies. Therefore, it is very important to study the time jitter of soliton microcombs. Here, we fabricate optical microresonators with perfect transmission spectrum that characterizes highly uniform extinction ratio and absence of mode interactions by laser machining high-purity silica fiber preforms. Based on such perfect whispering-gallery-mode cavity, We demonstrate that K-band microwave with ultra-low phase noise (-83 dBc/Hz@100 Hz; -112 dBc/Hz@1kHz; -133 dBc/Hz@10kHz) can be generated by photo-detecting the repetition rate of a soliton microcomb. Also, with the Raman scattering and dispersive wave emission largely restricted, we show that ultra-low time jitter soliton has a wide existence range. Our work illuminates a pathway toward low-noise photonic microwave generation as well as the quantum regime of soliton microcombs.

Versatile octave-spanning soliton crystals with high conversion efficiency in a Si3N4 microresonator

Microresonator-based soliton crystals are a key recent advancement in the study of the rich nonlinear dynamics of soliton states. The soliton crystals are self-organized temporal pulses filling the microresonator cavity and have strong comb lines with wide spacing making them of great interest in many potential applications such as communication and meteorology. However, achieving a broad spectrum, tunable repetition rates, and high conversion efficiency are still a challenge. Here, we report the deterministic generation of versatile octave-spanning soliton crystals with various repetition rates via avoided mode crossings. In addition, we investigate the conversion efficiency of the obtained soliton crystals and achieved above ∼50% in one of the devices with a suitable coupling. Our results pave the way for accessing coherent broad and tunable on-chip soliton crystals, thus requiring a rigorous and viable microcavity design to engineer the desired mode coupling position.

Nonclassical Crystallization Causes Dendritic and Band-Like Microscale Patterns in Inorganic Precipitates

The self-organization of complex solids can create patterns extending hierarchically from the atomic to the macroscopic scale. A frequently studied model is the chemical garden system which consists of life-like precipitate shapes. In this study, we examine the thin walls of chemical gardens using microfluidic devices that yield linear Ni(OH)2 precipitate membranes. We observe distinct light-scattering patterns within the compositionally pure membranes, including disorganized spots, dendrites, and parallel bands. The bands are tilted with respect to the membrane axis and their spacing (20-100 μm) increases with increasing flow rates. Scanning electron microscopy reveals that the bands consist of submicron particles embedded in a denser material and these particles are also found in the reactant stream. We propose that dendrites and bands arise from the attachment of solution-borne nanoparticles. The bands are generated by particle-aggregation zones moving upstream along the slowly advancing membrane surface. The speed of the aggregation zones is proportional to the band distance and defines the system's dispersion relation. This speed-wavelength dependence and the flow-opposing motion of the aggregation zones are likely caused by low particle concentrations in the wake of the zones that only slowly recover due to Brownian motion and particle nucleation.

Quantum decoherence of dark pulses in optical microresonators

Quantum fluctuations disrupt the cyclic motions of dissipative Kerr solitons (DKSs) in nonlinear optical microresonators and consequently cause timing jitter of the emitted pulse trains. This problem is translated to the performance of several applications that employ DKSs as compact frequency comb sources. Recently, device manufacturing and noise reduction technologies have advanced to unveil the quantum properties of DKSs. Here we investigate the quantum decoherence of DKSs existing in normal-dispersion microresonators known as dark pulses. By virtue of the very large material nonlinearity, we directly observe the quantum decoherence of dark pulses in an AlGaAs-on-insulator microresonator, and the underlying dynamical processes are resolved by injecting stochastic photons into the microresonators. Moreover, phase correlation measurements show that the uniformity of comb spacing of quantum-limited dark pulses is better than 1.2 × 10^-16 and 2.5 × 10^-13 when normalized to the optical carrier frequencies and repetition frequencies, respectively. Comparing DKSs generated in different material platforms explicitly confirms the advantages of dark pulses over bright solitons in terms of quantum-limited coherence. Our work establishes a critical performance assessment of DKSs, providing guidelines for coherence engineering of chip-scale optical frequency combs.

Inverse design of soliton microcomb based on genetic algorithm and deep learning

Soliton microcombs generated by the third-order nonlinearity of microresonators exhibit high coherence, low noise, and stable spectra envelopes, which can be designed for many applications. However, conventional dispersion engineering based design methods require iteratively solving Maxwell's equations through time-consuming electromagnetic field simulations until a local optimum is obtained. Moreover, the overall inverse design from soliton microcomb to the microcavity geometry has not been systematically investigated. In this paper, we propose a high accuracy microcomb-to-geometry inverse design method based on the genetic algorithm (GA) and deep neural network (DNN), which effectively optimizes dispersive wave position and power. The method uses the Lugiato-Lefever equation and GA (LLE-GA) to obtain second- and higher-order dispersions from a target microcomb, and it utilizes a pre-trained forward DNN combined with GA (FDNN-GA) to obtain microcavity geometry. The results show that the dispersive wave position deviations of the inverse designed MgF₂ and Si₃N₄ microresonators are less than 0.5%, and the power deviations are less than 5 dB, which demonstrates good versatility and effectiveness of our method for various materials and structures.

Synthesized spatiotemporal mode-locking and photonic flywheel in multimode mesoresonators

Dissipative Kerr soliton (DKS) frequency combs—also known as microcombs—have arguably created a new field in cavity nonlinear photonics, with a strong cross-fertilization between theoretical, experimental, and technological research. Spatiotemporal mode-locking (STML) not only adds new degrees of freedom to ultrafast laser technology, but also provides new insights for implementing analogue computers and heuristic optimizers with photonics. Here, we combine the principles of DKS and STML to demonstrate the STML DKS by developing an unexplored ultrahigh-quality-factor Fabry–Pérot (FP) mesoresonator based on graded index multimode fiber (GRIN-MMF). Complementing the two-step pumping scheme with a cavity stress tuning method, we can selectively excite either the eigenmode DKS or the STML DKS. Furthermore, we demonstrate an ultralow noise microcomb that enhances the photonic flywheel performance in both the fundamental comb linewidth and DKS timing jitter. The demonstrated fundamental comb linewidth of 400 mHz and DKS timing jitter of 500 attosecond (averaging times up to 25 μs) represent improvements of 25× and 2.5×, respectively, from the state-of-the-art. Our results show the potential of GRIN-MMF FP mesoresonators as an ideal testbed for high-dimensional nonlinear cavity dynamics and photonic flywheel with ultrahigh coherence and ultralow timing jitter.

Here the authors demonstrate spatiotemporal mode-locked dissipative Kerr soliton and enhanced photonic flywheel performances in both the fundamental comb linewidth and DKS timing jitter.

Spectral Interferometry with Frequency Combs

In this review paper, we provide an overview of the state of the art in linear interferometric techniques using laser frequency comb sources. Diverse techniques including Fourier transform spectroscopy, linear spectral interferometry and swept-wavelength interferometry are covered in detail. The unique features brought by laser frequency comb sources are shown, and specific applications highlighted in molecular spectroscopy, optical coherence tomography and the characterization of photonic integrated devices and components. Finally, the possibilities enabled by advances in chip scale swept sources and frequency combs are discussed.

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.

Vibrational Kerr Solitons in an Optomechanical Microresonator

Kerr soliton microcombs in microresonators have been a prominent miniaturized coherent light source. Here, for the first time, we demonstrate the existence of Kerr solitons in an optomechanical microresonator, for which a nonlinear model is built by incorporating a single mechanical mode and multiple optical modes. Interestingly, an exotic vibrational Kerr soliton state is found, which is modulated by a self-sustained mechanical oscillation. Besides, the soliton provides extra mechanical gain through the optical spring effect, and results in phonon lasing with a red-detuned pump. Various nonlinear dynamics is also observed, including limit cycle, higher periodicity, and transient chaos. This work provides a guidance for not only exploring many-body nonlinear interactions, but also promoting precision measurements by featuring superiority of both frequency combs and optomechanics.

Thermal noise reduction in soliton microcombs via laser self-cooling

Thermal noise usually dominates the low-frequency region of the optical phase noise of soliton microcombs, which leads to decoherence that limits many aspects of applications. In this work, we demonstrate a simple and reliable way to mitigate this noise by laser cooling with a 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 for laser cooling.

Ultrastable microwave and soliton-pulse generation from fibre-photonic-stabilized microcombs

The ability to generate lower-noise microwaves has greatly advanced high-speed, high-precision scientific and engineering fields. Microcombs have high potential for generating such low-noise microwaves from chip-scale devices. To realize an ultralow-noise performance over a wider Fourier frequency range and longer time scale, which is required for many high-precision applications, free-running microcombs must be locked to more stable reference sources. However, ultrastable reference sources, particularly optical cavity-based methods, are generally bulky, alignment-sensitive and expensive, and therefore forfeit the benefits of using chip-scale microcombs. Here, we realize compact and low-phase-noise microwave and soliton pulse generation by combining a silica-microcomb (with few-mm diameter) with a fibre-photonic-based timing reference (with few-cm diameter). An ultrastable 22-GHz microwave is generated with −110 dBc/Hz (−88 dBc/Hz) phase noise at 1-kHz (100-Hz) Fourier frequency and 10⁻¹³-level frequency instability within 1-s. This work shows the potential of fully packaged, palm-sized or smaller systems for generating both ultrastable soliton pulse trains and microwaves, thereby facilitating a wide range of field applications involving ultrahigh-stability microcombs.

A compact yet high-performance stabilization method has been the missing ingredient for microcombs. Here, optical fibre is used for stabilizing microcombs, enabling the generation of ultrastable soliton pulses and microwaves from palm-sized platforms

Self-frequency shift of AlN-on-sapphire Kerr solitons

We study the self-frequency shift of continuously pumped Kerr solitons in AlN-on-sapphire microcavities with Raman gain bandwidths narrower than the cavity free-spectral range. Solitons are generated in ∼230GHz microcavities via high-order mode dispersion engineering. The dependence of the self-frequency shift on soliton pulse width is measured and differs from amorphous material microcavities. Our measurement and simulation reveal the impact of frequency detuning between the cavity resonances and Raman gain peaks, as well as the importance of all three Raman gain peaks. The interplay between the Raman effect and dispersive wave recoil and a potential quiet point are also observed.