Kerr Solitons Research Articles

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.

The Effect of Instantaneous Noise Injection on the Behavior of Dissipative Kerr Solitons in a Fiber Kerr Resonator

We numerically investigated the behavior of dissipative Kerr solitons (DKSs) in fiber Kerr resonators when random noise fields are suddenly applied to the system. Simulation results based on an iterative computation of an Ikeda-map-like equation system show the first observation of the annihilation and excitation of DKS under the stimulation of the noise with different intensities. Switching among different states of DKSs triggered by high amplitude noise is observed. These results have confirmed the robustness of DKSs against noise perturbations and provide new insights into the DKS dynamics in Kerr resonators, thus opening a new way to achieve different DKS states in fiber Kerr resonators.

Phase noise of Kerr soliton dual microcombs.

Dissipative Kerr soliton microcombs are believed to be a promising technique to build a dual-comb source for applications including precision laser metrology, fast laser spectroscopy, and high-speed optical signal processing. In this Letter, we conduct a detailed experimental investigation on the phase coherence between two on-chip Kerr soliton microcombs, where the underlying physical and technical origins that lead to the mutual phase noise between microcombs are analyzed. Moreover, the techniques of 2-point locking and optical frequency division are explored to enhance the dual-microcomb phase coherence, and we demonstrate the best phase noise down to -50 dBc/Hz at 1-Hz offset, -90 dBc/Hz at 1-kHz offset, and -120 dBc/Hz at 1-MHz offset. Our study provides a basic reference for both fundamental studies and practical applications of Kerr soliton dual microcombs that entail high mutual phase coherence.

Monolithic Kerr and electro-optic hybrid microcombs

Microresonator-based soliton generation promises chip-scale integration of optical frequency combs for applications spanning from time keeping to frequency synthesis. Access to the soliton repetition rate is a prerequisite for those applications. While miniaturized cavities harness Kerr nonlinearity and enable terahertz soliton repetition rates, such high rates are not amenable to direct electronic detection. Here, we demonstrate hybrid Kerr and electro-optic microcombs using a lithium niobate thin film that exhibits both Kerr and Pockels nonlinearities. By interleaving the high-repetition-rate Kerr soliton comb with the low-repetition-rate electro-optic comb on the same waveguide, wide Kerr soliton mode spacing is divided within a single chip, allowing for direct electronic detection and feedback control of the soliton repetition rate. Our work establishes an integrated approach to electronically access terahertz solitons, paving the way for building chip-scale referenced comb sources.

Dissipative solitons in optical microresonators

<p indent="0mm">A soliton is a stationary local structure that keeps its waveform and spreading speed during propagation. Recent research shows that chip-scale optical microresonators can support dissipative solitons with surprisingly high energy efficiency and stability. The formation of optical microresonator dissipative solitons requires two balances, gain-loss balance and dispersion-nonlinearity balance. The gain-loss balance maintains the soliton’s amplitude while the dispersion-nonlinearity balance keeps its width. In this paper, we review the formation, development, and applications of dissipative optical solitons, as well as dissipative mechanical solitons in optical microresonators, and analyze the balances in different solitons. This review mainly consists of two parts: Optical microresonator dissipative solitons and opto-mechanical microresonator dissipative solitons. The first part discusses a typical kind of solitons named dissipative Kerr solitons. Dissipative Kerr solitons balance the propagation dispersion through Kerr nonlinearity in optical microresonators and are widely studied due to their easy implementation in silicon-based microcavities. In order to improve the practical performance of dissipative Kerr solitons, researchers have proposed many schemes to improve their stability and efficiency. Meanwhile, various high-precision sensing applications based on dissipative Kerr solitons, such as photonic radar, range measurement, and absorption spectrum detection, have drawn extensive attention. The second part introduces the dissipative solitons in optomechanical microresonators. A recently-discovered type of solitons, optomechanical dissipative solitons, is introduced. Unlike the dissipative Kerr solitons, the optomechanical dissipative solitons gain their power from phonon lasing, and compensate the propagation dispersion by optomechanical nonlinearity. The dynamics of the optomechanical dissipative solitons are described by the modified Korteweg-de Vries equation. Low-frequency optomechanical dissipative solitons can achieve kHz-accuracy acoustic signal measurement, which can be used in acoustic detection and communication. Finally, we summarize the formation, development, and applications of dissipative solitons in optomechanical microresonators. We also provide an outlook for future applications like radio-frequency calibration, radio-frequency communications, and underwater tomography.

Stimulated generation of deterministic platicon frequency microcombs

Dissipative Kerr soliton generation in chip-scale nonlinear resonators has recently observed remarkable advances, spanning from massively parallel communications, to self-referenced oscillators, and to dual-comb spectroscopy. Often working in the anomalous dispersion regime, unique driving protocols and dispersion in these nonlinear resonators have been examined to achieve the soliton and soliton-like temporal pulse shapes and coherent frequency comb generation. The normal dispersion regime provides a complementary approach to bridge the nonlinear dynamical studies, including the possibility of square pulse formation with flattop plateaus, or platicons. Here we report observations of square pulse formation in chip-scale frequency combs through stimulated pumping at one free spectral range and in silicon nitride rings with + 55 fs 2 / mm normal group velocity dispersion. Tuning of the platicon frequency comb via a varied sideband modulation frequency is examined in both spectral and temporal measurements. Determined by second-harmonic autocorrelation and cross correlation, we observe bright square platicon pulse of 17 ps pulse width on a 19 GHz flat frequency comb. With auxiliary-laser-assisted thermal stabilization, we surpass the thermal bistable dragging and extend the mode-locking access to narrower 2 ps platicon pulse states, supported by nonlinear dynamical modeling and boundary limit discussions.

Repetition rate locked single-soliton microcomb generation via rapid frequency sweep and sideband thermal compensation

Dissipative Kerr solitons (DKSs) with mode-locked pulse trains in high- Q optical microresonators possess low-noise and broadband parallelized comb lines, having already found plentiful cutting-edge applications. However, thermal bistability and thermal noise caused by the high microresonator power and large temperature exchange between microresonator and the environment would prevent soliton microcomb formation and deteriorate the phase and frequency noise. Here, a novel method that combines rapid frequency sweep with optical sideband thermal compensation is presented, providing a simple and reliable way to get into the single-soliton state. Meanwhile, it is shown that the phase and frequency noises of the generated soliton are greatly reduced. Moreover, by closing the locking loop, an in-loop repetition rate fractional instability of 5.5 × 10 − 15 at 1 s integration time and a triangular linear repetition rate sweep with 2.5 MHz could be realized. This demonstration provides a means for the generation, locking, and tuning of a soliton microcomb, paving the way for the application of single-soliton microcombs in low-phase-noise microwave generation and laser ranging.

Cold-resonance-mediated self-stabilization of Kerr frequency combs in a Si3N4 microring resonator

Kerr frequency combs (KFCs) generated from continuous-wave pumped microresonators have been vastly exploited for a plethora of applications. Along with an appreciable bandwidth, most of the applications demand a stable and coherent frequency comb, which is a challenging quest. Several complex experimental approaches were reported to attain stable frequency combs. In this paper, we report an innovative and simple approach to achieve stabilized KFCs in a ${\text{Si}}_{3}{\text{N}}_{4}$ racetrack microring resonator. Intensive numerical simulations reveal an enhancement of the comb bandwidth when the temperature is reduced slightly lower than the room temperature. The maximum temperature rise due to the propagating dissipative Kerr soliton (DKS) has also been studied through finite element simulations. Through homogeneous steady-state analysis we validate that the stability of a single DKS state is enhanced at the temperatures reported in this paper. We believe that the proposed thermal route may help in reducing the complex experimental procedures for stabilization of KFCs.

Polarization multiplexed dissipative Kerr solitons in an on-chip micro-resonator.

We demonstrate polarization multiplexed dissipative Kerr solitons in an on-chip silicon nitride micro-resonator. In our experiment, TE- and TM-polarized solitons can be individually generated and controlled, thanks to their weak mutual interaction as the result of sufficiently different repetition rates and orthogonal polarization states. Furthermore, we find that TE- and TM-polarized solitons usually exhibit uncorrelated time jitters. Therefore, the frequency and phase coherence between the polarization multiplexed soliton microcombs change dramatically as a function of pump laser parameters, where by optimization, we achieve a narrow dual-microcomb beat note linewidth as small as 4.4 kHz. Potential applications of on-chip polarization multiplexed soliton microcombs include Kerr comb spectral expansion, dual-comb metrology, and measurement of quantum entanglements.

Erratum: “Dual-mode microresonators as straightforward access to octave-spanning dissipative Kerr solitons” [APL Photonics 7, 066103 (2022)

Erratum: “Dual-mode microresonators as straightforward access to octave-spanning dissipative Kerr solitons” [APL Photonics 7, 066103 (2022)

Extending thermal stability of short-living soliton states in silicon nitride microring resonators

Dissipative Kerr solitons in microresonators enable on-chip chip generation of low-noise optical pulse trains with high repetition rates, finding applications in optical communication, distance measurement, spectroscopy and radiofrequency generation. However, the most common photonic integrated platforms often show very short living, hence difficult to achieve, soliton states. Here, we exploit an auxiliary resonance to access soliton regime in Si3N4 microresonators by simple wavelength scanning. We increase the likelihood of single soliton formation by more than two times using backward tuning of the laser, and we show that the increased thermal stability allows soliton formation by thermal tuning of the whole sample, keeping the laser at a fixed frequency.

Dual-mode microresonators as straightforward access to octave-spanning dissipative Kerr solitons

The Kerr soliton frequency comb is a revolutionary compact ruler of coherent light that allows applications from precision metrology to quantum information technology. The universal, reliable, and low-cost soliton microcomb source is key to these applications. As a development and extension of the direct creation of a soliton microcomb with the dual-mode scheme in an aluminum nitride microresonator, this paper thoroughly presents the design strategy to reliably attain such dual-modes in the silicon nitride (Si3N4) platform, separated by ∼10 GHz, which stabilizes soliton formation without using additional auxiliary laser or RF components. We demonstrate the deterministic generation of the refined single-solitons that span 1.5-octaves, i.e., near 200 THz, via adiabatic pump wavelength tuning. The ultra-wide soliton existence range up to 17 GHz not only suggests the robustness of the system but will also extend the applications of soliton combs. Moreover, the proposed scheme is found to easily give rise to multi-solitons as well as the soliton crystals featuring enhanced repetition rate (2 and 3 THz) and conversion efficiency greater than 10%. We also show the effective thermal tuning of mode separation to increase the possibility to access the single-soliton state. Our results are crucial for the chip-scale self-referenced frequency combs with a simplified configuration.

Quantum dynamics of dissipative Kerr solitons

Dissipative Kerr solitons arising from parametric gain in ring microresonators are usually described within a classical mean-field framework. Here, we develop a quantum-mechanical model of dissipative Kerr solitons in terms of the Lindblad master equation and study the model via the truncated Wigner method, which accounts for quantum effects to leading order. We show that, within this open quantum system framework, the soliton experiences a finite coherence time due to quantum fluctuations originating from losses. Reading the results in terms of the theory of open quantum systems allows us to estimate the Liouvillian spectrum of the system. It is characterized by a set of eigenvalues with a finite imaginary part and a vanishing real part in the limit of vanishing quantum fluctuations. This feature shows that dissipative Kerr solitons are a specific class of dissipative time crystals.

Modulation instability generation with blue-detuned pump laser in coupled microcavities

Optical frequency combs based on microcavities with Kerr nonlinearity are promising frequency comb sources for many applications. A typical Kerr soliton comb is generated in a nonlinear microcavity with anomalous dispersion pumped by a red-detuned continuous-wave laser. Modulation instability (MI) is the basis for Kerr soliton comb generation. In a microcavity with nearly zero dispersion, the first pair of MI modes can grow only with a red-detuned pump laser. In this paper, we find that MI generation is possible with blue-detuned pump lasers for coupled microcavities with nearly zero dispersion. We study a microcavity with Kerr nonlinearity coupled with an auxiliary microcavity, which has negligible nonlinearity. By theoretical analysis, we show that the coupled microcavities can create a region supporting MI generation in the blue-detuned side of the resonances of the nonlinear main cavity, whereas there is no blue-detuned MI generation in a single nonlinear microcavity. The properties of the blue-detuned MI region are determined by the coupling coefficient between the two microcavities, the loss of the auxiliary cavity, and the detuning between the modes of the two microcavities. The size and location of the blue-detuned MI region can be varied by tuning these parameters. Numerical simulations of MI generation based on the blue-detuned MI region in the coupled microcavities are presented. By considering more modes, MI comb generations with coupled microcavities having anomalous and normal dispersion are also numerically simulated.

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.

Compact, spatial-mode-interaction-free, ultralow-loss, nonlinear photonic integrated circuits

Multi-mode waveguides are ubiquitously used in integrated photonics. Although interaction among different spatial waveguide eigenmodes can induce novel nonlinear phenomena, spatial mode interaction is typically undesired. Adiabatic bends, such as Euler bends, have been favoured to suppress spatial mode interaction. Here, we adapt and optimize Euler bends to build compact racetrack microresonators based on ultralow-loss, multi-mode, silicon nitride photonic integrated circuits. The racetrack microresonators feature a footprint of only 0.21 mm2 for 19.8 GHz free spectral range, suitable for tight photonic integration. We quantitatively investigate the suppression of spatial mode interaction in the racetrack microresonators with Euler bends. We show that the low optical loss rate (15.5 MHz) is preserved, on par with the mode interaction strength (25 MHz). This results in an unperturbed microresonator dispersion profile. We further generate a single dissipative Kerr soliton of 19.8 GHz repetition rate without complex laser tuning schemes or auxiliary lasers. The optimized Euler bends and racetrack microresonators can be building blocks for integrated nonlinear photonic systems, as well as linear circuits for programmable processors or photonic quantum computing.

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.

Platicon microcomb generation using laser self-injection locking

The past decade has witnessed major advances in the development and system-level applications of photonic integrated microcombs, that are coherent, broadband optical frequency combs with repetition rates in the millimeter-wave to terahertz domain. Most of these advances are based on harnessing of dissipative Kerr solitons (DKS) in microresonators with anomalous group velocity dispersion (GVD). However, microcombs can also be generated with normal GVD using localized structures that are referred to as dark pulses, switching waves or platicons. Compared with DKS microcombs that require specific designs and fabrication techniques for dispersion engineering, platicon microcombs can be readily built using CMOS-compatible platforms such as thin-film (i.e., thickness below 300 nm) silicon nitride with normal GVD. Here, we use laser self-injection locking to demonstrate a fully integrated platicon microcomb operating at a microwave K-band repetition rate. A distributed feedback (DFB) laser edge-coupled to a Si3N4 chip is self-injection-locked to a high-Q ( > 107) microresonator with high confinement waveguides, and directly excites platicons without sophisticated active control. We demonstrate multi-platicon states and switching, perform optical feedback phase study and characterize the phase noise of the K-band platicon repetition rate and the pump laser. Laser self-injection-locked platicons could facilitate the wide adoption of microcombs as a building block in photonic integrated circuits via commercial foundry service.

Ultrafast dynamic RF-spectrum investigation of soliton microcombs

Dissipative Kerr solitons in microcavity systems exhibit remarkable nonlinear dynamics. The real-time measurement of soliton motion facilitates the comprehensive understanding of soliton physics. In this Letter, an all-optical radio frequency (RF) spectrum analyzer (named f-LISA) is used to characterize various stable soliton states and to track relative soliton motion in real time. By applying an inverse Fourier transform to the broadband RF spectrum, the autocorrelation traces are obtained with a temporal resolution of 373 fs and an ultrahigh frame rate of 20.6 MHz. We successfully characterize not only the stable single soliton state but also the stable multi-soliton states with different azimuthal angles between adjacent solitons. Furthermore, the dynamics of soliton switching from four-soliton state to single soliton state is observed in a temporal window of 60 µs. It is believed that the proposed scheme provides an alternative way to visualize the multi-soliton trajectories and enable the study of the soliton dynamics in integrated microcavities.