On timing jitter of mode locked Kerr frequency combs

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.

Theoretical Analysis of Microcavity Simultons Reinforced by χ^{(2)} and χ^{(3)} Nonlinearities

High-Q microcavities with quadratic and cubic nonlinearities add lots of versatility in controlling microcombs. Here, we study microcavity simulton and soliton dynamics reinforced by both χ^{(2)} and χ^{(3)} nonlinearities in a continuously pumped microcavity. Theoretical analysis based on the Lagrangian approach reveals the soliton peak power and gain-loss balance are impacted by the flat part of the intracavity pump, while the dark-pulse part of the pump leads to a nearly constant soliton group velocity change. We also derived a soliton conversion efficiency upper limit that is fully determined by the coupling condition and the quantum-limited soliton timing jitter in the χ^{(2,3)} system. Numerical simulations confirm the analytical results. Our theory is particularly useful for investigating AlN microcombs and sheds light on the interplay between χ^{(2)} and χ^{(3)} nonlinearities within microcavity simultons.

Turnkey photonic flywheel in a microresonator-filtered laser

Dissipative Kerr soliton (DKS) microcomb has emerged as an enabling technology that revolutionizes a wide range of applications in both basic science and technological innovation. Reliable turnkey operation with sub-optical-cycle and sub-femtosecond timing jitter is key to the success of many intriguing microcomb applications at the intersection of ultrafast optics and microwave electronics. Here we propose an approach and demonstrate the first turnkey Brillouin-DKS frequency comb to the best of our knowledge. Our microresonator-filtered laser design offers essential benefits, including phase insensitivity, self-healing capability, deterministic selection of the DKS state, and access to the ultralow noise comb state. The demonstrated turnkey Brillouin-DKS frequency comb achieves a fundamental comb linewidth of 100 mHz and DKS timing jitter of 1 femtosecond for averaging times up to 56 μs. The approach is universal and generalizable to various device platforms for user-friendly and field-deployable comb devices.

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.

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.

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.

Optical linewidth of soliton microcombs

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

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

Dissipative Kerr soliton microcombs for FEC-free optical communications over 100 channels

The demand for high-speed and highly efficient optical communication techniques has been rapidly growing due to the ever-increasing volume of data traffic. As well as the digital coherent communication used for core and metro networks, intensity modulation and direct detection (IM-DD) are still promising schemes in intra/inter data centers thanks to their low latency, high reliability, and good cost performance. In this work, we study a microresonator-based frequency comb as a potential light source for future IM-DD optical systems where applications may include replacing individual stabilized lasers with a continuous laser driven microresonator. Regarding comb line powers and spectral intervals, we compare a modulation instability comb and a soliton microcomb and provide a quantitative analysis with regard to telecom applications. Our experimental demonstration achieved a forward error correction (FEC) free operation of bit-error rate (BER) <10^-9 with a 1.45 Tbps capacity using a total of 145 lines over the entire C-band and revealed the possibility of soliton microcomb-based ultra-dense wavelength division multiplexing (WDM) with a simple, cost-effective IM-DD scheme, with a view to future practical use in data centers.

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.

Photonic Flywheel in a Monolithic Fiber Resonator

We demonstrate the first compact photonic flywheel with sub-fs time jitter (averaging times up to 10  μs) at the quantum-noise limit of a monolithic fiber resonator. Such quantum-limited performance is accessed through novel two-step pumping scheme for dissipative Kerr soliton generation. Controllable interaction between stimulated Brillouin lasing and Kerr nonlinearity enhances the DKS coherence and mitigates the thermal instability challenge, achieving a remarkable 22-Hz intrinsic comb linewidth and an unprecedented phase noise of -180  dBc/Hz at 945-MHz carrier at free running. The scheme can be generalized to various device platforms for field-deployable precision metrology.

Towards a stabilized Kerr optical frequency comb with spatial interference

We measured a soliton's carrier frequency created by a silicon nitride Kerr comb from an interference pattern created by a spatial interferometer. The optical frequencies were determined from the interference pattern by simultaneously calibrating against an interference pattern from the pump optical frequency. Results were compared to real-time measurements by an optical spectrum analyzer (OSA). The spatial interferometer and the OSA results tracked each other, and the resulting RMS error is presented.

Real-time transition dynamics and stability of chip-scale dispersion-managed frequency microcombs

Femtosecond mode-locked laser frequency combs have served as the cornerstone in precision spectroscopy, all-optical atomic clocks, and measurements of ultrafast dynamics. Recently frequency microcombs based on nonlinear microresonators have been examined, exhibiting remarkable precision approaching that of laser frequency combs, on a solid-state chip-scale platform and from a fundamentally different physical origin. Despite recent successes, to date, the real-time dynamical origins and high-power stabilities of such frequency microcombs have not been fully addressed. Here, we unravel the transitional dynamics of frequency microcombs from chaotic background routes to femtosecond mode-locking in real time, enabled by our ultrafast temporal magnifier metrology and improved stability of dispersion-managed dissipative solitons. Through our dispersion-managed oscillator, we further report a stability zone that is more than an order-of-magnitude larger than its prior static homogeneous counterparts, providing a novel platform for understanding ultrafast dissipative dynamics and offering a new path towards high-power frequency microcombs.

Ultralow-noise photonic microwave synthesis using a soliton microcomb-based transfer oscillator

The synthesis of ultralow-noise microwaves is of both scientific and technological relevance for timing, metrology, communications and radio-astronomy. Today, the lowest reported phase noise signals are obtained via optical frequency-division using mode-locked laser frequency combs. Nonetheless, this technique ideally requires high repetition rates and tight comb stabilisation. Here, a microresonator-based Kerr frequency comb (soliton microcomb) with a 14 GHz repetition rate is generated with an ultra-stable pump laser and used to derive an ultralow-noise microwave reference signal, with an absolute phase noise level below  -60 dBc/Hz at 1 Hz offset frequency and  -135 dBc/Hz at 10 kHz. This is achieved using a transfer oscillator approach, where the free-running microcomb noise (which is carefully studied and minimised) is cancelled via a combination of electronic division and mixing. Although this proof-of-principle uses an auxiliary comb for detecting the microcomb's offset frequency, we highlight the prospects of this method with future self-referenced integrated microcombs and electro-optic combs, that would allow for ultralow-noise microwave and sub-terahertz signal generators.

Quartic dissipative solitons in optical Kerr cavities

Solitons, ubiquitous in nonlinear sciences, are wavepackets which maintain their characteristic shape upon propagation. In optics, they have been observed and extensively studied in optical fibers. The spontaneous generation of a dissipative Kerr soliton (DKS) train in an optical microresonator pumped with continuous wave (CW) coherent light has placed solitons at the heart of optical frequency comb research in recent years. The commonly observed soliton has a "sech"-shaped envelope resulting from resonator cubic nonlinearity balanced by its quadratic anomalous group velocity dispersion (GVD). Here we exploit the Lagrangian variational method to show that CW pumping of a Kerr resonator featuring quartic GVD forms a pure quartic soliton (PQS) with Gaussian envelope. We find analytical expressions for pulse parameters in terms of experimentally relevant quantities and derive an area theorem. Analytical predictions are validated with extensive numerical simulations and apply also to fiber-based and spatial Kerr resonators. Broader bandwidth with flatter spectral envelope of a PQS, compared to a DKS of the same pulse width and peak power, make it superior for applications requiring small frequency comb line-to-line power variation.

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.

Single-mode dispersive waves and soliton microcomb dynamics

Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications.

Towards chip-scale optical frequency synthesis based on optical heterodyne phase-locked loop

An integrated heterodyne optical phase-locked loop was designed and demonstrated with an indium phosphide based photonic integrated circuit and commercial off-the-shelf electronic components. As an input reference, a stable microresonator-based optical frequency comb with a 50-dB span of 25 nm (~3 THz) around 1550 nm, having a spacing of ~26 GHz, was used. A widely-tunable on-chip sampled-grating distributed-Bragg-reflector laser is offset locked across multiple comb lines. An arbitrary frequency synthesis between the comb lines is demonstrated by tuning the RF offset source, and better than 100Hz tuning resolution with ± 5 Hz accuracy is obtained. Frequency switching of the on-chip laser to a point more than two dozen comb lines away (~5.6 nm) and simultaneous locking to the corresponding nearest comb line is also achieved in a time ~200 ns. A low residual phase noise of the optical phase-locking system is successfully achieved, as experimentally verified by the value of -80 dBc/Hz at an offset of as low as 200 Hz.

Bringing short-lived dissipative Kerr soliton states in microresonators into a steady state

Dissipative Kerr solitons have recently been generated in optical microresonators, enabling ultrashort optical pulses at microwave repetition rates, that constitute coherent and numerically predictable Kerr frequency combs. However, the seeding and excitation of the temporal solitons is associated with changes in the intracavity power that can lead to large thermal resonance shifts and render the soliton states in most commonly used resonator platforms short lived. Here we describe a "power kicking" method to overcome this instability by modulating the power of the pump laser. With this method also initially very short-lived (of the order of 100 ns) soliton states can be brought into a steady state in contrast to techniques reported earlier which relied on an adjustment of the laser scan speed only. Once the soliton state is in a steady state it can persist for hours and is thermally self-locked.

Theory and measurement of the soliton self-frequency shift and efficiency in optical microcavities

Dissipative Kerr cavity solitons experience a so-called self-frequency shift (SFS) as a result of Raman interactions. The frequency shift has been observed in several microcavity systems. The Raman process has also been shown numerically to influence the soliton pumping efficiency. Here, a perturbed Lagrangian approach is used to derive simple analytical expressions for the SFS and the soliton efficiency. The predicted dependences of these quantities on soliton pulse width are compared with measurements in a high-Q silica microcavity. The Raman time constant in silica is also inferred. Analytical expressions for the Raman SFS and soliton efficiency greatly simplify the prediction of soliton behavior over a wide range of microcavity platforms.

Optical Cherenkov radiation in overmoded microresonators

We show that an optical analog of Cherenkov radiation (dispersive wave) is observable in a nonlinear microring resonator generating Kerr frequency comb and containing linearly interacting families of equidistant modes. The radiation results from disruptions in the frequency dependent group velocity dispersion of the pumped cavity modes and is emitted into different mode families of the resonator. This effect reveals itself as a dispersive shaped structure in the spectral envelope of the frequency comb. We found that the dips in the comb spectrum correspond to peaks of the emission of the power in the other mode families of the resonator. The spectrum of the combs that includes both mode families does not have any dips, but peaks and resembles the Cherenkov radiation spectra frequently observed in Kerr comb systems. This Letter shows that a correct description of the Kerr comb in presence of mode anti-crossings should take into account not only the pumped mode family with modified dispersion parameter, but also the modes of the interacting families.

Active capture and stabilization of temporal solitons in microresonators

Soliton mode locking and femtosecond pulse generation have recently been demonstrated in high-Q optical microcavities and provide a new way to miniaturize frequency comb systems, as well as create integrated comb systems on a chip. However, triggering the mode-locking process is complicated by a well-known thermal hysteresis that can destabilize the solitons. Moreover, on a longer time scale, thermal drifting of the cavity resonant frequency relative to the pumping frequency causes loss of mode locking. In this Letter, an active feedback method is used both to capture specific soliton states and to stabilize the states indefinitely. The capture and stabilization method provides a reliable way to overcome thermal effects during soliton formation and to excite a desired number of circulating cavity solitons. It is also used to demonstrate a low pumping power of 22 mW for generation of microwave-repetition-rate solitons on a chip.

A broadband chip-scale optical frequency synthesizer at 2.7 × 10(-16) relative uncertainty

Optical frequency combs-coherent light sources that connect optical frequencies with microwave oscillations-have become the enabling tool for precision spectroscopy, optical clockwork, and attosecond physics over the past decades. Current benchmark systems are self-referenced femtosecond mode-locked lasers, but Kerr nonlinear dynamics in high-Q solid-state microresonators has recently demonstrated promising features as alternative platforms. The advance not only fosters studies of chip-scale frequency metrology but also extends the realm of optical frequency combs. We report the full stabilization of chip-scale optical frequency combs. The microcomb's two degrees of freedom, one of the comb lines and the native 18-GHz comb spacing, are simultaneously phase-locked to known optical and microwave references. Active comb spacing stabilization improves long-term stability by six orders of magnitude, reaching a record instrument-limited residual instability of [Formula: see text]. Comparing 46 nitride frequency comb lines with a fiber laser frequency comb, we demonstrate the unprecedented microcomb tooth-to-tooth relative frequency uncertainty down to 50 mHz and 2.7 × 10(-16), heralding novel solid-state applications in precision spectroscopy, coherent communications, and astronomical spectrography.

High spectral purity Kerr frequency comb radio frequency photonic oscillator

Femtosecond laser-based generation of radio frequency signals has produced astonishing improvements in achievable spectral purity, one of the basic features characterizing the performance of an radio frequency oscillator. Kerr frequency combs hold promise for transforming these lab-scale oscillators to chip-scale level. In this work we demonstrate a miniature 10 GHz radio frequency photonic oscillator characterized with phase noise better than -60 dBc Hz(-1) at 10 Hz, -90 dBc Hz(-1) at 100 Hz and -170 dBc Hz(-1) at 10 MHz. The frequency stability of this device, as represented by Allan deviation measurements, is at the level of 10(-10) at 1-100 s integration time-orders of magnitude better than existing radio frequency photonic devices of similar size, weight and power consumption.

Frequency comb formation and transition to chaos in microresonators with near-zero dispersion

We investigate the frequency comb formation in microresonators with near-zero dispersion, study the route from integrability to chaos in the corresponding nonlinear system, and demonstrate the key role of nonlinear dynamics of such a system for frequency comb generation and stability.

Generation of a coherent near-infrared Kerr frequency comb in a monolithic microresonator with normal GVD

We demonstrate experimentally, and describe theoretically, generation of a wide, fundamentally phase-locked Kerr frequency comb in a nonlinear resonator with a normal group velocity dispersion (GVD). A magnesium fluoride whispering-gallery mode resonator characterized with 10 GHz free spectral range and pumped either at 780 or 795 nm is used in the experiment. The envelope of the observed frequency comb differs significantly from the Kerr frequency comb spectra reported previously. We show via numerical simulation that, while the frequency comb does not correspond to generation of short optical pulses, the relative phase of the generated harmonics are fixed.

On the robustness of phase locking in Kerr optical frequency combs

We theoretically investigate the phase locking phenomena between the spectral components of Kerr optical frequency combs in the dynamical regime of Turing patterns. We show that these Turing patterns display a particularly strong and robust phase locking, originating from a cascade of phase locked triplets which asymptotically lead to a global phase locking between the modes. The local and global phase locking relationships defining the shape of the comb are analytically determined. Our analysis also shows that solitons display a much weaker phase locking that can be destroyed more easily than in the Turing pattern regime. Our results indicate that Turing patterns are generally the most suitable for applications requiring the highest stability. Experimental generation of such combs is also discussed in detail, and is in excellent agreement with the numerical simulations.

Focus issue introduction: nonlinear optics 2013

Nonlinear Optics has continued to develop over the last few years at an extremely fast pace, with significant advances being reported in nonlinear optical metamaterials, optical signal processing, quantum optics, nonlinear optics at subwavelength scale, and biophotonics. These exciting new developments have generated significant potential for a broad spectrum of technological applications in which nonlinear-optical processes play a central role.