Spectral Purification of Microwave Signals with Disciplined Dissipative Kerr Solitons

Soliton synchronization in microresonators with a modulated pump

Microresonator frequency comb generation from Kerr solitons has become a cutting edge technology, but challenges remain in creating, maintaining, and controlling the solitons. Pump modulation and dual pumping are promising techniques for meeting these challenges. Here we derive the equation of motion of solitons interacting with a modulated pump in the framework of synchronization theory. It implies that the soliton repetition rate locks to the modulation frequency whenever the latter is within a locking range of frequencies around an integer multiple of the free spectral range of the microresonator. We calculate explicitly, numerically, and in perturbation theory the width of the locking range as a function of the amplitude and frequency of the pump and the modulation phase. We show that a highly red-detuned, strong pump that is amplitude-modulated provides the best conditions for entrainment, and that the width of the locking range is proportional to the square of the modulation frequency, limiting the effectiveness of RF modulation as an entrainment method.

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.

Comparison of Microcomb-Based Radio-Frequency Photonic Transversal Signal Processors Implemented with Discrete Components Versus Integrated Chips

RF photonic transversal signal processors, which combine reconfigurable electrical digital signal processing and high-bandwidth photonic processing, provide a powerful solution for achieving adaptive high-speed information processing. Recent progress in optical microcomb technology provides compelling multi-wavelength sources with a compact footprint, yielding a variety of microcomb-based RF photonic transversal signal processors with either discrete or integrated components. Although they operate based on the same principle, the processors in these two forms exhibit distinct performances. This paper presents a comparative investigation of their performances. First, we compare the performances of state-of-the-art processors, focusing on the processing accuracy. Next, we analyze various factors that contribute to the performance differences, including the tap number and imperfect response of experimental components. Finally, we discuss the potential for future improvement. These results provide a comprehensive comparison of microcomb-based RF photonic transversal signal processors implemented using discrete and integrated components and provide insights for their future development.

Red narrow-linewidth lasing and frequency comb from gain-switched self-injection-locked Fabry-Pérot laser diode

Narrow-linewidth lasers are in extensive demand for numerous cutting-edge applications. Such lasers operating at the visible range are of particular interest. Self-injection locking of a laser diode frequency to a high-Q whispering gallery mode is an effective and universal way to achieve superior laser performance. We demonstrate ultranarrow lasing with less than 10 Hz instantaneous linewidth for 20 [Formula: see text]s averaging time at 638 nm using a Fabry-Pérot laser diode locked to a crystalline MgF[Formula: see text] microresonator. The linewidth measured with a [Formula: see text]-separation line technique that characterizes 10 ms stability is as low as 1.4 kHz. Output power exceeds 80 mW. Demonstrated results are among the best for visible-range lasers in terms of linewidth combined with solid output power. We additionally report the first demonstration of a gain-switched regime for such stabilized Fabry-Pérot laser diode showing a high-contrast visible frequency comb generation. Tunable linespacing from 10 MHz to 3.8 GHz is observed. We demonstrated that the beatnote between the lines has sub-Hz linewidth and experiences spectral purification in the self-injection locking regime. This result might be of special importance for spectroscopy in the visible range.

Soliton Microcomb on Chip Integrated Si3N4 Microresonators with Power Amplification in Erbium-Doped Optical Mono-Core Fiber

Soliton microcombs, offering large mode spacing and broad bandwidth, have enabled a variety of advanced applications, particularly for telecommunications, photonic data center, and optical computation. Yet, the absolute power of microcombs remains insufficient, such that optical power amplification is always required. Here, we demonstrate a combined technique to access power-sufficient optical microcombs, with a photonic-integrated soliton microcomb and home-developed erbium-doped gain fiber. The soliton microcomb is generated in an integrated Si3N4 microresonator chip, which serves as a full-wave probing signal for power amplification. After the amplification, more than 40 comb modes, with 115-GHz spacing, reach the onset power level of >−10 dBm, which is readily available for parallel telecommunications , among other applications.

Numerical characterization of soliton microcomb in an athermal hybrid Si3N4-TiO2 microring

We theoretically investigate the athermal constructions to cancel the thermorefractive effect of a hybrid Si₃N₄-TiO₂ microring, which merges two materials with opposite thermo-optical coefficients (TOCs). The analytical and numerical results predict that the thermorefractive effect can be reduced under the appropriate parameters. In addition, the soliton state is easily accessed under the athermal condition. The thermorefractive noise due to the fluctuation of the microresonator temperature caused by the heat exchange between the microresonator and the surrounding environment is also suppressed by one order of magnitude, which is critical for the potential applications of soliton microcombs, such as spectroscopy, optical clocks and microwave generation.

All-optical dissipative discrete time crystals

Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-independent or periodically-driven quantum many-body systems. Spontaneous modification of discrete time-translation symmetry in periodically-forced physical systems can create a discrete time crystal (DTC) constituting a state of matter possessing properties like temporal rigid long-range order and coherence, which are inherently desirable for quantum computing and information processing. Despite their appeal, experimental demonstrations of DTCs are scarce and significant aspects of their behavior remain unexplored. Here, we report the experimental observation and theoretical investigation of DTCs in a Kerr-nonlinear optical microcavity. Empowered by the self-injection locking of two independent lasers with arbitrarily large frequency separation simultaneously to two same-family cavity modes and a dissipative Kerr soliton, this versatile platform enables realizing long-awaited phenomena such as defect-carrying DTCs and phase transitions. Combined with monolithic microfabrication, this room-temperature system paves the way for chip-scale time crystals supporting real-world applications outside sophisticated laboratories.

Discrete time crystals are described by a subharmonic response with respect to an external drive and have been mostly observed in closed periodically-driven systems. Here, the authors demonstrate a dissipative discrete time crystal in a Kerr-nonlinear optical microcavity pumped by two lasers.

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

Architecture for microcomb-based GHz-mid-infrared dual-comb spectroscopy

Dual-comb spectroscopy (DCS) offers high sensitivity and wide spectral coverage without the need for bulky spectrometers or mechanical moving parts. And DCS in the mid-infrared (mid-IR) is of keen interest because of inherently strong molecular spectroscopic signatures in these bands. We report GHz-resolution mid-IR DCS of methane and ethane that is derived from counter-propagating (CP) soliton microcombs in combination with interleaved difference frequency generation. Because all four combs required to generate the two mid-IR combs rely upon stability derived from a single high-Q microcavity, the system architecture is both simplified and does not require external frequency locking. Methane and ethane spectra are measured over intervals as short as 0.5 ms, a time scale that can be further reduced using a different CP soliton arrangement. Also, tuning of spectral resolution on demand is demonstrated. Although at an early phase of development, the results are a step towards mid-IR gas sensors with chip-based architectures for chemical threat detection, breath analysis, combustion studies, and outdoor observation of trace gases.

Gain-switched semiconductor laser driven soliton microcombs

Dissipative Kerr soliton generation using self-injection-locked III-V lasers has enabled fully integrated hybrid microcombs that operate in turnkey mode and can access microwave repetition rates. Yet, continuous-wave-driven soliton microcombs exhibit low energy conversion efficiency and high optical power threshold, especially when the repetition frequencies are within the microwave range that is convenient for direct detection with off-the-shelf electronics. Here, by actively switching the bias current of injection-locked III-V semiconductor lasers with switching frequencies in the X-band and K-band microwave ranges, we pulse-pump both crystalline and integrated microresonators with picosecond laser pulses, generating soliton microcombs with stable repetition rates and lowering the required average pumping power by one order of magnitude to a record-setting level of a few milliwatts. In addition, we unveil the critical role of the phase profile of the pumping pulses, and implement phase engineering on the pulsed pumping scheme, which allows for the robust generation and the stable trapping of solitons on intracavity pulse pedestals. Our work leverages the advantages of the gain switching and the pulse pumping techniques, and establishes the merits of combining distinct compact comb platforms that enhance the potential of energy-efficient chipscale microcombs.

Brillouin-Kerr Soliton Frequency Combs in an Optical Microresonator

By generating a Brillouin laser in an optical microresonator, we realize a soliton Kerr microcomb through exciting the Kerr frequency comb using the generated Brillouin laser in the same cavity. The intracavity Brillouin laser pumping scheme enables us to access the soliton states with a blue-detuned input pump. Because of the ultranarrow linewidth and the low-noise properties of the generated Brillouin laser, the observed soliton microcomb exhibits narrow-linewidth comb lines and stable repetition rate. Also, we demonstrate a low-noise microwave signal with phase noise of -49  dBc/Hz at 10 Hz, -130  dBc/Hz at 10 kHz, and -149  dBc/Hz at 1 MHz offsets for a 10.43 GHz carrier with only a free-running input pump. The easy operation of the Brillouin-Kerr soliton microcomb with excellent performance makes our scheme promising for practical applications.

Deterministic access of broadband frequency combs in microresonators using cnoidal waves in the soliton crystal limit

We present a method to deterministically obtain broad bandwidth frequency combs in microresonators. These broadband frequency combs correspond to cnoidal waves in the limit when they can be considered soliton crystals or single solitons. The method relies on moving adiabatically through the (frequency detuning)×(pump amplitude) parameter space, while avoiding the chaotic regime. We consider in detail Si₃N₄ microresonators with small or intermediate dimensions and an SiO₂ microresonator with large dimensions, corresponding to prior experimental work. We also discuss the impact of thermal effects on the stable regions for the cnoidal waves. Their principal effect is to increase the detuning for all the stable regions, but they also skew the stable regions, since higher pump power corresponds to higher power and hence increased temperature and detuning. The change in the detuning is smaller for single solitons than it is for soliton crystals. Without temperature effects, the stable regions for single solitons and soliton crystals almost completely overlap. When thermal effects are included, the stable region for single solitons separates from the stable regions for the soliton crystals, explaining in part the effectiveness of backwards-detuning to obtaining single solitons.

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.

Frequency division using a soliton-injected semiconductor gain-switched frequency comb

With optical spectral marks equally spaced by a frequency in the microwave or the radio frequency domain, optical frequency combs have been used not only to synthesize optical frequencies from microwave references but also to generate ultralow-noise microwaves via optical frequency division. Here, we combine two compact frequency combs, namely, a soliton microcomb and a semiconductor gain-switched comb, to demonstrate low-noise microwave generation based on a novel frequency division technique. Using a semiconductor laser that is driven by a sinusoidal current and injection-locked to microresonator solitons, our scheme transfers the spectral purity of a dissipative soliton oscillator into the subharmonic frequencies of the microcomb repetition rate. In addition, the gain-switched comb provides dense optical spectral emissions that divide the line spacing of the soliton microcomb. With the potential to be fully integrated, the merger of the two chipscale devices may profoundly facilitate the wide application of frequency comb technology.

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.

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.

Terahertz wave generation using a soliton microcomb

The Terahertz or millimeter wave frequency band (300 GHz - 3 THz) is spectrally located between microwaves and infrared light and has attracted significant interest for applications in broadband wireless communications, space-borne radiometers for Earth remote sensing, astrophysics, and imaging. In particular optically generated THz waves are of high interest for low-noise signal generation. Here, we propose and demonstrate stabilized terahertz wave generation using a microresonator-based frequency comb (microcomb). A unitravelling-carrier photodiode (UTC-PD) converts low-noise optical soliton pulses from the microcomb to a terahertz wave at the soliton's repetition rate (331 GHz). With a free-running microcomb, the Allan deviation of the Terahertz signal is 4.5×10^-9 at 1 s measurement time with a phase noise of -72 dBc/Hz (-118 dBc/Hz) at 10 kHz (10 MHz) offset frequency. By locking the repetition rate to an in-house hydrogen maser, in-loop fractional frequency stabilities of 9.6×10^-15 and 1.9×10^-17 are obtained at averaging times of 1 s and 2000 s respectively, indicating that the stability of the generated THz wave is limited by the maser reference signal. Moreover, the terahertz signal is successfully used to perform a proof-of-principle demonstration of terahertz imaging of peanuts. Combining the monolithically integrated UTC-PD with an on-chip microcomb, the demonstrated technique could provide a route towards highly stable continuous terahertz wave generation in chip-scale packages for out-of-the-lab applications. In particular, such systems would be useful as compact tools for high-capacity wireless communication, spectroscopy, imaging, remote sensing, and astrophysical applications.