Phase shaping of dual-pumped Brillouin-Kerr frequency combs.

We investigate the spectral phase characteristics of dual-pumped Kerr frequency combs generated in a bichromatic Brillouin fiber laser architecture with normal dispersion, producing square-like pulse profiles. Using a pulse shaper, we measure the relative phase between the pump Stokes and adjacent lines, revealing a symmetric phase relationship. Our results highlight good phase coherence of the comb. By manipulating spectral amplitudes and phases, we demonstrate the transformation into various optical waveforms. The stability of our low-noise frequency comb ensures reliable performance in practical settings.

Stabilized single-frequency sub-kHz linewidth Brillouin fiber laser cavity operating at 1 µm.

We experimentally demonstrate a stabilized single-frequency Brillouin fiber laser operating at 1.06 µm by means of a passive highly nonlinear fiber (HNLF) ring cavity combined with a phase-locking loop scheme. The stimulated Brillouin scattering efficiency is first investigated in distinct single-mode germanosilicate core fibers with increasing G e O 2 content. The most suitable fiber, namely, 21 mol.% G e O 2 core fiber, is used as the Brillouin gain medium in the laser cavity made with a 15-m-long segment. A Stokes lasing threshold of 140 mW is reported. We also show significant linewidth narrowing (below 1 kHz) as well as frequency noise reduction compared to that of the initial pump in our mode-hop free Brillouin fiber laser.

Dispersion engineering in a Brillouin fiber laser cavity for Kerr frequency comb formation.

We conduct numerical and experimental investigations on Kerr comb generation in a nonlinear and non-reciprocal fiber cavity by leveraging both stimulated Brillouin backscattering and cascaded four-wave mixing. By engineering the net cavity dispersion to be either normal or anomalous, we enable the formation of diverse patterns and localized structures in the cavity field. The comb's properties depend crucially on the mismatch between the frequency spacing of the bichromatic pump and the free spectral range of the Brillouin laser cavity in both cases. Particularly, in the anomalous regime, adjusting this parameter yields coherent, stable frequency combs in the modulation instability regime. This allows control and expansion of the spectral bandwidth up to 2 THz in normal dispersion and to 6 THz under anomalous net dispersion. This versatile and easily reconfigurable method holds potential for applications in high-speed communications and microwave synthesis.

A continuum of bright and dark-pulse states in a photonic-crystal resonator.

Nonlinearity is a powerful determinant of physical systems. Controlling nonlinearity leads to interesting states of matter and new applications. In optics, diverse families of continuous and discrete states arise from balance of nonlinearity and group-velocity dispersion (GVD). Moreover, the dichotomy of states with locally enhanced or diminished field intensity depends critically on the relative sign of nonlinearity and either anomalous or normal GVD. Here, we introduce a resonator with unconditionally normal GVD and a single defect mode that supports both dark, reduced-intensity states and bright, enhanced-intensity states. We access and explore this dark-to-bright pulse continuum by phase-matching with a photonic-crystal resonator, which mediates the competition of nonlinearity and normal GVD. These stationary temporal states are coherent frequency combs, featuring highly designable spectra and ultralow noise repetition-frequency and intensity characteristics. The dark-to-bright continuum illuminates physical roles of Kerr nonlinearity, GVD, and laser propagation in a gapped nanophotonic medium.

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.

Monolithic piezoelectric control of soliton microcombs.

High-speed actuation of laser frequency1 is critical in applications using lasers and frequency combs2,3, and is a prerequisite for phase locking, frequency stabilization and stability transfer among optical carriers. For example, high-bandwidth feedback control of frequency combs is used in optical-frequency synthesis4, frequency division5 and optical clocks6. Soliton microcombs7,8 have emerged as chip-scale frequency comb sources, and have been used in system-level demonstrations9,10. Yet integrated microcombs using thermal heaters have limited actuation bandwidths11,12 of up to 10 kilohertz. Consequently, megahertz-bandwidth actuation and locking of microcombs have only been achieved with off-chip bulk component modulators. Here we demonstrate high-speed soliton microcomb actuation using integrated piezoelectric components13. By monolithically integrating AlN actuators14 on ultralow-loss Si3N4 photonic circuits15, we demonstrate voltage-controlled soliton initiation, tuning and stabilization with megahertz bandwidth. The AlN actuators use 300 nanowatts of power and feature bidirectional tuning, high linearity and low hysteresis. They exhibit a flat actuation response up to 1 megahertz-substantially exceeding bulk piezo tuning bandwidth-that is extendable to higher frequencies by overcoming coupling to acoustic contour modes of the chip. Via synchronous tuning of the laser and the microresonator, we exploit this ability to frequency-shift the optical comb spectrum (that is, to change the comb's carrier-envelope offset frequency) and make excursions beyond the soliton existence range. This enables a massively parallel frequency-modulated engine16,17 for lidar (light detection and ranging), with increased frequency excursion, lower power and elimination of channel distortions resulting from the soliton Raman self-frequency shift. Moreover, by modulating at a rate matching the frequency of high-overtone bulk acoustic resonances18, resonant build-up of bulk acoustic energy allows a 14-fold reduction of the required driving voltage, making it compatible with CMOS (complementary metal-oxide-semiconductor) electronics. Our approach endows soliton microcombs with integrated, ultralow-power and fast actuation, expanding the repertoire of technological applications of microcombs.

Massively parallel coherent laser ranging using a soliton microcomb.

Coherent ranging, also known as frequency-modulated continuous-wave (FMCW) laser-based light detection and ranging (lidar)1 is used for long-range three-dimensional distance and velocimetry in autonomous driving2,3. FMCW lidar maps distance to frequency4,5 using frequency-chirped waveforms and simultaneously measures the Doppler shift of the reflected laser light, similar to sonar or radar6,7 and coherent detection prevents interference from sunlight and other lidar systems. However, coherent ranging has a lower acquisition speed and requires precisely chirped8 and highly coherent5 laser sources, hindering widespread use of the lidar system and impeding parallelization, compared to modern time-of-flight ranging systems that use arrays of individual lasers. Here we demonstrate a massively parallel coherent lidar scheme using an ultra-low-loss photonic chip-based soliton microcomb9. By fast chirping of the pump laser in the soliton existence range10 of a microcomb with amplitudes of up to several gigahertz and a sweep rate of up to ten megahertz, a rapid frequency change occurs in the underlying carrier waveform of the soliton pulse stream, but the pulse-to-pulse repetition rate of the soliton pulse stream is retained. As a result, the chirp from a single narrow-linewidth pump laser is transferred to all spectral comb teeth of the soliton at once, thus enabling parallelism in the FMCW lidar. Using this approach we generate 30 distinct channels, demonstrating both parallel distance and velocity measurements at an equivalent rate of three megapixels per second, with the potential to improve sampling rates beyond 150 megapixels per second and to increase the image refresh rate of the FMCW lidar by up to two orders of magnitude without deterioration of eye safety. This approach, when combined with photonic phase arrays11 based on nanophotonic gratings12, provides a technological basis for compact, massively parallel and ultrahigh-frame-rate coherent lidar systems.

Heteronuclear soliton molecules in optical microresonators.

Optical soliton molecules are bound states of solitons that arise from the balance between attractive and repulsive effects. Having been observed in systems ranging from optical fibres to mode-locked lasers, they provide insights into the fundamental interactions between solitons and the underlying dynamics of the nonlinear systems. Here, we enter the multistability regime of a Kerr microresonator to generate superpositions of distinct soliton states that are pumped at the same optical resonance, and report the discovery of heteronuclear dissipative Kerr soliton molecules. Ultrafast electrooptical sampling reveals the tightly short-range bound nature of such soliton molecules, despite comprising cavity solitons of dissimilar amplitudes, durations and carrier frequencies. Besides the significance they hold in resolving soliton dynamics in complex nonlinear systems, such heteronuclear soliton molecules yield coherent frequency combs whose unusual mode structure may find applications in metrology and spectroscopy.

Chip-based soliton microcomb module using a hybrid semiconductor laser.

Photonic chip-based soliton microcombs have shown rapid progress and have already been used in many system-level applications. There has been substantial progress in realizing soliton microcombs that rely on compact laser sources, culminating in devices that only utilize a semiconductor gain chip or a self-injection-locked laser diode as the pump source. However, generating single solitons with electronically detectable repetition rates from a compact laser module has remained challenging. Here we demonstrate a current-initiated, Si3N4 chip-based, 99-GHz soliton microcomb driven directly by a compact, semiconductor-based laser. This approach does not require any complex soliton tuning techniques, and single solitons can be accessed by tuning the laser current. Further, we demonstrate a generic, simple, yet reliable, packaging technique to facilitate the fiber-chip interface, which allows building a compact soliton microcomb package that can benefit from the fiber systems operating at high power (> 100 mW). Both techniques can exert immediate impact on chip-based nonlinear photonic applications that require high input power, high output power, and interfacing chip-based devices to mature fiber systems.

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.

Author Correction: Electrically pumped photonic integrated soliton microcomb.

The original version of this Article contained an error in the first sentence of the Acknowledgements, which incorrectly read 'This publication was supported by Contract HR0011-15-C-0055 (DODOS) from the Defense Advanced Research Projects Agency (DARPA), Defense Sciences Office (DSO).' The correct version states 'Microsystems Technology Office (MTO)' in place of 'Defense Sciences Office (DSO)'. This has been corrected in both the PDF and HTML versions of the Article.

Spectral Purification of Microwave Signals with Disciplined Dissipative Kerr Solitons.

Continuous-wave-driven Kerr nonlinear microresonators give rise to self-organization in terms of dissipative Kerr solitons, which constitute optical frequency combs that can be used to generate low-noise microwave signals. Here, by applying either amplitude or phase modulation to the driving laser we create an intracavity potential trap to discipline the repetition rate of the solitons. We demonstrate that this effect gives rise to a novel spectral purification mechanism of the external microwave signal frequency, leading to reduced phase noise of the output signal. We experimentally observe that the microwave signal generated from disciplined solitons is injection locked by the external drive at long timescales, but exhibits an unexpected suppression of the fast timing jitter. Counterintuitively, this filtering takes place for frequencies that are substantially lower than the cavity decay rate. As a result, while the long timescale stability of the Kerr frequency comb's repetition rate is improved by more than 4 orders of magnitude, the purified microwave signal shows a reduction of the phase noise by 30 dB at offset frequencies above 10 kHz.

Electrically pumped photonic integrated soliton microcomb.

Microcombs provide a path to broad-bandwidth integrated frequency combs with low power consumption, which are compatible with wafer-scale fabrication. Yet, electrically-driven, photonic chip-based microcombs are inhibited by the required high threshold power and the frequency agility of the laser for soliton initiation. Here we demonstrate an electrically-driven soliton microcomb by coupling a III-V-material-based (indium phosphide) multiple-longitudinal-mode laser diode chip to a high-Q silicon nitride microresonator fabricated using the photonic Damascene process. The laser diode is self-injection locked to the microresonator, which is accompanied by the narrowing of the laser linewidth, and the simultaneous formation of dissipative Kerr solitons. By tuning the laser diode current, we observe transitions from modulation instability, breather solitons, to single-soliton states. The system operating at an electronically-detectable sub-100-GHz mode spacing requires less than 1 Watt of electrical power, can fit in a volume of ca. 1 cm3, and does not require on-chip filters and heaters, thus simplifying the integrated microcomb.

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.

Self-referenced photonic chip soliton Kerr frequency comb.

Self-referencing turns pulsed laser systems into self-referenced frequency combs. Such frequency combs allow counting of optical frequencies and have a wide range of applications. The required optical bandwidth to implement self-referencing is typically obtained via nonlinear broadening in optical fibers. Recent advances in the field of Kerr frequency combs have provided a path toward the development of compact frequency comb sources that provide broadband frequency combs, exhibit microwave repetition rates and are compatible with on-chip photonic integration. These devices have the potential to significantly expand the use of frequency combs. Yet to date, self-referencing of such Kerr frequency combs has only been attained by applying conventional, fiber-based broadening techniques. Here we demonstrate external broadening-free self-referencing of a Kerr frequency comb. An optical spectrum spanning two-thirds of an octave is directly synthesized from a continuous wave laser-driven silicon nitride microresonator using temporal dissipative Kerr soliton formation and soliton Cherenkov radiation. Using this coherent bandwidth and two continuous wave transfer lasers in a 2f-3f self-referencing scheme, we are able to detect the offset frequency of the soliton Kerr frequency comb. By stabilizing the repetition rate to a radio frequency reference, the self-referenced frequency comb is used to count and track the continuous wave pump laser's frequency. This work demonstrates the principal ability of soliton Kerr frequency combs to provide microwave-to-optical clockworks on a chip.