Observation of Breathing Dark Pulses in Normal Dispersion Optical Microresonators

A chip-integrated comb-based microwave oscillator

Low-noise microwave oscillators are cornerstones for wireless communication, radar and clocks. The employment and optimization of optical frequency combs have enabled photonic microwave synthesizers with unrivalled noise performance and bandwidth breaking the bottleneck of those electronic counterparts. Emerging interest is to use chip-based Kerr frequency combs, namely microcombs. Today microcombs built on photonic integrated circuits feature small size, weight and power consumption, and can be manufactured to oscillate at any frequency ranging from microwave to millimeter-wave band. A monolithic microcomb-based microwave oscillator requires integration of lasers, photodetectors and nonlinear microresonators on a common substrate, which however has still remained elusive. Here, we demonstrate the first, fully hybrid-integrated, microcomb-based microwave oscillator at 10.7 GHz. The chip device, powered by a customized microelectronic circuit, leverages hybrid integration of a high-power DFB laser, a silicon nitride microresonator of a quality factor exceeding 25 × 106, and a high-speed photodetector chip of 110 GHz bandwidth (3 dB) and 0.3 A/W responsivity. Each component represents the state of the art of its own class, yet also allows large-volume manufacturing with low cost using established CMOS and III-V foundries. The hybrid chip outputs an ultralow-noise laser of 6.9 Hz intrinsic linewidth, a coherent microcomb of 10.7 GHz repetition rate, and a 10.7 GHz microwave carrier of 6.3 mHz linewidth - all the three functions in one entity occupying a footprint of only 76 mm2. Furthermore, harnessing the nonlinear laser-microresonator interaction, we observe and maneuver a unique noise-quenching dynamics within discrete microcomb states, which offers immunity to laser current noise, suppression of microwave phase noise by more than 20 dB, and improvement of microwave power by up to 10 dB. The ultimate microwave phase noise reaches -75/-105/-130 dBc/Hz at 1/10/100 kHz Fourier offset frequency. Our results can reinvigorate our information society for communication, sensing, imaging, timing and precision measurement.

Design and pulse-formation properties of chirped pulse Kerr solitons

Kerr resonators generate stable frequency combs and ultrashort pulses with applications in telecommunications, biomedicine, and metrology. Chirped pulse solitons recently observed in normal dispersion Kerr resonators with an intracavity spectral filter can enable new material design freedom, reduced fabrication requirements, and the potential for improved ultrashort pulse peak powers. This study examines the design and formation properties of chirped-pulse Kerr solitons essential for enabling these advances. First, prior theoretical predictions that chirped pulse solitons are relatively insensitive to cavity loss and the strength of the dispersion map are experimentally validated. The loss insensitivity property is applied toward demonstrating high energy pulses in a cavity with large output coupling and the map insensitivity property is applied toward demonstrating femtosecond pulses, for the first time from chirped-pulse solitons, in a dispersion-mapped cavity with small net-normal dispersion. The relationship between chirped pulses and bright pulses enabled by higher order dispersion is examined with respect to pulse formation, cavity design parameters, and performance properties. Finally, guidelines for additional improvements are detailed for chirped pulse soliton-based high-performance pulse generation.

Multimode resonance transition to collapsed snaking in normal dispersive Kerr cavities: bright versus dark solitons

We study the dynamics of Kerr cavity solitons in the normal dispersion regime in the presence of an intracavity phase modulation. The associated parabolic potential introduces multimode resonances, which promote the formation of high-order bright solitons. By gradually reducing the potential strength, bright solitons undergo a transition into dark solitons. We describe this process as a shift from a multimode resonance to a collapsed snaking bifurcation structure. This work offers a comprehensive overview of cavity dynamics and may provide a potential pathway to access multi-stable states by effectively varying the phase modulation.

Impact of stimulated Raman scattering on dark soliton generation in a silica microresonator

Generating a coherent optical frequency comb at an arbitrary wavelength is important for fields such as precision spectroscopy and optical communications. Dark solitons which are coherent states of optical frequency combs in normal dispersion microresonators can extend the operating wavelength range of these combs. While the existence and dynamics of dark solitons has been examined extensively, requirements for the modal interaction for accessing the soliton state in the presence of a strong Raman interaction at near visible wavelengths has been less explored. Here, analysis on the parametric and Raman gain in a silica microresonator is performed, revealing that four-wave mixing parametric gain which can be created by a modal-interaction-aided additional frequency shift is able to exceed the Raman gain. The existence range of the dark soliton is analyzed as a function of pump power and detuning for given modal coupling conditions. We anticipate these results will benefit fields requiring optical frequency combs with high efficiency and selectable wavelength such as biosensing applications using silica microcavities that have a strong Raman gain in the normal dispersion regime.

Dissipative Kerr solitons, breathers, and chimera states in coherently driven passive cavities with parabolic potential

We analyze the stability and dynamics of dissipative Kerr solitons (DKSs) in the presence of a parabolic potential. This potential stabilizes oscillatory and chaotic regimes, favoring the generation of static DKSs. Furthermore, the potential induces the emergence of new dissipative structures, such as asymmetric breathers and chimera-like states. Based on a mode decomposition of these states, we unveil the underlying modal interactions.

Photo-induced cascaded harmonic and comb generation in silicon nitride microresonators

Silicon nitride (Si3N4) is an ever-maturing integrated platform for nonlinear optics but mostly considered for third-order [χ(3)] nonlinear interactions. Recently, second-order [χ(2)] nonlinearity was introduced into Si3N4 via the photogalvanic effect, resulting in the inscription of quasi-phase-matched χ(2) gratings. However, the full potential of the photogalvanic effect in microresonators remains largely unexplored for cascaded effects. Here, we report combined χ(2) and χ(3) nonlinear effects in a normal dispersion Si3N4 microresonator. We demonstrate that the photo-induced χ(2) grating also provides phase-matching for the sum-frequency generation process, enabling the initiation and successive switching of primary combs. In addition, the doubly resonant pump and second-harmonic fields allow for effective third-harmonic generation, where a secondary optically written χ(2) grating is identified. Last, we reach a broadband microcomb state evolved from the sum-frequency-coupled primary comb. These results expand the scope of cascaded effects in microresonators.

Chirped-pulsed Kerr solitons in the Lugiato-Lefever equation with spectral filtering

Optical Kerr resonators support a variety of stable nonlinear phenomena in a simple and compact design. The generation of ultrashort pulses and frequency combs has been shown to benefit several applications, including spectroscopy and telecommunications. The most common anomalous dispersion Kerr resonators can be accurately described by a well-studied mean-field Lugiato-Lefever equation (LLE). Recently observed highly chirped pulses in normal dispersion resonators with a spectral filter, however, cannot. Here we examine the LLE in the normal dispersion regime modified with a Gaussian spectral filter (LLE-F). In addition to solutions associated with the LLE, we find stable highly chirped pulses. Solutions are strongly dependent on the filter bandwidth. Because of the large changes per round trip, the validity of the LLE-F fails over a large range of experimentally relevant parameters. While the mean-field approach leads to accurate predictions with respect to the nonlinearity coefficient and the dispersion, the dependence of drive power on loss deviates significantly from an experimentally accurate model, which leads to opportunities for Kerr resonators including frequency comb generation from low-Q-factor cavities.

Dynamics of dark breathers and Raman-Kerr frequency combs influenced by high-order dispersion

We investigate the dark breathers and Raman-Kerr microcombs generation influenced by stimulated Raman scattering (SRS) and high-order dispersion (HOD) effects in silicon microresonators with an integrated spatiotemporal formalism. The strong and narrow Raman gain constitute a threshold behavior with respect to free spectral range above which stable dark pulses can exist. The breathing dark pulses induced by HOD mainly depend on the amplitude and sign of third-order dispersion coefficient and their properties are also affected by the Raman assisted four wave mixing process. Such dissipative structures formed through perturbed switching waves, mainly exist in a larger red detuning region than that of stable dark pulses. Their breathing characteristics related to driving conditions have been analyzed in detail. Furthermore, the octave spanning mid-infrared (MIR) frequency combs via Cherenkov radiation are demonstrated, which circumvent chaotic and multi-soliton states compared with their anomalous dispersion-based counterpart. Our findings provide a viable way to investigate the physics inside dark pulses and broadband MIR microcombs generation.

Excitation of switching waves in normally dispersive Kerr cavities

A coherently pumped, passive cavity supports, in the normal dispersion regime, the propagation of still interlocked fronts or switching waves that form invariant localized temporal structures. We address theoretically the problem of the excitation of this type of wave packet. First, we map all the dynamical behaviors of the switching waves as a function of accessible parameters, namely, the cavity detuning and input energy deficiency, using box-like excitation of the intracavity field. Then we show how a good degree of control can be obtained by applying a negative or positive external pulsed excitation.