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Relative phase noise between the primary and synthesis portions a Schematic of the measurement setup through which the relative phase noise of two comb teeth in the stitching region, one from the primary comb portion and one from the synthesis comb portion, is measured with the assistance of a 1300 nm EO comb. b Spectrum of the microcomb device under investigation. c Two microcomb teeth from the stitching region (blue) plotted along with the EO comb (purple). The EO comb teeth are not fully resolved due to the limited spectral resolution of the optical spectrum analyzer in comparison to the EO comb repetition frequency (6.0156 GHz). d Beat note of the EO comb with the two microcomb teeth. Only one out of the two beatnotes is present due to the limited spectrum analyser bandwidth (250 MHz). e Mixing of the two beat notes produced between the EO comb and the microcomb teeth to retrieve the relative phase noise of the microcomb teeth, without the (free-running) 1300 nm laser phase noise contribution. Both spectra have been taken with a resolution bandwidth of 230 kHz.
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Broadband and low-noise microresonator frequency combs (microcombs) are critical for deployable optical frequency measurements. Here we expand the bandwidth of a microcomb far beyond its anomalous dispersion region on both sides of its spectrum through spectral translation mediated by mixing of a dissipative Kerr soliton and a secondary pump. We in...
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... Moreover, recent demonstration showed that solitons can lock to an external CW pump, with fundamental impact in metrology [38,43]. Very importantly, pumping via dual external pump lasers operating at different wavelengths [44][45][46] can replicate, and effectively broaden, the spectrum of cavity-solitons by allowing the initially generated soliton comb to interact through nonlinear mixing with an additional pump. The new lines are dependent on the features of the initial comb, such as FSR and comb shape, due to phase-matching requirements in four-wave mixing [47]. ...
... The parametric interaction between a laser cavity-soliton and an externally coupled source to the resonator has not been reported to date, and it remains particularly important to establish if the self-oscillating microcombs can produce stable and persistent optical states, while being amenable to parametric interaction such as in purely externally driven configurations [44,45]. Lasing mode frequencies are determined by the properties of the system and can be perturbed by the presence of a driven wave, whose frequency is fixed and externally controlled. ...
We study the interaction of a laser cavity-soliton microcomb with an externally coupled, co-propagating tunable CW pump, observing parametric Kerr interactions which lead to the formation of both a cross-phase modulation and a four-wave mixing replica of the laser cavity-soliton. We compare and explain the dependence of the microcomb spectra from both the cavity-soliton and pump parameters, demonstrating the ability to adjust the microcomb externally without breaking or interfering with the soliton state. The parametric nature of the process agrees with numerical simulations. The parametric extended state maintains the typical robustness of laser-cavity solitons.
... Optical frequency combs (OFC), featuring an optical spectrum with uniformly spaced teeth and enabling high-precision measurements of complex signals, have been well recognized as a powerful tool for modern science and technology [1][2][3] . Typically, OFC can be generated through electro-optical modulation 4,5 , mode-locked laser 6,7 , and Kerr nonlinearity 8,9 . In recent years, such techniques have also been studied beyond purely optical systems [10][11][12][13][14] , especially the possibility of achieving acoustic frequency combs (AFC) [15][16][17][18] with micro-mechanical systems [19][20][21][22] . ...
Optical frequency combs have received increasing attention, thanks to their fundamental importance in optical computing, communication, sensing and metrology. Recently, thermal phonon counterparts of frequency combs have shown ~10² comb teeth and ~10³ teeth spacing, and limited to the high-frequency range over 100 kHz. In contrast, we report the first truly coherent acoustic frequency comb (AFC), with simultaneous giant enhancements in comb teeth number and teeth spacing, reaching the record teeth number of 10^4, covering six orders of magnitude in frequency; thus enabling a wide range of typical applications as force sensing, deep-sea monitoring or biomedical ultrasonics. In such a single device, two kinds of nonlinear couplings can emerge, i.e., the gain-assisted light-motion coupling and the mechanical wave mixing, the interplay of which can be flexibly tuned by rotating the angle of the membrane. Therefore, a single device could achieve a coherent switch from the multi-color phonon lasing regime to the coherent AFC regime, with almost perfectly uniform comb teeth. This work presents the first example merging phonon lasers and AFCs, and can stimulate more efforts on making and operating high-quality coherent AFC chips for diverse applications, by using phonon lasers already achieved in such diverse systems as membranes, levitated spheres, photonic crystals, semiconductor lattices, and cold ions.
... While this analogy may allude to the possibility of generating PDCSs in foundry-ready, pure-Kerr resonators with bichromatic driving 36 , fundamental differences between dispersive χ (2) and χ (3) parametric oscillators (for example, the number of potentially resonant fields, the frequency spacing of interacting waves, dispersive phase matching and spurious non-degenerate FWM interactions) prohibit a priori conclusions. The impact of bichromatic driving in the dynamics of conventional Kerr CSs has been considered [37][38][39][40][41] , but the possibility of using the scheme to generate temporal PDCSs remains entirely unexplored. ...
... We note that the prominent dip at about 275 THz arises due to the frequency dependence of the pulley coupler 46 , which was taken into account ad hoc in our simulations when estimating the spectrum of the out-coupled PDCS (shown as a blue curve in Fig. 3e; see also Methods and Supplementary Fig. 2). The spectral features around 350 THz originate from nonlinear Bragg-scattering-type FWM, whereby the two pumps at ω ± spectrally translate a portion of the soliton spectrum to an idler at higher frequencies 39 : we find that this process is linearly phase matched for soliton spectral components at ω S ≈ 2π × 232 THz, yielding a high-frequency idler at ω I ≈ 2π × 354 THz (see Extended Data Fig. 2). ...
... It is interesting to note that, in addition to the frequency comb around the degenerate FWM frequency at 253 THz, frequency combs arise also around both of the pump frequencies. These combs originate from FWM interactions between the pump fields and the comb lines around 253 THz (see also Supplementary Note 2), in a manner similar to spectral extension [38][39][40] and two-dimensional frequency comb 49 schemes studied in the context of conventional Kerr CSs. The combs around the pump frequencies share the line spacing with the comb around 253 THz, but there is a constant offset between the pump and PDCS combs. ...
The discovery that externally driven nonlinear optical resonators can sustain ultrashort pulses (solitons) corresponding to coherent optical frequency combs has enabled landmark advances in applications from telecommunications to sensing. Most previous research has focused on resonators with purely cubic (Kerr-type) nonlinearity that are externally driven with a monochromatic continuous-wave laser—in such systems, the solitons manifest themselves as unique attractors whose carrier frequency coincides with that of the external driving field. Recent experiments have, however, shown that a qualitatively different type of temporal soliton can arise via parametric downconversion in resonators with simultaneous quadratic and cubic nonlinearity. In contrast to conventional solitons in pure-Kerr resonators, these parametrically driven solitons come in two different flavours with opposite phases, and they are spectrally centred at half of the frequency of the driving field. Here we theoretically predict and experimentally demonstrate that parametrically driven solitons can also arise in resonators with pure-Kerr nonlinearity under conditions of bichromatic driving. In this case, the solitons arise through four-wave-mixing-mediated phase-sensitive amplification, come with two distinct phases and have a carrier frequency in between the two external driving fields. Our experiments are performed in an integrated silicon nitride microcavity, and we observe frequency comb spectra in remarkable agreement with theoretical predictions. In addition to representing the discovery of a new type of temporal dissipative soliton, our results constitute an unequivocal realization of parametrically driven soliton frequency combs in a microcavity platform that is compatible with foundry-ready mass fabrication.
... Among them, we can highlight microwave/THz photonics, [18][19][20][21][22] quantum state generation, [23][24][25][26][27][28][29][30][31] optical telecommunications, 32-37 spectroscopy, 38-41 computation, 42 astronomy, imaging, and optical ranging, 43-47 among other more fundamental topics. 48,49 However, despite these astounding successes, the field of Kerr comb science and technology is facing several challenges. We would like to highlight an arbitrary selection of three of them below. ...
Microresonator Kerr optical frequency combs currently constitute a well-established research area in integrated, nonlinear, and quantum photonics. These systems have found a plethora of technological applications, while serving as an excellent platform to investigate fundamental scientific topics such as light–matter interactions, pattern formation in driven-dissipative systems, or entangled twin-photon generation. We here provide a brief overview of the topic, highlight some of the most recent advances, and discuss a few of the main challenges ahead in this field.
... These demonstrations are intriguing, but by definition, systems exhibiting Ω = ∂Φ/∂t ≠ 0 are not synchronized. Until now, multi-driving of a DKS has been observed only when the primary and secondary combs are unsynchronized [27][28][29][30] or when soliton crystals are generated 31,32 . Here, we investigate the specific conditions to achieve phase-locking and demonstrate its appearance. ...
The phase-coherent frequency division of a stabilized optical reference laser to the microwave domain is made possible by optical-frequency combs (OFCs)1,2. OFC-based clockworks3–6 lock one comb tooth to a reference laser, which probes a stable atomic transition, usually through an active servo that increases the complexity of the OFC photonic and electronic integration for fieldable clock applications. Here, we demonstrate that the Kerr nonlinearity enables passive, electronics-free synchronization of a microresonator-based dissipative Kerr soliton (DKS) OFC⁷ to an externally injected reference laser. We present a theoretical model explaining this Kerr-induced synchronization (KIS), which closely matches experimental results based on a chip-integrated, silicon nitride, micro-ring resonator. Once synchronized, the reference laser captures an OFC tooth, so that tuning its frequency provides direct external control of the OFC repetition rate. We also show that the stability of the repetition rate is linked to that of the reference laser through the expected frequency division factor. Finally, KIS of an octave-spanning DKS exhibits enhancement of the opposite dispersive wave, consistent with the theoretical model, and enables improved self-referencing and access to the OFC carrier–envelope offset frequency. The KIS-mediated enhancements we demonstrate can be directly implemented in integrated optical clocks and chip-scale low-noise microwave generators.
... The SLW introduces a range of fascinating effects, such as frequency shifting or the emergence of new frequencies termed the idler-wave, which draws parallels with Hawking radiation [6]. In more recent developments, the SLW process has not only been identified in optical fibers but also in waveguide platforms and Kerr microresonators resonators [7][8][9][10]. In these scenarios, linear-waves undergo conversion into an idler-wave by interacting with cavity solitons. ...
Optical event horizons in fibers, driven by coherent pumps, have been a prominent subject of study within the field of nonlinear optics. Previously, optical event horizons involving a potent pump and a linear-wave were interpreted as phase-matching processes wherein new spectral components are derived from the linear-wave due to the influence of the strong pump. This nonlinear interaction, coupled with the wave mixing mechanism, has been elaborated upon in the spectral domain. It’s portrayed as a cascaded four-wave mixing process, achieving quasi-phase-matching through intermediate spectral components. Until now, research focused on event horizons or soliton linear-wave interactions has predominantly relied on coherent laser pump sources. However, there has been a recent resurgence in the exploration of incoherently pumped nonlinear optics. While the specific dynamics of incoherent light fields and their subsequent nonlinear processes might be elusive due to their inherent random field fluctuations, their incoherent nature unveils a multitude of statistical dynamics for nonlinear phenomena. In this work, we delve into optical event horizons encountered by linear-waves propelled by an incoherent light field within nonlinear optical fibers. Our numerical analysis scrutinizes the dynamics of linear-waves during optical event horizons under incoherent pumping. We further dissect the temporal statistics of the newly birthed idler-waves emerging from these event horizon processes.
... Moille-Perez-Stone-Rao et al. [19] designed an ultra-broadband microcomb which may contribute to the study of optical frequency synthesis, optical atomic clocks and reaching prescribed wavelengths. In fact, nω 1 ± (l − n)ω 2 in (1.10) can be viewed as spectral translation of {nω 1 } a (l − n)ω 2 length. ...
By modifying a Kuksin’s estimate, the coefficients of a one-dimensional quasi-periodic linear Schrödinger equation can be reduced to constants, and thus, the existence of the quasi-periodic solutions is obtained. Moreover, for the reduced system, the boundedness, the blowup and the specific form of the quasi-periodic solutions are analyzed in detail, via the depiction of the phase portrait with respect to the pseudo-time in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^3$$\end{document} and the growth of solutions from the spectrum theory of the associated lattice Schrödinger operator numerically. The result is based on infinite-dimensional KAM theory and bifurcation theory, which is original. The reduction techniques can also be used to the Ginzburg–Landau equation, which can be applied to traffic flow hydrodynamics. The solitary wavelike quasi-periodic solutions obtained can be further refined and applied to optical soliton communication.
... Although durations below 200 fs have been achieved using judicious fibre-based dispersion management [21][22][23] , and clusters of 100-fs-long CSs have recently been observed in centimetre-scale resonators made from highly nonlinear fibre 24 , the ability to generate single pulses with sub-100-fs durations has remained elusive-particularly in metre-scale resonators made from standard telecommunications fibre. State-of-the-art microresonator platforms permit dissipative solitons with durations measured in tens of femtoseconds, but they typically have a very large (hundreds of gigahertz) free-spectral range 10,25 , which makes them unsuitable for applications that require frequency combs with fine spacing (for example, high-resolution spectroscopy). Although mature mode-locked laser technologies exist that allow for sub-100-fs pulse generation at megahertz repetition rates, these do not benefit from some of the key advantages of dissipative solitons in passive resonators, including flexibility on operating wavelength and repetition rate, as well as the potential for on-chip integration. ...
External driving of passive, nonlinear optical resonators has emerged over the past decade as a novel route for the generation of ultrashort optical pulses and corresponding broadband frequency combs. Although the pulse formation dynamics in such systems dramatically differ from those manifesting themselves in conventional mode-locked lasers, the demarcation between the two traditionally distinct paradigms has recently begun to blur, with demonstrations of hybrid systems incorporating both external driving and active media shown to offer specific advantages. Here we explore a new pathway for ultrashort pulse generation at the interface of externally driven passive resonators and lasers. By leveraging the nonlinear Raman gain inherent in fused silica, we achieve the deterministic generation of low-noise dissipative solitons with durations well below 100 fs via the phase-coherent pulsed driving of resonators made of standard, commercially available optical fibre. We explore and explain the physics of the new dissipative Raman soliton states, identifying scaling laws that govern the pulses’ characteristics and that allow output repetition rates to be scaled at will without influencing the soliton duration. The scheme explored in our work enables the shortest-ever pulses generated in resonators (active or passive) made from a single commercially available optical fibre, to the best of our knowledge, and it has the potential to be transferred into a chip-scale format by using existing dispersion-engineered silica microresonators.
... The recent discovery of different types of solitonic pulses in optical microresonators, including bright solitons and dark pulses in the anomalous [1][2][3][4][5][6] and the normal [7][8][9][10][11][12] group velocity dispersion (GVD) regime, respectively, has facilitated the development of fully coherent, chip scale microcombs. Such phase-locked and low-noise multiwavelength laser sources have promoted plenty of applications in astronomy [13,14], spectroscopy [15][16][17][18][19], metrology [20][21][22], coherent communications [23][24][25] and optical clock [26][27][28]. ...
... Table 1 lists the normalized variables and their corresponding original symbol used in Eqns. (1)- (4). Some other parameters: L, δ 10 , α and T R are the total cavity length, external pump detuning, linear loss coefficient and single round-trip time, respectively. ...
We numerically investigate the excitation of vector solitonic pulse with orthogonally polarized components via free-carrier effects in microresonators with normal group velocity dispersion (GVD). The dynamics of single, dual and oscillated vector pulses are unveiled under turn-key excitation with a single frequency-fixed CW laser source. Parameter spaces associated with detuning, polarization angle, interval between the pumped orthogonal resonances and pump amplitude have been revealed. Different vector pulse states can also be observed exploiting the traditional pump scanning scheme. Simultaneous and independent excitation regimes are identified due to varying interval of the orthogonal pump modes. The nonlinear coupling between two modes contributes to the distortion of the vector pulses’ profile. The free-carrier effects and the pump polarization angle provide additional degrees of freedom for efficiently controlling the properties of the vector solitonic microcombs. Moreover, the crucial thermal dynamics in microcavities is discussed and weak thermal effects are found to be favorable for delayed vector pulse formation. These findings reveal complex excitation mechanism of solitonic structures and could provide novel routes for microcomb generation.
... In addition, broader bandwidth tuning of soliton spectra span and high sensitivity gas sensing was achieved by altering the Fermi level of the graphene-based resonator to successively modulate its second-and higher-order chromatic dispersions [18][19][20]. The microcircuit system composed of integrated piezoelectric actuators also provide additional method for tuning the mode resonance which is very attractive for initiating, tuning, and stabilizing the soliton microcombs [21], but the above schemes usually require high fabrication technology and cost, and its comb frequency interval of hundreds of GHz is still a regret for microwave generation in X-(10 GHz) and K-bands (20 GHz) [22,23]. Thus, there are still challenges to realize highly efficient and widely tunable soliton combs. ...
The dissipative Kerr soliton combs based on microresonators have attracted wide attention due to their high coherence and on-chip integration. Meanwhile, the soliton microcombs have shown broad applications in coherent communication, on-chip low-noise microwave synthesizer, optical clock, etc. However, the performance of these applications is typically limited by their bandwidth as the precise tuning of the soliton microcombs usually relies on the thermoelectric cooler, which is slow and may increase the system’s complexity. Here, we demonstrate the observation of dissipative solitons based on the magnesium fluoride resonator with an ultrahigh-quality (Q) factor of about 927 million. The ‘power-kicking’ scheme is employed to lock and stabilize the solitons actively. Also, tuning the acousto-optical modulator allows changing the bandwidth and recoil of the solitons. This approach enables more direct and concise feedback and reduces the system’s complexity.
