We demonstrate protected single-soliton formation and operation in a Kerr microresonator using a phase-modulated pump laser. Phase modulation gives rise to spatially varying effective loss and detuning parameters, which in turn lead to an operation regime in which multi-soliton degeneracy is lifted and a single soliton is the only observable behavior. Direct excitation of single solitons is indicated by observed reversal of the characteristic 'soliton step.' Phase modulation also enables precise control of the soliton pulse train's properties, and measured dynamics agree closely with simulations. We show that the technique can be extended to high repetition-frequency Kerr solitons through subharmonic phase modulation. These results facilitate straightforward generation and control of Kerr-soliton microcombs for integrated photonics systems.
We investigate the effects of Raman and Kerr gain in crystalline microresonators and determine the conditions required to generate modelocked frequency combs. We show theoretically that strong, narrowband Raman gain determines a maximum microresonator size allowable to achieve comb formation. We verify this condition experimentally in diamond and silicon microresonators and show that there exists a competition between Raman and Kerr effects that leads to the existence of two different comb states.
We experimentally demonstrate a negative Kerr nonlinearity for quasi-undoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2,gr = -10^(-13) m^2/W. Whereas the sign of n2,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the…
Mode interaction in silicon nitride micro-resonators is investigated. We provide clear experimental evidence of mode interaction between two family modes and mode interaction is demonstrated to be the cause of the comb generation in resonators with normal dispersion.
Soliton microcombs based on Kerr nonlinearity in microresonators have been a prominent miniaturized coherent light source. Here, for the first time, we demonstrate the existence of Kerr solitons in an optomechanical microresonator, for which a nonlinear model is built by incorporating a single mechanical mode and multiple optical modes. Interestingly, an exotic vibrational Kerr soliton state is found, which is modulated by a self-sustained mechanical oscillation. Besides, the soliton provides extra mechanical gain through the optical spring effect, and results in phonon lasing with a red-detun…
Taking advantage of an extended Lugiato--Lefever equation with third-order dispersion, we numerically show that dark cavity solitons formed in normal dispersion of microresonators are capable of emitting dispersive waves in both normal and anomalous dispersion regions, resembling the behavior of the commonly encountered bright cavity solitons. The generated dispersive waves can be accurately predicted by the dissipative radiation theory. In addition, we demonstrate the stability enhancement of Kerr frequency combs in normal dispersion regime in case the dispersive wave is emitted by dark solit…
We stabilize a chip-scale Si3N4 phase-locked Kerr frequency comb via locking the pump laser to an independent stable high-Q reference microresonator and locking the comb spacing to an external microwave oscillator. In this comb, the pump laser shift induces negligible impact on the comb spacing change. This scheme is a step towards miniaturization of the stabilized Kerr comb system as the microresonator reference can potentially be integrated on-chip. Fractional instability of the optical harmonics of the stabilized comb is limited by the microwave oscillator used for comb spacing lock below 1…
This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb gen…
Recent experiments have demonstrated the generation of widely-spaced parametric sidebands that can evolve into "clustered" optical frequency combs in Kerr microresonators. Here we describe the physics that underpins the formation of such clustered comb states. In particular, we show that the phase-matching required for the initial sideband generation is such that (at least) one of the sidebands experiences anomalous dispersion, enabling that sideband to drive frequency comb formation via degenerate and non-degenerate four-wave mixing. We validate our proposal through a combination of experimen…
The Kerr effect in optical microresonators plays an important role for integrated photonic devices and enables third harmonic generation, four-wave mixing, and the generation of microresonator-based frequency combs. Here we experimentally demonstrate that the Kerr nonlinearity can split ultra-high-Q microresonator resonances for two continuous-wave lasers. The resonance splitting is induced by self- and cross-phase modulation and counter-intuitively enables two lasers at different wavelengths to be simultaneously resonant in the same microresonator mode. We develop a pump-probe spectroscopy sc…
Dissipative Kerr solitons are localized structures that exist in optical microresonators. They lead to the formation of microcombs --- chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by capitalizing on advances in silicon photonics. Previous demonstrations have mainly focused on anomalous dispersion microresonators. Notwithstanding, localized structures also exist in the normal dispersion regime in the form of circulating dark pulses, but their physical dynamics is far from being understood. Here, we report the discovery of reversible switching betw…
Optical injection locking is implemented to faithfully transfer the phase noise of a dissipative Kerr microresonator soliton comb in addition to the amplification of the Kerr comb. Unlike Er-doped fiber and semiconductor optical amplifiers, the optical injection locking amplifies the comb mode without degrading the optical signal-to-noise ratio. In addition, we show that the residual phase noise of the optical injection locking is sufficiently small to transfer the relative phase noise of comb modes (equivalent to the repetition frequency) of low phase noise Kerr combs, concluding that the opt…
We study optical parametric oscillations in Kerr-nonlinear microresonators, revealing an intricate solution space -- parameterized by the pump-to-signal conversion efficiency -- that arises from an interplay of nonlinear processes. Using a three-mode approximation, we derive an efficiency-maximizing relation between pump power and frequency mismatch. To move beyond a three-mode approximation, a necessity for geometries such as integrated microring resonators, we numerically simulate the Lugiato-Lefever Equation that accounts for the full spectrum of nonlinearly-coupled resonator modes. We obse…
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, radiofrequency 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 degre…
Kerr frequency combs generated from microresonators are the subject of intense study. Most research employs microresonators with anomalous dispersion, for which modulation instability is believed to play a key role in initiation of the comb. Comb generation in normal dispersion microresonators has also been reported but is less well understood. Here we report a detailed investigation of few-moded, normal dispersion silicon nitride microresonators, showing that mode coupling can strongly modify the local dispersion, even changing its sign. We demonstrate a link between mode coupling and initiat…
Kerr microresonators generate interesting and useful fundamental states of electromagnetic radiation through nonlinear interactions of continuous-wave (CW) laser light. Using photonic-integration techniques, functional devices with low noise, small size, low-power consumption, scalable fabrication, and heterogeneous combinations of photonics and electronics can be realized. Kerr solitons, which stably circulate in a Kerr microresonator, have emerged as a source of coherent, ultrafast pulse trains and ultra-broadband optical-frequency combs. Using the f-2f technique, Kerr combs support carrier-…
Carrier-envelope phase stabilization of optical pulses enables exquisitely precise measurements by way of direct optical-frequency synthesis, absolute optical-to-microwave phase conversion, and control of ultrafast waveforms. We report such phase stabilization for Kerr-microresonator frequency combs integrated on silicon chips, and verify their fractional-frequency inaccuracy at <3x10-16. Our work introduces an interlocked Kerr-comb configuration comprised of one silicon-nitride and one silica microresonator, which feature nearly harmonic repetition frequencies and can be generated with one la…
We demonstrate stable microresonator Kerr soliton frequency combs in a III-V platform (AlGaAs on SiO$_2$) through quenching of thermorefractive effects by cryogenic cooling to temperatures between 4~K and 20~K. This cooling reduces the resonator's thermorefractive coefficient, whose room-temperature value is an order of magnitude larger than that of other microcomb platforms like Si$_3$N$_4$, SiO$_2$, and AlN, by more than two orders of magnitude, and makes soliton states adiabatically accessible. Realizing such phase-stable soliton operation is critical for applications that fully exploit the…
High-Q silicon nitride (SiN) microresonators enable optical Kerr frequency comb generation on a photonic chip and have recently been shown to support fully coherent combs based on temporal dissipative Kerr soliton formation. For bright soliton formation it is necessary to operate SiN waveguides in the multimode regime so as to produce anomalous group velocity dispersion. This can lead to local disturbances of the dispersion due to avoided crossings caused by coupling between different mode families, and therefore prevent the soliton formation. Here we demonstrate that a single mode "filtering"…
Temporal solitons in driven microresonator, fiber-resonator, and bulk enhancement cavities enable attractive optical sources for spectroscopy, communications, and metrology. Here we present theoretical and experimental observations of a new class of temporal optical soliton characterized by pulses with large and positive chirp in normal dispersion resonators with strong spectral filtering. Numerical simulations reveal stable waveforms over a wide new range of parameters including highly chirped pulses at large drive powers. Chirped temporal solitons matching predictions are observed in experim…
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. Due to the ultra-narrow linewidth and the low-noise properties of the generated Brillouin laser, the observed soliton microcomb exhibits narrow-linewidth comb lines and stable repetition rate even by using a diode laser with relatively broad linewidth. Also, we demonstrate a low-noise …
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 during the excitation process 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 t…
The realization of ultrahigh quality (Q) resonators regardless of the underpinning material platforms has been a ceaseless pursuit, because the high Q resonators provide an extreme environment of storage of light to enable observations of many unconventional nonlinear optical phenomenon with high efficiencies. Here, we demonstrate an ultra-high Q factor (7.1*10^6) microresonator on the 4H-silicon-carbide-on-insulator (4H-SiCOI) platform in which both \c{hi}^(2) and \c{hi}^(3) nonlinear processes of high efficiencies have been generated. Broadband frequency conversions, including second-, third…
We demonstrate experimentally, and explain theoretically, generation of a wide, fundamentally phase locked Kerr frequency comb in a nonlinear resonator with a normal group velocity dispersion. A magnesium fluoride whispering gallery resonator characterized with 10 GHz free spectral range and pumped either at 780 nm 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,…
Optical frequency combs allow for precise measurement of optical frequencies and are used in a growing number of applications beyond spectroscopy and optical frequency metrology. A class of compact microresonator based frequency comb generators has emerged recently based on (hyper)-parametric frequency conversion, mediated by the Kerr-non-linearity, of a continuous wave laser beam. Despite the rapid progress and the emergence of a wide variety of micro-resonator Kerr-comb platforms, an understanding of the dynamics of the Kerr comb formation is still lacking. In particular the question in whic…
The model, that is usually called Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a perfe…
We present measurements of silicon nitride nonlinear microresonators and frequency comb generation at cryogenic temperatures as low as 7~K. The resulting two orders of magnitude reduction in the thermo-refractive coefficient relative to room-temperature enables direct access to single bright Kerr soliton states through adiabatic frequency tuning of the pump laser while remaining in thermal equilibrium. Our experimental results, supported by theoretical modeling, show that single solitons are easily accessible at temperatures below 60~K for the microresonator device under study. We further demo…
Kerr soliton frequency comb generation in monolithic microresonators recently attracted great interests as it enables chip-scale few-cycle pulse generation at microwave rates with smooth octave-spanning spectra for self-referencing. Such versatile platform finds significant applications in dual-comb spectroscopy, low-noise optical frequency synthesis, coherent communication systems, etc. However, it still remains challenging to straightforwardly and deterministically generate and sustain the single-soliton state in microresonators. In this paper, we propose and theoretically demonstrate the ex…
We present and theoretically investigate a dispersion engineered GaP-OI microresonator containing a partially-etched gap of 250 nm x 410 nm in a 600 nm x 2990 nm waveguide. This gap enables a 3.25 μm wide anomalous dispersion spectral span covering both the near-infrared and the mid-infrared spectra. This anomalous dispersion is manifested by two mechanisms, being the hybridization of the fundamental TE modes around 1550 nm and the geometric dispersion of the higher order TE mode around the 3100 nm wavelengths, respectively. Two Kerr soliton combs can be numerically generated with 101 GHz and …
Microresonator-based Kerr frequency comb (microcomb) generation can potentially revolutionize a variety of applications ranging from telecommunications to optical frequency synthesis. However, phase-locked microcombs have generally had low conversion efficiency limited to a few percent. Here we report experimental results that achieve ~30% conversion efficiency (~200 mW on-chip comb power excluding the pump) in the fiber telecommunication band with broadband mode-locked dark-pulse combs. We present a general analysis on the efficiency which is applicable to any phase-locked microcomb state. Th…
Microresonator frequency combs harness the nonlinear Kerr effect in an integrated optical cavity to generate a multitude of phase-locked frequency lines. The line spacing can reach values in the order of 100 GHz, making it an attractive multi-wavelength light source for applications in fiber-optic communications. Depending on the dispersion of the microresonator, different physical dynamics have been observed. A recently discovered comb state corresponds to the formation of mode-locked dark pulses in a normal-dispersion microcavity. Such dark-pulse combs are particularly compelling for advance…
We report on the first experimental demonstration of widely-tunable parametric sideband generation in a Kerr microresonator. Specifically, by pumping a silica microsphere in the normal dispersion regime, we achieve the generation of phase-matched four-wave mixing sidebands at large frequency detunings from the pump. Thanks to the role of higher-order dispersion in enabling phase matching, small variations of the pump wavelength translate into very large and controllable changes in the wavelengths of the generated sidebands: we experimentally demonstrate over 720 nm of tunability using a low-po…
Microresonator-based optical frequency combs, or "microcombs", have attracted lots of attention in the last few years thanks to their promising applications in telecommunications, spectroscopy and optical clocks. The process of comb generation in microresonators can be modelled in the frequency domain using coupled mode equations, and has also recently been successfully described in the time domain using a nonlinear Schrödinger equation known as the Lugiato-Lefever equation. Though time-domain approaches have brought many interesting insights for the understanding of microcombs, an intuitive f…
The formation of temporal dissipative solitons in continuous wave laser driven microresonators enables the generation of coherent, broadband and spectrally smooth optical frequency combs as well as femtosecond pulses with compact form factor. Here we report for the first time on the observation of a Raman-induced soliton self-frequency shift for a microresonator soliton. The Raman effect manifests itself in amorphous SiN microresonator based single soliton states by a spectrum that is hyperbolic secant in shape, but whose center is spectrally red-shifted (i.e. offset) from the continuous wave …
High-Q microresonator has been suggested a promising platform for optical frequency comb generation, via dissipative soliton formation. To achieve a higher Q and obtain the necessary anomalous dispersion, $Si_3N_4$ microresonators made of multi-mode waveguides were previously implemented. However, coupling between different transverse mode families in the multi-mode waveguides results in periodic disruption of dispersion and quality factor, introducing perturbation to dissipative soliton formation and amplitude modulation to the corresponding spectrum. Careful choice of pump wavelength to avoi…
Thermal noise is ubiquitous in microscopic systems and in high-precision measurements. Controlling thermal noise, especially using laser light to apply dissipation, substantially affects science in revealing the quantum regime of gases, in searching for fundamental physics, and in realizing practical applications. Recently, nonlinear light-matter interactions in microresonators have opened up new classes of microscopic devices. A key example is Kerr-microresonator frequency combs; so-called soliton microcombs not only explore nonlinear science but also enable integrated-photonics devices, such…
Broadband Kerr combs with a flat comb spectral profile are expected in a number of applications, such as high-capacity optical communication. Here, we propose novel concentric dual-ring microresonators (DRMs) for advanced dispersion engineering to tailor the comb spectral profile. The dispersion can be flexibly engineered not only by the cross-section of the DRMs, but also by the gap between concentric dual-ring microresonators, which provides a new path to geometrically control the spectral profile of the soliton Kerr combs. An octave-spanning dissipative Kerr soliton comb with superior spect…
All-optical Synchronization of Breather Solitons in a Kerr Microresonator
The University of Auckland（奥克兰大学）；The Dodd-Walls Centre for Photonics and Quantum technologies（光子与量子技术多德-沃尔斯中心）；Joint Quantum Institute, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学联合量子研究所）；NIST（美国国家标准与技术研究院）
Dissipative temporal Kerr solitons in optical microresonators enable to convert a continuous wave laser into a train of femtosecond pulses. Of particular interest are single soliton states, whose $\mathrm{sech}^{2}$ spectral envelope provides a spectrally smooth and low noise optical frequency comb, and that recently have been generated in crystalline, silica, and silicon-nitride resonators. Here, we study the dynamics of multiple soliton states containing ${N}$ solitons and report the discovery of a novel, yet simple mechanism which makes it possible to reduce deterministically the number of …
Temporal-dissipative Kerr solitons are self-localized light pulses sustained in driven nonlinear optical resonators. Their realization in microresonators has enabled compact sources of coherent optical frequency combs as well as the study of dissipative solitons. A key parameter of their dynamics is the effective-detuning of the pump laser to the thermally- and Kerr-shifted cavity resonance. Together with the free spectral range and dispersion, it governs the soliton-pulse duration, as predicted by an approximate analytical solution of the Lugiato-Lefever equation. Yet, a precise experimental …
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 fibers 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 electroopt…
Optical frequency combs enable coherent data transmission on hundreds of wavelength channels and have the potential to revolutionize terabit communications. Generation of Kerr combs in nonlinear integrated microcavities represents a particularly promising option enabling line spacings of tens of GHz, compliant with wavelength-division multiplexing (WDM) grids. However, Kerr combs may exhibit strong phase noise and multiplet spectral lines, and this has made high-speed data transmission impossible up to now. Recent work has shown that systematic adjustment of pump conditions enables low phase-n…
Microresonator optical frequency combs based on cascaded four-wave mixing are potentially attractive as a multi-wavelength source for on-chip optical communications. In this paper we compare time domain coherence, radio-frequency (RF) intensity noise, and individual line optical communications performance for combs generated from two different silicon nitride microresonators. The comb generated by one microresonator forms directly with lines spaced by a single free spectral range (FSR) and exhibits high coherence, low noise, and excellent 10 Gbit/s optical communications results. The comb gene…
We report the experimental observation of oscillatory antiphase switching between counter-propagating light beams in Kerr ring microresonators, including the emergence of periodic behaviour from a chaotic regime. Self-switching occurs in balanced regimes of operation and is well captured by a simple coupled dynamical system featuring only the self- and cross-phase Kerr nonlinearities. Switching phenomena are due to temporal instabilities of symmetry-broken states combined with attractor merging that restores the broken symmetry on average. Self-switching of counter-propagating light is robust …
We consider interaction of counter-propagating waves in a bi-directionally pumped ring microresonator with Kerr nonlinearity. We introduce a hierarchy of the mode expansions and envelope functions evolving on different time scales set by the cavity linewidth and nonlinearity, dispersion, and repetition rate, and provide a detailed derivation of the corresponding hierarchy of the coupled mode and of the Lugiato-Lefever-like equations. An effect of the washout of the repetition rate frequencies from the equations governing dynamics of the counter-propagating waves is elaborated in details.
Octave-spanning, self-referenced frequency combs are applied in diverse fields ranging from precision metrology to astrophysical spectrometer calibration. In the past decade, Kerr frequency comb generators have emerged as alternative scheme offering chip-scale integration, high repetition rate and bandwidths that are only limited by group velocity dispersion. The recent observation of Kerr frequency combs operating in the dissipative Kerr soliton (DKS) regime, along with dispersive wave formation, has provided the means for fully coherent, broadband Kerr frequency comb generation with engineer…
Parametric nonlinear optical processes allow for the generation of new wavelengths of coherent electromagnetic radiation. Their ability to create radiation that is widely tunable in wavelength is particularly appealing, with applications ranging from spectroscopy to quantum information processing. Unfortunately, existing tunable parametric sources are marred by deficiencies that obstruct their widespread adoption. Here we show that ultrahigh-Q crystalline microresonators made of magnesium fluoride can overcome these limitations, enabling compact and power-efficient devices capable of generatin…
We report that an instability boundary of a single-mode state in Kerr ring microresonators with ultrahigh quality factors breaks the parameter space span by the pump laser power and frequency into a sequence of narrow in frequency and broad in power resonance domains - Arnold tongues. Arnold resonances are located between the Lugiato-Lefever (lower) and universal (higher) thresholds. Pump power estimates corresponding to the universal threshold are elaborated in details. RF-spectra generated within the tongues reveal a transition between the repetition-rate locked and unlocked regimes of the s…
