With demonstrated applications ranging from metrology to telecommunications, soliton microresonator frequency combs have emerged over the past decade as a remarkable new technology. However, standard implementations only allow for the generation of combs whose repetition rate is tied close to the fundamental resonator free-spectral range (FSR), offering little or no dynamic control over the comb line spacing. Here we propose and experimentally demonstrate harmonic and rational harmonic driving as novel techniques that allow for the robust generation of soliton frequency combs with discretely adjustable frequency spacing. By driving an integrated Kerr microresonator with a periodic train of picosecond pulses whose repetition rate is set close to an integer harmonic of the 3.23 GHz cavity FSR, we deterministically generate soliton frequency combs with frequency spacings discretely adjustable between 3.23 GHz and 19.38 GHz. More remarkably, we also demonstrate that driving the resonator at rational fractions of the FSR allows for the generation of combs whose frequency spacing corresponds to an integer harmonic of the pump repetition rate. By measuring the combs' radio-frequency spectrum, we confirm operation in the low-noise soliton regime with no supermode noise. The novel techniques demonstrated in our work provide new degrees of freedom for the design of synchronously pumped soliton frequency combs.
Dissipative Kerr-microresonator soliton combs (hereafter called soliton combs) are promising to realize chip scale integration of full soliton comb systems providing high precision, broad spectral coverage and a coherent link to the micro/mm/THz domain with diverse applications coming on line all the time. However, the large soliton comb spacing hampers some applications. For example, for spectroscopic applications, there are simply not enough comb lines available to sufficiently cover almost any relevant absorption features. Here, we overcome this limitation by scanning the comb mode spacing …
We report the thermal control of a dissipative Kerr microresonator soliton comb via an optical sideband generated from an electro-optic modulator. Same as the previous reports using an independent auxiliary laser, our sideband-based (S-B) auxiliary light also enables to access a stable soliton comb and to reduce the phase noise of the soliton comb, greatly simplifying the setup with an auxiliary laser. More importantly, because of the intrinsically high frequency/phase correlation between the pump and S-B auxiliary light, the detuning between the pump and resonance frequency is automatically a…
Microresonator-based optical frequency combs emitted from high-quality-factor microresonators, also known as microcombs, have opened up new horizons to areas of optical frequency comb technology including frequency metrology, precision sensing, and optical communication. To extend the capability of microcombs for such applications, large and reliable tunability is of critical importance. Here, we show broad spectral tuning of Kerr soliton microcombs in a thermally controlled crystalline microresonator with pump-detuning stabilization. The fundamental elements composing frequency combs, namely …
Dissipative Kerr soliton microcombs in microresonators has enabled fundamental advances in chip scale precision metrology, communication, spectroscopy, and parallel signal processing. Here we demonstrate polarization diverse soliton transitions and deterministic switching dynamics of a self stabilized microcomb in a strongly coupled dispersion-managed microresonator driven with a single pump laser. The switching dynamics are induced by the differential thermorefractivity between coupled transverse magnetic and transverse electric supermodes during the forward backward pump detunings. The achie…
We investigate soliton generation dynamics with the influence of thermal effects. Either soliton annihilation or survival can occur in different trials with the same tuning method, and a spontaneous route to soliton formation is observed.
Rapid and large scanning of a dissipative Kerr-microresonator soliton comb with the characterization of all comb modes along with the separation of the comb modes is imperative for the emerging applications of the frequency-scanned soliton combs. However, the scan speed is limited by the gain of feedback systems and the measurement of the frequency shift of all comb modes has not been demonstrated. To overcome the limitation of the feedback, we incorporate the feedback with the feedforward. With the additional gain of > 40 dB by a feedforward signal, a dissipative Kerr-microresonator soliton c…
THz oscillators generated via frequency-multiplication of microwaves are facing difficulty in achieving low phase noise. Photonics-based techniques, in which optical two tones are translated to a THz wave through opto-electronic conversion, are promising if the relative phase noise between the two tones is well suppressed. Here, a THz ($\approx$ 560 GHz) wave with a low phase noise is provided by a frequency-stabilized, dissipative Kerr microresonator soliton comb. The repetition frequency of the comb is stabilized to a long fiber in a two-wavelength delayed self-heterodyne interferometer, sig…
We report the first demonstration of thermally controlled soliton modelocked frequency comb generation in microresonators. By controlling the electric current through heaters integrated with silicon nitride microresonators, we demonstrate a systematic and repeatable pathway to single- and multi-soliton modelocked states without adjusting the pump laser wavelength. Such an approach could greatly simplify the generation of modelocked frequency combs and facilitate applications such as chip-based dual-comb spectroscopy.
A shaped doublet pump pulse is proposed for simultaneous octave-spanning soliton Kerr frequency comb generation and second-harmonic conversion in a single microresonator. The temporal soliton in the cavity is trapped atop a doublet pulse pedestal, resulting in a greatly expanded soliton region compared to that with a general Gaussian pulse pump. The possibility of single-microresonator comb self-referencing in a single silicon nitride microring, which can facilitate compact on-chip optical clocks, is demonstrated via simulation.
We investigate, numerically and experimentally, the effect of thermo-optical (TO) chaos on direct soliton generation (DSG) in microresonators. When the pump laser is scanned from blue to red and then stopped at a fixed wavelength, we find that the solitons generated sometimes remain (survive) and sometimes annihilate subsequent to the end of the scan. We refer to the possibility of these different outcomes arising under identical laser scan conditions as coexistence of soliton annihilation and survival. Numerical simulations that include the thermal dynamics show that the coexistence of solito…
The recent discovery of dissipative Kerr solitons in microresonators has facilitated the development of fully coherent, chip-scale frequency combs. In addition, dark soliton pulses have been observed in microresonators in the normal dispersion regime. Here, we report bound states of mutually trapped dark-bright soliton pairs in a microresonator. The soliton pairs are generated seeding two modes with opposite dispersion but with similar group velocities. One laser operating in the anomalous dispersion regime generates a bright soliton microcomb, while the other laser in the normal dispersion re…
Soliton microcombs constitute chip-scale optical frequency combs, and have the potential to impact a myriad of applications from frequency synthesis and telecommunications to astronomy. The requirement on external driving lasers has been significantly relaxed with the demonstration of soliton formation via self-injection locking of the pump laser to the microresonator. Yet to date, the dynamics of this process has not been fully understood. Prior models of self-injection locking were not able to explain sufficiently large detunings, crucial for soliton formation. Here we develop a theoretical …
We demonstrate the generation of counter-rotating cavity solitons in a silicon nitride microresonator using a fixed, single-frequency laser. We demonstrate a dual 3-soliton state with a difference in the repetition rates of the soliton trains that can be tuned by varying the ratio of pump powers in the two directions. Such a system enables a highly compact, tunable dual comb source that can be used for applications such as spectroscopy and distance ranging.
The generation of temporal cavity solitons in microresonators results in low-noise optical frequency combs which are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems with a localized temporal structure that exhibits oscillatory behavior. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here, we demonstrate the excitation of breather solitons in two different microre…
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 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 simulatio…
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…
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…
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…
We report a method to control - disrupt and restore, a regime of the unidirectional soliton generation in a bidirectionally pumped ring microresonator. This control, i.e., the soliton blockade, is achieved by tuning pump frequency of the counterrotating field. The blockade effect is correlated with the emergence of a dark-bright nonlinear resonance of the cw-states.
Fast-responding detector arrays are commonly used for imaging rapidly-changing scenes. Besides array detectors, a single-pixel detector combined with a broadband optical spectrum can also be used for rapid imaging by mapping the spectrum into a spatial coordinate grid and then rapidly measuring the spectrum. Here, optical frequency combs generated from high-$Q$ silica microresonators are used to implement this method. The microcomb is dispersed in two spatial dimensions to measure a test target. The target-encoded spectrum is then measured by multi-heterodyne beating with another microcomb hav…
We present, experimentally and numerically, the observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in a high-Q SiN microresonator. Breather solitons can be excited by increasing the pump power at a relatively small pump phase detuning in microresonators. Out of phase power evolution is observed for groups of comb lines around the center of the spectrum compared to groups of lines in the spectral wings. The evolution of the power spectrum is not symmetric with respect to the spectrum center. Numerical simulations based on the generalized Lugiato-Lefever equation are in good…
Solitons occur in many physical systems when a nonlinearity compensates wave dispersion. Their recent formation in microresonators opens a new research direction for nonlinear optical physics and provides a platform for miniaturization of spectroscopy and frequency metrology systems. These microresonator solitons orbit around a closed waveguide path and produce a repetitive output pulse stream at a rate set by the round-trip time. In this work counter-propagating solitons that simultaneously orbit in an opposing sense (clockwise/counter-clockwise) are studied. Despite sharing the same spatial …
The perfect soliton crystal (PSC) was recently discovered as an extraordinary Kerr soliton state with regularly distributed soliton pulses and enhanced comb line power spaced by multiples of the cavity free spectral ranges (FSRs). The modulation of continuous-wave excitation in optical microresonators and the tunable repetition rate characteristic will significantly enhance and extend the application potential of soliton microcombs for self-referencing comb source, terahertz wave generation, and arbitrary waveform generation. However, the reported PSC spectrum is generally narrow. Here, we dem…
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…
We report on experimental observation of localized structures in two mutually coupled broad-areahttp://hal.archives-ouvertes.fr/images/calendar.gif semiconductor resonators. These structures coexist with a dark homogeneous background and they have the same properties as cavity solitons without requiring the presence of a driving beam into the system. They can be switched individually on and off by means of a local addressing beam.
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 …
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 observation of temporal dissipative Kerr solitons in optical microresonators provides, on the applied side, compact sources of coherent optical frequency combs that have already been applied in coherent communications, dual comb spectroscopy and metrology. On a fundamental level, it enables the study of soliton physics in driven nonlinear cavities. Microresonators are commonly multimode and, as a result, inter-mode interactions inherently occur among mode families - a condition referred to as "avoided mode crossings". Avoided mode crossings can cause soliton decay, but can also modify the …
We present an explicit sech-squared-soliton solution associated with the optical Pockels effect, achieved through the generation of the frequency combs via parametric down-conversion in optical microresonators with quadratic nonlinearity. This soliton contrasts the parametric sech-soliton describing the half-harmonic field in the limit of the large index mismatch, and associated with the cascaded-Kerr effect. We predict differences in the spectral profiles and powers of the Pockels and cascaded-Kerr solitons, and report that the pump power threshold of the former agree with the recent experime…
Microresonator based optical frequency combs (MFC) have demonstrated promise in extending the capabilities of optical frequency combs. Here we demonstrate all optical stabilization of a low noise temporal soliton based MFC in a crystalline resonator via a new technique to control the repetition rate. This is accomplished by thermally heating the microresonator with an additional probe laser coupled to an auxiliary optical resonator mode. The offset frequency is controlled by stabilization of the pump laser frequency to a reference optical frequency comb. We analyze the stabilization by perform…
Dissipative Kerr soliton offers broadband coherent and low-noise frequency comb and stable temporal pulse train, having shown great potential applications in spectroscopy, communications, and metrology. Breathing soliton is a particular dissipative Kerr soliton that the pulse duration and peak intensity show periodic oscillation. However, the noise and stability of the breathing soliton is still remaining unexplored, which would be the main obstacle for future applications. Here, we have investigated the breathing dissipative Kerr solitons in the silicon nitride (SiN) microrings, while the bre…
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"…
Optical frequency combs in microresonators (microcombs) have a wide range of applications in science and technology, due to its compact size and access to considerably larger comb spacing. Despite recent successes, the problems of self-starting, high mode efficiency as well as high output power have not been fully addressed for conventional soliton microcombs. Recent demonstration of laser cavity soliton microcombs by nesting a microresonator into a fiber cavity, shows great potential to solve the problems. Here we comprehensively study the dissipative soliton generation and interaction dynami…
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…
Optical frequency comb generation in microresonators has attracted significant attention over the past decade, as it offers the promising potential for chip-scale optical frequency synthesis, optical clocks and precise optical spectroscopy. However, accessing temporal dissipative Kerr soliton (DKSs) is known to be severely hampered by thermal effects. Furthermore, due to the degeneracy of soliton existence range with respect to soliton number, deterministically accessing single soliton state is another challenge. Here, we demonstrate stable and deterministic single soliton generation in AlN-on…
The recent demonstration of dissipative Kerr solitons in microresonators has opened a new pathway for the generation of ultrashort pulses and low-noise frequency combs with gigahertz to terahertz repetition rates, enabling applications in frequency metrology, astronomy, optical coherent communications, and laser-based ranging. A main challenge for soliton generation, in particular in ultra-high-Q resonators, is the sudden change of circulating intracavity power during the onset of soliton generation. This sudden power change requires precise control of the seed laser frequency and power or fas…
Considering a bidirectionally pumped ring microresonator, we provide a concise derivation of the model equations allowing us to eliminate the repetition rate terms and reduce the nonlinear interaction between the counter-propagating waves to the power-dependent shifts of the resonance frequencies. We present the simulation results of the soliton control by swiping the frequency of the counter-propagating wave in the forward and backward directions and with the soliton-blockade effect either present or not. We highlight the non-reciprocity of the forward and backward scans. Furthermore, we repo…
Continuous-wave laser driven Kerr-nonlinear, optical microresonators have enabled a variety of novel applications and phenomena including the generation of optical frequency combs, ultra-low noise microwaves, as well as, ultra-short optical pulses. In this work we break with the paradigm of the continuous-wave optical drive and use instead periodic, pico-second optical pulses. We observe the deterministic generation of stable femtosecond dissipative cavity solitons on-top of the resonantly enhanced driving pulse. Surprisingly, the soliton pulse locks to the driving pulse enabling direct all-op…
Frequency conversion in microresonators has revolutionised modern-day nonlinear and quantum optics. Here, we present a theory of the multimode second harmonic generation in microresonators under conditions when the parametric conversion back to the pump spectrum dominates through the large domain in the resonator parameter space. We demonstrate that the spectral tunability of the sideband generation in this regime is governed by a discrete sequence of the so-called Eckhaus instabilities. We report the transition to modelocking and generation of solitons, which have a double-pulse structure in …
Fragmentation of Stability Domains of Dark Solitons and Dark Breathers and Drifting Solitons at High Pump Intensities in Normal Dispersion Kerr Microresonators
The formation of temporal dissipative solitons in optical microresonators enables compact, high repetition rate sources of ultra-short pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the resonator mode spectrum on temporal soliton formation. Using frequency comb assisted diode laser spectroscopy, the measured mode structure of crystalline MgF2 resonators are correlated with temporal soliton formation. While an overal general anomalous dispersion is required, it is found that higher order dispersion can be tolerated a…
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…
Chip-integrated optical frequency combs are attractive optical sources in comb applications requiring high-repetition-rate, low power consumption, or compact size. Spontaneous soliton formation via Kerr parametric oscillation is a promising generation principle in these frequency combs, and has been demonstrated in several material platforms over the past decade. Of these materials, AlGaAs has one of the largest Kerr nonlinearity coefficients allowing low pump threshold comb generation. However, bright soliton generation using this material has only been possible at cryogenic temperature becau…
The influence of thermo-optic effects on shape profiles of soliton crystals in optical Kerr microresonators is investigated. The study rests on a model that consists of the Lugiato-Lefever equation, coupled to the one-dimensional heat diffusion equation with a source term proportional to the average power of the optical field. Using appropriate variable changes the model equations are transformed into a set of coupled first-order nonlinear ordinary differential equations. These equations are solved numerically with emphasis on the influence of thermo-optic effects on the amplitude and instanta…
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…
Octave-wide frequency combs in microresonators are essential for self-referencing. However, it is difficult for the small-size and high-repetition-rate microresonators to achieve perfect soliton modelocking over the broad frequency range due to the detrimental impact of dispersion. Here we examine the stability of the soliton states consisting of one hundred modes in silicon-nitride microresonators with the one-THz free spectral range. We report the coexistence of fast and slow solitons in a narrow detuning range, which is surrounded on either side by the breather states. We decompose the brea…
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 …
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…
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 …
We report how a doublet of the symmetric oppositely tilted bistable resonance peaks in a microring resonator with quadratic nonlinearity set for generation of the second harmonic can transform into a Kerr-like peak on one side of the linear cavity resonance and into a closed loop structure disconnected from the quasi-linear resonance on the other. Both types of the nonlinear resonances are associated with the formation of the soliton combs for dispersion profiles of a typical LiNbO$_3$ microring. We report bright quasi-solitons propagating on a weakly modulated low intensity background when th…
We present a novel compact dual-comb source based on a monolithic optical crystalline MgF$_2$ multi-resonator stack. The coherent soliton combs generated in two microresonators of the stack with the repetition rate of 12.1 GHz and difference of 1.62 MHz provided after heterodyning a 300 MHz wide radio-frequency comb. Analogous system can be used for dual-comb spectroscopy, coherent LIDAR applications and massively parallel optical communications.
