We studied numerically the generation of the coherent frequency combs at second harmonic generation in $χ^{(2)}$ microresonators via conventional frequency scan method. It was demonstrated for the first time that under particular conditions it is possible to generate two-color flat-top solitonic pulses, platicons, using pump amplitude modulation or controllable mode interaction approach, if the signs of the group velocity coefficients at pump frequency and its second harmonic are opposite but absolute values of these coefficients are rather close. It was revealed that platicons may be observed on both sides of the linear microresonator resonance (at positive, as well as negative pump frequency detunings). For the efficient platicon excitation, one needs simultaneous accurate matching of both microresonator free spectral ranges and resonant eigenfrequencies. Platicon generation processes were simulated numerically, excitation conditions and platicon generation domains were found for different generation methods, and the properties of generated platicons were studied for the different combinations of the medium parameters.
We demonstrate numerically novel mechanism providing generation of the flat-top solitonic pulses, platicons, in optical microresonators at normal GVD via negative thermal effects. We found that platicon excitation is possible if the ratio of the photon lifetime to the thermal relaxation time is large enough. We show that there are two regimes of the platicon generation depending on the pump amplitude: the smooth one and the oscillatory one. Parameter ranges providing platicon excitation are found and analysed for different values of the thermal relaxation time, frequency-scan rate and GVD coef…
We demonstrate that flat-topped dissipative solitonic pulses, platicons, and corresponding frequency combs can be excited in optical microresonators with normal group velocity dispersion using either amplitude modulation of the pump or bichromatic pump. Soft excitation may occur in particular frequency range if modulation depth is large enough and modulation frequency is close to the free spectral range of the microresonator.
We describe the generation of stable mode-locked pulse trains from on-chip normal dispersion microresonators. The excitation of hyper-parametric oscillation is facilitated by the local dispersion disruptions induced by mode interactions. The system is then driven from hyper-parametric oscillation to the mode-locked state with over 200 nm spectral width by controlled pump power and detuning. With the continuous-wave driven nonlinearity, the pulses sit on a pedestal, akin to a cavity soliton. We identify the importance of pump detuning and wavelength-dependent quality factors in stabilizing and …
We predict the existence of a novel type of the flat-top dissipative solitonic pulses, "platicons", in microresonators with normal group velocity dispersion (GVD). We propose methods to generate these platicons from cw pump. Their duration may be altered significantly by tuning the pump frequency. The transformation of a discrete energy spectrum of dark solitons of the Lugiato-Lefever equation into a quasicontinuous spectrum of platicons is demonstrated. Generation of similar structures is also possible with bi-harmonic, phase/amplitude modulated pump or via laser injection locking.
We investigate experimentally and theoretically effects of the inter-core propagation mismatch on nonlinear switching in dual-core high-index-contrast soft-glass optical fibers. Incident femtosecond pulses of various energy are fed into a single ("straight") core, to identify transitions between different dynamical regimes, viz., inter-core oscillations, self-trapping in the cross core, and retaining the pulse in the straight core. The transfer between channels, which has solitonic character, is controlled by the pulse's energy. A model based on the system of coupled nonlinear Schrödinger equa…
We studied numerically the generation of the two-color flat-top solitonic pulses, platicons, in the microresonator based doubly resonant optical parametric oscillator. We revealed that if the signs of the group velocity dispersion (GVD) coefficients at interacting harmonics are opposite, platicon excitation is possible via pump amplitude modulation or controllable mode interaction approach. Upon pump frequency scan generation of platicons was observed at positive pump frequency detunings for the normal GVD at pump frequency and at negative detunings in the opposite case. Interestingly, we foun…
We studied generation and dynamics of solitonic pulses, platicons, at normal group velocity dispersion due to the pump amplitude modulation. We proposed, that if the required frequency of amplitude modulation is too large for available modulators, it is possible to use subharmonic phase modulation for platicon generation. It was also demonstrated that it is possible to control the repetition rate of platicons by tuning modulation frequency. Tuning range for platicons was found to be much wider than for bright solitons. We also studied the influence of the high-order dispersion on platicon prop…
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…
Soliton microcombs are helping to advance the miniaturization of a range of comb systems. These combs mode lock through the formation of short temporal pulses in anomalous dispersion resonators. Here, a new microcomb is demonstrated that mode locks through the formation of pulse pairs in normal-dispersion coupled-ring resonators. Unlike conventional microcombs, pulses in this system cannot exist alone, and instead must phase lock in pairs to form a bright soliton comb. Also, the pulses can form at recurring spectral windows and the pulses in each pair feature different optical spectra. This pa…
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…
We developed an original model describing the process of the frequency comb generation in the self-injection locking regime and performed numerical simulation of this process.Generation of the dissipative Kerr solitons in the self-injection locking regime at anomalous group velocity dispersion was studied numerically. Different regimes of the soliton excitation depending on the locking phase, backscattering parameter and pump power were identified. It was also proposed and confirmed numerically that self-injection locking may provide an easy way for the generation of the frequency combs at nor…
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 observe a transition to a coherent-comb state in a SiN-microresonator with anomalous dispersion. Although ~300 fs pulse trains are generated after line-by-line shaping, the intensity within the microring does not appear to be pulse-like.
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…
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…
Light pulses entering an elongated bottle microresonator (BMR) from a transversely oriented input-output waveguide (microfiber) slowly propagate along the BMR length and bounce between turning points at its constricting edges. To avoid insertion losses and processing errors, a pulse should completely transfer from the waveguide into the BMR and, after being processed, completely return back into the waveguide. For this purpose, the waveguide and BMR should be impedance matched along the pulse bandwidth. Here we show how to enhance the impedance matched bandwidth by optimization of the BMR effe…
We report, for the first time to the best of our knowledge, spectral phase characterization and line-by-line pulse shaping of an optical frequency comb generated by nonlinear wave mixing in a microring resonator. Through programmable pulse shaping the comb is compressed into a train of near-transform-limited pulses of \approx 300 fs duration (intensity full width half maximum) at 595 GHz repetition rate. An additional, simple example of optical arbitrary waveform generation is presented. The ability to characterize and then stably compress the frequency comb provides new data on the stability …
Kerr frequency combs from microresonators are now extensively investigated as a potentially portable technology for a variety of applications. Most studies employ anomalous dispersion microresonators that support modulational instability for comb initiation, and mode-locking transitions resulting in coherent bright soliton-like pulse generation have been reported. However, some experiments show comb generation in normal dispersion microresonators; simulations suggest the formation of dark pulse temporal profiles. Excitation of dark pulse solutions is difficult due to the lack of modulational i…
We perform the first theoretical modeling of the spectral-temporal dynamics of parametric microresonator comb generation with octave-spanning bandwidths through use of the Lugiato-Lefever model extended to include higher-order dispersion and self-steepening. We show that three distinct stages are necessary to achieve single-pulse modelocking and ultrabroadband, stabilized combs. Our simulations agree well with previous experimental demonstrations and predict many of the observed features, including multi-pulse generation, dispersive wave generation, modelocking and comb stabilization.
Spin waves in magnetic microresonators are at the core of modern magnonics. Here we demonstrate a new method of tunable excitation of different spin wave modes in magnetic microdisks by using a train of laser pulses coming at a repetition rate higher than the decay rate of spin precession. The microdisks are etched in a transparent bismuth iron garnet film and the light pulses influence the spins nonthermally through the inverse Faraday effect. The high repetition rate of the laser stimulus of 10 GHz establishes an interplay between the spin wave resonances in the frequency and momentum domain…
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 …
Breathers are localized waves, that are periodic in time or space. The concept of breathers is useful for describing many physical systems including granular lattices, Bose-Einstein condensation, hydrodynamics, plasmas and optics. Breathers could exist in both the anomalous and the normal dispersion regime. However, the demonstration of optical breathers in the normal dispersion regime remains elusive to our knowledge. Kerr comb generation in optical microresonators provides an array of oscillators that are highly coupled via the Kerr effect, which can be exploited to explore the breather dyna…
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…
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…
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 …
Temporally stabilized optical pules, confined in microresonators driven by a continuous-wave laser, have attracted tremendous attention due to their fascinating features with many applications. Here we report the observations of mode-locked platicon frequency microcomb formation in normal dispersion dispersion-managed microresonators operating at microwave K-band repetition rate for the first time. Facilitated by the thermally controllable modulated background induced by avoided mode-crossings, various platicon bound state patterns with regular and irregular temporal separation are stably gene…
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-…
Coherent inter-conversion between an optical and a mechanical excitation in an optomechanical resonator can be used for the storage of an optical pulse as an excitation in a mechanical oscillator. This optomechanical light storage is enabled by external writing and readout pulses at one mechanical frequency below the optical resonance. In this paper, we expand an earlier experimental study [Phys. Rev. Lett. 107, 133601 (2011)] on storing an optical pulse as a radial breathing mode in a silica microsphere. We show that the heterodyne beating between a readout pulse and the corresponding retriev…
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…
A tunable bottle microresonator can trap an optical pulse of the given spectral width, hold it as long as the material losses permit, and release without distortion.
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…
We numerically study, by means of the single envelope equation, the generation of optical frequency combs ranging from the visible to the mid-infrared spectral regions in resonators with quadratic and cubic nonlinearities. Phase-matched quadratic wave-mixing processes among the comb lines can be activated by low-power continuous wave pumping in the near infrared of a radially poled lithium niobate whispering gallery resonator (WGR). We examine both separate and co-existing intra-cavity doubly resonant second-harmonic generation and parametric oscillation processes, and find that modulation ins…
Solitons are shape preserving waveforms that are ubiquitous across nonlinear dynamical systems and fall into two separate classes, that of bright solitons, formed in the anomalous group velocity dispersion regime, and `dark solitons' in the normal dispersion regime. Both types of soliton have been observed in BEC, hydrodynamics, polaritons, and mode locked lasers, but have been particularly relevant to the generation of chipscale microresonator-based frequency combs (microcombs), used in numerous system level applications in timing, spectroscopy, and communications. For microcombs, both bright…
We report on the fabrication of high-Q, fused-quartz microresonators and the parametric generation of a frequency comb with 36 GHz line spacing using them. We have characterized the intrinsic stability of the comb in both the time and frequency domains to assess its suitability for future precision metrology applications. Intensity autocorrelation measurements and line-by-line comb control reveal near-transform-limited picosecond pulse trains that are associated with good relative phase and amplitude stability of the comb lines. The comb's 36 GHz line spacing can be readily photodetected, whic…
Dissipative Kerr solitons in optical microresonators provide a unifying framework for nonlinear optical physics with photonic-integrated technologies and have recently been employed in a wide range of applications from coherent communications to astrophysical spectrometer calibration. Dissipative Kerr solitons can form a rich variety of stable states, ranging from breathers to multiple-soliton formations, among which, the recently discovered soliton crystals stand out. They represent temporally-ordered ensembles of soliton pulses, which can be regularly arranged by a modulation of the continuo…
Spectroscopy of whispering-gallery mode (WGM) microresonators has become a powerful scientific tool, enabling detection of single viruses, nanoparticles, and even single molecules. Yet the demonstrated timescale of these schemes has been limited so far to milliseconds or more. Here we introduce a novel scheme that is orders of magnitude faster, capable of capturing complete spectral snapshots of WGM resonances at nanosecond timescales: cavity ring-up spectroscopy (CRUS). Based on sharply-rising detuned probe pulses, CRUS combines the sensitivity of heterodyne measurements with the highest poss…
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…
We use a drop-port geometry to study power transfer in silicon nitride on-chip microresonator frequency comb generators. In sharp contrast with the traditional transmission geometry, we observe smooth output spectra with comparable powers in the pump and adjacent comb lines. An observation of saturation in the drop-port output power is explained semi-empirically by introducing pump saturation into a coupling of modes model. Autocorrelation measurements are performed on the drop-port output, without the need to filter out or suppress the strong pump line as is necessary in thru-port experiments…
We demonstrate that the optical spectrum of a soliton microcomb generated in a microresonator can be coherently extended by using bichromatic pumping: one pump with a frequency in the anomalous dispersion regime of the microresonator is used to generate a bright soliton microcomb while a second pump in the normal dispersion regime both compensates the thermal effect of the microresonator and generates a second frequency comb via cross-phase modulation with the bright soliton, thus extending the spectrum of the microcomb. Experimental results for different microresonators show that the mode spa…
The nonlinear propagation of optical pulses in dielectric waveguides and resonators provides a laboratory to investigate a wide range of remarkable interactions. Many of the resulting phenomena find applications in optical systems. One example is dispersive wave generation, the optical analog of Cherenkov radiation. These waves have an essential role in fiber spectral broadeners that are routinely used in spectrocopy and metrology. Dispersive waves form when a soliton pulse begins to radiate power as a result of higher-order dispersion. Recently, dispersive wave generation in microcavities has…
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…
Development of ultrashort pulse sources has had an immense impact on condensed-matter physics, biomedical imaging, high-field physics, frequency metrology, telecommunications, nonlinear optics, and molecular spectroscopy. Although numerous advancements of such sources have been made, it remains a challenge to create a highly compact, robust platform capable of producing femtosecond pulses over a wide range of wavelengths, durations, and repetition rates. Recent observations of frequency comb generation via cascaded parametric oscillation in microresonators11 suggest a path for achieving this g…
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 …
We report on 'slow' pulsing dynamics in a silica resonator-based laser system: by nesting a high-Q rod-resonator inside an amplifying fiber cavity, we demonstrate that trains of microsecond pulses can be generated with repetition rates in the hundreds of kilohertz. We show that such pulses are produced with a period equivalent to several hundreds of laser cavity roundtrips via the interaction between the gain dynamics in the fiber cavity and the thermo-optical effects in the high-Q resonator. Experiments reveal that the pulsing properties can be controlled by adjusting the amplifying fiber cav…
Temporal cavity solitons (CSs) are persisting pulses of light that can manifest themselves in continuously driven passive resonators, such as macroscopic fiber ring cavities and monolithic microresonators. Experiments so far have demonstrated two techniques for their excitation, yet both possess drawbacks in the form of system complexity or lack of control over soliton positioning. Here we experimentally demonstrate a new CS writing scheme that alleviates these deficiencies. Specifically, we show that temporal CSs can be excited at arbitrary positions through direct phase modulation of the cav…
We demonstrate ultrafast soliton-based nonlinear balancing of dual-core asymmetry in highly nonlinear photonic crystal fiber at sub-nanojoule pulse energy level. The effect of fiber asymmetry was studied experimentally by selective excitation and monitoring of individual fiber cores at different wavelengths between 1500 nm and 1800 nm. Higher energy transfer rate to non-excited core was observed in the case of fast core excitation due to nonlinear asymmetry balancing of temporal solitons, which was confirmed by the dedicated numerical simulations based on the coupled generalized nonlinear Schr…
Pulsed driving of Kerr microresonators represents a promising avenue for the efficient generation of soliton states associated with coherent optical frequency combs. The underlying physics has not, however, yet been comprehensively investigated. Here, we report on a numerical and theoretical study of the impact of de-synchronization between the periodic pump field and the train of solitons circulating in the cavity. We show that de-synchronization can affect the soliton configurations that can be sustained for given parameters, and that it can be leveraged to guarantee operation in the attract…
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,…
Soliton crystals are periodic patterns of multi-spot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with emphasis on their one-to-one correspondance with Elliptic solitons. In th…
