Stimulated Raman Scattering Imposes Fundamental Limits to the Duration and Bandwidth of Temporal Cavity Solitons

Theory of soliton self-frequency shift in silica optical microresonators with a modified Raman response by the Boson peak

We theoretically study the Raman-induced self-frequency shift of dissipative Kerr soliton in silica optical resonators by taking into consideration the Boson peak. We find that the Boson peak will greatly increase the soliton self-frequency shift and contribute even more than the shift induced by the Lorentzian response for certain pulse durations. We also show that the revised Raman shock time is associated with the pulse width even for a relatively long pulse. Moreover, we demonstrate that the background continuous wave decreases the self-frequency shift of the soliton via the interference with the soliton. Our theoretical and simulated results display excellent agreement with the previous experimental values in the silica-based Kerr-soliton microcomb.

Binding dynamics of cavity solitons in a Kerr resonator with high order dispersion

Cavity solitons are persistent light pulses arising from the externally driven Kerr resonators. Thanks to the passive parametric gain, cavity soliton has been endowed with the natural advantage of the chip-scaled integration since it was first experimentally generated in the fiber-based platform. Deterministic single soliton with smooth spectrum is a preferred state for numerous applications. However, multiple solitons are more common in the resonators with anomalous dispersion. In this condition, adjacent solitons are easily perturbed to attract and collide with each other. Some experimental observations deviated from the aforementioned description have recorded the stable soliton intervals that can last for a long time scale. This phenomenon is known as soliton binding and is attributed to the presence of narrow resonant sidebands in the spectrum. While the stationary configuration of two binding solitons has been investigated, the dynamical evolution remains an area for further exploration. In this paper, we discuss the binding dynamics of the cavity solitons in the presence of high-order dispersion. The proposed theoretical predictions match well with the numerical results, encompassing both the stationary stable intervals and dynamic trajectories. Our research will provide a comprehensive insight into the soliton motion induced by the internal perturbations.

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

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

Thermo-Optical Control of Raman Solitons in a Functionalized Silica Microsphere

The investigation of optical microcavity solitons is in demand both for applications and basic science. Despite the tremendous progress in the study of microresonator solitons, there is still no complete understanding of all features of their nonlinear dynamics in various regimes. Controlling soliton properties is also of great interest. We proposed and investigated experimentally and theoretically a simple and easily reproducible way to generate Raman solitons with controllable spectral width in an anomalous dispersion region in a functionalized silica microsphere with whispering gallery modes (WGMs) driven in a normal dispersion regime. To functionalize the microsphere, coating (TiO₂ + graphite powder) was applied at the pole. The coating is used for effective thermalization of the radiation of an auxiliary laser diode launched through the fiber stem holding the microsphere to control detuning of the pump frequency from exact resonance due to the thermo-optical shift of the WGM frequencies. We demonstrated that the thermo-optical control by changing the power of an auxiliary diode makes it possible to switch on/off the generation of Raman solitons and control their spectral width, as well as to switch Raman generation to multimode or single-mode. We also performed a detailed theoretical analysis based on the Raman-modified Lugiato-Lefever equation and explained peculiarities of intracavity nonlinear dynamics of Raman solitons. All experimental and numerically simulated results are in excellent agreement.

120-fs single-pulse generation from stretched-pulse fiber Kerr resonators

Fiber Kerr resonators are simple driven resonators with desirable wavelength and repetition rate flexibility for generating ultrashort pulses for applications including telecommunications, biomedicine, and materials processing. However, fiber Kerr resonators to date often generate longer pulses and require more complicated techniques for generating single pulses than would be desirable for applications. Here we address these limits by demonstrating robust single-pulse performance supporting 120-fs pulse durations in fiber Kerr resonators based on stretched-pulse solitons. Through matching numerical and experimental studies, stretched-pulse soliton performance is found to strongly depend on the total cavity length, and the optimum length is found to depend on the drive, Raman scattering, and the total pulse stretching. The bandwidth increases with decreasing net dispersion, enabled by shorter total cavity lengths. In a cavity with an optimized length and the described setup, stable stretched-pulse solitons corresponding to 120-fs duration are experimentally observed. In addition, soliton trapping is demonstrated with a pulsed drive source despite large intracavity breathing, and single-pulse performance is observed. Robust with high performance single-pulse generation is a critical step toward useful femtosecond pulse generation.

Mode-locking induced by coherent driving in fiber lasers

Mode-locking is a broad concept that encompasses different processes enabling short optical pulse formation in lasers. It typically requires an intracavity mechanism that discriminates between single and collective mode lasing, which can be complex and sometimes adds noise. Moreover, known mode-locking schemes do not guarantee phase stability of the carrier wave. Here, we theoretically propose that injecting a detuned signal seamlessly leads to mode-locking in fiber lasers. We show that phase-locked pulses, akin to cavity solitons, exist in a wide range of parameters. In that regime the laser behaves as a passive resonator due to the non-instantaneous gain saturation.

Vibrational Kerr Solitons in an Optomechanical Microresonator

Kerr soliton microcombs 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-detuned pump. Various nonlinear dynamics is also observed, including limit cycle, higher periodicity, and transient chaos. This work provides a guidance for not only exploring many-body nonlinear interactions, but also promoting precision measurements by featuring superiority of both frequency combs and optomechanics.

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

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

Conversion efficiency of soliton Kerr combs

We investigate the conversion efficiency (CE) of soliton modelocked Kerr frequency combs. Our analysis reveals three distinct scaling regimes of CE with the cavity free spectral range (FSR), which depends on the relative contributions of the coupling and propagation loss to the total cavity loss. Our measurements, for the case of critical coupling, verify our theoretical prediction over a range of FSRs and pump powers. Our numerical simulations also indicate that mode crossings have an adverse effect on the achievable CE. Our results indicate that microresonator combs operating with spacings in the electronically detectable regime are highly inefficient, which could have implications for integrated Kerr comb devices.

Raman pure quartic solitons in Kerr microresonators

Pure quartic solitons (PQSs) are a unique class of solitons advantageous for developing promising applications due to their broad and flat-top spectrum, as well as the distinctive energy scaling law. Here we investigate the characteristics and dynamics of the PQS in the presence of the Raman effect based on Kerr microresonators. Stimulated Raman scattering leads to reduced pulse peak power, self-frequency shifts, and distortion of the symmetry pulse shape of the PQS. Besides, dynamical evolution of the Raman PQS, especially the breathing state, is investigated. We discover the appearance of an intermediate stable state between the existence region of breathers and chaos in the parameter space, which has not been discovered yet in other soliton regimes. A stability analysis is performed to investigate the spatial dynamics in the context of the Raman PQS.

Tunable Raman lasing in an As2S3 chalcogenide glass microsphere

We demonstrate experimentally Raman lasing in an As₂S₃ chalcogenide glass microsphere pumped by a C-band narrow line laser. Single-mode Raman lasing tunable from 1.610 μm to 1.663 μm is attained when tuning a pump laser wavelength in the 1.522-1.574 μm range. When the pump power significantly exceeds the threshold, multimode cascade Raman lasing is achieved with the maximum Raman order of four at a wavelength of 2.01 μm. We also report an up-converted wave generation at 1.38 μm which is interpreted as the result of four-wave mixing between the pump wave and the wave generated in the second Raman order. The numerical results based on the simulation of the Lugiato-Lefever equation agree with the experimental results.

Photonic Dissipation Control for Kerr Soliton Generation in Strongly Raman-Active Media

Microcavity solitons enable miniaturized coherent frequency comb sources. However, the formation of microcavity solitons can be disrupted by stimulated Raman scattering, particularly in the emerging crystalline microcomb materials with high Raman gain. Here, we propose and implement dissipation control-tailoring the energy dissipation of selected cavity modes-to purposely raise or lower the threshold of Raman lasing in a strongly Raman-active lithium niobate microring resonator and realize on-demand soliton mode locking or Raman lasing. Numerical simulations are carried out to confirm our analyses and agree well with experiment results. Our work demonstrates an effective approach to address strong stimulated Raman scattering for microcavity soliton generation.

Microsphere-Based Optical Frequency Comb Generator for 200 GHz Spaced WDM Data Transmission System

Optical frequency comb (OFC) generators based on whispering gallery mode (WGM) microresonators have a massive potential to ensure spectral and energy efficiency in wavelength-division multiplexing (WDM) telecommunication systems. The use of silica microspheres for telecommunication applications has hardly been studied but could be promising. We propose, investigate, and optimize numerically a simple design of a silica microsphere-based OFC generator in the C-band with a free spectral range of 200 GHz and simulate its implementation to provide 4-channel 200 GHz spaced WDM data transmission system. We calculate microsphere characteristics such as WGM eigenfrequencies, dispersion, nonlinear Kerr coefficient with allowance for thermo-optical effects, and simulate OFC generation in the regime of a stable dissipative Kerr soliton. We show that by employing generated OFC lines as optical carriers for WDM data transmission, it is possible to ensure error-free data transmission with a bit error rate (BER) of 4.5 × 10−30, providing a total of 40 Gbit/s of transmission speed on four channels.

Stretched-Pulse Soliton Kerr Resonators

Kerr resonators support novel nonlinear wave phenomena including technologically important optical solitons. Fiber Kerr resonator solitons enable wavelength and repetition-rate versatile femtosecond-pulse and frequency-comb generation. However, key performance parameters, such as pulse duration, lag behind those from traditional mode-locked laser-based sources. Here we present new pulse generation in dispersion-managed Kerr resonators based on stretched-pulse solitons, which support the shortest pulses to date from a fiber Kerr resonator. In contrast to established Kerr resonator solitons, stretched-pulse solitons feature Gaussian temporal profiles that stretch and compress each round trip. Experimental results are in excellent agreement with numerical simulations. The dependence on dispersion and drive power are detailed theoretically and experimentally and design guidelines are presented for optimizing performance. Kerr resonator stretched-pulse solitons represent a new stable nonlinear waveform and a promising technique for femtosecond pulse generation.

Massively parallel coherent laser ranging using a soliton microcomb

Coherent ranging, also known as frequency-modulated continuous-wave (FMCW) laser-based light detection and ranging (lidar)¹ is used for long-range three-dimensional distance and velocimetry in autonomous driving^2,3. FMCW lidar maps distance to frequency^4,5 using frequency-chirped waveforms and simultaneously measures the Doppler shift of the reflected laser light, similar to sonar or radar^6,7 and coherent detection prevents interference from sunlight and other lidar systems. However, coherent ranging has a lower acquisition speed and requires precisely chirped⁸ and highly coherent⁵ laser sources, hindering widespread use of the lidar system and impeding parallelization, compared to modern time-of-flight ranging systems that use arrays of individual lasers. Here we demonstrate a massively parallel coherent lidar scheme using an ultra-low-loss photonic chip-based soliton microcomb⁹. By fast chirping of the pump laser in the soliton existence range¹⁰ of a microcomb with amplitudes of up to several gigahertz and a sweep rate of up to ten megahertz, a rapid frequency change occurs in the underlying carrier waveform of the soliton pulse stream, but the pulse-to-pulse repetition rate of the soliton pulse stream is retained. As a result, the chirp from a single narrow-linewidth pump laser is transferred to all spectral comb teeth of the soliton at once, thus enabling parallelism in the FMCW lidar. Using this approach we generate 30 distinct channels, demonstrating both parallel distance and velocity measurements at an equivalent rate of three megapixels per second, with the potential to improve sampling rates beyond 150 megapixels per second and to increase the image refresh rate of the FMCW lidar by up to two orders of magnitude without deterioration of eye safety. This approach, when combined with photonic phase arrays¹¹ based on nanophotonic gratings¹², provides a technological basis for compact, massively parallel and ultrahigh-frame-rate coherent lidar systems.

Subharmonic Entrainment of Kerr Breather Solitons

We predict subharmonic entrainment of breather-soliton oscillations to a periodic perturbation at the round-trip time T_{R} in Kerr-nonlinear optical resonators; an integer ratio T_{b}/T_{R}=N≫1 results for breathing period T_{b}. Rigid entrainment is observed with intermediate finesse (F∼30-40) for N up to 20, and we propose a way to realize higher entrainment ratios at higher finesse. This nontrivial synchronization across the widely separated timescales of the photon lifetime and round-trip time points to a new direction for research in this field and may find application, for example, in the measurement of a pulse train repetition rate that is electronically inaccessible.

Interplay of Polarization and Time-Reversal Symmetry Breaking in Synchronously Pumped Ring Resonators

Optically induced breaking of symmetries plays an important role in nonlinear photonics, with applications ranging from optical switching in integrated photonic circuits to soliton generation in ring lasers. In this work we study for the first time the interplay of two types of spontaneous symmetry breaking that can occur simultaneously in optical ring resonators. Specifically we investigate a ring resonator that is synchronously pumped with short pulses of light. In this system we numerically study the interplay and transition between regimes of temporal symmetry breaking (in which pulses in the resonator either run ahead or behind the seed pulses) and polarization symmetry breaking (in which the resonator spontaneously generates elliptically polarized light out of linearly polarized seed pulses). We find ranges of pump parameters for which each symmetry breaking can be independently observed, but also a regime in which a dynamical interplay takes place. Besides the fundamentally interesting physics of the interplay of different types of symmetry breaking, our work contributes to a better understanding of the nonlinear dynamics of optical ring cavities which are of interest for future applications including all-optical logic gates, synchronously pumped optical frequency comb generation, and resonator-based sensor technologies.

Imaging soliton dynamics in optical microcavities

Solitons are self-sustained wavepackets that occur in many physical systems. Their recent demonstration in optical microresonators has provided a new platform for the study of nonlinear optical physics with practical implications for miniaturization of time standards, spectroscopy tools, and frequency metrology systems. However, despite its importance to the understanding of soliton physics, as well as development of new applications, imaging the rich dynamical behavior of solitons in microcavities has not been possible. These phenomena require a difficult combination of high-temporal-resolution and long-record-length in order to capture the evolving trajectories of closely spaced microcavity solitons. Here, an imaging method is demonstrated that visualizes soliton motion with sub-picosecond resolution over arbitrary time spans. A wide range of complex soliton transient behavior are characterized in the temporal or spectral domain, including soliton formation, collisions, spectral breathing, and soliton decay. This method can serve as a visualization tool for developing new soliton applications and understanding complex soliton physics in microcavities.

Experimental observations of breathing Kerr temporal cavity solitons at large detunings

It was recently predicted that, due to stimulated Raman scattering, temporal Kerr cavity solitons may exhibit oscillatory instabilities at large cavity detunings [Phys. Rev. Lett.120, 053902 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.053902]. Here, we report experimental observations of this behavior. To access the appropriate oscillatory regime, we construct a macroscopic fiber ring resonator with a high finesse of F≈240. By synchronously driving the resonator with flat-top nanosecond pulses, we can reach very large intracavity power levels, where Raman-induced soliton oscillations can be observed. We also surprisingly find that, in the limit of large cavity driving strengths, new soliton instability regimes that are not accounted for in the known bifurcation structure of driven Kerr resonators can emerge even in the absence of Raman effects. Our experimental results are in good agreement with numerical simulations.

Universal isocontours for dissipative Kerr solitons

Dissipative Kerr solitons can be generated within an existence region defined on a space of normalized pumping power versus cavity-pump detuning frequency. The contours of constant soliton power and constant pulse width in this region are studied through measurement and simulation. Such isocontours impart structure to the existence region and improve understanding of soliton locking and stabilization methods. As part of the study, dimensionless, closed-form expressions for soliton power and pulse width are developed (including Raman contributions). They provide isocontours in close agreement with those from the full simulation, and, as universal expressions, can simplify the estimation of soliton properties across a wide range of systems.