Kerr Solitons In Optical Microresonators Research Articles

Soliton Burst and Bi‐Directional Switching in the Platform with Positive Thermal‐Refractive Coefficient Using an Auxiliary Laser

AbstractDissipative Kerr solitons in optical microresonators enable the generation of stable ultrashort pulses and phase‐locked frequency combs, leading to their widespread applications. For traditional platforms with positive thermal‐refractive coefficient, strong thermal effect increases the difficulties of soliton triggering and prohibits the deterministic control of soliton number. Here, using an auxiliary laser to tune thermal effect, soliton burst and bi‐directional switching are demonstrated in high‐index doped silica glass platform. First, by varying the parameters of the auxiliary laser, the thermal effect tuning of the microresonator is studied with different thermal compensation states achieved, leading to distinct soliton switching features. Especially, the solitons burst and bi‐directional switch in over‐compensated state. The corresponding process is recorded in real time based on a temporal magnification system, uncovering transient dynamics from continuum background noise to soliton formation. Finally, the deterministic generation of solitons is enabled with controllable soliton number spanning from 1 to 21. The present work provides insight into soliton dynamics and enables soliton generation on demand with a large range of soliton numbers inside a single device.

Dissipative Kerr solitons in optical microresonators with Raman effect and third-order dispersion* *Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0304203 and 2019YFA0705000), the National Natural Science Foundation of China (Grant Nos. 12004116 and 11804204), and 1331KSC.

Using the mean-field normalized Lugiato–Lefever equation, we theoretically investigate the dynamics of cavity soliton and comb generation in the presence of Raman effect and the third-order dispersion. Both of them can induce the temporal drift and frequency shift. Based on the moment analysis method, we analytically obtain the temporal and frequency shift, and the results agree with the direct numerical simulation. Finally, the compensation and enhancement of the soliton spectral between the Raman-induced self-frequency shift and soliton recoil are predicted. Our results pave the way for further understanding the soliton dynamics and spectral characteristics, and providing an effective route to manipulate frequency comb.

Dynamics of soliton crystals in optical microresonators

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 continuous-wave intracavity driving field. To date, however, the dynamics of soliton crystals remains mainly unexplored. Moreover, the vast majority of the reported crystals contained defects - missing or shifted pulses, breaking the symmetry of these states, and no procedure to avoid such defects was suggested. Here we explore the dynamical properties of soliton crystals and discover that often-neglected chaotic operating regimes of the driven optical microresonator are the key to their understanding. In contrast to prior work, we prove the viability of deterministic generation of $\mathrm{perfect}$ soliton crystal states, which correspond to a stable, defect-free lattice of optical pulses inside the cavity. We discover the existence of critical pump power, below which the stochastic process of soliton excitation suddenly becomes deterministic enabling faultless, device-independent access to perfect soliton crystals. Furthermore, we demonstrate the switching of soliton crystal states and prove that it is also tightly linked to the pump power and is only possible in the regime of transient chaos. Finally, we report a number of other dynamical phenomena experimentally observed in soliton crystals including the formation of breathers, transitions between soliton crystals, their melting, and recrystallization.

Ultralow-power chip-based soliton microcombs for photonic integration

The generation of dissipative Kerr solitons in optical microresonators has provided a route to compact frequency combs of high repetition rate, which have already been employed for optical frequency synthesizers, ultrafast ranging, coherent telecommunication and dual-comb spectroscopy. Silicon nitride (Si$_3$N$_4$) microresonators are promising for photonic integrated soliton microcombs. Yet to date, soliton formation in Si$_3$N$_4$ microresonators at electronically detectable repetition rates, typically less than 100 GHz, is hindered by the requirement of external power amplifiers, due to the low quality ($Q$) factors, as well as by thermal effects which necessitate the use of frequency agile lasers to access the soliton state. These requirements complicate future photonic integration, heterogeneous or hybrid, of soliton microcomb devices based on Si$_3$N$_4$ microresonators with other active or passive components. Here, using the photonic Damascene reflow process, we demonstrate ultralow-power single soliton formation in high-Q ($Q_0>15\times10^6$) Si$_3$N$_4$ microresonators with 9.8 mW input power (6.2 mW in the waveguide) for devices of electronically detectable, 99 GHz repetition rate. We show that solitons can be accessed via simple, slow laser piezo tuning, in many resonances in the same sample. These power levels are compatible with current silicon-photonics-based lasers for full photonic integration of soliton microcombs, at repetition rates suitable for applications such as ultrafast ranging and coherent communication. Our results show the technological readiness of Si$_3$N$_4$ optical waveguides for future all-on-chip soliton microcomb devices.

Intermode Breather Solitons in Optical Microresonators

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 soliton spectrum, leading to e.g. the formation of dispersive wave and inducing a spectral recoil. Yet, to date, the entailing temporal soliton dynamics from inter-mode interactions has rarely been studied, but is critical to understand regimes of soliton-stability. Here we report the discovery of an inter-mode breather soliton. Such breathing dynamics occurs within a laser detuning range where conventionally stationary dissipative solitons are expected. We demonstrate experimentally the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators), and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We demonstrate experimentally that the breathing is associated with a periodic energy exchange between the soliton and another optical mode family. We further show that inter-mode interactions can be modeled by a response function acting on dissipative solitons. The observation of breathing dynamics in the conventionally stable soliton regime is critical to applications, ranging from low-noise microwave generation, frequency synthesis to spectroscopy. On a fundamental level, our results provide new understandings of the rich dissipative soliton dynamics in multimode nonlinear cavities.

Detuning-dependent properties and dispersion-induced instabilities of temporal dissipative Kerr solitons in optical microresonators

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 verification of this relation was lacking so far. Here, by measuring and controlling the effective-detuning, we establish a new way of stabilizing solitons in microresonators and demonstrate that the measured relation linking soliton width and detuning deviates by less than 1 % from the approximate expression, validating its excellent predictive power. Furthermore, a detuning-dependent enhancement of specific comb lines is revealed, due to linear couplings between mode-families. They cause deviations from the predicted comb power evolution, and induce a detuning-dependent soliton recoil that modifies the pulse repetition-rate, explaining its unexpected dependence on laser-detuning. Finally, we observe that detuning-dependent mode-crossings can destabilize the soliton, leading to an unpredicted soliton breathing regime (oscillations of the pulse) that occurs in a normally-stable regime. Our results test the approximate analytical solutions with an unprecedented degree of accuracy and provide new insights into dissipative-soliton dynamics.

Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators

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 solitons, one by one, i.e. ${N\! \to\! N\!-\!1\! \to\! \dots \!\to\! 1}$. By applying weak phase modulation, we directly characterize the soliton state via a double-resonance response. The dynamical probing demonstrates that transitions occur in a predictable way, and thereby enables us to map experimentally the underlying multi-stability diagram of dissipative Kerr solitons. These measurements reveal the "lifted" degeneracy of soliton states as a result of the power-dependent thermal shift of the cavity resonance (i.e. the thermal nonlinearity). The experimental results are in agreement with theoretical and numerical analysis that incorporate the thermal nonlinearity. By studying two different microresonator platforms (integrated $\mathrm{Si_{3}N_{4}}$ microresonators and crystalline $\mathrm{MgF_{2}}$ resonators) we confirm that these effects have a universal nature. Beyond elucidating the fundamental dynamical properties of dissipative Kerr solitons the observed phenomena are also of practical relevance, providing a manipulation toolbox which enables to sequentially reduce, monitor and stabilize the number ${N}$ of solitons, preventing it from decay. Achieving reliable single soliton operation and stabilization in this manner in optical resonators is imperative to applications.