We report on the interaction between stimulated Brillouin scattering and temporal cavity solitons in doubly resonant ring resonators. Our experiments are performed in coherently driven passive optical-fibre resonators. We demonstrate that the interplay between four-wave mixing and cascade Brillouin lasing spontaneously generates patterns of CSs on a temporal grid at twice the Brillouin-shift. These patterns are shown to be highly stable owing to a long-range locking mechanism mediated by the acoustic oscillation generated by the solitons. We introduce a unified mean-field model of the cavity to describe the dynamics between the coupled forward and backward waves under coherent driving. This model reproduces very well the experiments and explains the paracrystalline structures of the soliton pattern. Our findings significantly advance the understanding of hybrid Brillouin-Kerr optical frequency combs.

Temporal cavity solitons are ultrashort optical pulses circulating in driven Kerr resonators. Their intrinsic stability and ability to generate coherent broadband frequency combs have led to breakthroughs in fields such as sensing, metrology, and signal synthesis. However, this robustness limits control over soliton dynamics and constrains comb characteristics. Here, we demonstrate that stationary and moving trapping potentials, generated through intracavity phase modulation, provide unprecedented control over cavity soliton properties. We theoretically show that, for deep potentials, the soliton spectral shift and repetition rate tuning range are primarily limited by a Hopf bifurcation, and reveal the role of dissipation in soliton dynamics. Using a fibre resonator, we observe stable blue- and red-shifted solitons up to 0.4 times their spectral width, at least an order of magnitude larger than with external phase modulation of the drive. We also investigate the interplay between the trapping potential and stimulated Raman scattering, showing that Raman self-frequency shift can be fully compensated, extending the existence range of cavity solitons. Our results provide a new means for stabilising or rapidly tuning the repetition rate of Kerr combs over a wide range, broadening the applications of Kerr frequency combs.

Temporal cavity solitons (CSs) are ultra-stable self-sustaining light pulses circulating indefinitely within a resonator [1]. They are sustained through a balance between the anomalous chromatic dispersion, cavity loss, Kerr nonlinearity and a coherent drive, detuned relative to a cavity resonance. CSs have been demonstrated across various platforms, with fiber ring resonators [1] and integrated microcombs [2] being the most common. Recent studies have explored the interaction between CSs-based frequency combs and stimulated Brillouin scattering (SBS), with the aim of developing hybrid combs. SBS arises from photon scattering onto an acoustic wave generated by the beating between two mutually coherent counter-propagating beams. For a single beam, this interaction results in an ultranarrow backward gain, enabling the generation of a highly coherent Brillouin laser from a lower coherence source. The combination of Brillouin laser coherence and high bandwidth of CSs-based combs motivates the development of hybrid CS-Brillouin frequency combs. Recent developments include using a Brillouin laser driven by a low-coherence external pump to drive counterpropagating CSs within the same cavity, in both a singly resonant fiber resonator [3] and a doubly resonant microcomb [4]. Brillouin dual-comb sources have also been demonstrated to generate both backward and forward microcombs [5]. Brillouin-enhanced Kerr frequency combs were also unexpectedly observed in a Fabry-Perot fiber resonator [6].

Temporal cavity solitons (CSs) are stable, localized particle-like objects in the form of optical pulses that circulate indefinitely in coherently driven nonlinear resonators. In the spectral domain, they form highly coherent frequency combs. Owing to their remarkable stability, they are attracting attention for applications in sensing, metrology, or optical signal synthesis. In this work, we report on the dynamics of CSs interacting with a trapping potential. We demonstrate that this interaction provides a powerful means to control their properties such as position, speed, and central frequency. Our theoretical analysis predicts fundamental limitations on the spectral shift of CSs relative to the driving frequency. Specifically, it reveals that within a broad range of detunings, frequency-shifted CSs encounter destabilization through a Hopf bifurcation. Moreover, we find that with periodic potentials, the Kelly sidebands emitted by trapped solitons undergo Bloch oscillations. In our experiments, we use an intracavity phase modulator to create the equivalent of an external real potential. We observe stable blue- and red- shifted solitons up to a limit close to our theoretical predictions. We then show theoretically and experimentally that this unprecedented level of control over the CS spectrum can be leveraged to cancel the Raman-induced self-frequency shift and even to stabilize CSs beyond the limitation imposed by stimulated Raman scattering. Our results provide valuable insights for applications requiring robust and potentially rapid tunable control over the cavity soliton properties.

Active cavity solitons suffer from gain saturation preventing high average cavity power. We overcome this limitation by optical gain clamping and demonstrate the generation of numerous solitons, opening the way to high power soliton crystals.

Cavity solitons are self-sustaining ultrastable pulses looping in an externally driven cavity [1], [2]. They exist in an equilibrium state between the nonlinear phase accumulation from the Kerr Effect counterbalancing the chromatic dispersion and cavity detuning, while the energy lost in the cavity is supplied through the driving laser. They offer an attractive way of generating optical frequency combs by simply extracting a fraction of the cavity power each roundtrip. The extracted signal, taking the form of a pulses train with a repetition rate equal to the cavity roundtrip, acts naturally as a frequency comb source. Several limitations still prevent their use for real-life applications. Both the comb bandwidth and the soliton peak power are limited by the intracavity losses and are typically lower than what can be obtained with mode-locked lasers. Minimum possible losses are desirable which contrasts with the desired output for which the highest possible tapping ratio is desired. This is also particularly critical for fiber resonators in which the loss budget is usually tight. This means that typically only a small fraction of the useful signal can be extracted. To overcome this limitation, active cavity solitons (ACS) were recently introduced [3]. They are hosted in an active cavity, for which the gain medium, pumped under the lasing threshold, compensates a major part of the cavity loss, including large input/output coupling ratios. This near-all loss compensation allows very low effective losses, even with the extraction of a large part of the cavity signal. This design however suffers from gain saturation as the gain decreases with increasing intracavity power, meaning that the effective low loss is only maintained at low average power. This intrinsically limits the number of solitons the cavity can sustain and prevents the spontaneous generation of solitons through a detuning sweep [4], [5]. The energetic efficiency is also low as only a small fraction of the pump power is absorbed in the gain medium.

We report theoretically and experimentally on the formation of temporal cavity solitons shorter than the fundamental limit imposed by the stimulated Raman scattering in a fiber Kerr resonator that includes a phase modulator.

Kerr cavity solitons (CSs) are pulses that propagate unperturbed in a driven nonlinear optical resonator. They currently play a crucial role in the formation of highly coherent optical frequency combs [1]. CSs are well described by the so-called Lugiato-Lefever equation (LLE) [1]–[2]. The CS peak power as a function of the driving laser phase detuning from the closest cavity resonance, $\delta_{0}$ , obtained by numerical continuation of the LLE, is shown in Fig. 1a. The highest reachable detuning, $\delta_{\max}$ , is proportional to the driving power $P_{in}$ . In particular, the CS peak power (duration) increases (decreases) with the cavity detuning. Then, to generate the shortest CSs with the highest peak power, one should operate at the largest detuning [2]–[3]. However, for short CSs in resonators made of silica, the stimulated Raman scattering (SRS) must be considered. This inelastic scattering is responsible for red-shifting the CS spectrum from the driving frequency (see Fig 1a, inset). A few years ago, Wang et al. demonstrated in [4] that the SRS imposes a fundamental limit to the peak power and the temporal duration of CSs, as the highest detuning for which a stable CS exists $(\delta_{\mathrm{H}2})$ is severely reduced with respect to the SRS-free case $(\delta_{\mathrm{H}2} < \delta_{\max})$ . Recently, it has been shown that an intracavity electro-optics phase modulator (EOM) can red and blue shift the CS spectrum [8]. In this work, we propose and demonstrate experimentally that an intracavity EOM can be leveraged to cancel the spectral red-shift caused by the SRS to overcome the fundamental limitation it imposes. The simplified experimental setup is depicted in Fig. 1b. It consists of a fiber ring resonator incorporating an EOM driven by a cosine waveform of amplitude $J=0.6$ rad and frequency $\Omega\simeq 2\pi\times 9.3\ \text{GHz}$ , an integer multiple of the cavity free-spectral-range. It also includes a short piece of erbium-doped fiber whose gain compensates for the EOM insertion loss [6]. The resonator is driven by 700 ps-long flat-top pulses $(P_{in}=100\ \text{mW})$ synchronized with the FSR. Given the experimental parameters, we find $\delta_{\max}=4.6$ rad (see Fig. 1a), at which CSs have a full width at half maximum duration of 730 fs [2]. Likewise, $\delta_{\mathrm{H}2}=2.8$ rad [4], corresponding to a 990 fs-long soliton. The corresponding CS peak power evolution with the cavity detuning is given in Fig. 1a (black curve). It clearly suggests the ability to reach a detuning $(\delta_{\text{EOM}}\simeq 4.2\ \text{rad})$ close to the maximum value ( $\delta_{\max}$ , set by $P_{in}$ ), and clearly larger than the limit imposed by the SRS. Here, this limit coincides with the detuning for which the SRS red-shift equals the maximum blue-shift induced by the intracavity EOM $(\Delta \omega=J\varOmega)$ .