Dissipative Raman solitons in passive Kerr resonators have emerged as a promising route to broadband coherent frequency comb generation. Yet, their centre frequency has so far been mostly fixed near the Raman gain peak (13~THz downshifted from the pump centre frequency in silica-based fibres), constraining spectral coverage and compatibility with standard optical amplifiers. This limitation arises because the frequency shift of Raman solitons that fulfills phase-matching and group-velocity-matching conditions has to fall within the Raman gain band, leaving little room for spectral tuning when using a single conventional optical fibre. Here, we demonstrate that dispersion management of the fibre Fabry-Pérot resonator which allows us to directly shift the soliton centre frequency. By combining two fibres with complementary dispersion profiles, we tailor the resonator's average dispersion to satisfy the phase-matching conditions for soliton formation at a target frequency downshifted by 7.8~THz from a pulsed pump, which is well outside the conventional 13~THz Raman gain band. This allows us to optically amplify the dissipative Raman soliton with a commercial L-band erbium-doped fibre amplifier, and fully characterise its temporal profile via the frequency-resolved optical gating technique.

We theoretically and numerically investigate the formation of soliton crystals in Kerr microresonators in the presence of an avoided mode crossing (AMX). Our study combines dynamical simulations based on a modified Lugiato-Lefever equation (LLE) with a stability analysis of its stationary solutions. We show that, depending on its strength and spectral position, the AMX can either stabilize otherwise unstable soliton crystals or induce Turing patterns which subsequently seeds soliton crystal formation. Both perfect and imperfect soliton crystals can form below the pump threshold for spatiotemporal chaos, and we identify the conditions required for perfect crystals. Finally, we investigate modulation instability in the presence of an AMX, showing that it modifies the parametric gain and can suppress or promote Turing pattern formation depending on its spectral position.

A controlled pump bias between faticon components enables deliberate tuning of their propagation velocity, repetition rate, and frequency-comb line spacing, providing a flexible and robust method for engineering soliton dynamics and tailored comb generation.

Fluctuations of nonequilibrium localized waves are shaped not only by direct stochastic forcing but also by deterministic transfer among coupled collective degrees of freedom. We develop a pathway-resolved stochastic collective-coordinate theory that makes this transfer explicit for stationary driven-dissipative solitons of the generalized Lugiato–Lefever equation with Raman response. The reduction yields a refined stationary phase-locking relation, providing a fixed point for the subsequent stochastic theory. Projecting field-level fluctuations onto four soliton coordinates: amplitude, frequency shift, temporal position, and global phase, yields a reduced Langevin model and, after linearization about a stable stationary state, an analytic power-spectral-density matrix. This framework separates direct stochastic injection from deterministic inter-coordinate conversion and thereby resolves how each observable spectrum is assembled from distinct internal fluctuation pathways. It shows that timing jitter is governed primarily by Gordon–Haus-type frequency-to-timing conversion, while phase noise is often dominated by amplitude-to-phase transfer rather than by direct phase diffusion. Raman response opens additional cascaded pathways, and the low-detuning hump in the intensity and phase spectra is traced to the driven response of an underdamped amplitude–phase subsystem preceding the breathing instability. Comparisons with stochastic simulations of both the reduced model and the full generalized Lugiato–Lefever equation show good agreement throughout most of the stable stationary single-soliton regime, with systematic deviations mainly near the Hopf boundary. The theory provides a general route for connecting internal fluctuation-transfer mechanisms of dissipative solitons to measurable noise observables.

Time-multiplexed networks of degenerate optical parametric oscillators have demonstrated remarkable success in simulating coupled Ising spins, thus providing a promising route to solving complex combinatorial optimization problems. In these systems, referred to as coherent Ising machines, spins are encoded in the oscillator phases, and measured at the system output using phase-sensitive techniques, making intricate phase stabilization necessary. Here, we introduce an optical Ising machine based on spontaneous polarization symmetry breaking in a coherently driven fiber Kerr nonlinear resonator. In our architecture, the spins are encoded in the polarization state, allowing robust, all-intensity readout with off-the-shelf telecom components. By operating in a newly-discovered regime where nonlinearity and topology lock the system's symmetry, we eliminate drift and bias, enabling uninterrupted Ising trials at optical speeds for over an hour, without manual intervention. This all-fiber platform not only simplifies the hardware but also opens a path to more stable, high-throughput coherent optical optimization devices for applications from finance to drug design and beyond.

Kerr frequency combs have recently emerged as an exciting new photonic technology, with applications across science and engineering. Their formation within driven optical resonators that possess a Kerr nonlinearity is enabled through the rich landscape of localized nonlinear dissipative structures intrinsic to these systems. This article offers a comprehensive review of the physics that underpins these nonlinear comb-generating structures. Particular attention is placed on bright temporal cavity solitons and nonlinear switching waves – the canonical stable comb-generating states in the anomalous and normal dispersion regimes, respectively. Written as both a review and tutorial, the article also includes an in-depth treatment of the numerical methods required to simulate driven Kerr resonators, alongside a comprehensive discussion of the laboratory techniques used to experimentally realize and characterize Kerr combs.

Microresonator Kerr solitons are promising candidates for the realization of miniaturized on-chip optical frequency combs. For specific system parameters, these solitons are associated with oscillatory instabilities, leading to breathing dynamics characterized by periodically modulated temporal and spectral profiles. In this regime, the solitons form a frequency comb comprised of primary comb lines surrounded by sidebands separated by the breathing frequency. Here, we numerically and experimentally demonstrate that the breathing sidebands can be all-optically synchronized to a weak monochromatic laser injected into the cavity, thus providing direct control of the soliton oscillation frequency. We judiciously characterize the synchronization process, and show that it is accompanied by a strong reduction of noise in the soliton's breathing. Our results provide fundamental insights on oscillatory dissipative structures, and could enable new forms of composite optical frequency combs.

We theoretically and numerically investigate the formation of soliton frequency combs in driven, passive resonators with novel dispersion profiles. Specifically, we explore multi-peak and purely high-order even dispersion. These novel solitons could be observed experimentally in integrated Kerr microresonators and passive fiber cavities, offering strong potential for applications in frequency comb spectroscopy, self-referencing, and telecommunications.

We report on the experimental generation of polarization symmetry-broken cavity solitons (SB-CSs) in a passive, fiber-based, coherently driven, Fabry-Pérot (FP) Kerr resonator. Polarization-resolved measurements reveal the spontaneous transition of initially symmetric CSs into asymmetrical vectorial states, triggered by a cross-phase modulation-induced polarization bifurcation. Most notably, due to counter-propagation of light occurring in FP resonators, we unveil a collective polarization conformity effect, whereby multiple CSs circulating in the cavity converge to the same asymmetric polarization state once their number exceeds a certain threshold. These results demonstrate that Fabry-Pérot resonators support novel collective soliton dynamics that are absent in ring architectures.

We report the existence of multi-peaked vector soliton families in normally dispersive passive Kerr resonators. Through cross-phase modulation between two orthogonal polarization components, each peak becomes tightly interlocked, enabling robust localization of the entire wave packet in defocusing cavities. Analysis using snakes-and-ladder diagrams demonstrates the diversity of these vector soliton families, which include dark-bright multi-peak solitons, flat-topped solitons, and modulation instability patterns, among others. Furthermore, stability analysis based on the coupled Lugiato-Lefever equations reveals that specific combinations of parameters can sustain stable vector cavity solitons, whose peak numbers can be continuously tuned by adding appropriate perturbations. These findings significantly expand the scope of soliton dynamics and optical frequency comb generation in pumped-dissipative systems, independent of dispersion conditions.

Through numerical simulations, we demonstrate the existence of an infinite family of temporal cavity solitons (CSs), which balance arbitrary negative pure, even-order dispersion k and self-phase modulation, as well as loss and parametric gain. These correspond to frequency combs with increasingly flatter spectra as k increases. We determine the analytic forms of these solitons at high pump power and detuning and derive that their energy is related to the pulse duration Δτ as Δτ-(k-1).

Coherent Ising machines (CIMs) are optical devices that can offer efficient solutions to many complex combinatorial optimization problems too challenging to solve with traditional computing methods [1]–[3]. CIMs typically utilize networks of degenerate optical parametric oscillators, where the bistable phases of optical pulses represent spin states, and coupling is achieved through electronic measurement and feedback. While offering a powerful approach, exemplified by exceptional scaling [4], complex phase stabilization techniques make continuous operation of these machines quite challenging. Here, we provide an experimental demonstration of a novel CIM platform, with spin-states defined based on the polarization of optical pulses, and resolved with straightforward intensity measurements, leading to simple and robust operation [5]. The device is made up of a Kerr nonlinear optical fiber ring resonator synchronously-driven with multiple laser pulses. As the driving frequency is swept across a cavity resonance, each circulating pulse undergoes spontaneous polarization symmetry breaking, producing independent spin states. Crucially, we operate in a period-2 regime, where the polarization state of each intracavity pulse alternates at each roundtrip, imparting topological protection against external perturbations [6]. This guarantees highly robust performance, confirmed by high-fidelity all-optical random number generation [7].

Spontaneous symmetry breaking (SSB) is an ubiquitous phenomenon of fundamental interest, potentially leading to promising applications in nonlinear optics. In coherently-driven Kerr ring resonators, SSB has been observed between counter-propagating beams [1] and co-propagating waves of orthogonal polarizations [2]. Experimental demonstrations of polarization SSB in optical fibre rings have also unveiled peculiar nonlinear dynamics such as topological protection of SSB phenomena as well as novel localized vectorial structures, including polarization domain walls (PDWs) [3], vectorial cavity solitons (CSs) [4], and polarization faticons [5]. Complementary to ring architectures, Fabry-Pérot (FP) Kerr resonators are also good candidates for practical applications including frequency comb generation [6] and polarization SSB [7]–[8]. FP Kerr resonators are typically made of a short segment of optical fibre encapsulated in-between two Bragg dielectric mirrors [6]–[7]. They benefit from the flexibility, interconnectivity, and stability of fibre-based systems, free-spectral ranges (FSR) from hundreds of MHz to tens of GHz, dispersion engineering using various types of optical fibres or mirror properties, whilst preserving high quality-factors. Here we show that fibre-based FP resonators can provide an efficient protection of polarization SSB phenomena through the introduction of a $\pi / 2$ -phase birefringent defect between the two orthogonal eigenmodes of the cavity, enabling the generation of robust vectorial localized temporal structures such as PDWs and CSs.

Dissipative temporal Kerr cavity solitons (CSs) are ultra-short pulses of light that can circulate indefinitely and without distortion within an optical cavity [1]. Over recent years they have attracted considerable attention thanks to a suite of applications being demonstrated from real-time spectroscopy to ultra-fast ranging [2]. With the commercial potential of this technology beginning to be realised, there has been a push towards tackling practical issues, chief among them being the reliable and robust generation of CSs. In this contribution, we demonstrate within a pulse-driven Kerr resonator that there exists a novel regime of CS auto-generation in which the CS state is the only available optical state of the system. Operating in this regime not only provides the CS states an enhanced level of robustness to environmental factors, but also guarantees the direct and automatic generation of CSs from an empty cavity without the need of any external seed or parameter ramp (i.e., soft excitation). Experimentally, our setup is comprised of a 0.3 m length of dispersion-shifted fiber with two dielectric end caps creating a Fabry-Perot cavity. The cavity is driven with a periodic train of 1.6-ps-long pulses created via standard electro-optic means [1], and with the help of a weak control beam we can precisely control the cavity detuning over the whole free-spectral range. Figure 1(a) illustrates this CS auto-generation with a pseudo-coloured plot of the intracavity spectrum as we periodically turn our picosecond driving pulse off and on again, showing the intracavity field automatically evolve into a CS from noise given that the cavity parameters lie within the auto-generative regime. A single trace of the experimental CS spectrum is shown in Fig. 1(b) in red (with the prominent spectral peak corresponding to a phase-matched dispersive wave), overlaid with a numerical simulation obtained with the same parameters (with the inset showing the temporal intensity profile) using the governing Lugiato-Lefever model [1]. Furthermore, due to the interplay between higher-order dispersion and our pulsed driving field, the deterministic selection of CS bound-states [3] becomes possible by simply tuning cavity parameters such as the pump desynchronisation or cavity detuning.

The generation of temporal cavity solitons (CSs) in Kerr resonators is well known to lead to the formation of stable frequency combs. In a resonator with pure second-order anomalous dispersion, the soliton's center frequency is pinned to that of the pump field. In this Letter, we consider the operation of CSs in a cavity that possesses a significant component of fourth-order dispersion, which provides a broadband region of parametric gain from which a CS can extract energy. Through the application of a pulsed driving field, temporally desynchronized from the natural roundtrip time of the resonator, we are able to demonstrate the generation of group-velocity-matched CSs, offset in frequency from the pump, and tunable over a ∼1.5 THz range. In addition, we observe a new spectral feature that forms on the opposite side of the pump to the CS that we identify as arising from linear-wave scattering from the CS field.