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Microcavity-based frequency combs, or ‘microcombs’1,2, have enabled many fundamental breakthroughs3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21 through the discovery of temporal cavity-solitons. These self-localized waves, described by the Lugiato–Lefever equation22, are sustained by a background of radiation usually containing 95% of the total power23. Simple methods for their efficient generation and control are currently being investigated to finally establish microcombs as out-of-the-lab tools24. Here, we demonstrate microcomb laser cavity-solitons. Laser cavity-solitons are intrinsically background-free and have underpinned key breakthroughs in semiconductor lasers22,25,26,27,28. By merging their properties with the physics of multimode systems29, we provide a new paradigm for soliton generation and control in microcavities. We demonstrate 50-nm-wide bright soliton combs induced at average powers more than one order of magnitude lower than the Lugiato–Lefever soliton power threshold22, measuring a mode efficiency of 75% versus the theoretical limit of 5% for bright Lugiato–Lefever solitons23. Finally, we can tune the repetition rate by well over a megahertz without any active feedback.

Microcombs are optical frequency combs based on microcavity resonators [1] . They find multiple applications, including metrology, spectroscopy, frequency synthesis, and optical communications. Temporal cavity solitons (TCS), the temporal counterpart of spatial cavity solitons [2] , have been shown to produce microcombs with optimal spectral features [1] and are well modeled by the Lugiato-Lefever equation in passive systems. High contrast TCS can be also obtained in active systems inclusive of laser gain [3] .

Novel metamaterial platforms exhibiting time-dependent electromagnetic properties enable the investigation of previously unexplored light-matter interactions [1] - [2] . A variation in the dielectric function on a timescale shorter than the electric field period is perceived as an ultrafast temporal boundary [3] , thus resulting in a time-dependent "Snell’s law" which connects the polarisation field frequency before and after the transition [4] , [5] . The onset of a frequency shift therefore enables the engineering of exotic nonlinear phenomena such as time refraction and photon acceleration [5] - [7] , with key fundamental and practical implications [8] . In one scheme, a temporal boundary is induced via photoexcitation of semiconducting metamaterials excited by ultrashort optical pulses. Above-bandgap photons drive an ultrafast transition from a dielectric to a metallic state. Temporal-boundaries-mediated nonlinearities become relevant for transition times shorter than the wave-period timescale, a challenging regime in optics. This condition is achieved in a hybrid approach, exploiting the interaction of terahertz (THz) fields and ultrafast photo-excited transients. The peculiar advantage of THz Time-Domain-Spectroscopy techniques is that they allow the agile reconstruction of full-field dynamics with sub-wave-period resolution. In addition, in all the considered schemes, terahertz waves impinge from vacuum onto a positionally static transient, in other words a large velocity mismatch always exists. An unexplored physical scenario is then when the transient is applied directly to a source where the transient exists in the same positional reference as the THz wave.

A complex problem in terahertz photonics is the need for thin emitters [1] . Traditional free-space terahertz (THz) emission crystals rely on relatively thick crystals (on the orders of millimetres), as the terahertz emission scales with the length of the crystal. Thick crystals, however, come with a number of drawbacks. One such drawback is that the emitted THz bandwidth is limited by phase-matching conditions [2] . This amounts to thicker crystals giving a lower bandwidth, making them unsuitable for broadband spectroscopy. In near-field imaging, the image resolution depends critically on how close one can approach the sample [3] : in this regime, thick crystals can quickly become unpractical as they effectively limit the achievable resolution.

Controlling the propagation of waves in random scattering media is a recurring challenge in several physical settings. Multiple scattering has a ubiquitous impact in wave domains like sound and mechanical [1] , and electromagnetic [2] . A fundamental limitation in the study of random wave propagation is the limited experimental access to the time-resolved oscillations of the electric field. At optical frequencies, in particular, the instantaneous electric field of optical wave-packets is, in general, not a directly measurable quantity, although particular settings, e.g., in the domain of optical frequency combs, allows for indirect reconstruction [3] . Conversely, full-wave characterization is quite mature in the state of the art of ultrafast terahertz (THz) photonics. The possibility of field-sensitive detection raises the important question of whether operating on the time-space domain of the electric field could provide insight on random wave propagate on typically not accessible in the optical domain. Indeed, this scenario recalls, in some fashion, the way random wave propagation is handled in the microwave and ultrasound domains, where multiple-path and scattering modelling allows specific deterministic approaches (e.g., time-reversal). A quite apt example is how the scattering matrix of a complex sample can be retrieved at optical frequency through measurements of the transmitted intensity profile [2] . This approach typically leads to a massive loss of information since scattering operates simultaneously in time and space [4] . However, it is conceivable that a more direct approach can be cast in a domain like THz, where the field is measurable in space and time. This ability would not only have a profound impact on THz imaging as a whole [5] , [6] , but it could also define novel approaches to the imaging of objects hidden behind scattering media while preserving their spectral fingerprint.

In photonics, the study of wave propagation in scattering media is limited by the inherent challenges in detecting the time-varying electric field oscillations, as detectors and cameras are only sensitive to the optical intensity. In the Terahertz (THz) domain, however, Time-Domain Spectroscopy (TDS) is an established technique capable of directly measuring the electric field and provide full-wave characterisation (amplitude and optical delay) in time. The combination of THz time-resolved measurements with the theory of wave propagation in scattering media is a rapidly emerging subject. It opens a promising route to gain coherent control over multiple-scattering phenomena in ways not previously accessible in optics [1] . Besides, the combination of broadband excitation and coherent, field-sensitive detection could allow investigating the transmission properties of a scattering medium in unprecedented detail and retrieve its coherent transfer-matrix representation, a task out-of-reach at optical frequencies. In this work, we theoretically demonstrate spatiotemporal refocusing of THz waves following a direct measurement of the transfer matrix of the scattering medium. Our approach combines the advantages offered by field-sensitive detection with the nonlinear wavefront shaping of THz waves. Wavefront shaping represents the state-of-the-art in the control of complex wave propagation at optical frequencies, as it allows to sequentially retrieve the transfer matrix elements of the scatterer [2] . To overcome the limited availability of THz Spatial Light Modulator (SLM) devices, we employ a recently proposed technique based on the nonlinear conversion of structured optical beams to THz patterns [3] . Specifically, we take inspiration from nonlinear Ghost-Imaging techniques and project a complete set of orthogonal Hadamard patterns on the scatterer [4] . This technique allows us to retrieve the complex-valued elements of the transfer matrix by numerical inversion ( Fig. 1a,b ). We apply the direct knowledge of the transfer matrix elements to identify the optimal focusing pattern in a deterministic fashion ( Fig. 1c,d ). Unlike iterative optimisation techniques [2] , our deterministic approach takes advantage of the full amount of spatiotemporal information encoded in the transfer matrix elements. Under this view, the task of identifying the optimal input wavefront is rewritten into an inverse problem that can be solved via constraint least-square optimisation methods. An exemplary result is shown in Fig. 1c,d , where our technique is employed to achieve spatiotemporal refocusing (i.e., focusing in space and compression in time) of a single cycle THz pulse.

In many disciplines, states that emerge in open systems far from equilibrium are determined by a few global parameters1,2. These states can often mimic thermodynamic equilibrium, a classic example being the oscillation threshold of a laser3 that resembles a phase transition in condensed matter. However, many classes of states cannot form spontaneously in dissipative systems, and this is the case for cavity solitons2 that generally need to be induced by external perturbations, as in the case of optical memories4,5. In the past decade, these highly localized states have enabled important advancements in microresonator-based optical frequency combs6,7. However, the very advantages that make cavity solitons attractive for memories—their inability to form spontaneously from noise—have created fundamental challenges. As sources, microcombs require spontaneous and reliable initiation into a desired state that is intrinsically robust8–20. Here we show that the slow non-linearities of a free-running microresonator-filtered fibre laser21 can transform temporal cavity solitons into the system’s dominant attractor. This phenomenon leads to reliable self-starting oscillation of microcavity solitons that are naturally robust to perturbations, recovering spontaneously even after complete disruption. These emerge repeatably and controllably into a large region of the global system parameter space in which specific states, highly stable over long timeframes, can be achieved.

Solitary waves — solitons — occur in a wide range of physical systems with a broad array of attributes and applications. Carefully engineered light–matter interactions have now produced an optomechanical dissipative soliton with promising properties.

Turing patterns and solitons are a common occurrence in systems that are out of equilibrium. For example, they regulate the emergence of organised structures in biology and chemistry. In optics, the study of temporal Turing rolls and cavity-solitons in nonlinear micro-cavity resonators has been key to the understanding of optical frequency comb formation in these structures. Over a decade, the impact of microresonator-based approaches to generating frequency combs – so-called "Micro-combs or "Kerr combs" – has reached far beyond metrology applications. Here we summarise our theoretical and experimental results for solitons and Turing patterns in a system comprising a micro-resonator nested in an auxiliary fibre-gain cavity.

We theoretically present a design of self-starting operation of microcombs based on laser-cavity solitons in a system composed of a micro-resonator nested in and coupled to an amplifying laser cavity. We demonstrate that it is possible to engineer the modulational-instability gain of the system's zero state to allow the start-up with a well-defined number of robust solitons. The approach can be implemented by using the system parameters, such as the cavity length mismatch and the gain shape, to control the number and repetition rate of the generated solitons. Because the setting does not require saturation of the gain, the results offer an alternative to standard techniques that provide laser mode-locking., Comment: To be published in Optics Express

Optical-Pump Terahertz (THz) Near-Field Microscopy (OP-TNFM) is a novel technique for trans- carrier hyperspectral imaging, capable of extracting recombination dynamics and the spatially distributed complex refractive index that results from thermalised carriers in semiconducting materials.

In an open nonlinear system, emergent complex structures are generally determined by a set of global parameters. Cavity-solitons are an example of such structures and, in their temporal form, have seeded the last decade of major developments in microresonator-based optical frequency combs. These optical pulses typically require complex procedures and external feedback to be induced and maintained. Recent progress has seen the microresonators directly embedded into a laser cavity [1] , [2] where it is possible to simply initiate cavity-soliton formation by increasing the laser-diode driving current [3] . Hybrid laser-microresonator schemes have been considered since 2012 [4] , and extremely efficient laser cavity-solitons have been experimentally and theoretically demonstrated in a laser microcomb [5] .

We present a theoretical investigation of broadband, spatio-temporal control of THz light in random media. We consider the refocusing and compression of a THz pulse by optimising the spatiotemporal features of the transmitted field.

A cartographical study is conducted within the parameter space of a microresonator- filtered fiber laser. We identify a region in which solitons are spontaneously formed and maintained, and we investigate the effects which govern their emergence.

We provide the first demonstration of two-color optical rectification from semiconductors in an extreme absorption regime. The THz generation is free from phase-matching constraints due to the confinement of the interaction within a 25-atomic-layer region.

International audience; We summarize our results on the generation of temporal laser cavity-solitons in a system comprising an optical micro-cavity nested in a fiber laser. We will discuss their features, region of existence, potential and challenges ahead. Dissipative solitons are self-confined pulses which appear in driven and lossy systems when the phase dispersion is balanced by the nonlinear phase-shift. Ultrashort pulses generated by passive mode-locking lasers are a very important example of temporal dissipative solitons in optics. Temporal cavity-solitons [1,2,3] also belong to this class of pulses and have been instrumental in the development of optical frequency combs in nonlinear micro-cavities, or "micro-combs" [1]. Temporal cavity-solitons have been largely studied in a 'driven' configuration, where an external pumping source is resonantly coupled in the nonlinear micro-resonator to sustain and excite the solitary pulses. More recently, we demonstrated that it is possible to generate localised pulses in a configuration where the micro-cavity is inserted in a fiber laser loop, as described in Figure 1. In particular, we reported the observation of laser cavity-solitons [4], which have previously attracted large attention especially in spatial configurations, such as in semiconductor lasers [5]. By merging their properties with the physics of both micro-resonators and multi-mode systems, this scheme represents a fundamentally new paradigm for the generation, stabilisation and control of solitary optical pulses in micro-cavities. Fig. 1. Scheme of the nested, travelling-wave cavities configuration: a Kerr micro-resonator (green loop) is nested in an amplifying fibre-loop (black). The amplifying cavity comprises a gain fibre (erbium-ytterbium doped amplifier, EYDFA), a tuneable delay line with optical couplers (OC), polarising beam splitter (PBS), polarisation control and a band-pass filter (BPF). The output of the laser is monitored with an optical spectrum analyser (OSA), a second-harmonic non-collinear autocorrelator and an oscilloscope to measure the radio-frequency noise of the system. © 2 0 2 0 T h e Au t h o r (s)

Microcombs based on Turing patterns have been extensively studied in configurations that can be modelled by the Lugiato-Lefever equation. Typically, such schemes are implemented experimentally by resonant coupling of a continuous wave laser to a Kerr microcavity in order to generate highly coherent and robust waves. Here, we study the formation of such patterns in a system composed of a microresonator nested in an amplifying laser cavity, a scheme recently used to demonstrate laser cavity solitons with high optical efficiency and easy repetition rate control. Utilizing this concept, we study different regimes of Turing patterns, unveiling their formation dynamics and demonstrating their controllability and robustness. By conducting a comprehensive modulational instability study with a mean-field model of the system, we explain the pattern formation in terms of its evolution from background noise, paving the way towards complete self-starting operation. Our theoretical and experimental paper provides a clear pathway for repetition rate control of these waves over both fine (Megahertz) and large (Gigahertz) scales, featuring a fractional frequency nonuniformity better than 7 × 10−14 with a 100-ms time gate and without the need for active stabilization.

We theoretically analyze and experimentally demonstrate optical bi-stability and multi-stability in an integrated nonlinear high-order microring resonator filter based on high-index contrast doped silica glass. We use a nonlinear model accounting for both the Kerr and thermal effects to analyze the instability behavior of the coupled-resonator based filter. The model also accurately predicts the multi-stable behavior of the filter when the input frequency is slightly detuned. To understand the role of the intracavity power distribution, we investigate the detuning of the individual rings of the filter from the optical response with a pump–probe experiment. Such a measurement is performed scanning the filter with a low-power probe beam tuned a few free spectral ranges away from the resonance where the pump is coupled. A comprehensive understanding of the relationship between the nonlinear behavior and the intracavity power distribution for the high-order microring resonator filter will help the design and implementation of future all-optical switching systems using this type of filter.

The stability of laser temporal cavity solitons in micro-ring cavities nested in an externally pumped fibre loop with gain is investigated. The crucial roles of group velocity mismatch and gain dispersion are identified.

Supplementary Material

We demonstrate a Terahertz Ghost-Imaging technique combining nonlinear pattern generation and single-pixel Time-Domain-Spectroscopy (TDS) detection. Our technique allows reconstructing the morphology and spectral features of subwavelength samples.

Terahertz (THz) spectroscopy systems are widely employed to retrieve the chemical and material composition of a sample. This is single-handed the most important driving motivation in the field and has largely contributed to shaping THz science as an independent subject. The limited availability of high-resolution imaging devices, however, still represents a major technological challenge in this promising field of research. In this theoretical work, we tackle this challenge by developing a novel nonlinear Ghost Imaging (GI) approach that conceptually outperforms established single-pixel imaging protocols at inaccessible wavelengths. Our methodology combines nonlinear THz generation with time-resolved field measurements, as enabled by state-of-the-art Time Domain Spectroscopy (TDS) techniques. As an ideal application target, we consider hyperspectral THz imaging of semi-transparent samples with nonnegligible delay contribution and we demonstrate how time-resolved, full-wave acquisition enables accurate spatiotemporal reconstruction of complex inhomogeneous samples.