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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.

Modern optical systems increasingly rely on complex physical processes. Advanced light sources, such as supercontinuum (SC) [1], are highly sought for imaging and metrology, and are based on nonlinear dynamics where the output properties must often finely match target performance characteristics. However, in these systems, the availability of control parameters and the means to adjust them in a versatile manner are usually limited. Moreover, finding the ideal parameters for a specific application can become inherently complex. Here, we use an actively-controlled photonic chip to prepare and manipulate patterns of femtosecond optical pulses seeding supercontinuum generation [1]. Taking advantage of machine learning concepts [2], we exploit this access to an enhanced and tunable parameter space and experimentally demonstrate the customization of nonlinear interactions responsible for tailoring supercontinuum properties [3].

Plasmonic metasurfaces provide a compact platform to engineer the wave-front of optical beams by tuning the material and its morphology, hence enabling advanced functionalities in ultra-thin photonic systems [1,2]. In standard metasurfaces, however, the optical response is usually static and fixed by design. An appealing possibility to achieve ultrafast dynamical tuning is given by optically-induced plasmonic systems, where the metallic response of narrow-bandgap semiconductors is driven by high-fluence illumination. Under these conditions, the surface of the semiconductor can be overflown with photo-carriers inducing a transient metallic state [3]. An intriguing question is whether the transient metallization could be employed to dynamically engineer the optical response and to control light-matter interactions on the surface.

Micro-resonator-based frequency combs, or micro-combs, have gained considerable interest in recent years due to their many potential applications such as high-speed communication systems, spectroscopy and ultrafast optical clocks [1]. Most micro-combs systems are based on laser pumped optical parametric oscillation and are typically non-self-starting, requiring a well-defined warm-up strategy involving smart control [2]. An alternative approach to micro-combs is represented by the Filter-Driven Four-Wave Mixing (FD-FWM) laser [3–5], based on a nonlinear micro-resonator nested in a main amplifying fibre cavity. Although this system has demonstrated self-starting regimes, stable operation typically imposes a strict relation between the minimum free-spectral range (FSR) of the main-cavity and the Q-factor of the micro-resonator. The use of longer main-cavity fibre lengths (highly desirable for several positive features, such as a larger gain) results in unrecoverable unstable regimes, i.e. in super-mode instability, which arises from the existence of many oscillating main-cavity modes within each micro-resonator resonance.

One of the major challenges in photonics is the full-wave reconstruction of arbitrary field distributions. Indeed, measuring both the amplitude and the optical delay (or optical phase) entails achieving breakthroughs in a wide range of scenarios, spanning from bio-imaging to material characterisation [1]. Time-Domain Spectroscopy (TDS) is routinely employed to perform field-sensitive measurements at terahertz (THz) frequencies. THz has been widely employed in developing advanced spectroscopy applications, thanks to its non-ionizing nature and to the fact that several materials possess a distinctive THz signature. All these features allow to precisely determine the composition of complex samples with critical implications in several fields, such as in-vivo biological imaging, medical diagnosis, security scanners and manufacturing control [2–3]. Despite the large body of research, however, the limited availability of high-resolution, full-wave imaging devices (i.e. field-sensitive THz cameras) poses a critical technological limit in this promising field.

Nonlinear optics in sub-wavelength structures plays a crucial role in the development of integrated photonics platforms and devices [1]. Surfaces, nanostructures and two-dimensional media are inherently free from longitudinal phase matching constraints and constitute an attractive framework to engineer complex forms of lightmatter interactions [2–3]. Most recent efforts in this area have focused on the generation of frequencies in the optical and infrared regions, e.g., second or third harmonic generation. An open question, however, is whether the broadband frequency conversion enabled by nanoscale nonlinear media could lead to the generation of long-wavelength radiation in a process known as Optical Rectification (OR). To date, OR of ultrafast optical pulses in nonlinear media has been subject of intense research, since it provides a robust and versatile approach to generate and manipulate broadband Terahertz (THz) fields. Using non-centrosymmetric crystals such as ZnTe and LiNbO 3 , large bandwidth THz pulses limited mainly by longitudinal phase-matching constraints, could be achieved [4]. Highly nonlinear Quasi-2D structures represent an intriguing alternative to this popular approach.

The FD-FWM is a proven approach to implement coherent Microcomb generation. Comb repetition rates can be finely controlled in a robust way, while maintaining the coherence during the whole process, whereas full-coherent type-I and type-II combs can be accessible. We present our recent advances towards effective control of optical combs exploiting integrated chip-based resonators.

In this contribution, we will review our recent activities in the development of double nested cavity lasers. Several stable operating regimes can be achieved over a wide range of conditions.

The interplay between ultrafast and slow nonlinearities, like Kerr and thermo-optical nonlinearities, is well-known for generating bistability, self-pulsing and chaotic regimes in optical microcavities. These effects have been observed in different kinds of devices, such as doped silica glass optical microcavities with high refractive index [1], and numerical models have been investigated to provide a description of such dynamics, e.g. in semiconductor nanocavities [2-3]. Specifically, self-pulsing can be explored to generate all-optical stochastic sources, and it has been recently demonstrated with opto-mechanical nonlinearities [4].