Periodic Reporting for period 4 - ExCoMet (CONTROLLING AND MEASURING RELATIVISTIC MOTION OF MATTER WITH ULTRAINTENSE STRUCTURED LIGHT) Reporting period: 2021-04-01 to 2021-12-31 Summary of the context and overall objectives of the project One of the major achievements of Optics in the last decades has been the generation of light pulses of extremely short duration, down to attoseconds (1 as=10^-18 s). In the femtosecond range (1 fs=10^-15 s), these pulses are now produced with sufficient energies to expose matter to considerable light intensities, exceeding 10^21 W/cm^2. This has opened the development of Ultra-High Intensity (UHI) Physics, a quickly growing research field that investigates the interaction of these incredibly intense lasers with matter. When such UHI laser beams interacts with a target of any kind, a plasma is instantly created due to the strong ionization of the target. In this regime of very short time scales and extreme intensities, the physics of the subsequent laser-plasma interaction is very different from the one at play in more ‘conventional’ laser-produced plasmas. First, when the laser intensity exceeds typically 10^18 W/cm^2, the laser-induced motion of the electrons in the plasma becomes relativistic. Second, the plasma dynamics is largely dominated by the collective ‘coherent’ motion of large numbers of electrons, directly driven by the light fields E(r,t) and B(r,t). The elementary laws that govern such collective interactions are well known, but from the point of view of fundamental physics the challenge here is to reach a detailed understanding of the key processes hidden behind their apparent complexity. This is a prerequisite to fulfil the ultimate goal of this research field, which is to drive and control collective relativistic motion of matter with light. Such a control is not only of fundamental interest; it also has potential ground-breaking applications in different fields. Indeed, as a result of the collective relativistic motion of charges, ultrashort bursts of coherent light are emitted by the plasma electrons and beams of high-energy particles (electrons or ions) are expelled from the plasma. Because the laser field is so huge, particles can reach relativistic energies in very short distances before being expelled, and the light they emit extends up to the X-ray range. Such beams of high-energy photons and particles are known to be of high interest for many research fields, as probes of matter on very small scales. They also have societal applications, e.g. for non-destructive testing, or in medicine, for imaging or therapy (e.g. cancer protontherapy). Until now, advances in Ultra-High Intensity Physics have largely relied on a quest for the highest laser intensities, pursued by pushing the technology to its limits (highest possible laser pulse energy, focused to a diffraction-limited focal spot, with a Fourier-transform limited pulse duration), in order to reach more extreme interaction regimes. In contrast, this project has established a new paradigm in Ultra-High Intensity Physics, by demonstrating the huge potential of using sophisticated ‘structured’ laser beams to drive UHI laser plasma-interactions –in other words, the potential of intentionally ‘distorting’ the laser field in space-time in controlled ways, at the expense of only slight reductions in laser intensities. Based on this general paradigm, we have established two novel concepts, which will impact both the physics of UHI interactions and their foreseen applications: A. Metrology of the plasma dynamics using structured light beams: we have shown that by measuring the response of the system to structured laser fields, time- and space-resolved information on the collective charge dynamics driven by the laser field in the plasma can be accessed, down to the attosecond (sub-laser cycle) and sub-micrometre temporal and spatial scales on which the laser-driven plasma dynamics occurs. This new approach for the metrology of UHI interactions partially solve one of the main present issues of UHI physics, by bridging the considerable gap that separates the detailed predictions of numerical simulations or models, from the much more limited ‘integrated’ information that can be collected in experiments, due to the insufficient spatial and temporal resolutions of measurements. B. Control of UHI laser-plasma interactions using structured light beams: we have shown that structured laser fields can be exploited to introduce new physics in UHI experiments, and can provide advanced degrees of freedom to achieve the ultimate goal of UHI physics, i.e. controlling the relativistic motion of charges with light. In other words, we have not only driven collective relativistic motion of charges with light as in previous experiments, but we have also finely controlled this motion by using structured laser fields as an advanced control knob. This improved control will make it possible to investigate new physical effects in UHI interactions, and will be essential for the development of new generations of ultrashort sources of particles and light . The project, combining experiments with theory and/or simulations, has focused on the two main physical systems being key in UHI physics -plasma mirrors and laser-plasma accelerators. The obtained results have clearly demonstrated the strength of the new paradigm of UHI structured light. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far Several important results have been obtained, which have been presented in 21 peer-reviewed scientific publications. The main outcomes have been the following:- Advanced metrology of femtosecond laser beams. We have developed new optical techniques to measure the spatio-temporal structure of femtosecond laser beams. These developments have led to a technology transfer agreement with a company that is now commercializing a measurement device based on one of the techniques we have demonstrated. In the final part of the project, we have used these new metrology tools to carry out the very first extensive experimental survey of spatio-temporal couplings in high-power ultrashort lasers.-Laser-plasma interactions driven by laser beams carrying orbital angular momentum. We have demonstrated experimentally the feasibility of generating such beams at extreme intensities, and we have investigated their interaction with dense plasmas.-Light bursts with controllable velocity using spatio-temporally shaped laser beams. We have demonstrated theoretically and then experimentally how to shape a femtosecond laser in space and time to produce light bursts that propagate at arbitrary and controllable velocity in vacuum. This theoretical prediction has been followed by considerable work, both theoretical and experimental, by other research groups especially in the USA. This should become a major scheme for the control of laser-driven particle acceleration..- Advanced metrology of laser-plasma interactions using structured laser beams. We have used spatio-temporally shaped laser beams to control the surface shape of dense plasmas, and have exploited these shaped plasmas to measure the spatial properties of the short-wavelength light that they generate, using an advanced technique known as ptychography. In a second step, we have exploited spatio-temporally shaped ultrashort laser beams to measure the spatio-temporal structure of attosecond pulses generated from plasmas mirrors, for the very first time. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) All results obtained so far are beyond the state of the art since, prior to this project, hardly any experiment and very few theoretical studies had been carried out on the use of spatio-temporally structured laser beams for ultrahigh intensity physics. Temporal profile of attosecond pulses generated from plasma mirrors, measured for the first time.