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Reporting period: 2019-10-01 to 2021-03-31

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). They are however very difficult to obtain by ‘conventional’ means, often requiring large particle accelerators. UHI physics instead holds the promise of getting these beams from laser-driven table-top sources, with the additional benefit of ultrashort durations, suitable to probe matter with extreme resolutions in both time and space.

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. The ultimate limit of this approach is the so-called 'lambda cubed' regime , where a ‘light bullet’ of lambda/c duration is focused on a focal spot of ≈lambda^2 area, where lambda is the laser wavelength.

In contrast, this project aims at establishing 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. These structured beams will in general consist of light fields E(r,t) and B(r,t) whose direction, amplitude or phase are shaped in space and/or time, such as beams with ultrafast wavefront rotation, or beams carrying orbital angular momentum (OAM). Based on this general paradigm, we will establish 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 will show 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 will 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. This will enable much more stringent comparisons between theory and experiments, and hence contribute to a deeper understanding of the physics of UHI interactions.

B. Control of UHI laser-plasma interactions using structured light beams: we will show 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 will not only drive collective relativistic motion of charges with light as in present experiments, but also finely control 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 (e.g. coupling with surface plasmons, effect of orbital angular momentum of light), and will be essential for the development of new generations of ultrashort sources of particles and light (e.g. new sources of isolated attosecond pulses or electron vortex beams).

To achieve these general goals, we will need to induce sophisticated types of structures on the laser beam, in a large multidimensional space. This has never been achieved so far for femtosecond UHI lasers, because the combination of their large diameters (typically > 50 mm), broad spectra (>50 nm) and high fluences (>100 mJ/cm^2) makes them extremely difficult to manipulate. We have however identified simple ways to induce the sophisticated beam structures required for this project, using limited numbers of optical elements. These elements will often rely on the state-of-the-art of optical manufacturing.

The project, combining experiments with theory and/or simulations, will focus on a set of well-defined objectives, for two main physical systems being key in UHI physics -plasma mirrors and laser-plasma accelerators. This set of objectives aims at demonstrating the strength of the new paradigm of UHI structured light, but each of them can individually lead to important and strong impact results.
Several important results have already been obtained, which have been presented in 9 peer-reviewed scientific publications. As planned in the initial project proposal, most of these publications investigate the use of structured laser beams to drive laser-plasma interactions at extreme laser intensities, aiming at new degrees of control and new methods of measurement. The main aspects investigated so far have been the following:

-Laser-plasma interactions driven by laser beams carrying orbital angular momentum (e.g. Laguerre-Gaussian beams). We have demonstrated experimentally the feasibility of generating such beams at extreme intensities, and we have investigated their interaction with dense plasmas. We have also performed a theoretical study on the interaction of so-called ‘spatio-temporal light springs’ with low density plasmas, and explored its potential for compact laser-driven particle accelerators.

- 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.

-Light bursts with controllable velocity using spatio-temporally shaped laser beams. We have demonstrated theoretically 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 groups especially in the USA.

- Advanced metrology of femtosecond laser beams. We have developed new optical techniques to measure the spatio-temporal structure of femtosecond laser beams, and used these techniques to measure for the first time the complete properties of one of the most powerful femtosecond lasers in operation to date (BELLA laser, USA). 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.
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 structured laser beams for ultrahigh intensity physics. Other results have also already been obtained, which are still under analysis and will be presented in future publications. In particular, we have used different types of structured laser fields to drive ultrahigh intensity interactions with plasma mirrors, and have obtained new physical effects: these include laser fields that are temporally-shaped on the sub-laser-period time scale, radially-polarized laser beams, and laser fields with wavefronts that oscillate on the scale of the laser period. This last scheme has enabled us to perform the first temporal characterization of attosecond pulses generated by ultraintense laser pulses on dense plasmas, which was one of the major objectives of the project –and probably the most challenging one.
Other projects objectives are still being addressed and are not totally fufilled yet. This includes all objectives related to the attosecond lighthouse scheme. Numerical studies have been performed and have provided promising results. Experiments on this aspect will take place by the end of the project, at Laboratoire d'Optique Appliquee (the second partner of the project).