In the past years, there has been a growing interest in innovative applications of radially polarized laser beams. Among them, the particular field of laser-driven electron acceleration has received much attention. Recent developments in high-power infrared laser sources at the INRS Advanced Laser Light Source (Varennes, Qc, Canada) allowed the experimental observation of a quasi-monoenergetic 23-keV electron beam produced by a radially polarized laser pulse tightly focused into a low density gas. Theoretical analyses suggest that the production of collimated attosecond electron pulses is within reach of the actual technology. Such an ultrashort electron pulse source would be a unique tool for fundamental and applied research. In this paper, we propose an overview of this emerging topic and expose some of the challenges to meet in the future.

We propose a simple laser-driven electron acceleration scheme based on tightly focused radially polarized laser pulses for the production of femtosecond electron bunches with energies in the few-hundreds-of-keV range. In this method, the electrons are accelerated forward in the focal volume by the longitudinal electric field component of the laser pulse. Three-dimensional test-particle and particle-in-cell simulations reveal the feasibility of generating well-collimated electron bunches with an energy spread of 5% and a temporal duration of the order of 1 fs. These results offer a route towards unprecedented time resolution in ultrafast electron diffraction experiments.

We introduce a microscopic particle-in-cell approach that allows bridging the microscopic and macroscopic realms of laser-driven plasma physics. As a first application, resonantly driven cluster nanoplasmas are investigated. Our analysis reveals an attosecond plasma-wave dynamics in clusters with radii R$\simeq${}30\,\,nm. The plasma waves are excited by electrons recolliding with the cluster surface and travel toward the center, where they collide and break. In this process, energetic electron hot spots are generated along with highly localized attosecond electric field fluctuations, whose intensity exceeds the driving laser by more than 2 orders of magnitude. The ionization enhancement resulting from both effects generates a strongly nonuniform ion charge distribution. The observed nonlinear plasma-wave phenomena have a profound effect on the ionization dynamics of nanoparticles and offer a route to extreme nanoplasmonic field enhancements.

The dynamics of solid-density nanoplasmas driven by intense lasers takes place in the strongly-coupled plasma regime, where collisions play an important role. The microscopic particle-in-cell method has enabled the complete classical electromagnetic description of these processes. The theoretical foundation of the approach and its relation to existing methods are reviewed. Selected applications to laser cluster processes are presented that have been inaccessible to numerical simulation so far.

Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but it tends to be unstable and inappropriate for studying strong-field phenomena like laser filamentation. In this paper, we show that nonlinear susceptibility can be provided instead by a harmonic oscillator driven by a nonlinear force, chosen in a way to reproduce the polarization obtained from the solution of the quantum mechanical two-level equations. The resulting saturable, nonlinearly-driven, harmonic oscillator model reproduces quantitatively the quantum mechanical solutions of harmonic generation in the under-resonant limit, up to the 9th harmonic. Finally, we demonstrate that fully explicit leapfrog integration of the saturable harmonic oscillator is stable, even for the intense laser fields that characterize laser filamentation and high harmonic generation.

Using three-dimensional particle-in-cell (3DPIC) simulations, we show that few-MeV electrons can be produced by tightly focusing few-cycle radially-polarized laser pulses in a low-density atomic gas. In particular, it is observed that for the few-TW laser power needed to reach relativistic electron energies, longitudinal attosecond microbunching occurs naturally, resulting in femtosecond structures with high-contrast attosecond density modulations. The 3DPIC simulations show that in the relativistic regime the leading pulse of these attosecond substructures survives to propagation over extended distances, suggesting that it could be delivered to a distant target, with the help of a properly designed transport beamline.