With the escalating laser peak power, modulating and detecting the intensity, duration, phase and polarization of ultra-intense laser pulses progressively becomes increasingly arduous due to the limited damage thresholds of conventional optical components. In particular, the generation and detection of ultra-intense vortex lasers pose great challenges for current laser technologies, which has limited the widely potential applications of relativistic vortex lasers in various domains. In this study, we propose to reconstruct the vortex phase and generate and amplify the relativistic vortex lasers via surface plasma holograms (SPHs). By interfering with the object laser and reference laser, SPHs are formed on the target and the phase of the interfering laser is imprinted through the modulation of surface plasma density. In particular, using the quadrature phase-shift interference, the vortex phase of the object laser can be well reconstructed. The generated vortex lasers can be focused and enhanced further by one order of magnitude, up to $1.7\times {10}^{21}$ W/cm${}^2$, which has been demonstrated by full three-dimensional particle-in-cell simulations. For the first time, we provide a practical way to detect the phase of relativistic vortex lasers, which can be applied in large 1–10 PW laser facilities. This will promote future experimental research of vortex-laser–plasma interaction and open a new avenue of plasma optics in the ultra-relativistic regime.

The propagation of multiple ultraintense femtosecond lasers in underdense plasmas is investigated theoretically and numerically. We find that the energy merging effect between two in-phase seed lasers can be improved by using two obliquely incident guiding lasers whose initial phase is $\pi$ and $\pi /2$ ahead of the seed laser. Particle-in-cell simulations show that due to the repulsion and energy transfer of the guiding laser, the peak intensity of the merged light is amplified by more than five times compared to the seed laser. The energy conversion efficiency from all incident lasers to the merged light is up to approximately 60$\%$. The results are useful for many applications, including plasma-based optical amplification, charged particle acceleration and extremely intense magnetic field generation.

Low-density polymer foams pre-ionized by a well-controlled nanosecond pulse are excellent plasma targets to trigger direct laser acceleration (DLA) of electrons by sub-picosecond relativistic laser pulses. In this work, the influence of the nanosecond pulse on the DLA process is investigated. The density profile of plasma generated after irradiating foam with a nanosecond pulse was simulated with a two-dimensional hydrodynamic code, which takes into account the high aspect ratio of interaction and the microstructure of polymer foams. The obtained plasma density profile was used as input to the three-dimensional particle-in-cell code to simulate energy, angular distributions and charge carried by the directional fraction of DLA electrons. The modelling shows good agreement with the experiment and in general a weak dependence of the electron spectra on the plasma profiles, which contain a density up-ramp and a region of near-critical electron density. This explains the high DLA stability in pre-ionized foams, which is important for applications.