Complementary diagnostics of high-intensity femtosecond laser pulses via vacuum acceleration of protons and electrons

Taking advantage of complementary measurements of the characteristics of both protons and electrons accelerated by a laser in a vacuum, we propose an advanced diagnostics of the parameters of the tightly focused high-intensity femtosecond laser pulse. The laser field description is based on Stratton-Chu integrals, which allow simulating laser pulses with different spatial-temporal profiles focused by an off-axis parabolic mirror down to the diffraction limit. The free particles, whose dynamics are calculated by the test particle method, are accelerated from a rarefied gas (almost a vacuum). We analyze the dependence of the particle spectra on the laser parameters: the laser peak intensity, focal spot size, and pulse duration. The results show that diagnostics obtained by simultaneously using protons and electrons allow increasing the estimation accuracy of measuring the focal spot size and the peak intensity and thus allow evaluating the laser pulse duration in the femtosecond range. Our proposal is a response to the urgent need to measure pulse durations in the focal spot for new PW-level class lasers of super-short duration up to similar to 10 to 20 fs, which clearly demonstrate a current trend in laser technology.