Description
Plasma mirrors are versatile optical elements for manipulating ultra-intense light. In particular, plasma mirrors can be used for high-order harmonic generation (HHG). The irradiation at ultra-high intensities drives relativistic oscillations of the plasma surface, producing harmonics that extend into the extreme ultraviolet (XUV) via the Doppler effect.
Doppler harmonic generation has recently gained attention as a promising approach to amplify PW-class laser intensities by several orders of magnitude [1]. Simulations indicate that operating plasma mirrors in the multi-PW regime could produce intensities exceeding $10^{25}\,$W/cm$^2$, enabling access to the strong-field regime of quantum electrodynamics (SF-QED). In order to access these regimes, driving plasma mirrors at intensities of $10^{22}\,$W/cm$^2$ is necessary. However, this regime is virtually unexplored in experiments.
To study Doppler harmonic generation from plasma mirrors at intensities substantially exceeding $10^{21}\,$W/cm$^2$, the first experiment was conducted at the BELLA PW laser facility LBNL (US). High-order harmonics up to the 40th and 30th orders were observed for 1.3 and $2.4\times10^{21}\,$W/cm$^2$, respectively, but a very low harmonic signal is detected at $6.6\times10^{21}\,$W/cm$^2$.
In this contribution, we present the results of a recent numerical simulation campaign aimed at a reliable modelling plasma mirrors at such extreme intensities [2]. In particular, we have investigated plasma instabilities triggered by the sub-picosecond pedestal preceding the main laser pulse. We examine how the pedestal duration and amplitude influence the efficiency of HHG and provide a detailed characterisation of the resulting instabilities. The simulations reveal a clear decrease in HHG efficiency at higher main-pulse intensities, which is attributed to the increased pedestal intensity and the stronger plasma instabilities it causes. This simulation campaign was crucial for interpreting and understanding the experimental results and demonstrates good agreement with the measurements.
All numerical simulations presented in this work are performed using the Particle-In-Cell code WarpX [3]. WarpX is an open-source, advanced electromagnetic and electrostatic Particle-In-Cell code developed under the High Performance Software Foundation (HPSF).
[1] H. Vincenti, Phys. Rev. Lett. 123, 105001 (2019).
[2] B. Groussin, P. Sikorski et al., arXiv:2602.10709 [physics.plasm-ph] (2026) (submitted to Phys.Rev.Lett., under review).
[3] J.-L. Vay et al., WarpX v 25.10 10.5281/zenodo.17261711 (2025).