Fundamental limit of intensity scaling for harmonic generation on plasma mirrors

Plasma mirrors have the potential to considerably boost the intensity of ultra-intense laser pulses through high-order harmonic generation, offering a promising route to the extreme fields required for probing the strong-field regime of quantum electrodynamics (SF-QED). This prospect relies on the favorable scaling of harmonic generation with increasing laser intensity, a longstanding assumption that has remained untested at extreme intensities. Combining the first measurements of Doppler harmonic generation approaching $10^{22}\,\mathrm{W/cm^2}$ with advanced particle-in-cell modeling, our study reveals fundamental limitations to this scaling. We notably observe a strong reduction of the harmonic yield as the laser intensity is increased, and show using simulations that this originates from the interaction of the sub-picosecond laser pedestal with the plasma mirror. This pedestal drives a rapid evolution of the plasma surface, through radiation-pressure compression and surface modulations, which progressively suppress harmonic generation. By extending our simulations up to intensities of $10^{23}\,\mathrm{W/cm^2}$, we show that this evolution accelerates strongly with increasing intensity, eventually leading to plasma mirror disruption on the timescale of the main laser pulse itself, making pulse duration, in addition to temporal contrast, a second key parameter for efficient harmonic generation. These results reveal the fundamental limits of the intensity scaling of harmonic generation from plasma mirrors and establish the conditions required to preserve efficient harmonic generation at extreme intensities, providing critical guidance for their use as intensity boosters toward the SF-QED regime.