High-order harmonic generation (HHG) from relativistically intense laser irradiation of solid-density plasmas provides novel coherent light sources in the extreme-ultraviolet (XUV) to x-ray spectral region with attosecond duration and high intensity even toward the Schwinger limit. However, whether the HHG process and mechanism are effective at extremely high laser intensities in the QED-plasma regime remains unclear, since QED processes, such as discrete synchrotron radiation, quantum radiation reaction, and pair creation, would change the energy partition and particle dynamics. In this work, through particle-in-cell simulations, we numerically demonstrate that the HHG process with the relativistically oscillating mirror mechanism can be scaled to an ultrahigh intensity level of 1024 W/cm2. The high harmonic spectrum, attosecond pulses, and conversion efficiency are not significantly affected by the QED processes. This result is of great benefit to the generation of coherent XUV and x-ray light sources with higher intensity, higher cutoff frequency, and shorter duration.

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