Coherent Harmonic Focusing and the Light Extreme

We demonstrate analytically and numerically that focusing of high harmonics produced by the reflection of a few femtosecond laser pulse from a concave plasma surface opens a new way towards unprecedentally high intensities. The key features allowing for boosting of the focal intensity is the harmonic coherency and the small exponent of the power-law decay of the harmonic spectrum. Using the similarity theory and direct particle-in-cell simulations we find that the intensity at the Coherent Harmonic Focus (CHF) scales as $I_{\tiny CHF} \propto a_0^3 I_0$, where $a_0$ and $I_0\propto a_0^2$ are the dimensionless relativistic amplitude and the intensity of the incident laser pulse. The scaling suggests that due to the CHF, the Schwinger intensity limit can be achieved using lasers with $I_0 \approx 10^{22}$ W/cm$^2$. The pulse duration at the focus scales as $\tau_{\tiny CHF} \propto 1/a_0^2$ and reaches the subattosecond range.