Coherent focusing of high harmonics: a new way towards the extreme intensities.

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 to unprecedentally high intensities. The key features allowing the boosting of the focal intensity are the harmonics coherency and the small exponent of the power-law decay of the harmonics spectrum. Using similarity theory and direct particle-in-cell simulations, we find that the intensity at the focus scales as I(CHF) alpha a(3)(0)I(0), where a(0) and I(0) alpha a(2)(0) are the dimensionless relativistic amplitude and the intensity of the incident laser pulse. The scaling suggests that due to the coherent harmonic focusing (CHF), the Schwinger intensity limit can be reached using lasers with I(0) approximately 10(22) W/cm(2). The pulse duration at the focus scales as tau(CHF) alpha 1/a(2)(0) and reaches the subattosecond range.