Phase-matched high-order harmonic generation in pre-ionized noble gases

One of the main difficulties of efficiently generating high-order harmonics in long neutral-gas targets is to reach the phase-matching conditions. The issue is that the medium cannot be sufficiently ionized by the driving laser due to plasma defocusing. We propose a method to improve the phase-matching by pre-ionizing the gas using a weak capillary discharge. We have demonstrated this mechanism, for the first time, in absorption-limited XUV generation by an 800 nm femtosecond laser in argon and krypton. The ability to control phase-mismatch is confirmed by an analytical model and numerical simulations of the entire generation process. Our method allows to increase the efficiency of the harmonic generation significantly, paving the way towards photon-hungry applications of these compact short-wavelength sources.