Phase-matched extreme-ultraviolet frequency-comb generation

Laser-driven high-order harmonic generation(1,2) provides spatially(3) and temporally(4) coherent tabletop sources of broadband extreme-ultraviolet (XUV) light. These sources typically operate at low repetition rates, frep. 100 kHz, where phase-matched HHG is readily achieved(5,6). However, many applications demand the improved counting statistics or frequency-comb precision afforded by high repetition rates, f(rep) > 10 MHz. Unfortunately, at such high frep, phase matching is prevented by steady-state plasma accumulated in the generation volume(7-11), strongly limiting the XUV average power. Here, we use high-temperature gas mixtures as the generation medium to increase the gas translational velocity, thereby reducing the steady-state plasma in the laser focus. This allows phase-matched XUV emission inside a femtosecond enhancement cavity at f(rep) = 77 MHz, enabling a record generated power of similar to 2 mW in a single harmonic order. This power scaling opens up many demanding applications, including XUV frequency-comb spectroscopy(12,13) of few-electron atoms and ions for precision tests of fundamental physical laws and constants(14-20).