Phase-matched extreme-ultraviolet frequency-comb generation

Abstract

Laser-driven high-order harmonic generation 1,2 (HHG) provides tabletop sources of broadband extreme-ultraviolet (XUV) light with excellent spatial 3 and temporal 4 coherence. These sources are typically operated at low repetition rates, f rep 100 kHz, where phase-matched frequency conversion into the XUV is readily achieved 5,6 . However, there are many applications that demand the improved counting statistics or frequency-comb precision afforded by operation at high repetition rates, f rep > 10 MHz. Unfortunately, at such high f rep , phase matching is prevented by the accumulated steady-state plasma in the generation volume 7-11 , setting stringent limitations on the XUV average power. Here, we use gas mixtures at high temperatures as the generation medium to increase the translational velocity of the gas, thereby reducing the steady-state plasma in the laser focus. This allows phase-matched XUV emission inside a femtosecond enhancement cavity at a repetition rate of 77 MHz, enabling a record generated power of ∼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 .The highly-nonlinear HHG process requires peak laser intensities around 10 14 W/cm 2 , which necessitates large laser pulse energies 10 µJ, and short pulse durations 100 fs, as typically reached with low repetition rate, chirped-pulse amplified 21 laser systems. However, high repetition rates are desirable for applications such as photoelectron spectroscopy 22-24 and microscopy 25 as well as electron-ion coincidence spectroscopy 26,27 , which are limited by counting detection or space-charge effects to few XUV ionization events per shot. Most notably, precision frequency-comb spectroscopy 12,13 requires f rep 10 MHz in order to stabilize the comb. Recent efforts allowed HHG to be directly driven at f rep 1 MHz, using either the direct output of a high-power oscillator 22,28 or the coherent combination of several fibre amplifiers 29,30 . Achieving the necessary intensity for HHG with f rep 10 MHz requires lasers with average power in the kW range. Apart from one demonstration at 20 MHz, where the measured XUV power was extremely low 31 , higher repetition rates up to 250 MHz 32 have been facilitated only by using passive enhancement cavities, which store ∼10 kW of laser power, where a gas jet is introduced at an intracavity focus 7,10-12,33-35 .In a macroscopic extended medium, efficient HHG requires matching the phase velocities of the generating laser and the generated fields. This can be achieved by balancing neutral and plasma dispersion, the geometric phase shift due to focusing (the Gouy phase), and the HHG intrinsic dipole phase 5,36 . Achieving this balance becomes increasingly challenging as the repetition rate increases above ∼10 MHz. The reason for this difficulty is that the plasma generated by one pulse does not have time to clear the focal volume before t...

Frequency comb spectroscopy

“…The approach is complex, as it also requires suitable out--coupling of the ultraviolet light and optimization of phase-matching effects that control the build--up of the harmonic signal over the interaction length. Recently, a record average power of 0.7 mW for a harmonic at 63 nm (4,760 THz) has been reported 46 at a repetition frequency of 77 MHz, using a swept cavity.…”

Cavity-enhanced noncollinear high-harmonic generation

“…This led to the first space-charge-free PES experiments at multi-MHz repetition rates [8,9], in particular also with attosecond temporal resolution [8]. Significant efforts have addressed the understanding of cavity-enhanced HHG conversion efficiency limitations related to plasma nonlinearity [10][11][12] and plasma cumulative effects [13,14]. Accelerating the gas to provide (nearly) single-pass conditions even at several tens of MHz has been shown to strongly mitigate the latter limitation, resulting in mW-level VUV frequency combs [13].…”

“…Significant efforts have addressed the understanding of cavity-enhanced HHG conversion efficiency limitations related to plasma nonlinearity [10][11][12] and plasma cumulative effects [13,14]. Accelerating the gas to provide (nearly) single-pass conditions even at several tens of MHz has been shown to strongly mitigate the latter limitation, resulting in mW-level VUV frequency combs [13]. In addition, novel, nonlinearity-optimized ultrashort-pulse enhancement regimes [12,15] promise a path to circumvent the blueshift-related intensity clamping [10][11][12].…”

Characterization of high-harmonic emission from ZnO up to 11 eV pumped with a Cr:ZnS high-repetition-rate source

“…Coherent addition of successive pulses in the train then leads to the required field enhancement; however, the need for stable phase-locked operation of the cavity renders these experiments extremely challenging. Additional limitations imposed by the dispersion of the ionized gas have only been circumvented recently [9]. Intense development of high average power MHz-rate sources has recently enabled extra-cavity high-harmonic generation with a thin-disk oscillator [10], and fs fiber lasers have also been used up to 0.6 MHz [11].…”