Vacuum-ultraviolet frequency combs from below-threshold harmonics

Abstract

Recent demonstrations of high-harmonic generation (HHG) at very high repetition frequencies (∼100 MHz) may allow for the revolutionary transfer of frequency combs to the vacuumultraviolet range. This advance necessitates unifying optical frequency-comb technology with strong-field atomic physics. Whereas strong-field studies of HHG have often focused on above-threshold harmonic generation (photon energy above the ionization potential), for vacuum-ultraviolet frequency combs an understanding of below-threshold harmonic orders and their generation process is crucial. Here, we present a new and quantitative study of the harmonics 7-13 generated below and near the ionization threshold in xenon gas with an intense 1,070 nm driving field. We show multiple generation pathways for these harmonics that are manifested as on-axis interference in the harmonic yield. This discovery provides a new understanding of the strong-field, below-threshold dynamics under the influence of an atomic potential and allows us to quantitatively assess the achievable coherence of a vacuum-ultraviolet frequency comb generated through below-threshold harmonics. We find that under reasonable experimental conditions, temporal coherence is maintained. As evidence, we present the first explicit vacuum-ultraviolet frequency-comb structure beyond the third harmonic.High-repetition-frequency HHG has recently been enabled through the use of femtosecond enhancement cavities 1,2 . In addition to potentially transferring frequency comb techniques 3,4 to the vacuum-ultraviolet range for possible applications such as direct frequency-comb spectroscopy 5-7 , the enhancementcavity technique allows for greater harmonic photon flux and a near-perfect Gaussian fundamental beam, which provides for exceptionally clean and high signal-to-noise studies of the HHG process itself. Here, we use these techniques and present a new set of experimental and theoretical studies of harmonics 7 to 13, generated below and near the ionization threshold in xenon gas with an intense 1,070 nm laser pulse. These harmonic orders are of great interest for the development of vacuum-ultraviolet frequency combs and it is crucial to understand how fluctuations in the driving-laser intensity influence the pulse-to-pulse coherence properties of the train of vacuum-ultraviolet pulses through the nonlinear HHG process. Production of frequency combs through HHG thus requires a systematic understanding of strong-field atomic physics [8][9][10][11] , but at the same time it provides a good probe for the latter subject.Surprisingly, we find that harmonics as low as the seventh contain several contributions with different intensitydependent phases. Our laser system permits a clean observation of interference between these phase contributions at unprecedented signal-to-noise ratios. In particular, we see experimentally a strong contribution from a component that has a large, intensitydependent phase and we show theoretically that it originates in semi-classical laser-driven continuum dynamics. We ...

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