Coherent phase-matched VUV generation by field-controlled bound states

The generation of high-order harmonics1 and attosecond pulses2 at ultrahigh repetition rates (>1 MHz) promises to revolutionize ultrafast spectroscopy. Such vacuum ultraviolet (VUV) and soft X-ray sources could potentially be driven directly by plasmonic enhancement of laser pulses from a femtosecond oscillator3,4, but recent experiments suggest that the VUV signal is actually dominated by incoherent atomic line emission5,6. Here, we demonstrate a new regime of phase-matched below-threshold harmonic generation, for which the generation and phase matching is enabled only near resonance structures of the atomic target. The coherent VUV line emission exhibits low divergence and quadratic growth with increasing target density up to nearly 1,000 torr mm and can be controlled by the sub-cycle field of a few-cycle driving laser with an intensity of only ∼13 10 W cm, which is achievable directly from few-cycle femtosecond oscillators with nanojoule energy7. High-order harmonic generation (HHG) has been the enabling technology for ultrafast science in the VUV and soft-X-ray spectral regions. Recently, ultrafast sources of below-threshold harmonics1,3, with photon energies below the target ionization potential, have been demonstrated. Such harmonics are critical to the extension of time-resolved photoemission spectroscopy8 to megahertz repetition rates and to the development of high-average-power VUV sources, because they can be generated with relatively low driving laser intensities ( 1× 10 W cm). Ultrafast VUV sources of low-order harmonics are also critical tools for studying wave packet dynamics in bound states of atoms9 and molecules10. However, compared to the high-order above-threshold harmonics, which have been extensively studied, little attention has been devoted to the development and characterization of below-threshold harmonic sources. Although below-threshold harmonic generation is largely incompatible with the three-step model of HHG11, recent experiments1,12 indicate that below-threshold harmonics can arise from a non-perturbative process. This non-perturbative generation mechanism has been attributed to negative energy returns of electron trajectories initiated by over-the-barrier ionization and driven by the oscillating laser field13. However, such semi-classical treatment minimizes the influence of the target atom, an approach that may not be valid for below-threshold harmonics, where resonance enhancement has been observed for moderate driving laser intensities14. Here, we uncover a novel regime of below-threshold harmonic generation accompanied by bright, coherent VUV line emission. The coherent VUV source results from the interaction of moderately intense few-cycle driving laser pulses with atomic targets, wherein below-threshold harmonics are enhanced near atomic resonances. In contrast to the incoherent plasma line emission observed in HHG with high laser intensities or with plasmonic enhancement5,6, the resonance-enhanced VUV emission is spatially coherent, with high conversion efficiency and phase-matched growth. We further find that the VUV emission exhibits non-perturbative behaviour and can be controlled by the field of the driving laser. Because the VUV source requires few-cycle driving lasers with an intensity of only 1× 10 W cm, it is readily extendable to ultrahigh repetition rates with commercially available Ti:sapphire oscillators7. In the experiment, below-threshold harmonics were generated from argon and the angularly resolved VUV spectrum was measured using a flat-field grating spectrometer15. The harmonic generation was driven with few-cycle ( 5 fs) near-infrared ( 730 nm) laser pulses, loosely focused to moderate intensities ( 1× 10 to 1× 10 W cm) sufficient to generate harmonics around the ionization threshold, but not so high as to destroy the atomic resonances16. The use of few-cycle driving lasers results in spectrally broad harmonics, and multiple resonances can be observed within a single harmonic. Figure 1a shows the spectrally and angularly resolved VUV signal in the vicinity of the 9th and 11th harmonics with a driving laser intensity of (3.3+0.3)× 10 W cm and a target pressure–length product of 10 torr mm. Whereas the 11th harmonic is above the argon ionization threshold (Ip1⁄4 15.76 eV), the 9th harmonic spans photon energies both above and below threshold. Below threshold, the 9th harmonic exhibits narrow-linewidth spectral enhancements in the vicinity of the atomic resonances. Figure 1b shows the evolution of these resonance-enhanced structures (RESs) as a function of the driving laser intensity within three different regimes. At relatively low intensities ( 1× 10 W cm to 3× 10 W cm), the RESs exhibit narrow linewidths and dominate the harmonic spectrum. For intensities between 3× 10 W cm and 8× 10 W cm, the above-threshold harmonic emission becomes comparable to the RESs and the lines in general become shifted and broadened until no resonances can be observed at intensities higher than 1× 10 W cm. The positions of the RESs agree qualitatively with the resonance energies of argon, and the resonance enhancement is further confirmed by below-threshold harmonic generation in neon and xenon gases, and by numerical solution of the timedependent Schrödinger equation (see Supplementary Section ‘Simulated harmonic spectra’).