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 1 × 1013 W cm−2, which is achievable directly from few-cycle femtosecond oscillators with nanojoule energy7.

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Figure 1: Resonance-enhanced structures in below-threshold harmonic generation.
Figure 2: Strong-field control of resonance-enhanced structures.
Figure 3: Phase-matching of resonance-enhanced structures.
Figure 4: Resonance-assisted phase-matching.


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This work was funded by the Defense Advanced Research Projects Agency (DARPA) program in ultrafast laser science and engineering (PULSE) programme through a grant from Aviation and Missile Research, Development, and Engineering Center (AMRDEC), by the US Army Research Office (grant no. W911 NF-12-1-0456), and by the National Science Foundation (grant no. 106860). D.A.T. and S.-I.C. were partially supported by the US Department of Energy. P.-C.L., J.H. and S.-I.C. would also like to acknowledge the partial support of the National Science Council of Taiwan and National Taiwan University (grants nos 103R104021 and 103R8700-2).

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M.C. and Z.C. conceived the study. M.C., X.W. and Y.C. designed the apparatus, performed the experiments and analysed the data. Y.W. and E.C. contributed to the carrier-envelope phase-dependent measurements and absolute energy calibration. M.C., H.W. and Z.C. developed the phase-matching model and interpreted the results. J.H. and D.A.T. performed the single-atom time-dependent Schrödinger equation calculations, while P.-C.L. performed the macroscopic calculations. The theoretical effort was coordinated by S.-I.C. All authors contributed to writing and editing the manuscript.

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Correspondence to Zenghu Chang.

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The authors declare no competing financial interests.

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Chini, M., Wang, X., Cheng, Y. et al. Coherent phase-matched VUV generation by field-controlled bound states. Nature Photon 8, 437–441 (2014).

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