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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.


  1. Yost, D. C. et al. Vacuum-ultraviolet frequency combs from below-threshold harmonics. Nature Phys. 5, 815–820 (2009).

    ADS  Article  Google Scholar 

  2. Krebs, M. et al. Towards isolated attosecond pulses at megahertz repetition rates. Nature Photon. 7, 555–559 (2013).

    ADS  Article  Google Scholar 

  3. Kim, S. et al. High-harmonic generation by resonant plasmon field enhancement. Nature 453, 757–760 (2008).

    ADS  Article  Google Scholar 

  4. Park, I.-Y. et al. Plasmonic generation of ultrashort extreme-ultraviolet light pulses. Nature Photon. 5, 677–681 (2011).

    ADS  Article  Google Scholar 

  5. Sivis, M., Duwe, M., Abel, B. & Ropers, C. Extreme-ultraviolet light generation in plasmonic nanostructures. Nature Phys. 9, 304–309 (2013).

    ADS  Article  Google Scholar 

  6. Sivis, M. & Ropers, C. Generation and bistability of a waveguide nanoplasma observed by enhanced extreme-ultraviolet fluorescence. Phys. Rev. Lett. 111, 085001 (2013).

    ADS  Article  Google Scholar 

  7. Miranda, M. N., Oliveira, P. B., Bernardo, L. M., Kartner, F. X. & Crespo, H. M. Space–time focusing of phase-stabilized nanojoule-level 2.5-cycle pulses to peak intensities >3×1013 W/cm2 at 80 MHz. CLEO Europe (2009).

  8. Rohwer, T. et al. Collapse of long-range charge order tracked by time-resolved photoemission at high momenta. Nature 471, 490–493 (2011).

    ADS  Article  Google Scholar 

  9. Chini, M. et al. Sub-cycle oscillations in virtual states brought to light. Sci. Rep. 3, 1105 (2013).

    Article  Google Scholar 

  10. Tao, H. et al. Ultrafast internal conversion in ethylene. I. The excited state lifetime. J. Chem. Phys. 134, 244306 (2011).

    ADS  Article  Google Scholar 

  11. Corkum, P. B. Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993).

    ADS  Article  Google Scholar 

  12. Power, E. P. et al. XFROG phase measurement of threshold harmonics in a Keldysh-scaled system. Nature Photon. 4, 352–356 (2010).

    ADS  Article  Google Scholar 

  13. Hostetter, J. A., Tate, J. L., Schafer, K. J. & Gaarde, M. B. Semiclassical approaches to below-threshold harmonics. Phys. Rev. A 82, 023401 (2010).

    ADS  Article  Google Scholar 

  14. Toma, E. S., Antoine, Ph., de Bohan, A. & Muller, H. G. Resonance-enhanced high-harmonic generation. J. Phys. B 32, 5843–5852 (1999).

    ADS  Article  Google Scholar 

  15. Wang, X., Chini, M., Cheng, Y., Wu, Y. & Chang, Z. In situ calibration of an extreme ultraviolet spectrometer for attosecond transient absorption experiments. Appl. Opt. 52, 323–329 (2013).

    ADS  Article  Google Scholar 

  16. Mevel, E. et al. Atoms in strong optical fields: evolution from multiphoton to tunnel ionization. Phys. Rev. Lett. 70, 406–409 (1993).

    ADS  Article  Google Scholar 

  17. Sola, I. J. et al. Controlling attosecond electron dynamics by phase-stabilized polarization gating. Nature Phys. 2, 319–322 (2006).

    ADS  Article  Google Scholar 

  18. Burnett, N. H., Kan, C. & Corkum, P. B. Ellipticity and polarization effects in harmonic generation in ionizing neon. Phys. Rev. A 51, R3418 (1995).

    ADS  Article  Google Scholar 

  19. Mashiko, H. et al. Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers. Phys. Rev. Lett. 100, 103906 (2008).

    ADS  Article  Google Scholar 

  20. Gaarde, M. B., Tate, J. L. & Schafer, K. J. Macroscopic aspects of attosecond pulse generation. J. Phys. B 41, 132001 (2008).

    ADS  Article  Google Scholar 

  21. Constant, E. et al. Optimizing high harmonic generation in absorbing gases: model and experiment. Phys. Rev. Lett. 82, 1668–1671 (1999).

    ADS  Article  Google Scholar 

  22. Kung, A. H., Young, J. F. & Harris, S. E. Generation of 1182-Å radiation in phase-matched mixtures of inert gases. Appl. Phys. Lett. 22, 301–302 (1973).

    ADS  Article  Google Scholar 

  23. Mahon, R., McIlrath, T. J., Myerscough, V. P. & Koopman, D. W. Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α. IEEE J. Quantum Electron. 15, 444–451 (1979).

    ADS  Article  Google Scholar 

  24. Hellmann, S., Rossnagel, K., Marczynski-Bühlow, M. & Kipp, L. Vacuum space–charge effects in solid-state photoemission. Phys. Rev. B 79, 035402 (2009).

    ADS  Article  Google Scholar 

  25. Sandberg, R. L. et al. Lensless diffractive imaging using tabletop coherent high-harmonic soft-X-ray beams. Phys. Rev. Lett. 99, 098103 (2007).

    ADS  Article  Google Scholar 

  26. Khan, S. D. et al. Ellipticity dependence of 400 nm-driven high harmonic generation. Appl. Phys. Lett. 99, 161106 (2011).

    ADS  Article  Google Scholar 

  27. Budil, K. S., Saliéres, P., L'Huillier, A., Ditmire, T. & Perry, M. D. Influence of ellipticity on harmonic generation. Phys. Rev. A 48, R3437 (1993).

    ADS  Article  Google Scholar 

  28. Tong, X.-M. & Chu, S.-I. Time-dependent density-functional theory for strong-field multiphoton processes: application to the study of the role of dynamical electron correlation in multiple high-order harmonic generation. Phys. Rev. A 57, 452–461 (1998).

    ADS  Article  Google Scholar 

  29. Telnov, D. A., Sosnova, K. E., Rozenbaum, E. & Chu, S.-I. Exterior complex scaling method in time-dependent density-functional theory: multiphoton ionization and high-order harmonic generation of Ar atoms. Phys. Rev. A 87, 053406 (2013).

    ADS  Article  Google Scholar 

  30. Chu, S.-I. Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields. J. Chem. Phys. 123, 062207 (2005).

    ADS  Article  Google Scholar 

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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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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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