Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz


Optical waveforms of light reproducible with subcycle precision underlie applications of lasers in ultrafast spectroscopies, quantum control of matter and light-based signal processing. Nonlinear upconversion of optical pulses via high-harmonic generation in gas media extends these capabilities to the extreme ultraviolet (EUV). However, the waveform reproducibility of the generated EUV pulses in gases is inherently sensitive to intensity and phase fluctuations of the driving field. We used photoelectron interferometry to study the effects of intensity and carrier-envelope phase of an intense single-cycle optical pulse on the field waveform of EUV pulses generated in quartz nanofilms, and contrasted the results with those obtained in gas argon. The EUV waveforms generated in quartz were found to be virtually immune to the intensity and phase of the driving field, implying a non-recollisional character of the underlying emission mechanism. Waveform-sensitive photonic applications and precision measurements of fundamental processes in optics will benefit from these findings.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Photoelectron interferometric tracing of the phase of EUV pulses.
Fig. 2: EUV waveform dependence on intensity of optical driver.
Fig. 3: CEP effects of driving field on EUV waveform.


  1. 1.

    Baltuska, A. et al. Attosecond control of electronic processes by intense light fields. Nature 421, 611–615 (2003).

  2. 2.

    Hassan, M. T. et al. Optical attosecond pulses and tracking the nonlinear response of bound electrons. Nature 530, 66–70 (2015).

  3. 3.

    Schubert, O. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photon. 8, 119–123 (2014).

  4. 4.

    Rybka, T. et al. Sub-cycle optical phase control of nanotunnelling in the single-electron regime. Nat. Photon. 10, 667–670 (2016).

  5. 5.

    Wirth, A. et al. Synthesized light transients. Science 334, 195–200 (2011).

  6. 6.

    Huang, S. W. et al. High-energy pulse synthesis with sub-cycle waveform control for strong-field physics. Nat. Photon. 5, 475–479 (2011).

  7. 7.

    Sansone, G. et al. Electron localization following attosecond molecular photoionization. Nature 465, 763–766 (2010).

  8. 8.

    Kling, M. F. et al. Control of electron localization in molecular dissociation. Science 312, 246–248 (2006).

  9. 9.

    Huismans, Y. et al. Time-resolved holography with photoelectrons. Science 331, 61–64 (2011).

  10. 10.

    Schiffrin, A. et al. Optical-field-induced current in dielectrics. Nature 493, 70–74 (2013).

  11. 11.

    Higuchi, T., Heide, C., Ullmann, K., Weber, H. B. & Hommelhoff, P. Light-field-driven currents in graphene. Nature 550, 224–228 (2017).

  12. 12.

    Sivis, M. et al. Tailored semiconductors for high-harmonic optoelectronics. Science 357, 303–306 (2017).

  13. 13.

    Goulielmakis, E. et al. Single-cycle nonlinear optics. Science 320, 1614–1617 (2008).

  14. 14.

    Sansone, G. et al. Isolated single-cycle attosecond pulses. Science 314, 443–446 (2006).

  15. 15.

    Li, J. et al. 53-attosecond X-ray pulses reach the carbon K-edge. Nat. Commun. 8, 186 (2017).

  16. 16.

    Cavalieri, A. L. et al. Attosecond spectroscopy in condensed matter. Nature 449, 1029–1032 (2007).

  17. 17.

    Schultze, M. et al. Delay in photoemission. Science 328, 1658–1662 (2010).

  18. 18.

    Guenot, D. et al. Measurements of relative photoemission time delays in noble gas atoms. J. Phys. B 47, 245602 (2014).

  19. 19.

    Wang, H. et al. Practical issues of retrieving isolated attosecond pulses. J. Phys. B 42, 134007 (2009).

  20. 20.

    Gagnon, J. & Yakovlev, V. S. The robustness of attosecond streaking measurements. Opt. Express 17, 17678–17693 (2009).

  21. 21.

    Peng, L. Y. & Starace, A. F. Attosecond pulse carrier-envelope phase effects on ionized electron momentum and energy distributions. Phys. Rev. A 76, 043401 (2007).

  22. 22.

    Lewenstein, M., Salières, P. & L’Huillier, A. Phase of the atomic polarization in high-order harmonic generation. Phys. Rev. A 52, 4747–4754 (1995).

  23. 23.

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

  24. 24.

    Corsi, C., Pirri, A., Sali, E., Tortora, A. & Bellini, M. Direct interferometric measurement of the atomic dipole phase in high-order harmonic generation. Phys. Rev. Lett. 97, 023901 (2006).

  25. 25.

    Sansone, G. et al. Measurement of harmonic phase differences by interference of attosecond light pulses. Phys. Rev. Lett. 94, 193903 (2005).

  26. 26.

    Sansone, G. et al. Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime. Phys. Rev. Lett. 92, 113904 (2004).

  27. 27.

    Haworth, C. A. et al. Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval. Nat. Phys. 3, 52–57 (2007).

  28. 28.

    Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011).

  29. 29.

    Vampa, G. et al. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015).

  30. 30.

    Luu, T. T. et al. Extreme ultraviolet high-harmonic spectroscopy of solids. Nature 521, 498–502 (2015).

  31. 31.

    Garg, M. et al. Multi-petahertz electronic metrology. Nature 538, 359–363 (2016).

  32. 32.

    Langer, F. et al. Symmetry-controlled temporal structure of high-harmonic carrier fields from a bulk crystal. Nat. Photon. 11, 227–231 (2017).

  33. 33.

    Hohenleutner, M. et al. Real-time observation of interfering crystal electrons in high-harmonic generation. Nature 523, 572–575 (2015).

  34. 34.

    Higuchi, T., Stockman, M. I. & Hommelhoff, P. Strong-field perspective on high-harmonic radiation from bulk solids. Phys. Rev. Lett. 113, 213901 (2014).

  35. 35.

    Vampa, G. et al. Theoretical analysis of high-harmonic generation in solids. Phys. Rev. Lett. 113, 073901 (2014).

  36. 36.

    Golde, D., Meier, T. & Koch, S. W. High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations. Phys. Rev. B 77, 075330 (2008).

  37. 37.

    Golde, D., Meier, T. & Koch, S. W. Microscopic analysis of extreme nonlinear optics in semiconductor nanostructures. J. Opt. Soc. Am. B 23, 2559–2565 (2006).

  38. 38.

    You, Y. S. et al. Laser waveform control of extreme ultraviolet high harmonics from solids. Opt. Lett. 42, 1816–1819 (2017).

  39. 39.

    Hammond, T. J. et al. Integrating solids and gases for attosecond pulse generation. Nat. Photon. 11, 594–599 (2017).

  40. 40.

    You, Y. S. et al. High-harmonic generation in amorphous solids. Nat. Commun. 8, 724 (2017).

  41. 41.

    Liu, C. D. et al. Carrier-envelope phase effects of a single attosecond pulse in two-color photoionization. Phys. Rev. Lett. 111, 123901 (2013).

  42. 42.

    Goulielmakis, E. et al. Direct measurement of light waves. Science 305, 1267–1269 (2004).

  43. 43.

    He, P. L., Ruiz, C. & He, F. Carrier-envelope-phase characterization for an isolated attosecond pulse by angular streaking. Phys. Rev. Lett. 116, 203601 (2016).

  44. 44.

    Benko, C. et al. Extreme ultraviolet radiation with coherence time greater than 1 s. Nat. Photon. 8, 530–536 (2014).

  45. 45.

    Lewenstein, M., Balcou, P., Ivanov, M. Y., L’Huillier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994).

  46. 46.

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

  47. 47.

    Schafer, K. J., Yang, B., Dimauro, L. F. & Kulander, K. C. Above threshold ionization beyond the high harmonic cutoff. Phys. Rev. Lett. 70, 1599–1602 (1993).

  48. 48.

    Wu, M. X., Ghimire, S., Reis, D. A., Schafer, K. J. & Gaarde, M. B. High-harmonic generation from Bloch electrons in solids. Phys. Rev. A 91, 043839 (2015).

  49. 49.

    Ott, C. et al. Strong-field spectral interferometry using the carrier-envelope phase. New J. Phys. 15, 073031 (2013).

  50. 50.

    Fordell, T., Miranda, M., Arnold, C. L. & L’Huillier, A. High-speed carrier-envelope phase drift detection of amplified laser pulses. Opt. Express 19, 23652–23657 (2011).

  51. 51.

    Kruger, M., Schenk, M. & Hommelhoff, P. Attosecond control of electrons emitted from a nanoscale metal tip. Nature 475, 78–81 (2011).

  52. 52.

    Herink, G., Solli, D. R., Gulde, M. & Ropers, C. Field-driven photoemission from nanostructures quenches the quiver motion. Nature 483, 190–193 (2012).

  53. 53.

    Piglosiewicz, B. et al. Carrier-envelope phase effects on the strong-field photoemission of electrons from metallic nanostructures. Nat. Photon. 8, 37–42 (2014).

Download references


We thank D. Bauer and C. Gohle for discussions. This work was supported by the Max Planck Society, a European Research Council grant (Attoelectronics-258501), the Deutsche Forschungsgemeinschaft, the Cluster of Excellence, Munich Centre for Advanced Photonics, and the European Research Training Network (MEDEA-641789).

Author information




M.G. and H.Y.K. conducted the experiments; M.G. and E.G. conceived the experiments. E.G. planned the experiments and supervised the project; all authors interpreted data and contributed to the preparation of the manuscript.

Corresponding author

Correspondence to E. Goulielmakis.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Photoelectron interferometry of ATI- and EUV-generated photoelectrons, semiclassical modelling of EUV emission in quartz and argon, and the direct link between the formed interference fringes and the phase of the EUV pulse.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Garg, M., Kim, H.Y. & Goulielmakis, E. Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz. Nature Photon 12, 291–296 (2018). https://doi.org/10.1038/s41566-018-0123-6

Download citation

Further reading