High-harmonic generation from solids


High-harmonic generation in atomic gases has been studied for decades, and has formed the basis of attosecond science. Observation of high-order harmonics from bulk crystals was, however, reported much more recently, in 2010. This Review surveys the subsequent efforts aimed at understanding the microscopic mechanism of solid-state harmonics in terms of what it can tell us about the electronic structure of the source materials, how it can be used to probe driven ultrafast dynamics and its prospects for novel, compact short-wavelength light sources. Although most of this work has focused on bulk materials as the source, recent experiments have investigated high-harmonic generation from engineered structures, which could form flexible platforms for attosecond photonics.

Fig. 1: High-order harmonic generation in ZnO crystals.
Fig. 2: Microscopic mechanisms for atomic and solid-state HHG.
Fig. 3: Recent progress in high harmonics from solids.
Fig. 4: CEP dependence of high-order harmonics from various solid materials.
Fig. 5: The use of engineered solid materials to generate and manipulate high harmonics.

Change history

  • 14 January 2019

    In the version of this Review Article originally published, in Fig. 2b, the label ‘Inter-band current’ should have read ‘Intra-band current’. This error has now been corrected in the online versions.


  1. 1.

    Ferray, M. et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B 21, L31 (1988).

    Article  Google Scholar 

  2. 2.

    Krause, J. L., Schafer, K. J. & Kulander, K. C. High-order harmonic generation from atoms and ions in the high intensity regime. Phys. Rev. Lett. 68, 3535–3538 (1992).

    ADS  Article  Google Scholar 

  3. 3.

    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).

    ADS  Article  Google Scholar 

  4. 4.

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

    ADS  Article  Google Scholar 

  5. 5.

    Reiss, H. R. Complete Keldysh theory and its limiting cases. Phys. Rev. A 42, 1476–1486 (1990).

    ADS  Article  Google Scholar 

  6. 6.

    Itatani, J. et al. Tomographic imaging of molecular orbitals. Nature 432, 867–871 (2004).

    ADS  Article  Google Scholar 

  7. 7.

    McFarland, B. K., Farrell, J. P., Bucksbaum, P. H. & Guhr, M. High harmonic generation from multiple orbitals in N2. Science 322, 1232–1235 (2008).

    ADS  Article  Google Scholar 

  8. 8.

    Baltuška, A. et al. Attosecond control of electronic. Nature 421, 611–615 (2003).

    ADS  Article  Google Scholar 

  9. 9.

    Goulielmakis, E. et al. Real-time observation of valence electron motion. Nature 466, 739–743 (2010).

    ADS  Article  Google Scholar 

  10. 10.

    Schultze, M. Attosecond band-gap dynamics in silicon. Science 346, 1348–1352 (2014).

    ADS  Article  Google Scholar 

  11. 11.

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

    Article  Google Scholar 

  12. 12.

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

    ADS  Article  Google Scholar 

  13. 13.

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

    ADS  Article  Google Scholar 

  14. 14.

    Ndabashimiye, G. Solid-state harmonics beyond the atomic limit. Nature 534, 520–523 (2016).

    ADS  Article  Google Scholar 

  15. 15.

    You, Y. S., Reis, D. A. & Ghimire, S. Anisotropic high-harmonic generation in bulk crystals. Nat. Phys. 13, 345–349 (2017).

    Article  Google Scholar 

  16. 16.

    Kim, H., Han, S., Kim, Y. W., Kim, S. & Kim, S.-W. Generation of coherent extreme-ultraviolet radiation from bulk sapphire crystal. ACS Photon. 4, 1627–1632 (2017).

    Article  Google Scholar 

  17. 17.

    Yoshikawa, N., Tamaya, T. & Tanaka, K. High-harmonic generation in graphene enhanced by elliptically polarized light excitation. Science 356, 736–738 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  18. 18.

    Vampa, G. et al. All-optical reconstruction of crystal band structure. Phys. Rev. Lett. 115, 193603 (2015).

    ADS  Article  Google Scholar 

  19. 19.

    Silva, R. E. F., Blinov, I. V., Rubtsov, A. N., Smirnova, O. & Ivanov, M. High-harmonic spectroscopy of ultrafast many-body dynamics in strongly correlated systems. Nat. Photon. 12, 266–270 (2018).

    ADS  Article  Google Scholar 

  20. 20.

    Wu, M., 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).

    ADS  Article  Google Scholar 

  21. 21.

    Garg, M., Kim, H. Y. & Goulielmakis, E. Ultimate waveform reproducibility of extreme ultraviolet pulses by high harmonic generation in bulk dielectrics. Nat. Photon. 12, 291–296 (2018).

    ADS  Article  Google Scholar 

  22. 22.

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

    ADS  Article  Google Scholar 

  23. 23.

    Park, H. et al. High-order harmonic generations in intense mid IR fields by cascade 3-wave mixing in a fractal-poled LiNbO3 photonic crystal. Opt. Lett. 42, 4020–4023 (2017).

    ADS  Article  Google Scholar 

  24. 24.

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

    ADS  Article  Google Scholar 

  25. 25.

    Huttner, U., Kira, M. & Koch, S. W. Ultrahigh off-resonant field effects in semiconductors. Laser Photon. Rev. 11, 1700049 (2017).

    ADS  Article  Google Scholar 

  26. 26.

    Houston, W. V. Acceleration of electrons in a crystal lattice. Phys. Rev. 57, 184–186 (1940).

    ADS  MathSciNet  Article  Google Scholar 

  27. 27.

    Zener, C. A theory of the electrical breakdown of solid dielectrics. Proc. R. Soc. Lond. A 145, 523–529 (1934).

    ADS  Article  Google Scholar 

  28. 28.

    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, 75330 (2008).

    ADS  Article  Google Scholar 

  29. 29.

    Ghimire, S. et al. Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field. Phys. Rev. Lett. 107, 167407 (2011).

    ADS  Article  Google Scholar 

  30. 30.

    Vampa, G. Theoretical analysis of high-harmonic generation in solids. Phys. Rev. Lett. 113, 73901 (2014).

    ADS  Article  Google Scholar 

  31. 31.

    Wu, M., 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).

    ADS  Article  Google Scholar 

  32. 32.

    Hawkins, P. G., Ivanov, M. Y. & Yakovlev, V. S. Effect of multiple conduction bands on high-harmonic emission from dielectrics. Phys. Rev. A 91, 013405 (2015).

    ADS  Article  Google Scholar 

  33. 33.

    Osika, E. N. et al. Wannier-Bloch approach to localization in high-harmonics generation in solids. Phys. Rev. X 7, 021017 (2017).

    Google Scholar 

  34. 34.

    Brunel, F. Harmonic generation due to plasma effects in a gas undergoing multiphoton ionization in the high-intensity limit. J. Opt. Soc. Am. B 7, 521–526 (1990).

    ADS  Article  Google Scholar 

  35. 35.

    Wu, M., Ghimire, S., Reis, D. A., Schafer, K. J. & Gaarde, M. B. High-harmonic generation from Bloch electrons in solids. Phys. Rev. A 91, 43839 (2015).

    ADS  Article  Google Scholar 

  36. 36.

    Ghimire, S. Generation and propagation of high-order harmonics in crystals. Phys. Rev. A 85, 43836 (2012).

    ADS  Article  Google Scholar 

  37. 37.

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

    ADS  Article  Google Scholar 

  38. 38.

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

    ADS  Article  Google Scholar 

  39. 39.

    Wu, M., Browne, D. A., Schafer, K. J. & Gaarde, M. B. Multi-level perspective on high-order harmonic generation in solids. Phys. Rev. A 94, 063403 (2016).

    ADS  Article  Google Scholar 

  40. 40.

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

    ADS  Article  Google Scholar 

  41. 41.

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

    ADS  Article  Google Scholar 

  42. 42.

    Vampa, G., Ou, Y. S. Y., Iu, H. L., Ghimire, S. & Reis, D. A. Observation of backward high-harmonic emission from solids. Opt. Express 26, 12210–12218 (2018).

    ADS  Article  Google Scholar 

  43. 43.

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

    ADS  Article  Google Scholar 

  44. 44.

    Velotta, R., Hay, N., Mason, M. B., Castillejo, M. & Marangos, J. P. High-order harmonic generation in aligned molecules. Phys. Rev. Lett. 87, 183901 (2001).

    ADS  Article  Google Scholar 

  45. 45.

    You, Y. S., Cunningham, E., Reis, D. A. & Ghimire, S. Probing periodic potential of the crystal via strong-field re-scattering. J. Phys. B 51, 114002 (2018).

    ADS  Article  Google Scholar 

  46. 46.

    Itatani, J. et al. Tomographic imaging of molecular orbitals. Nature 432, 867–871 (2004).

    ADS  Article  Google Scholar 

  47. 47.

    Han, S. et al. High-harmonic generation by field enhanced femtosecond pulses in metal-sapphire nanostructure. Nat. Commun. 7, 13105 (2016).

    ADS  Article  Google Scholar 

  48. 48.

    Vampa, G. et al. Plasmon-enhanced high-harmonic generation from silicon. Nat. Phys. 13, 659–662 (2017).

    Article  Google Scholar 

  49. 49.

    Liu, H. et al. High-harmonic generation from an atomically thin semiconductor. Nat. Phys. 13, 262–265 (2016).

    Article  Google Scholar 

  50. 50.

    Wang, Y. H., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Observation of Floquet-Bloch states on the surface of a topological insulator. Science 342, 453–457 (2013).

    ADS  Article  Google Scholar 

  51. 51.

    Chang, Z., Corkum, P. B. & Leone, S. R. Attosecond optics and technology: progress to date and future prospects [Invited]. J. Opt. Soc. Am. B 33, 1081–1097 (2016).

    ADS  Article  Google Scholar 

  52. 52.

    Saito, N. et al. Observation of selection rules for circularly polarized fields in high-harmonic generation from a crystalline solid. Optica 4, 1333–1336 (2017).

    Article  Google Scholar 

  53. 53.

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

    ADS  Article  Google Scholar 

  54. 54.

    Vampa, G. et al. Strong-field optoelectronics in solids. Nat. Photon. 12, 465–468 (2018).

    ADS  Article  Google Scholar 

Download references


This work is supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, primarily through the Early Career Research Program (S.G.). D.A.R. was supported through AMOS programme.

Author information



Corresponding author

Correspondence to Shambhu Ghimire.

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.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ghimire, S., Reis, D.A. High-harmonic generation from solids. Nature Phys 15, 10–16 (2019). https://doi.org/10.1038/s41567-018-0315-5

Download citation

Further reading


Quick links

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing