Review Article | Published:

High-harmonic generation from solids

Abstract

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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

References

  1. 1.

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

  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).

  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).

  4. 4.

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

  5. 5.

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

  6. 6.

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

  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).

  8. 8.

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

  9. 9.

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

  10. 10.

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

  11. 11.

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

  12. 12.

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

  13. 13.

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

  14. 14.

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

  15. 15.

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

  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).

  17. 17.

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

  18. 18.

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

  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).

  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).

  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).

  22. 22.

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

  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).

  24. 24.

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

  25. 25.

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

  26. 26.

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

  27. 27.

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

  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).

  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).

  30. 30.

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

  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).

  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).

  33. 33.

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

  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).

  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).

  36. 36.

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

  37. 37.

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

  38. 38.

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

  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).

  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).

  41. 41.

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

  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).

  43. 43.

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

  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).

  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).

  46. 46.

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

  47. 47.

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

  48. 48.

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

  49. 49.

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

  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).

  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).

  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).

  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).

  54. 54.

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

Download references

Acknowledgements

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

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

Further reading

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.