Abstract

Intraband high-order harmonics in solids reflect the nonlinear motion of carriers in the energy bands and have important applications. In general, multiple energy bands contribute to the intraband harmonics. We reveal the interference mechanism of intraband harmonics between electrons and holes by using the k-resolved semiclassical intraband model. The model gives a quantitative relationship between the intraband radiation yield, the energy band dispersion, and the laser parameters. Based on a preexcitation scheme, we present a method to reconstruct energy bands by using the intraband harmonics. We simulate the intraband harmonics of photo-carriers polarized by a bias field. The variation of harmonic yields as a function of a delay time results from the k-resolved energy band dispersion and reflects the Bloch oscillation of photo-carriers driven by the bias field.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31–L35 (1988).
    [Crossref]
  2. M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
    [Crossref]
  3. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
    [Crossref]
  4. J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
    [Crossref]
  5. O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
    [Crossref]
  6. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” J. Exp. Theor. Phys. 20(5), 1307–1314 (1965).
  7. M. Y. Ivanov, M. Spanner, and O. Smirnova, “Anatomy of strong field ionization,” J. Mod. Opt. 52(2-3), 165–184 (2005).
    [Crossref]
  8. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
    [Crossref]
  9. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
    [Crossref]
  10. M. W. Feise and D. S. Citrin, “Semi-classical theory of terahertz multiple-harmonic generation in semiconductor superlattices,” Appl. Phys. Lett. 75(22), 3536–3538 (1999).
    [Crossref]
  11. D. Golde, T. Meier, and S. W. Koch, “High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations,” Phys. Rev. B 77(7), 075330 (2008).
    [Crossref]
  12. S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys.: Condens. Matter 20(38), 384204 (2008).
    [Crossref]
  13. O. D. Mücke, “Isolated high-order harmonics pulse from two-color-driven Bloch oscillations in bulk semiconductors,” Phys. Rev. B 84(8), 081202 (2011).
    [Crossref]
  14. S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
    [Crossref]
  15. G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, “Theoretical analysis of high-harmonic generation in solids,” Phys. Rev. Lett. 113(7), 073901 (2014).
    [Crossref]
  16. O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
    [Crossref]
  17. M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
    [Crossref]
  18. G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
    [Crossref]
  19. K. K. Hansen, D. Bauer, and L. B. Madsen, “Finite-system effects on high-order harmonic generation: From atoms to solids,” Phys. Rev. A 97(4), 043424 (2018).
    [Crossref]
  20. T. Y. Du, D. Tang, X. H. Huang, and X. B. Bian, “Multichannel high-order harmonic generation from solids,” Phys. Rev. A 97(4), 043413 (2018).
    [Crossref]
  21. Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
    [Crossref]
  22. N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
    [Crossref]
  23. T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature (London) 521(7553), 498–502 (2015).
    [Crossref]
  24. A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (2017).
    [Crossref]
  25. F. Bloch, “Über die quantenmechanik der elekronen in kristallgittern,” Eur. Phys. J. A 52(7-8), 555–600 (1929).
    [Crossref]
  26. C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. A 145(855), 523–529 (1934).
    [Crossref]
  27. A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82(25), 5140–5143 (1999).
    [Crossref]
  28. J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
    [Crossref]
  29. C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, “Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice,” Phys. Rev. Lett. 70(21), 3319–3322 (1993).
    [Crossref]
  30. J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
    [Crossref]
  31. I. Bloch, “Quantum coherence and entanglement with ultracold atoms in optical lattices,” Nature (London) 453(7198), 1016–1022 (2008).
    [Crossref]
  32. W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Coherent ballistic motion of electrons in a periodic potential,” Phys. Rev. Lett. 104(14), 146602 (2010).
    [Crossref]
  33. T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
    [Crossref]
  34. G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
    [Crossref]
  35. C. R. McDonald, G. Vampa, P. B. Corkum, and T. Brabec, “Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals,” Phys. Rev. A 92(3), 033845 (2015).
    [Crossref]
  36. T. J. Shao, Y. Xu, X. H. Huang, and X. B. Bian, “Strain effects on high-order harmonic generation in solids,” Phys. Rev. A 99(1), 013432 (2019).
    [Crossref]
  37. L. J. Lü and X. B. Bian, “Multielectron interference of intraband harmonics in solids,” Phys. Rev. B 100(21), 214312 (2019).
    [Crossref]
  38. Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
    [Crossref]
  39. C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
    [Crossref]
  40. G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91(6), 064302 (2015).
    [Crossref]

2019 (4)

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
[Crossref]

T. J. Shao, Y. Xu, X. H. Huang, and X. B. Bian, “Strain effects on high-order harmonic generation in solids,” Phys. Rev. A 99(1), 013432 (2019).
[Crossref]

L. J. Lü and X. B. Bian, “Multielectron interference of intraband harmonics in solids,” Phys. Rev. B 100(21), 214312 (2019).
[Crossref]

2018 (2)

K. K. Hansen, D. Bauer, and L. B. Madsen, “Finite-system effects on high-order harmonic generation: From atoms to solids,” Phys. Rev. A 97(4), 043424 (2018).
[Crossref]

T. Y. Du, D. Tang, X. H. Huang, and X. B. Bian, “Multichannel high-order harmonic generation from solids,” Phys. Rev. A 97(4), 043413 (2018).
[Crossref]

2017 (2)

A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (2017).
[Crossref]

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

2016 (1)

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

2015 (5)

G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91(6), 064302 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature (London) 521(7553), 498–502 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

C. R. McDonald, G. Vampa, P. B. Corkum, and T. Brabec, “Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals,” Phys. Rev. A 92(3), 033845 (2015).
[Crossref]

2014 (3)

G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, “Theoretical analysis of high-harmonic generation in solids,” Phys. Rev. Lett. 113(7), 073901 (2014).
[Crossref]

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

2013 (1)

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[Crossref]

2011 (2)

O. D. Mücke, “Isolated high-order harmonics pulse from two-color-driven Bloch oscillations in bulk semiconductors,” Phys. Rev. B 84(8), 081202 (2011).
[Crossref]

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

2010 (1)

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Coherent ballistic motion of electrons in a periodic potential,” Phys. Rev. Lett. 104(14), 146602 (2010).
[Crossref]

2009 (1)

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
[Crossref]

2008 (3)

D. Golde, T. Meier, and S. W. Koch, “High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations,” Phys. Rev. B 77(7), 075330 (2008).
[Crossref]

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys.: Condens. Matter 20(38), 384204 (2008).
[Crossref]

I. Bloch, “Quantum coherence and entanglement with ultracold atoms in optical lattices,” Nature (London) 453(7198), 1016–1022 (2008).
[Crossref]

2005 (1)

M. Y. Ivanov, M. Spanner, and O. Smirnova, “Anatomy of strong field ionization,” J. Mod. Opt. 52(2-3), 165–184 (2005).
[Crossref]

2004 (1)

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

2003 (1)

J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
[Crossref]

2001 (2)

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

1999 (2)

M. W. Feise and D. S. Citrin, “Semi-classical theory of terahertz multiple-harmonic generation in semiconductor superlattices,” Appl. Phys. Lett. 75(22), 3536–3538 (1999).
[Crossref]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82(25), 5140–5143 (1999).
[Crossref]

1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref]

1993 (2)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref]

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, “Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice,” Phys. Rev. Lett. 70(21), 3319–3322 (1993).
[Crossref]

1992 (1)

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

1988 (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31–L35 (1988).
[Crossref]

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” J. Exp. Theor. Phys. 20(5), 1307–1314 (1965).

1934 (1)

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. A 145(855), 523–529 (1934).
[Crossref]

1929 (1)

F. Bloch, “Über die quantenmechanik der elekronen in kristallgittern,” Eur. Phys. J. A 52(7-8), 555–600 (1929).
[Crossref]

Agostini, P.

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

Bai, L.

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

Balcou, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref]

Bauer, D.

K. K. Hansen, D. Bauer, and L. B. Madsen, “Finite-system effects on high-order harmonic generation: From atoms to solids,” Phys. Rev. A 97(4), 043424 (2018).
[Crossref]

Bian, X. B.

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

T. J. Shao, Y. Xu, X. H. Huang, and X. B. Bian, “Strain effects on high-order harmonic generation in solids,” Phys. Rev. A 99(1), 013432 (2019).
[Crossref]

L. J. Lü and X. B. Bian, “Multielectron interference of intraband harmonics in solids,” Phys. Rev. B 100(21), 214312 (2019).
[Crossref]

T. Y. Du, D. Tang, X. H. Huang, and X. B. Bian, “Multichannel high-order harmonic generation from solids,” Phys. Rev. A 97(4), 043413 (2018).
[Crossref]

Blaga, C. I.

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

Bloch, F.

F. Bloch, “Über die quantenmechanik der elekronen in kristallgittern,” Eur. Phys. J. A 52(7-8), 555–600 (1929).
[Crossref]

Bloch, I.

I. Bloch, “Quantum coherence and entanglement with ultracold atoms in optical lattices,” Nature (London) 453(7198), 1016–1022 (2008).
[Crossref]

Borja, L. J.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Brabec, T.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

C. R. McDonald, G. Vampa, P. B. Corkum, and T. Brabec, “Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals,” Phys. Rev. A 92(3), 033845 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91(6), 064302 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, “Theoretical analysis of high-harmonic generation in solids,” Phys. Rev. Lett. 113(7), 073901 (2014).
[Crossref]

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

Cao, X.

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

Ciappina, M.

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

Citrin, D. S.

M. W. Feise and D. S. Citrin, “Semi-classical theory of terahertz multiple-harmonic generation in semiconductor superlattices,” Appl. Phys. Lett. 75(22), 3536–3538 (1999).
[Crossref]

Corkum, P.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
[Crossref]

Corkum, P. B.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91(6), 064302 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

C. R. McDonald, G. Vampa, P. B. Corkum, and T. Brabec, “Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals,” Phys. Rev. A 92(3), 033845 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, “Theoretical analysis of high-harmonic generation in solids,” Phys. Rev. Lett. 113(7), 073901 (2014).
[Crossref]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref]

Cunningham, J. E.

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Delahaye, J.

J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
[Crossref]

DiChiara, A. D.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

DiMauro, L. F.

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Drescher, M.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

Du, T. Y.

T. Y. Du, D. Tang, X. H. Huang, and X. B. Bian, “Multichannel high-order harmonic generation from solids,” Phys. Rev. A 97(4), 043413 (2018).
[Crossref]

Dudovich, N.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
[Crossref]

Elsaesser, T.

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Coherent ballistic motion of electrons in a periodic potential,” Phys. Rev. Lett. 104(14), 146602 (2010).
[Crossref]

Fedotov, A. B.

Feise, M. W.

M. W. Feise and D. S. Citrin, “Semi-classical theory of terahertz multiple-harmonic generation in semiconductor superlattices,” Appl. Phys. Lett. 75(22), 3536–3538 (1999).
[Crossref]

Feldmann, J.

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Ferray, M.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31–L35 (1988).
[Crossref]

Gaal, P.

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Coherent ballistic motion of electrons in a periodic potential,” Phys. Rev. Lett. 104(14), 146602 (2010).
[Crossref]

Gandman, A.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Garg, M.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature (London) 521(7553), 498–502 (2015).
[Crossref]

Ghimire, S.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Golde, D.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

D. Golde, T. Meier, and S. W. Koch, “High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations,” Phys. Rev. B 77(7), 075330 (2008).
[Crossref]

Goulielmakis, E.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature (London) 521(7553), 498–502 (2015).
[Crossref]

Hakonen, P.

J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
[Crossref]

Hammond, T. J.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Han, S.

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

Hansen, K. K.

K. K. Hansen, D. Bauer, and L. B. Madsen, “Finite-system effects on high-order harmonic generation: From atoms to solids,” Phys. Rev. A 97(4), 043424 (2018).
[Crossref]

Hassel, J.

J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
[Crossref]

Hentschel, M.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

Hey, R.

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Coherent ballistic motion of electrons in a periodic potential,” Phys. Rev. Lett. 104(14), 146602 (2010).
[Crossref]

Hohenleutner, M.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Huang, X. H.

T. J. Shao, Y. Xu, X. H. Huang, and X. B. Bian, “Strain effects on high-order harmonic generation in solids,” Phys. Rev. A 99(1), 013432 (2019).
[Crossref]

T. Y. Du, D. Tang, X. H. Huang, and X. B. Bian, “Multichannel high-order harmonic generation from solids,” Phys. Rev. A 97(4), 043413 (2018).
[Crossref]

Huber, R.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Hunsche, S.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82(25), 5140–5143 (1999).
[Crossref]

Huttner, U.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Itatani, J.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

Ivanov, M. Y.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
[Crossref]

M. Y. Ivanov, M. Spanner, and O. Smirnova, “Anatomy of strong field ionization,” J. Mod. Opt. 52(2-3), 165–184 (2005).
[Crossref]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref]

Jiang, S.

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

Kampfrath, T.

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[Crossref]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” J. Exp. Theor. Phys. 20(5), 1307–1314 (1965).

Kieffer, J. C.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

Kienberger, R.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

Kim, H.

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

Kim, S.

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

Kim, S. W.

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

Kim, Y. W.

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

Kira, M.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Klug, D. D.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, “Theoretical analysis of high-harmonic generation in solids,” Phys. Rev. Lett. 113(7), 073901 (2014).
[Crossref]

Knox, W. H.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82(25), 5140–5143 (1999).
[Crossref]

Koch, S. W.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

D. Golde, T. Meier, and S. W. Koch, “High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations,” Phys. Rev. B 77(7), 075330 (2008).
[Crossref]

Köhler, K.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, “Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice,” Phys. Rev. Lett. 70(21), 3319–3322 (1993).
[Crossref]

Krausz, F.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

Kuehn, W.

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Coherent ballistic motion of electrons in a periodic potential,” Phys. Rev. Lett. 104(14), 146602 (2010).
[Crossref]

Kurz, H.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, “Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice,” Phys. Rev. Lett. 70(21), 3319–3322 (1993).
[Crossref]

L’Huillier, A.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref]

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31–L35 (1988).
[Crossref]

Lai, Y. H.

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

Lange, C.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Langer, F.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Lanin, A. A.

Légaré, F.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

Leitenstorfer, A.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82(25), 5140–5143 (1999).
[Crossref]

Leo, K.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, “Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice,” Phys. Rev. Lett. 70(21), 3319–3322 (1993).
[Crossref]

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Leone, S. R.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Levesque, J.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

Lewenstein, M.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref]

Li, X. F.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31–L35 (1988).
[Crossref]

Lindell, R.

J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
[Crossref]

Lompre, L. A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31–L35 (1988).
[Crossref]

Lu, R.

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

Lü, L. J.

L. J. Lü and X. B. Bian, “Multielectron interference of intraband harmonics in solids,” Phys. Rev. B 100(21), 214312 (2019).
[Crossref]

Luu, T. T.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature (London) 521(7553), 498–502 (2015).
[Crossref]

Madsen, L. B.

K. K. Hansen, D. Bauer, and L. B. Madsen, “Finite-system effects on high-order harmonic generation: From atoms to solids,” Phys. Rev. A 97(4), 043424 (2018).
[Crossref]

Mainfray, G.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31–L35 (1988).
[Crossref]

Mairesse, Y.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
[Crossref]

Manus, C.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31–L35 (1988).
[Crossref]

McDonald, C. R.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

C. R. McDonald, G. Vampa, P. B. Corkum, and T. Brabec, “Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals,” Phys. Rev. A 92(3), 033845 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91(6), 064302 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, “Theoretical analysis of high-harmonic generation in solids,” Phys. Rev. Lett. 113(7), 073901 (2014).
[Crossref]

Meier, T.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

D. Golde, T. Meier, and S. W. Koch, “High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations,” Phys. Rev. B 77(7), 075330 (2008).
[Crossref]

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Mikhailov, S. A.

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys.: Condens. Matter 20(38), 384204 (2008).
[Crossref]

Miller, D. B. A.

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Miyata, Y.

N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
[Crossref]

Moulet, A.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature (London) 521(7553), 498–502 (2015).
[Crossref]

Mücke, O. D.

O. D. Mücke, “Isolated high-order harmonics pulse from two-color-driven Bloch oscillations in bulk semiconductors,” Phys. Rev. B 84(8), 081202 (2011).
[Crossref]

Muller, H. G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

Nagai, K.

N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
[Crossref]

Nelson, K. A.

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[Crossref]

Neumark, D. M.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Niikura, H.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

Nuss, M. C.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82(25), 5140–5143 (1999).
[Crossref]

Orlando, G.

G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91(6), 064302 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, “Theoretical analysis of high-harmonic generation in solids,” Phys. Rev. Lett. 113(7), 073901 (2014).
[Crossref]

Paalanen, M.

J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
[Crossref]

Park, H.

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

Patchkovskii, S.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
[Crossref]

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

Pemmaraju, C.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Pepin, H.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

Prell, J. S.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Prendergast, D.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Ramasesha, K.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Reider, G. A.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

Reimann, K.

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Coherent ballistic motion of electrons in a periodic potential,” Phys. Rev. Lett. 104(14), 146602 (2010).
[Crossref]

Reis, D. A.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Roskos, H. G.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, “Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice,” Phys. Rev. Lett. 70(21), 3319–3322 (1993).
[Crossref]

Sasaki, S.

N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
[Crossref]

Sato, S.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Schmidt, B. E.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

Schmitt-Rink, S.

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Schubert, O.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Schultze, M.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Schulze, A.

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Schwedler, R.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, “Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice,” Phys. Rev. Lett. 70(21), 3319–3322 (1993).
[Crossref]

Seppa, H.

J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
[Crossref]

Shah, J.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82(25), 5140–5143 (1999).
[Crossref]

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Shao, T. J.

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

T. J. Shao, Y. Xu, X. H. Huang, and X. B. Bian, “Strain effects on high-order harmonic generation in solids,” Phys. Rev. A 99(1), 013432 (2019).
[Crossref]

Sillanpaa, M.

J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
[Crossref]

Sistrunk, E.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Smirnova, O.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
[Crossref]

M. Y. Ivanov, M. Spanner, and O. Smirnova, “Anatomy of strong field ionization,” J. Mod. Opt. 52(2-3), 165–184 (2005).
[Crossref]

Spanner, M.

M. Y. Ivanov, M. Spanner, and O. Smirnova, “Anatomy of strong field ionization,” J. Mod. Opt. 52(2-3), 165–184 (2005).
[Crossref]

Spielmann, C.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

Stepanov, E. A.

Takaguchi, Y.

N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
[Crossref]

Tanaka, K.

N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
[Crossref]

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[Crossref]

Tang, D.

T. Y. Du, D. Tang, X. H. Huang, and X. B. Bian, “Multichannel high-order harmonic generation from solids,” Phys. Rev. A 97(4), 043413 (2018).
[Crossref]

Tempea, G.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

Th. Hassan, M.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature (London) 521(7553), 498–502 (2015).
[Crossref]

Thiré, N.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

Thomas, P.

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

Uchida, K.

N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
[Crossref]

Urbanek, B.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Vampa, G.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

C. R. McDonald, G. Vampa, P. B. Corkum, and T. Brabec, “Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals,” Phys. Rev. A 92(3), 033845 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91(6), 064302 (2015).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, “Theoretical analysis of high-harmonic generation in solids,” Phys. Rev. Lett. 113(7), 073901 (2014).
[Crossref]

Villeneuve, D.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
[Crossref]

Villeneuve, D. M.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

von Plessen, G.

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Wang, Z.

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

Waschke, C.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, “Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice,” Phys. Rev. Lett. 70(21), 3319–3322 (1993).
[Crossref]

Whitmore, D.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Woerner, M.

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Coherent ballistic motion of electrons in a periodic potential,” Phys. Rev. Lett. 104(14), 146602 (2010).
[Crossref]

Wu, T.

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

Xu, J.

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

Xu, Y.

T. J. Shao, Y. Xu, X. H. Huang, and X. B. Bian, “Strain effects on high-order harmonic generation in solids,” Phys. Rev. A 99(1), 013432 (2019).
[Crossref]

Yabana, K.

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

Yang, F.

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

Yoshikawa, N.

N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
[Crossref]

Yu, C.

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

Yu. Kruchinin, S.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature (London) 521(7553), 498–502 (2015).
[Crossref]

Yuan, G.

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

Zeidler, D.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

Zener, C.

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. A 145(855), 523–529 (1934).
[Crossref]

Zhang, X.

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

Zheltikov, A. M.

Ziegler, K.

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys.: Condens. Matter 20(38), 384204 (2008).
[Crossref]

ACS Photonics (1)

Y. W. Kim, T. J. Shao, H. Kim, S. Han, S. Kim, M. Ciappina, X. B. Bian, and S. W. Kim, “Spectral interference in high harmonic generation from solids,” ACS Photonics 6(4), 851–857 (2019).
[Crossref]

Appl. Phys. Lett. (1)

M. W. Feise and D. S. Citrin, “Semi-classical theory of terahertz multiple-harmonic generation in semiconductor superlattices,” Appl. Phys. Lett. 75(22), 3536–3538 (1999).
[Crossref]

Eur. Phys. J. A (1)

F. Bloch, “Über die quantenmechanik der elekronen in kristallgittern,” Eur. Phys. J. A 52(7-8), 555–600 (1929).
[Crossref]

J. Exp. Theor. Phys. (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” J. Exp. Theor. Phys. 20(5), 1307–1314 (1965).

J. Mod. Opt. (1)

M. Y. Ivanov, M. Spanner, and O. Smirnova, “Anatomy of strong field ionization,” J. Mod. Opt. 52(2-3), 165–184 (2005).
[Crossref]

J. Phys. B (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21(3), L31–L35 (1988).
[Crossref]

J. Phys.: Condens. Matter (1)

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys.: Condens. Matter 20(38), 384204 (2008).
[Crossref]

Nat. Commun. (2)

N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, “Interband resonant high-harmonic generation by valley polarized electron–hole pairs,” Nat. Commun. 10(1), 3709 (2019).
[Crossref]

Z. Wang, H. Park, Y. H. Lai, J. Xu, C. I. Blaga, F. Yang, P. Agostini, and L. F. DiMauro, “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nat. Commun. 8(1), 1686 (2017).
[Crossref]

Nat. Photonics (2)

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[Crossref]

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Nat. Phys. (1)

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Nature (1)

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Nature (London) (4)

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432(7019), 867–871 (2004).
[Crossref]

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460(7258), 972–977 (2009).
[Crossref]

I. Bloch, “Quantum coherence and entanglement with ultracold atoms in optical lattices,” Nature (London) 453(7198), 1016–1022 (2008).
[Crossref]

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature (London) 521(7553), 498–502 (2015).
[Crossref]

Optica (1)

Phys. Rev. A (6)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref]

C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of HHG on dipole moments in SiO2 crystals,” Phys. Rev. A 94(1), 013846 (2016).
[Crossref]

C. R. McDonald, G. Vampa, P. B. Corkum, and T. Brabec, “Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals,” Phys. Rev. A 92(3), 033845 (2015).
[Crossref]

T. J. Shao, Y. Xu, X. H. Huang, and X. B. Bian, “Strain effects on high-order harmonic generation in solids,” Phys. Rev. A 99(1), 013432 (2019).
[Crossref]

K. K. Hansen, D. Bauer, and L. B. Madsen, “Finite-system effects on high-order harmonic generation: From atoms to solids,” Phys. Rev. A 97(4), 043424 (2018).
[Crossref]

T. Y. Du, D. Tang, X. H. Huang, and X. B. Bian, “Multichannel high-order harmonic generation from solids,” Phys. Rev. A 97(4), 043413 (2018).
[Crossref]

Phys. Rev. B (5)

O. D. Mücke, “Isolated high-order harmonics pulse from two-color-driven Bloch oscillations in bulk semiconductors,” Phys. Rev. B 84(8), 081202 (2011).
[Crossref]

D. Golde, T. Meier, and S. W. Koch, “High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations,” Phys. Rev. B 77(7), 075330 (2008).
[Crossref]

L. J. Lü and X. B. Bian, “Multielectron interference of intraband harmonics in solids,” Phys. Rev. B 100(21), 214312 (2019).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91(6), 064302 (2015).
[Crossref]

J. Feldmann, K. Leo, J. Shah, D. B. A. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schulze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46(11), 7252–7255 (1992).
[Crossref]

Phys. Rev. Lett. (6)

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, “Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice,” Phys. Rev. Lett. 70(21), 3319–3322 (1993).
[Crossref]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82(25), 5140–5143 (1999).
[Crossref]

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Coherent ballistic motion of electrons in a periodic potential,” Phys. Rev. Lett. 104(14), 146602 (2010).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115(19), 193603 (2015).
[Crossref]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref]

G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, “Theoretical analysis of high-harmonic generation in solids,” Phys. Rev. Lett. 113(7), 073901 (2014).
[Crossref]

Proc. R. Soc. A (1)

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. A 145(855), 523–529 (1934).
[Crossref]

Science (4)

J. Delahaye, J. Hassel, R. Lindell, M. Sillanpaa, M. Paalanen, H. Seppa, and P. Hakonen, “Low-noise current amplifier based on mesoscopic Josephson junction,” Science 299(5609), 1045–1048 (2003).
[Crossref]

M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014).
[Crossref]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001).
[Crossref]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. The HHG spectrum of SiO$_2$ simulated by solving the SBE and adopting the pump-probe scheme. The dephasing time is $\infty$ (a), 100 fs (b), 10 fs (c), and 3 fs (d), respectively. The black vertical line indicates the location of the minimum bandgap.
Fig. 2.
Fig. 2. The seventh harmonic amplitudes and intensities as a function of $A_0$. (a) The blue-solid, magenta-dashed-dotted, and green-dashed curves represent the seventh intraband harmonic amplitudes of electrons, holes, and the total of them at $k_0$=0 varying with the vector potential peak, respectively. (b) The green-dashed and red-dashed-dotted curves represent the seventh harmonic intensity calculated by the semiclassical model at $k_0$=0 and the SBE using the preexcitation scheme, respectively. The thin black curve is the square of the first term of $Y_{t,7}$.
Fig. 3.
Fig. 3. The solid-blue line represents the difference between the lowest conduction band and the highest valence band of SiO$_2$. The dashed-red line represents the bandgap reconstructed with the first, third, fifth, seventh, and ninth harmonics generated by probe lights with $A_0$=0.385 a.u. (the wavelength is 3500 nm, $F_b$=0.005 a.u., and the FWHM is 100 fs, as in Fig. 1) obtained by calculating the SBE. Because it is a Gaussian pulse, using 0.95$A_0$ here can better reconstruct the energy bands. There is no quantitative number of carriers in our analysis, the reconstructed bandgaps are multiplied by a constant and plus the minimum bandgap.
Fig. 4.
Fig. 4. The $k$-resolved intraband harmonic amplitudes of SiO$_2$ with $A_0$=0.269 a.u. Since the harmonic amplitudes of holes [ (c) and (d)] are one order of magnitude smaller than that of electrons [ (a) and (b)], the total harmonic amplitudes which are almost the same as that of electrons are not shown here.
Fig. 5.
Fig. 5. The blue curves show harmonic intensities at different delay times calculated by the SBE. Green-dotted lines are the $k$-resolved harmonic intensities calculated by the semiclassical method, which are mapped to one $T_{bo}$ for comparison. The black vertical lines indicate the delay times for carriers to return to the $\Gamma$ point after a BO period.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

d k / d t = F .
k ( t ) = k 0 + A 0 sin ( ω t ) ,
ε m ( k ) = c m , 0 + c m , 1 ( k k 0 ) + c m , 2 ( k k 0 ) 2 + .
v ˙ m ( k 0 , A 0 , t ) = Y m , 1 cos ( ω t ) + Y m , 2 cos ( 2 ω t π / 2 ) + + Y m , n cos [ n ω t + ( 1 n ) π / 2 ] ,
Y m , n = n ω H m , n ,
Y t , 1 = ω [ 2 ( c e , 2 c h , 2 ) A 0 + 3 ( c e , 4 c h , 4 ) A 0 3 + ] , Y t , 3 = 3 ω [ ( c e , 4 c h , 4 ) A 0 3 + 15 8 ( c e , 6 c h , 6 ) A 0 5 + ] , Y t , 5 = 5 ω [ 3 8 ( c e , 6 c h , 6 ) A 0 5 + 7 8 ( c e , 8 c h , 8 ) A 0 7 + ] , .
ε e ( k ) ε h ( k ) = c e , 0 c h , 0 + ( c e , 2 c h , 2 ) k 2 + .
Δ k = F c t d e l a y .

Metrics