Abstract

We introduce a quasi-classical model in the k space combined with the energy band structure of solids to understand the mechanisms of high-order harmonic generation (HHG) process occurring in a subcycle timescale. This model interprets the multiple plateau structure in HHG spectra well and the linear dependence of cutoff energies on the amplitude of vector potential A0 of the laser fields. It also predicts the emission time of HHG, which agrees well with the results by solving the time-dependent Schrödinger equation (TDSE). It provides a scheme to reconstruct the energy dispersion relations in Brillouin zone and to control the trajectories of HHG by varying the shape of laser pulses. This model is instructive for experimental measurements.

© 2017 Optical Society of America

Full Article  |  PDF Article

Corrections

Tao-Yuan Du and Xue-Bin Bian, "Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids: erratum," Opt. Express 25, 7731-7731 (2017)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-25-7-7731

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  4. K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37(18), 3891–3893 (2012).
    [Crossref] [PubMed]
  5. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
    [Crossref] [PubMed]
  6. J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
    [Crossref] [PubMed]
  7. H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
    [Crossref] [PubMed]
  8. M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
    [Crossref] [PubMed]
  9. A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
    [Crossref] [PubMed]
  10. M. Krüger, M. Schenk, and P. Hommelhoff, “Attosecond control of electrons emitted from a nanoscale metal tip,” Nature 475(7354), 78–81 (2011).
    [Crossref] [PubMed]
  11. 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]
  12. 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).
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  13. T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  16. B. Zaks, R. B. Liu, and M. S. Sherwin, “Experimental observation of electron-hole recollisions,” Nature 483(7391), 580–583 (2012).
    [Crossref] [PubMed]
  17. 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] [PubMed]
  18. M. Wu, S. Ghimire, D. A. Reis, K. J. Schafer, and M. B. Gaarde, “High-harmonic generation from Bloch electrons in solids,” Phys. Rev. A 91(4), 043839 (2015).
    [Crossref]
  19. Z. Guan, X. X. Zhou, and X. B. Bian, “High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses,” Phys. Rev. A 93(3), 033852 (2016).
    [Crossref]
  20. G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
    [Crossref] [PubMed]
  21. 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]
  22. P. G. Hawkins, M. Y. Ivanov, and V. S. Yakovlev, “Effect of multiple conduction bands on high-harmonic emission from dielectrics,” Phys. Rev. A 91(1), 013405 (2015).
    [Crossref]
  23. P. G. Hawkins and M. Y. Ivanov, “Role of subcycle transition dynamics in high-order-harmonic generation in periodic structures,” Phys. Rev. A 87(6), 063842 (2013).
    [Crossref]
  24. S. Ghimire, A. D. DiChiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. DiMauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
    [Crossref]
  25. 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]
  26. 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] [PubMed]
  27. 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]
  28. S. Glutsch, “Nonresonant and resonant Zener tunneling,” Phys. Rev. B 69(23), 235317 (2004).
    [Crossref]
  29. M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-Field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116(19), 197401 (2016).
    [Crossref] [PubMed]
  30. M. Goano, F. Bertazzi, M. Penna, and E. Bellotti, “Electronic structure of wurtzite ZnO: Nonlocal pseudopotential and ab initio calculations,” J. Appl. Phys. 102(8), 083709 (2007).
    [Crossref]
  31. J. C. Slater, “A soluble problem in energy bands,” Phys. Rev. 87(5), 807–835 (1952).
    [Crossref]
  32. T. Y. Du, Z. Guan, X. X. Zhou, and X. B. Bian, “Enhanced high-order harmonic generation from periodic potentials in inhomogeneous laser fields,” Phys. Rev. A 94(2), 023419 (2016).
    [Crossref]
  33. C. Chandre, S. Wiggins, and T. Uzer, “Time-frequency analysis of chaotic systems,” Physica D 181(3-4), 171–196 (2003).
    [Crossref]
  34. P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in a strong electromagnetic field,” Phys. Rev. A 51(3), R1750–R1753 (1995).
    [Crossref] [PubMed]

2016 (5)

F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
[Crossref] [PubMed]

Z. Guan, X. X. Zhou, and X. B. Bian, “High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses,” Phys. Rev. A 93(3), 033852 (2016).
[Crossref]

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-Field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116(19), 197401 (2016).
[Crossref] [PubMed]

T. Y. Du, Z. Guan, X. X. Zhou, and X. B. Bian, “Enhanced high-order harmonic generation from periodic potentials in inhomogeneous laser fields,” Phys. Rev. A 94(2), 023419 (2016).
[Crossref]

2015 (7)

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]

P. G. Hawkins, M. Y. Ivanov, and V. S. Yakovlev, “Effect of multiple conduction bands on high-harmonic emission from dielectrics,” Phys. Rev. A 91(1), 013405 (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, 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] [PubMed]

M. Wu, S. Ghimire, D. A. Reis, K. J. Schafer, and M. B. Gaarde, “High-harmonic generation from Bloch electrons in solids,” Phys. Rev. A 91(4), 043839 (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 521(7553), 498–502 (2015).
[Crossref] [PubMed]

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

2014 (2)

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]

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] [PubMed]

2013 (2)

P. G. Hawkins and M. Y. Ivanov, “Role of subcycle transition dynamics in high-order-harmonic generation in periodic structures,” Phys. Rev. A 87(6), 063842 (2013).
[Crossref]

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
[Crossref] [PubMed]

2012 (4)

K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37(18), 3891–3893 (2012).
[Crossref] [PubMed]

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
[Crossref] [PubMed]

B. Zaks, R. B. Liu, and M. S. Sherwin, “Experimental observation of electron-hole recollisions,” Nature 483(7391), 580–583 (2012).
[Crossref] [PubMed]

S. Ghimire, A. D. DiChiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. DiMauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

2011 (3)

M. Krüger, M. Schenk, and P. Hommelhoff, “Attosecond control of electrons emitted from a nanoscale metal tip,” Nature 475(7354), 78–81 (2011).
[Crossref] [PubMed]

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]

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

2009 (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

2008 (2)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
[Crossref] [PubMed]

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]

2007 (1)

M. Goano, F. Bertazzi, M. Penna, and E. Bellotti, “Electronic structure of wurtzite ZnO: Nonlocal pseudopotential and ab initio calculations,” J. Appl. Phys. 102(8), 083709 (2007).
[Crossref]

2004 (2)

S. Glutsch, “Nonresonant and resonant Zener tunneling,” Phys. Rev. B 69(23), 235317 (2004).
[Crossref]

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

2003 (1)

C. Chandre, S. Wiggins, and T. Uzer, “Time-frequency analysis of chaotic systems,” Physica D 181(3-4), 171–196 (2003).
[Crossref]

2000 (1)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[Crossref]

1995 (1)

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in a strong electromagnetic field,” Phys. Rev. A 51(3), R1750–R1753 (1995).
[Crossref] [PubMed]

1993 (1)

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

1952 (1)

J. C. Slater, “A soluble problem in energy bands,” Phys. Rev. 87(5), 807–835 (1952).
[Crossref]

Agostini, P.

S. Ghimire, A. D. DiChiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. DiMauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[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]

Antoine, P.

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in a strong electromagnetic field,” Phys. Rev. A 51(3), R1750–R1753 (1995).
[Crossref] [PubMed]

Apalkov, V.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
[Crossref] [PubMed]

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
[Crossref] [PubMed]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
[Crossref] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
[Crossref] [PubMed]

Barth, J. V.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
[Crossref] [PubMed]

Bellotti, E.

M. Goano, F. Bertazzi, M. Penna, and E. Bellotti, “Electronic structure of wurtzite ZnO: Nonlocal pseudopotential and ab initio calculations,” J. Appl. Phys. 102(8), 083709 (2007).
[Crossref]

Bertazzi, F.

M. Goano, F. Bertazzi, M. Penna, and E. Bellotti, “Electronic structure of wurtzite ZnO: Nonlocal pseudopotential and ab initio calculations,” J. Appl. Phys. 102(8), 083709 (2007).
[Crossref]

Bertrand, J. B.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

Bian, X. B.

Z. Guan, X. X. Zhou, and X. B. Bian, “High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses,” Phys. Rev. A 93(3), 033852 (2016).
[Crossref]

T. Y. Du, Z. Guan, X. X. Zhou, and X. B. Bian, “Enhanced high-order harmonic generation from periodic potentials in inhomogeneous laser fields,” Phys. Rev. A 94(2), 023419 (2016).
[Crossref]

Blanchet, V.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

Bothschafter, E. M.

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
[Crossref] [PubMed]

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] [PubMed]

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]

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] [PubMed]

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[Crossref]

Browne, D. A.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

Chandre, C.

C. Chandre, S. Wiggins, and T. Uzer, “Time-frequency analysis of chaotic systems,” Physica D 181(3-4), 171–196 (2003).
[Crossref]

Chang, Z.

Chini, M.

Ciappina, M.

M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-Field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116(19), 197401 (2016).
[Crossref] [PubMed]

Constant, E.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
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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).
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H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
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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).
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T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
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Z. Guan, X. X. Zhou, and X. B. Bian, “High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses,” Phys. Rev. A 93(3), 033852 (2016).
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T. Y. Du, Z. Guan, X. X. Zhou, and X. B. Bian, “Enhanced high-order harmonic generation from periodic potentials in inhomogeneous laser fields,” Phys. Rev. A 94(2), 023419 (2016).
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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).
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T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
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M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
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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).
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M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
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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).
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F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
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M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
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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).
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J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
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P. G. Hawkins, M. Y. Ivanov, and V. S. Yakovlev, “Effect of multiple conduction bands on high-harmonic emission from dielectrics,” Phys. Rev. A 91(1), 013405 (2015).
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P. G. Hawkins and M. Y. Ivanov, “Role of subcycle transition dynamics in high-order-harmonic generation in periodic structures,” Phys. Rev. A 87(6), 063842 (2013).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
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J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
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F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
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M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
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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).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
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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).
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M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
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F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
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M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
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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).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
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F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
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F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
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T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
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Krüger, M.

M. Krüger, M. Schenk, and P. Hommelhoff, “Attosecond control of electrons emitted from a nanoscale metal tip,” Nature 475(7354), 78–81 (2011).
[Crossref] [PubMed]

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.

F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
[Crossref] [PubMed]

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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]

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] [PubMed]

Levesque, J.

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

Liu, R. B.

B. Zaks, R. B. Liu, and M. S. Sherwin, “Experimental observation of electron-hole recollisions,” Nature 483(7391), 580–583 (2012).
[Crossref] [PubMed]

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 521(7553), 498–502 (2015).
[Crossref] [PubMed]

Mairesse, Y.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

Maquet, A.

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in a strong electromagnetic field,” Phys. Rev. A 51(3), R1750–R1753 (1995).
[Crossref] [PubMed]

McDonald, C. R.

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, 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] [PubMed]

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] [PubMed]

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]

Mével, E.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

Mohammad, A.

S. Ghimire, A. D. DiChiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. DiMauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[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 521(7553), 498–502 (2015).
[Crossref] [PubMed]

Mühlbrandt, S.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
[Crossref] [PubMed]

Nagler, P.

F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
[Crossref] [PubMed]

Ndabashimiye, G.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

S. Ghimire, A. D. DiChiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. DiMauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

Niikura, H.

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

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] [PubMed]

Paasch-Colberg, T.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
[Crossref] [PubMed]

Patchkovskii, S.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

Penna, M.

M. Goano, F. Bertazzi, M. Penna, and E. Bellotti, “Electronic structure of wurtzite ZnO: Nonlocal pseudopotential and ab initio calculations,” J. Appl. Phys. 102(8), 083709 (2007).
[Crossref]

Pépin, H.

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

Piraux, B.

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in a strong electromagnetic field,” Phys. Rev. A 51(3), R1750–R1753 (1995).
[Crossref] [PubMed]

Poellmann, C.

F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
[Crossref] [PubMed]

Reichert, J.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
[Crossref] [PubMed]

Reis, D. A.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

M. Wu, S. Ghimire, D. A. Reis, K. J. Schafer, and M. B. Gaarde, “High-harmonic generation from Bloch electrons in solids,” Phys. Rev. A 91(4), 043839 (2015).
[Crossref]

S. Ghimire, A. D. DiChiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. DiMauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[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]

Ruf, H.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

Schafer, K. J.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

M. Wu, S. Ghimire, D. A. Reis, K. J. Schafer, and M. B. Gaarde, “High-harmonic generation from Bloch electrons in solids,” Phys. Rev. A 91(4), 043839 (2015).
[Crossref]

Schenk, M.

M. Krüger, M. Schenk, and P. Hommelhoff, “Attosecond control of electrons emitted from a nanoscale metal tip,” Nature 475(7354), 78–81 (2011).
[Crossref] [PubMed]

Schiffrin, A.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
[Crossref] [PubMed]

Schmid, C. P.

F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
[Crossref] [PubMed]

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] [PubMed]

Schubert, O.

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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]

Schüller, C.

F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
[Crossref] [PubMed]

Schultze, M.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
[Crossref] [PubMed]

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
[Crossref] [PubMed]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
[Crossref] [PubMed]

Schweinberger, W.

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
[Crossref] [PubMed]

Sherwin, M. S.

F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
[Crossref] [PubMed]

B. Zaks, R. B. Liu, and M. S. Sherwin, “Experimental observation of electron-hole recollisions,” Nature 483(7391), 580–583 (2012).
[Crossref] [PubMed]

Sistrunk, E.

S. Ghimire, A. D. DiChiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. DiMauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[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]

Slater, J. C.

J. C. Slater, “A soluble problem in energy bands,” Phys. Rev. 87(5), 807–835 (1952).
[Crossref]

Sommer, A.

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
[Crossref] [PubMed]

Spanner, M.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

Steiner, J. T.

F. Langer, M. Hohenleutner, C. P. Schmid, C. Poellmann, P. Nagler, T. Korn, C. Schüller, M. S. Sherwin, U. Huttner, J. T. Steiner, S. W. Koch, M. Kira, and R. Huber, “Lightwave-driven quasiparticle collisions on a subcycle timescale,” Nature 533(7602), 225–229 (2016).
[Crossref] [PubMed]

Stockman, M. I.

M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-Field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116(19), 197401 (2016).
[Crossref] [PubMed]

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493(7430), 70–74 (2013).
[Crossref] [PubMed]

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2012).
[Crossref] [PubMed]

Szafruga, U. B.

S. Ghimire, A. D. DiChiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. DiMauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[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] [PubMed]

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008).
[Crossref] [PubMed]

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]

Uzer, T.

C. Chandre, S. Wiggins, and T. Uzer, “Time-frequency analysis of chaotic systems,” Physica D 181(3-4), 171–196 (2003).
[Crossref]

Vampa, G.

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, 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] [PubMed]

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] [PubMed]

Villeneuve, D. M.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

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

Wang, X.

Wiggins, S.

C. Chandre, S. Wiggins, and T. Uzer, “Time-frequency analysis of chaotic systems,” Physica D 181(3-4), 171–196 (2003).
[Crossref]

Wismer, M. S.

M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-Field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116(19), 197401 (2016).
[Crossref] [PubMed]

Wörner, H. J.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334(6053), 208–212 (2011).
[Crossref] [PubMed]

Wu, M.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

M. Wu, S. Ghimire, D. A. Reis, K. J. Schafer, and M. B. Gaarde, “High-harmonic generation from Bloch electrons in solids,” Phys. Rev. A 91(4), 043839 (2015).
[Crossref]

Wu, Y.

Yakovlev, V. S.

M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-Field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116(19), 197401 (2016).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 (a) The first conduction (red line) and the valence (blue line) bands of ZnO along the Γ-M direction of the Brillouin zone from [30]. (b) The band gap between the conduction and valence bands along the Γ-M direction as a function of wave vector k. (c) Comparison of the cutoff energies of HHG from the experimental results [11] and the proposed quasi-classical model.
Fig. 2
Fig. 2 HHG spectra and field dependence of the cutoff. (a) and (b) show the whole HHG spectra calculated by Bloch states and B splines, the wavelengths of laser fields are 3.2 µm and 3.6 µm, respectively. The strength of the laser fields is fixed at 0.005 a.u. The arrows show the cutoffs calculated by the quasi-classical model. (c) and (d) show the bandgap between the conduction bands C1, C3 and the valence band, respectively. (e) and (f) show the field strength dependence of cutoff for the first and second plateaus, respectively. The wavelength of laser fields is fixed at 3.2 µm. (g) and (h) show the wavelength dependence of cutoff for the first and second plateaus, respectively. The strength of laser fields is fixed at 0.005 a.u.
Fig. 3
Fig. 3 Time-Frequency analysis of HHG. (a) is the time-dependent displacement k(t) in k space and electric field E of the laser pulses. The values have been normalized. (b) and (d) are the time-frequency analysis of the second and first plateaus in Fig. 2(a), respectively. η1, η2 and η3 represent the emission time of HHG predicted by the quasi-classical model involving transition from the conduction band C1, C2 and C3 to V, respectively. η4 represents the result involving the transition between the conduction band C3 and C1, which is similar to the transition between continuum-continuum states in the atomic systems. (c) Populations of conduction bands C1, C2 and C3. The starting times of population on conduction bands are labeled by t1, t 2, t3 values. Laser parameters are the same as those in Fig. 2(a). The envelope of the pulse is a cos2 function, and the total duration is 6 cycles. The symbol o.c. represents optical cycle.
Fig. 4
Fig. 4 Microscopic motion within sub-cycle timescale and electron-hole pair recombination in energy bands driven by laser pulses. (a) is the electronic dynamic processes of the first plateau including the conduction bandC1 and Valence band. (b) and (c) are the electronic dynamic processes of the second plateau including conduction bands C2 or C3 and Valence band, respectively. In (c), the recombination channel 3′ corresponds to quasi-classical trajectories η4 in Fig. 3(b). The starting times of transitions between neighbor bands are labeled by t1, 2, 3 values.

Equations (4)

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k(t)= k 0 + e A(t),
η(t)= ε c (k(t)) ε v (k(t)) ω 0
η cutoff =Δ ε k max k max A 0 E 0 λ
H ^ (t)= H ^ 0 + e m A(t) p ^ ,

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