Abstract

High order harmonic generation (HHG) in semiconductors opens a new frontier in strong field physics and attosecond science. However, the underlying physical mechanisms are not yet fully understood and lively debated. Here, we identify and discuss carrier-wave population transfer as a novel and important dynamical effect. We find that the interband excitation occurs in an extremely short time window due to the intraband motion. Our analysis based on this finding allows for a physically intuitive interpretation of the anomalous carrier-envelope phase dependence observed in HHG from MgO and to understand the dominant role of the interband polarization as reported in a series of recent semiconductor HHG experiments. Motivated by the discovered coupling mechanism, we demonstrate that the interband excitation can be controlled by an appropriately tailored two-color field. An ultrabroad supercontinuum spectrum covering the entire plateau region can be generated which directly creates an isolated-attosecond pulse even without phase compensation. Our results provide remarkable insight into the basic physics governing the sub-cycle electron motion with significant implications for the generation of isolated-attosecond light pulses in semiconductor materials.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  20. O. Schubert and et al., “Sub-cycle control of terahertz high-harmonic generation by dynamical bloch oscillations,” Nature Photonics 8, 119–123 (2014).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  23. Y. S. You and et al., “Laser waveform control of extreme ultraviolet high harmonics from solids,” Opt. Lett. 42, 1816–1819 (2017).
    [Crossref] [PubMed]
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    [Crossref]
  25. F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, “Attosecond optical-field-enhanced carrier injection into the GaAs conduction band,” Nature Phys. 14, 560–565 (2018).
    [Crossref]
  26. M. Garg, H. Y. Kim, and E. Goulielmakis, “Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz,” Nature Photonics 12, 291–296 (2018).
    [Crossref]
  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, 075330 (2008).
    [Crossref]
  28. Z. Wang and et al., “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nature Comm. 8, 1686 (2017).
    [Crossref]
  29. M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
    [Crossref]
  30. F. Catoire and H. Bachau, “Above-Threshold Ionization of Quasiperiodic Structures by Low-Frequency Laser Fields,” Phys. Rev. Lett. 115, 163602 (2015).
    [Crossref] [PubMed]
  31. F. Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Phys. 52, 555 (1929).
    [Crossref]
  32. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89, 127401 (2002).
    [Crossref] [PubMed]
  33. T. Tritschler, O. D. Mücke, and M. Wegener, “Extreme nonlinear optics of two-level systems,” Phys. Rev. A 68, 033404 (2003).
    [Crossref]
  34. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
    [Crossref]
  35. M. Nisoli and G. Sansone, “New frontiers in attosecond science,” Prog. Quant. Electron. 33, 17–59 (2009).
    [Crossref]
  36. V. S. Yakovlev and A. Scrinzi, “High hiarmonic imaging of few-cycle pulses,” Phys. Rev. Lett. 91, 153901 (2003).
    [Crossref]
  37. Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98, 203901 (2007).
    [Crossref] [PubMed]

2018 (5)

S. Yu. Kruchinin, F. Krausz, and V. S. Yakovlev, “Strong-field phenomena in periodic systems,” Rev. Mod. Phys. 90, 021002 (2018).
[Crossref]

S. Jiang, J. Chen, H. Wei, C. Yu, R. Lu, and C. D. Lin, “Role of the transition dipole amplitude and phase on the generation of odd and even high-order harmonics in crystals,” Phys. Rev. Lett. 120, 253201 (2018).
[Crossref] [PubMed]

X. Song, G. Shi, G. Zhang, J. Xu, C. Lin, J. Chen, and W. Yang, “Attosecond time delay of retrapped resonant ionization,” Phys. Rev. Lett. 121, 103201 (2018).
[Crossref] [PubMed]

F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, “Attosecond optical-field-enhanced carrier injection into the GaAs conduction band,” Nature Phys. 14, 560–565 (2018).
[Crossref]

M. Garg, H. Y. Kim, and E. Goulielmakis, “Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz,” Nature Photonics 12, 291–296 (2018).
[Crossref]

2017 (8)

Y. S. You and et al., “Laser waveform control of extreme ultraviolet high harmonics from solids,” Opt. Lett. 42, 1816–1819 (2017).
[Crossref] [PubMed]

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, 516–519 (2017).
[Crossref]

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
[Crossref]

Z. Wang and et al., “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nature Comm. 8, 1686 (2017).
[Crossref]

X. Gong and et al., “Energy-resolved ultrashort delays of photoelectron emission clocked by orthogonal two-color laer fields,” Phys. Rev. Lett. 118, 143203 (2017).
[Crossref]

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13, 262–265 (2017).
[Crossref]

Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13, 345 (2017).
[Crossref]

L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
[Crossref]

2016 (5)

Z. Tao, C. Chen, T. Szivási, M. Keller, M. Mavrikakis, H. Kapteyn, and M. Murnane, “Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids,” Science 353, 62–67 (2016).
[Crossref] [PubMed]

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, 520–523 (2016).
[Crossref] [PubMed]

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref] [PubMed]

M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
[Crossref]

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

2015 (6)

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, 572–575 (2015).
[Crossref] [PubMed]

F. Catoire and H. Bachau, “Above-Threshold Ionization of Quasiperiodic Structures by Low-Frequency Laser Fields,” Phys. Rev. Lett. 115, 163602 (2015).
[Crossref] [PubMed]

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, 462–464 (2015).
[Crossref] [PubMed]

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, 193603 (2015).
[Crossref] [PubMed]

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, 498–502 (2015).
[Crossref] [PubMed]

M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, “Carrier-wave rabi-flopping signatures in high-order harmonic generation for alkali atoms,” Phys. Rev. Lett. 114, 143902 (2015).
[Crossref] [PubMed]

2014 (2)

O. Schubert and et al., “Sub-cycle control of terahertz high-harmonic generation by dynamical bloch oscillations,” Nature Photonics 8, 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, 073901 (2014).
[Crossref] [PubMed]

2011 (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,” Nature Phys. 7, 138–141 (2011).
[Crossref]

2009 (2)

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

M. Nisoli and G. Sansone, “New frontiers in attosecond science,” Prog. Quant. Electron. 33, 17–59 (2009).
[Crossref]

2008 (1)

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, 075330 (2008).
[Crossref]

2007 (1)

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98, 203901 (2007).
[Crossref] [PubMed]

2003 (2)

T. Tritschler, O. D. Mücke, and M. Wegener, “Extreme nonlinear optics of two-level systems,” Phys. Rev. A 68, 033404 (2003).
[Crossref]

V. S. Yakovlev and A. Scrinzi, “High hiarmonic imaging of few-cycle pulses,” Phys. Rev. Lett. 91, 153901 (2003).
[Crossref]

2002 (1)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89, 127401 (2002).
[Crossref] [PubMed]

2001 (1)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Signatures of carrier-wave rabi flopping in GaAs,” Phys. Rev. Lett. 87, 057401 (2001).
[Crossref] [PubMed]

1929 (1)

F. Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Phys. 52, 555 (1929).
[Crossref]

Agostini, P.

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,” Nature Phys. 7, 138–141 (2011).
[Crossref]

Bachau, H.

F. Catoire and H. Bachau, “Above-Threshold Ionization of Quasiperiodic Structures by Low-Frequency Laser Fields,” Phys. Rev. Lett. 115, 163602 (2015).
[Crossref] [PubMed]

Bloch, F.

F. Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Phys. 52, 555 (1929).
[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, 462–464 (2015).
[Crossref] [PubMed]

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, 193603 (2015).
[Crossref] [PubMed]

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, 073901 (2014).
[Crossref] [PubMed]

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, 520–523 (2016).
[Crossref] [PubMed]

M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
[Crossref]

M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
[Crossref]

Calegari, F.

L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
[Crossref]

Castrovilli, M. C.

L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
[Crossref]

Catoire, F.

F. Catoire and H. Bachau, “Above-Threshold Ionization of Quasiperiodic Structures by Low-Frequency Laser Fields,” Phys. Rev. Lett. 115, 163602 (2015).
[Crossref] [PubMed]

Chang, Z.

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
[Crossref]

Chen, C.

Z. Tao, C. Chen, T. Szivási, M. Keller, M. Mavrikakis, H. Kapteyn, and M. Murnane, “Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids,” Science 353, 62–67 (2016).
[Crossref] [PubMed]

Chen, J.

X. Song, G. Shi, G. Zhang, J. Xu, C. Lin, J. Chen, and W. Yang, “Attosecond time delay of retrapped resonant ionization,” Phys. Rev. Lett. 121, 103201 (2018).
[Crossref] [PubMed]

S. Jiang, J. Chen, H. Wei, C. Yu, R. Lu, and C. D. Lin, “Role of the transition dipole amplitude and phase on the generation of odd and even high-order harmonics in crystals,” Phys. Rev. Lett. 120, 253201 (2018).
[Crossref] [PubMed]

Cheng, Y.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98, 203901 (2007).
[Crossref] [PubMed]

Chew, A.

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
[Crossref]

Chini, M.

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
[Crossref]

Ciappina, M.

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

Ciappina, M. F.

M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, “Carrier-wave rabi-flopping signatures in high-order harmonic generation for alkali atoms,” Phys. Rev. Lett. 114, 143902 (2015).
[Crossref] [PubMed]

Corkum, P. B.

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, 193603 (2015).
[Crossref] [PubMed]

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, 462–464 (2015).
[Crossref] [PubMed]

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, 073901 (2014).
[Crossref] [PubMed]

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,” Nature Phys. 7, 138–141 (2011).
[Crossref]

DiMauro, L. F.

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,” Nature Phys. 7, 138–141 (2011).
[Crossref]

Fedotov, A. B.

Fennel, T.

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M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
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Z. Tao, C. Chen, T. Szivási, M. Keller, M. Mavrikakis, H. Kapteyn, and M. Murnane, “Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids,” Science 353, 62–67 (2016).
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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, 193603 (2015).
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Z. Tao, C. Chen, T. Szivási, M. Keller, M. Mavrikakis, H. Kapteyn, and M. Murnane, “Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids,” Science 353, 62–67 (2016).
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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, 520–523 (2016).
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Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13, 345 (2017).
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H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13, 262–265 (2017).
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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, 520–523 (2016).
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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,” Nature Phys. 7, 138–141 (2011).
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Ren, X.

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
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M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, “Carrier-wave rabi-flopping signatures in high-order harmonic generation for alkali atoms,” Phys. Rev. Lett. 114, 143902 (2015).
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F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, “Attosecond optical-field-enhanced carrier injection into the GaAs conduction band,” Nature Phys. 14, 560–565 (2018).
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L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
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L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
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L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
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F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, “Attosecond optical-field-enhanced carrier injection into the GaAs conduction band,” Nature Phys. 14, 560–565 (2018).
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M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
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M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
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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, 520–523 (2016).
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Schlaepfer, F.

F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, “Attosecond optical-field-enhanced carrier injection into the GaAs conduction band,” Nature Phys. 14, 560–565 (2018).
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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, 193603 (2015).
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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, 462–464 (2015).
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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, 572–575 (2015).
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O. Schubert and et al., “Sub-cycle control of terahertz high-harmonic generation by dynamical bloch oscillations,” Nature Photonics 8, 119–123 (2014).
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V. S. Yakovlev and A. Scrinzi, “High hiarmonic imaging of few-cycle pulses,” Phys. Rev. Lett. 91, 153901 (2003).
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L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
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X. Song, G. Shi, G. Zhang, J. Xu, C. Lin, J. Chen, and W. Yang, “Attosecond time delay of retrapped resonant ionization,” Phys. Rev. Lett. 121, 103201 (2018).
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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,” Nature Phys. 7, 138–141 (2011).
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X. Song, G. Shi, G. Zhang, J. Xu, C. Lin, J. Chen, and W. Yang, “Attosecond time delay of retrapped resonant ionization,” Phys. Rev. Lett. 121, 103201 (2018).
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Stepanov, E. A.

Stierle, J.

L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
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M. S. Wismer, S. Yu. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116, 197401 (2016).
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L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
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Z. Tao, C. Chen, T. Szivási, M. Keller, M. Mavrikakis, H. Kapteyn, and M. Murnane, “Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids,” Science 353, 62–67 (2016).
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Z. Tao, C. Chen, T. Szivási, M. Keller, M. Mavrikakis, H. Kapteyn, and M. Murnane, “Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids,” Science 353, 62–67 (2016).
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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, 498–502 (2015).
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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, 462–464 (2015).
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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, 193603 (2015).
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Trabattoni, A.

L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
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T. Tritschler, O. D. Mücke, and M. Wegener, “Extreme nonlinear optics of two-level systems,” Phys. Rev. A 68, 033404 (2003).
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O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89, 127401 (2002).
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O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Signatures of carrier-wave rabi flopping in GaAs,” Phys. Rev. Lett. 87, 057401 (2001).
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Vampa, G.

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, 193603 (2015).
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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, 462–464 (2015).
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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, 073901 (2014).
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F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, “Attosecond optical-field-enhanced carrier injection into the GaAs conduction band,” Nature Phys. 14, 560–565 (2018).
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Z. Wang and et al., “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nature Comm. 8, 1686 (2017).
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T. Tritschler, O. D. Mücke, and M. Wegener, “Extreme nonlinear optics of two-level systems,” Phys. Rev. A 68, 033404 (2003).
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O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89, 127401 (2002).
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O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Signatures of carrier-wave rabi flopping in GaAs,” Phys. Rev. Lett. 87, 057401 (2001).
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S. Jiang, J. Chen, H. Wei, C. Yu, R. Lu, and C. D. Lin, “Role of the transition dipole amplitude and phase on the generation of odd and even high-order harmonics in crystals,” Phys. Rev. Lett. 120, 253201 (2018).
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Wintersperger, K.

L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
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M. S. Wismer, S. Yu. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116, 197401 (2016).
[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, 520–523 (2016).
[Crossref] [PubMed]

M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
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Wu, Y.

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
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Xu, J.

X. Song, G. Shi, G. Zhang, J. Xu, C. Lin, J. Chen, and W. Yang, “Attosecond time delay of retrapped resonant ionization,” Phys. Rev. Lett. 121, 103201 (2018).
[Crossref] [PubMed]

Xu, Z.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98, 203901 (2007).
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S. Yu. Kruchinin, F. Krausz, and V. S. Yakovlev, “Strong-field phenomena in periodic systems,” Rev. Mod. Phys. 90, 021002 (2018).
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M. S. Wismer, S. Yu. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116, 197401 (2016).
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V. S. Yakovlev and A. Scrinzi, “High hiarmonic imaging of few-cycle pulses,” Phys. Rev. Lett. 91, 153901 (2003).
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X. Song, G. Shi, G. Zhang, J. Xu, C. Lin, J. Chen, and W. Yang, “Attosecond time delay of retrapped resonant ionization,” Phys. Rev. Lett. 121, 103201 (2018).
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Yin, Y.

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
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You, Y. S.

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
[Crossref]

Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13, 345 (2017).
[Crossref]

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13, 262–265 (2017).
[Crossref]

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

S. Jiang, J. Chen, H. Wei, C. Yu, R. Lu, and C. D. Lin, “Role of the transition dipole amplitude and phase on the generation of odd and even high-order harmonics in crystals,” Phys. Rev. Lett. 120, 253201 (2018).
[Crossref] [PubMed]

Yu. Kruchinin, S.

S. Yu. Kruchinin, F. Krausz, and V. S. Yakovlev, “Strong-field phenomena in periodic systems,” Rev. Mod. Phys. 90, 021002 (2018).
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M. S. Wismer, S. Yu. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, “Strong-field resonant dynamics in semiconductors,” Phys. Rev. Lett. 116, 197401 (2016).
[Crossref] [PubMed]

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, 498–502 (2015).
[Crossref] [PubMed]

Zeng, Z.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98, 203901 (2007).
[Crossref] [PubMed]

Zhan, M.

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref] [PubMed]

Zhang, G.

X. Song, G. Shi, G. Zhang, J. Xu, C. Lin, J. Chen, and W. Yang, “Attosecond time delay of retrapped resonant ionization,” Phys. Rev. Lett. 121, 103201 (2018).
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Zheltikov, A. M.

Zherebtsov, S.

L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
[Crossref]

Zhuang, F.

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
[Crossref]

Zimmermann, T.

M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, “Carrier-wave rabi-flopping signatures in high-order harmonic generation for alkali atoms,” Phys. Rev. Lett. 114, 143902 (2015).
[Crossref] [PubMed]

Nat. Phys. (2)

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13, 262–265 (2017).
[Crossref]

Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13, 345 (2017).
[Crossref]

Nature (5)

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, 520–523 (2016).
[Crossref] [PubMed]

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref] [PubMed]

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, 498–502 (2015).
[Crossref] [PubMed]

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, 462–464 (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, 572–575 (2015).
[Crossref] [PubMed]

Nature Comm. (2)

Y. S. You, Y. Yin, Y. Wu, A. Chew, X. Ren, F. Zhuang, S. Gholam-Mirzaei, M. Chini, Z. Chang, and S. Ghimire, “High-harmonic generation in amorphous solids,” Nature Comm. 8, 724 (2017).
[Crossref]

Z. Wang and et al., “The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor,” Nature Comm. 8, 1686 (2017).
[Crossref]

Nature Photonics (2)

M. Garg, H. Y. Kim, and E. Goulielmakis, “Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz,” Nature Photonics 12, 291–296 (2018).
[Crossref]

O. Schubert and et al., “Sub-cycle control of terahertz high-harmonic generation by dynamical bloch oscillations,” Nature Photonics 8, 119–123 (2014).
[Crossref]

Nature Phys. (2)

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,” Nature Phys. 7, 138–141 (2011).
[Crossref]

F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, “Attosecond optical-field-enhanced carrier injection into the GaAs conduction band,” Nature Phys. 14, 560–565 (2018).
[Crossref]

Nature Physics (1)

L. Seiert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nature Physics 13, 766–770 (2017).
[Crossref]

Opt. Lett. (1)

Optica (1)

Phys. Rev. A (2)

T. Tritschler, O. D. Mücke, and M. Wegener, “Extreme nonlinear optics of two-level systems,” Phys. Rev. A 68, 033404 (2003).
[Crossref]

M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
[Crossref]

Phys. Rev. B (1)

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, 075330 (2008).
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Phys. Rev. Lett. (12)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89, 127401 (2002).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Simulated CEP-dependent HHG spectra for MgO with field strength 1.3 V/Å and excitation carrier wave central wavelength 1.7 μm, corresponding to a laser period T0 = 5.665 fs. We use a temporal Gaussian envelope with a FWHM τp = 2T0 and a dephasing time of T2 = T0/4. (a) with two-band model, (b) with three-band model, and (c) considering only interband transitions.
Fig. 2
Fig. 2 (a), (c), (e) The total HHG spectrum Irad (black dash line), interband polarization I rad pol (blue solid line), and intraband current I rad curr (red solid line) for coupled inter- and intraband dynamics, and pure interband HHG (green solid line) when the intraband motion is artificially switched off. (b), (d), (f) The corresponding time-dependent population nC1[(K(t), t] for coupled (blue line) and pure interband (green line) motion. The red dash and green dot-dash lines in (b), (d), and (e) show the normalized electric field and vector potential, respectively. with ϕCEP = 0 and a field strength 1.3 V/Å. (a) and (b) show the results for τp = 2T0 and field strength 1.3 V/Å, (c) and (d) are same with (a) and (b) but for τp = 10T0. (e) and (f) are same with (c) and (d) but for ΩR = 0.7ω0 and ΩB = 8.45ω0. The dotted grey vertical lines in (a), (c), and (e) represent the minimum band gap at the center of the Brillouin zone. The blue dots on the curves in (b), (d) and (f) denote moments when the electrons pass through the Γ point. The magenta dots in (f) denote moments when the electrons after Bragg-reflection at the boundary of the first Brillouin zone pass through the Γ point again.
Fig. 3
Fig. 3 CEP-dependent HHG spectra from MgO. (a) for τp = 10T0 and (b) for τp = 4T0.
Fig. 4
Fig. 4 (a) and (b) HHG spectra and the corresponding time-dependent population nC[(K(t), t] for the two-color field with relative phase φ = 0; (c) the temporal profiles of the attosecond pulse generated from supercontinuum spectrum ranging from the 9th to the 21th harmonics without the phase compensation. (d) and (e) same with (a) and (b), but for φ = π
Fig. 5
Fig. 5 Excitation and emission instant analysis for a single driving pulse (a) (d), a two-color pulse with relative phase φ = 0 (b) (e), and a two-color pulse with φ = π (c) (f). (a)–(c) show the electric field (red dash line), the vector potential (green dot-dash line), the time-dependent population of conduction band nC[(K(t), t] (blue solid line), and attosecond pulse generation (black line), respectively. (d)–(e) show the corresponding time-frequency analysis.

Equations (2)

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K ( t ) = k A ( t ) = k + e t 0 t E ( t ) d t ,
E ( t ) = [ E 1 cos ( ω 1 t ) + E 2 cos ( ω 2 t + φ ) ] f ( t ) .

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