Abstract

We studied the multi-plateau high-order harmonic generation (HHG) from solids numerically. It is found that the HHG spectra in the second and higher plateaus are redshifted in short laser pulses due to the nonadiabatic effect. The corresponding FWHMs also increase as a function of the harmonic order, suggesting the step-by-step excitation of higher conduction bands in the HHG process. Although the system is symmetric in the coordinate space, even-order harmonics are present. It is due to the fact that the symmetry of electron motions and the population in the higher conduction bands is broken in the k space and time domain based on the indirect step-by-step excitation model. Our numerical results are in good agreement with recent experimental measurements of Ndabashimiye et al. [Nature 534, 520 (2016)].

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2017 (6)

K. F. Lee, X. Ding, T. J. Hammond, M. E. Fermann, G. Vampa, and P. B. Corkum, “Harmonic generation in solids with direct fiber laser pumping,” Opt. Lett. 42(6), 1113–1116 (2017).
[Crossref] [PubMed]

T.-Y. Du and X.-B. Bian, “Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids,” Opt. Express 25(1), 151–158 (2017).
[Crossref] [PubMed]

T. Ikemachi, Y. Shinohara, T. Sato, J. Yumoto, M. Kuwata-Gonokami, and K. L. Ishikawa, “Trajectory analysis of high-order-harmonic generation from periodic crystals,” Phys. Rev. A 95(4), 043416 (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, 262–266 (2017).
[Crossref]

M.-Z. Li, G.-R. Jia, and X.-B. Bian, “Alignment dependent ultrafast electron-nuclear dynamics in molecular high-order harmonic generation,” J. Chem. Phys. 146(8), 084305 (2017).
[Crossref] [PubMed]

S. Jiang, C. Yu, G. Yuan, T. Wu, Z. Wang, and R. Lu, “Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields,” J. Phys.: Condens. Matter 29, 275702 (2017).

2016 (7)

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

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[Crossref] [PubMed]

X. Yuan, P. Wei, C. Liu, X. Ge, Y. Zheng, Z. Zeng, and R. Li, “Effect of nuclear motion on spectral broadening of high-order harmonic generation,” Opt. Express 24(8), 8194–8201 (2016).
[Crossref] [PubMed]

M. Wu, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94(6), 063403 (2016).
[Crossref]

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]

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]

2015 (6)

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]

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575, 1–71 (2015).
[Crossref]

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

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]

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of high-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (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]

2014 (1)

X.-B. Bian and A. D. Bandrauk, “Probing nuclear motion by frequency modulation of molecular high-order harmonic generation,” Phys. Rev. Lett. 113(19), 193901 (2014).
[Crossref] [PubMed]

2013 (1)

X.-B. Bian and A. Bandrauk, “Spectral shifts of nonadiabatic high-order harmonic generation,” Appl. Sci. 3(1), 267–277 (2013).
[Crossref]

2012 (1)

X.-B. Bian and A. D. Bandrauk, “Orientation dependence of nonadiabatic molecular high-order-harmonic generation from resonant polar molecules,” Phys. Rev. A 86(5), 053417 (2012).
[Crossref]

2011 (3)

S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field,” Phys. Rev. Lett. 107, 167407 (2011).
[Crossref] [PubMed]

X.-B. Bian and A. D. Bandrauk, “Nonadiabatic molecular high-order harmonic generation from polar molecules: Spectral redshift,” Phys. Rev. A 83(4), 041403 (2011).
[Crossref]

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

2009 (1)

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

2006 (1)

K. A. Pronin and A. D. Bandrauk, “Coherent control of harmonic generation in superlattices: single-mode response,” Phys. Rev. Lett. 97(2), 020602 (2006)
[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]

1995 (2)

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]

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
[Crossref] [PubMed]

1994 (1)

K. A. Pronin, A. D. Bandrauk, and A. A. Ovchinnikov, “Harmonic generation by a one-dimensional conductor: Exact results,” Phys. Rev. B 50(5), R3473 (1994).
[Crossref]

1993 (1)

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

Agostini, P.

S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field,” Phys. Rev. Lett. 107, 167407 (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]

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]

Bai, L.

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

Bandrauk, A.

X.-B. Bian and A. Bandrauk, “Spectral shifts of nonadiabatic high-order harmonic generation,” Appl. Sci. 3(1), 267–277 (2013).
[Crossref]

Bandrauk, A. D.

X.-B. Bian and A. D. Bandrauk, “Probing nuclear motion by frequency modulation of molecular high-order harmonic generation,” Phys. Rev. Lett. 113(19), 193901 (2014).
[Crossref] [PubMed]

X.-B. Bian and A. D. Bandrauk, “Orientation dependence of nonadiabatic molecular high-order-harmonic generation from resonant polar molecules,” Phys. Rev. A 86(5), 053417 (2012).
[Crossref]

X.-B. Bian and A. D. Bandrauk, “Nonadiabatic molecular high-order harmonic generation from polar molecules: Spectral redshift,” Phys. Rev. A 83(4), 041403 (2011).
[Crossref]

K. A. Pronin and A. D. Bandrauk, “Coherent control of harmonic generation in superlattices: single-mode response,” Phys. Rev. Lett. 97(2), 020602 (2006)
[Crossref] [PubMed]

K. A. Pronin, A. D. Bandrauk, and A. A. Ovchinnikov, “Harmonic generation by a one-dimensional conductor: Exact results,” Phys. Rev. B 50(5), R3473 (1994).
[Crossref]

Y. Pertot, X.-B. Bian, M. A. Fareed, A. D. Bandrauk, and T. Ozaki, “Wavelength tuning of highly stable high-order harmonics generated from carbon plasma,” in 2013 IEEE Photonics Conference, IPC 2013 (2013), p. 51.

Beaulieu, S.

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[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]

Bian, X.-B.

M.-Z. Li, G.-R. Jia, and X.-B. Bian, “Alignment dependent ultrafast electron-nuclear dynamics in molecular high-order harmonic generation,” J. Chem. Phys. 146(8), 084305 (2017).
[Crossref] [PubMed]

T.-Y. Du and X.-B. Bian, “Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids,” Opt. Express 25(1), 151–158 (2017).
[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]

X.-B. Bian and A. D. Bandrauk, “Probing nuclear motion by frequency modulation of molecular high-order harmonic generation,” Phys. Rev. Lett. 113(19), 193901 (2014).
[Crossref] [PubMed]

X.-B. Bian and A. Bandrauk, “Spectral shifts of nonadiabatic high-order harmonic generation,” Appl. Sci. 3(1), 267–277 (2013).
[Crossref]

X.-B. Bian and A. D. Bandrauk, “Orientation dependence of nonadiabatic molecular high-order-harmonic generation from resonant polar molecules,” Phys. Rev. A 86(5), 053417 (2012).
[Crossref]

X.-B. Bian and A. D. Bandrauk, “Nonadiabatic molecular high-order harmonic generation from polar molecules: Spectral redshift,” Phys. Rev. A 83(4), 041403 (2011).
[Crossref]

Y. Pertot, X.-B. Bian, M. A. Fareed, A. D. Bandrauk, and T. Ozaki, “Wavelength tuning of highly stable high-order harmonics generated from carbon plasma,” in 2013 IEEE Photonics Conference, IPC 2013 (2013), p. 51.

T.-Y. Du, X.-H. Huang, and X.-B. Bian, “Insight into High-order Harmonic Generation from Solids: The Contributions of the Bloch Wave-packets Moving on the Group and Phase Velocities,” arXiv:1707.05689 (2017).

T.-Y. Du and X.-B. Bian, “Mechanism of High-Order Harmonic Generation from Periodic Potentials,” arXiv:1606.06433 (2016).

Brabec, T.

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]

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]

M. Wu, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94(6), 063403 (2016).
[Crossref]

Camp, S.

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[Crossref] [PubMed]

Cao, X.

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

Catoire, F.

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (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]

Comby, A.

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[Crossref] [PubMed]

Corkum, P. B.

K. F. Lee, X. Ding, T. J. Hammond, M. E. Fermann, G. Vampa, and P. B. Corkum, “Harmonic generation in solids with direct fiber laser pumping,” Opt. Lett. 42(6), 1113–1116 (2017).
[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]

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

Descamps, D.

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[Crossref] [PubMed]

DiChiara, A. D.

S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field,” Phys. Rev. Lett. 107, 167407 (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]

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,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field,” Phys. Rev. Lett. 107, 167407 (2011).
[Crossref] [PubMed]

Ding, X.

Du, H.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of high-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Du, T.-Y.

T.-Y. Du and X.-B. Bian, “Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids,” Opt. Express 25(1), 151–158 (2017).
[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]

T.-Y. Du and X.-B. Bian, “Mechanism of High-Order Harmonic Generation from Periodic Potentials,” arXiv:1606.06433 (2016).

T.-Y. Du, X.-H. Huang, and X.-B. Bian, “Insight into High-order Harmonic Generation from Solids: The Contributions of the Bloch Wave-packets Moving on the Group and Phase Velocities,” arXiv:1707.05689 (2017).

Fareed, M. A.

Y. Pertot, X.-B. Bian, M. A. Fareed, A. D. Bandrauk, and T. Ozaki, “Wavelength tuning of highly stable high-order harmonics generated from carbon plasma,” in 2013 IEEE Photonics Conference, IPC 2013 (2013), p. 51.

Fermann, M. E.

Gaarde, M. B.

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. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[Crossref] [PubMed]

M. Wu, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94(6), 063403 (2016).
[Crossref]

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]

Ge, X.

Geng, J.-W.

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575, 1–71 (2015).
[Crossref]

Ghimire, S.

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, 262–266 (2017).
[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. 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, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field,” Phys. Rev. Lett. 107, 167407 (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]

Gong, Q.

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575, 1–71 (2015).
[Crossref]

Guan, Z.

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]

Hammond, T. J.

Hawkins, P. G.

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]

He, L.

L. He, P. Lan, C. Zhai, F. Wang, W. Shi, Q. Zhang, X. Zhu, and P. Lu, “Frequency shift in high order harmonic generation from isotopic molecules,” arXiv:1601.04835v2 (2016).

Heinz, T. F.

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, 262–266 (2017).
[Crossref]

Hohenleutner, M.

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]

Hu, B.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of high-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Huang, X.-H.

T.-Y. Du, X.-H. Huang, and X.-B. Bian, “Insight into High-order Harmonic Generation from Solids: The Contributions of the Bloch Wave-packets Moving on the Group and Phase Velocities,” arXiv:1707.05689 (2017).

Huber, R.

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]

Huttner, U.

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]

Ikemachi, T.

T. Ikemachi, Y. Shinohara, T. Sato, J. Yumoto, M. Kuwata-Gonokami, and K. L. Ishikawa, “Trajectory analysis of high-order-harmonic generation from periodic crystals,” Phys. Rev. A 95(4), 043416 (2017).
[Crossref]

Ishikawa, K. L.

T. Ikemachi, Y. Shinohara, T. Sato, J. Yumoto, M. Kuwata-Gonokami, and K. L. Ishikawa, “Trajectory analysis of high-order-harmonic generation from periodic crystals,” Phys. Rev. A 95(4), 043416 (2017).
[Crossref]

Ivanov, M.

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

Á. Jiménez-Galán, N. Zhavoronkov, M. Schloz, F. Morales, and M. Ivanov, “Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields,” arXiv:1707.05590 (2017).

Ivanov, M. Y.

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]

Jia, G.-R.

M.-Z. Li, G.-R. Jia, and X.-B. Bian, “Alignment dependent ultrafast electron-nuclear dynamics in molecular high-order harmonic generation,” J. Chem. Phys. 146(8), 084305 (2017).
[Crossref] [PubMed]

Jiang, S.

S. Jiang, C. Yu, G. Yuan, T. Wu, Z. Wang, and R. Lu, “Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields,” J. Phys.: Condens. Matter 29, 275702 (2017).

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

Jiang, W.-C.

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575, 1–71 (2015).
[Crossref]

Jiménez-Galán, Á.

Á. Jiménez-Galán, N. Zhavoronkov, M. Schloz, F. Morales, and M. Ivanov, “Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields,” arXiv:1707.05590 (2017).

Kira, M.

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]

Knorr, M.

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]

Koch, S. W.

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]

Krausz, F.

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

Kuwata-Gonokami, M.

T. Ikemachi, Y. Shinohara, T. Sato, J. Yumoto, M. Kuwata-Gonokami, and K. L. Ishikawa, “Trajectory analysis of high-order-harmonic generation from periodic crystals,” Phys. Rev. A 95(4), 043416 (2017).
[Crossref]

L’Huillier, A.

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
[Crossref] [PubMed]

Lan, P.

L. He, P. Lan, C. Zhai, F. Wang, W. Shi, Q. Zhang, X. Zhu, and P. Lu, “Frequency shift in high order harmonic generation from isotopic molecules,” arXiv:1601.04835v2 (2016).

Langer, F.

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]

Lee, K. F.

Légaré, F.

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[Crossref] [PubMed]

Lewenstein, M.

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
[Crossref] [PubMed]

Li, M.-Z.

M.-Z. Li, G.-R. Jia, and X.-B. Bian, “Alignment dependent ultrafast electron-nuclear dynamics in molecular high-order harmonic generation,” J. Chem. Phys. 146(8), 084305 (2017).
[Crossref] [PubMed]

Li, R.

Li, Y.

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, 262–266 (2017).
[Crossref]

Liu, C.

Liu, H.

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, 262–266 (2017).
[Crossref]

Lu, P.

L. He, P. Lan, C. Zhai, F. Wang, W. Shi, Q. Zhang, X. Zhu, and P. Lu, “Frequency shift in high order harmonic generation from isotopic molecules,” arXiv:1601.04835v2 (2016).

Lu, R.

S. Jiang, C. Yu, G. Yuan, T. Wu, Z. Wang, and R. Lu, “Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields,” J. Phys.: Condens. Matter 29, 275702 (2017).

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

Mairesse, Y.

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[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.

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]

Morales, F.

Á. Jiménez-Galán, N. Zhavoronkov, M. Schloz, F. Morales, and M. Ivanov, “Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields,” arXiv:1707.05590 (2017).

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]

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]

Ovchinnikov, A. A.

K. A. Pronin, A. D. Bandrauk, and A. A. Ovchinnikov, “Harmonic generation by a one-dimensional conductor: Exact results,” Phys. Rev. B 50(5), R3473 (1994).
[Crossref]

Ozaki, T.

Y. Pertot, X.-B. Bian, M. A. Fareed, A. D. Bandrauk, and T. Ozaki, “Wavelength tuning of highly stable high-order harmonics generated from carbon plasma,” in 2013 IEEE Photonics Conference, IPC 2013 (2013), p. 51.

Peng, L.-Y.

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575, 1–71 (2015).
[Crossref]

Pertot, Y.

Y. Pertot, X.-B. Bian, M. A. Fareed, A. D. Bandrauk, and T. Ozaki, “Wavelength tuning of highly stable high-order harmonics generated from carbon plasma,” in 2013 IEEE Photonics Conference, IPC 2013 (2013), p. 51.

Petit, S.

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[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]

Pronin, K. A.

K. A. Pronin and A. D. Bandrauk, “Coherent control of harmonic generation in superlattices: single-mode response,” Phys. Rev. Lett. 97(2), 020602 (2006)
[Crossref] [PubMed]

K. A. Pronin, A. D. Bandrauk, and A. A. Ovchinnikov, “Harmonic generation by a one-dimensional conductor: Exact results,” Phys. Rev. B 50(5), R3473 (1994).
[Crossref]

Reis, D. A.

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, 262–266 (2017).
[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. 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, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field,” Phys. Rev. Lett. 107, 167407 (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]

Salières, P.

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
[Crossref] [PubMed]

Sato, T.

T. Ikemachi, Y. Shinohara, T. Sato, J. Yumoto, M. Kuwata-Gonokami, and K. L. Ishikawa, “Trajectory analysis of high-order-harmonic generation from periodic crystals,” Phys. Rev. A 95(4), 043416 (2017).
[Crossref]

Schafer, K. J.

M. Wu, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94(6), 063403 (2016).
[Crossref]

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (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(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]

Schloz, M.

Á. Jiménez-Galán, N. Zhavoronkov, M. Schloz, F. Morales, and M. Ivanov, “Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields,” arXiv:1707.05590 (2017).

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]

Shi, W.

L. He, P. Lan, C. Zhai, F. Wang, W. Shi, Q. Zhang, X. Zhu, and P. Lu, “Frequency shift in high order harmonic generation from isotopic molecules,” arXiv:1601.04835v2 (2016).

Shinohara, Y.

T. Ikemachi, Y. Shinohara, T. Sato, J. Yumoto, M. Kuwata-Gonokami, and K. L. Ishikawa, “Trajectory analysis of high-order-harmonic generation from periodic crystals,” Phys. Rev. A 95(4), 043416 (2017).
[Crossref]

Sistrunk, E.

S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field,” Phys. Rev. Lett. 107, 167407 (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]

Szafruga, U. B.

S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field,” Phys. Rev. Lett. 107, 167407 (2011).
[Crossref] [PubMed]

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.

K. F. Lee, X. Ding, T. J. Hammond, M. E. Fermann, G. Vampa, and P. B. Corkum, “Harmonic generation in solids with direct fiber laser pumping,” Opt. Lett. 42(6), 1113–1116 (2017).
[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]

Wang, F.

L. He, P. Lan, C. Zhai, F. Wang, W. Shi, Q. Zhang, X. Zhu, and P. Lu, “Frequency shift in high order harmonic generation from isotopic molecules,” arXiv:1601.04835v2 (2016).

Wang, H.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of high-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Wang, Z.

S. Jiang, C. Yu, G. Yuan, T. Wu, Z. Wang, and R. Lu, “Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields,” J. Phys.: Condens. Matter 29, 275702 (2017).

Wanie, V.

S. Beaulieu, S. Camp, D. Descamps, A. Comby, V. Wanie, S. Petit, F. Légaré, K. J. Schafer, M. B. Gaarde, F. Catoire, and Y. Mairesse, “Role of excited states in high-order harmonic generation,” Phys. Rev. Lett. 117(20), 203001 (2016).
[Crossref] [PubMed]

Wei, P.

Wiggins, S.

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

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, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94(6), 063403 (2016).
[Crossref]

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, T.

S. Jiang, C. Yu, G. Yuan, T. Wu, Z. Wang, and R. Lu, “Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields,” J. Phys.: Condens. Matter 29, 275702 (2017).

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

Xiong, W.-H.

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575, 1–71 (2015).
[Crossref]

Xue, S.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of high-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Yakovlev, V. S.

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]

You, Y. S.

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, 262–266 (2017).
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Yu, C.

S. Jiang, C. Yu, G. Yuan, T. Wu, Z. Wang, and R. Lu, “Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields,” J. Phys.: Condens. Matter 29, 275702 (2017).

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

Yuan, G.

S. Jiang, C. Yu, G. Yuan, T. Wu, Z. Wang, and R. Lu, “Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields,” J. Phys.: Condens. Matter 29, 275702 (2017).

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

Yuan, X.

Yumoto, J.

T. Ikemachi, Y. Shinohara, T. Sato, J. Yumoto, M. Kuwata-Gonokami, and K. L. Ishikawa, “Trajectory analysis of high-order-harmonic generation from periodic crystals,” Phys. Rev. A 95(4), 043416 (2017).
[Crossref]

Zeng, Z.

Zhai, C.

L. He, P. Lan, C. Zhai, F. Wang, W. Shi, Q. Zhang, X. Zhu, and P. Lu, “Frequency shift in high order harmonic generation from isotopic molecules,” arXiv:1601.04835v2 (2016).

Zhang, Q.

L. He, P. Lan, C. Zhai, F. Wang, W. Shi, Q. Zhang, X. Zhu, and P. Lu, “Frequency shift in high order harmonic generation from isotopic molecules,” arXiv:1601.04835v2 (2016).

Zhang, X.

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

Zhang, Z.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of high-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Zhavoronkov, N.

Á. Jiménez-Galán, N. Zhavoronkov, M. Schloz, F. Morales, and M. Ivanov, “Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields,” arXiv:1707.05590 (2017).

Zheng, Y.

Zhou, X. X.

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]

Zhou, X.-X.

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]

Zhu, X.

L. He, P. Lan, C. Zhai, F. Wang, W. Shi, Q. Zhang, X. Zhu, and P. Lu, “Frequency shift in high order harmonic generation from isotopic molecules,” arXiv:1601.04835v2 (2016).

Appl. Sci. (1)

X.-B. Bian and A. Bandrauk, “Spectral shifts of nonadiabatic high-order harmonic generation,” Appl. Sci. 3(1), 267–277 (2013).
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J. Chem. Phys. (1)

M.-Z. Li, G.-R. Jia, and X.-B. Bian, “Alignment dependent ultrafast electron-nuclear dynamics in molecular high-order harmonic generation,” J. Chem. Phys. 146(8), 084305 (2017).
[Crossref] [PubMed]

J. Phys.: Condens. Matter (1)

S. Jiang, C. Yu, G. Yuan, T. Wu, Z. Wang, and R. Lu, “Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields,” J. Phys.: Condens. Matter 29, 275702 (2017).

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, 262–266 (2017).
[Crossref]

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

Nature (2)

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).
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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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Opt. Express (2)

Opt. Lett. (1)

Phys. Rep. (1)

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575, 1–71 (2015).
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Phys. Rev. A (10)

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).
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M. Wu, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94(6), 063403 (2016).
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T. Ikemachi, Y. Shinohara, T. Sato, J. Yumoto, M. Kuwata-Gonokami, and K. L. Ishikawa, “Trajectory analysis of high-order-harmonic generation from periodic crystals,” Phys. Rev. A 95(4), 043416 (2017).
[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]

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

X.-B. Bian and A. D. Bandrauk, “Nonadiabatic molecular high-order harmonic generation from polar molecules: Spectral redshift,” Phys. Rev. A 83(4), 041403 (2011).
[Crossref]

X.-B. Bian and A. D. Bandrauk, “Orientation dependence of nonadiabatic molecular high-order-harmonic generation from resonant polar molecules,” Phys. Rev. A 86(5), 053417 (2012).
[Crossref]

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of high-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (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).
[Crossref]

Phys. Rev. B (2)

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K. A. Pronin and A. D. Bandrauk, “Coherent control of harmonic generation in superlattices: single-mode response,” Phys. Rev. Lett. 97(2), 020602 (2006)
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S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field,” Phys. Rev. Lett. 107, 167407 (2011).
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Other (5)

T.-Y. Du and X.-B. Bian, “Mechanism of High-Order Harmonic Generation from Periodic Potentials,” arXiv:1606.06433 (2016).

T.-Y. Du, X.-H. Huang, and X.-B. Bian, “Insight into High-order Harmonic Generation from Solids: The Contributions of the Bloch Wave-packets Moving on the Group and Phase Velocities,” arXiv:1707.05689 (2017).

Y. Pertot, X.-B. Bian, M. A. Fareed, A. D. Bandrauk, and T. Ozaki, “Wavelength tuning of highly stable high-order harmonics generated from carbon plasma,” in 2013 IEEE Photonics Conference, IPC 2013 (2013), p. 51.

L. He, P. Lan, C. Zhai, F. Wang, W. Shi, Q. Zhang, X. Zhu, and P. Lu, “Frequency shift in high order harmonic generation from isotopic molecules,” arXiv:1601.04835v2 (2016).

Á. Jiménez-Galán, N. Zhavoronkov, M. Schloz, F. Morales, and M. Ivanov, “Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields,” arXiv:1707.05590 (2017).

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Figures (7)

Fig. 1
Fig. 1 Band structure of the system and schematic illustration of the motion of photoelectrons in different bands with multi-plateau HHG emissions in the k space.
Fig. 2
Fig. 2 Schematic illustration of the motion of electrons in the conduction bands in the first cycle of the time domain. (a) The electron motions in C3. (b) The electron motions in C2. (c) The electron motions in C1. (d) Vector potential of the laser field. (e) Electric field of the laser.
Fig. 3
Fig. 3 HHG spectrum. The parameters of the laser field: λ=3.2μm, I=8.77×1011 W/cm2, and τ=15 cycles. f (t) = 1. The black, blue, and red arrows correspond to the predicted cutoff energies of HHG from the first, second, and third conduction band, respectively.
Fig. 4
Fig. 4 Population of conduction bands C1, C2, and C3 as a function of time. The laser parameters are the same as in Fig. 3. f (t) = 1.
Fig. 5
Fig. 5 Spectrum of HHG. The laser parameters are the same as in Fig. 3, except f (t) = cos2(π(tτ/2)) and τ = 10 cycles.
Fig. 6
Fig. 6 The same as Fig. 5 except τ=15 cycles.
Fig. 7
Fig. 7 The asymmetric coefficients as a function of harmonic order. In the upper panel, the total pulse duration τ=10 cycles. In the lower panel, τ=15 cycles.

Equations (5)

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k ( t ) = k 0 + A ( t )
E ( t ) = E 0 f ( t ) cos ( ω ( t τ / 2 ) )
N 1 = [ ε C 1 ( k m a x ) ε v ( k m a x ) ] / ω 32
A ( N ) = S f S r S f + S r
S f = τ / 2 τ g ( N ω , t ) d t , S r = 0 τ / 2 g ( N ω , t ) d t ,

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