Abstract

We theoretically investigate the high-order harmonic generation driven by sawtooth-like laser fields. It is found that the coherence of the high-order harmonic spectrum could be controlled by adjusting the sawtooth shape parameter α (0 ≤ α ≤ 0.5). With proper α, the intensity of the high-order harmonic spectra come from the electrons with long trajectories can be greatly weakened and the harmonic photons in the plateau burst with high coherence in a broad frequency range. Selecting these harmonics, a phase-stabilized attosecond pulse train with regular pulse structure could be obtained.

© 2013 OSA

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  1. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81,163–234 (2009).
    [CrossRef]
  2. 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]
  3. 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,” Science320,1614–1617(2008).
    [CrossRef] [PubMed]
  4. Z. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A71,023813(2005).
    [CrossRef]
  5. W. Chen, G. Chen, and D. Kim, “Two-color field for the generation of an isolated attosecond pulse in water-window region,” Opt. Express19,20610–20615(2011).
  6. P. Li, I. Liu, and Shih-I Chu, “Optimization of three-color laser field for the generation of single ultrashort attosecond pulse,” Opt. Express19,23857–23866(2011).
  7. S. Chelkowski, T. Bredtmann, and A. D. Bandrauk, “High-order-harmonic generation from coherent electron wave packets in atoms and molecules as a tool for monitoring attosecond electrons,” Phys. Rev. A85,033404 (2012).
    [CrossRef]
  8. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett.71,1994 (1993).
  9. J. Mauritsson, P. Johnsson, E. Gustafsson, A. LHuillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett.97,013001 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B40,2321–2331 (2007).
    [CrossRef]
  12. P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A76,021801(R) (2007).
    [CrossRef]
  13. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
    [CrossRef] [PubMed]
  14. H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
    [CrossRef] [PubMed]
  15. D. R. Hartree, The Calculation of Atomic Structures (Wiley, New York, 1957).
  16. M. Gavrila, Atoms in Intense Laser Fields (Academic, New York, 1992).
  17. K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A45,3347 (2000).
    [CrossRef]
  18. X. M. Tong and Shih-I Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A61,021802 (2000).
    [CrossRef]

2012 (1)

S. Chelkowski, T. Bredtmann, and A. D. Bandrauk, “High-order-harmonic generation from coherent electron wave packets in atoms and molecules as a tool for monitoring attosecond electrons,” Phys. Rev. A85,033404 (2012).
[CrossRef]

2011 (3)

2009 (1)

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

2008 (1)

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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

2007 (3)

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]

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B40,2321–2331 (2007).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A76,021801(R) (2007).
[CrossRef]

2006 (1)

J. Mauritsson, P. Johnsson, E. Gustafsson, A. LHuillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett.97,013001 (2006).
[CrossRef] [PubMed]

2005 (2)

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Z. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A71,023813(2005).
[CrossRef]

2003 (1)

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

2000 (2)

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A45,3347 (2000).
[CrossRef]

X. M. Tong and Shih-I Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A61,021802 (2000).
[CrossRef]

1994 (1)

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

Agostini, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[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,” Science320,1614–1617(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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Balcou, Ph.

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Bandrauk, A. D.

S. Chelkowski, T. Bredtmann, and A. D. Bandrauk, “High-order-harmonic generation from coherent electron wave packets in atoms and molecules as a tool for monitoring attosecond electrons,” Phys. Rev. A85,033404 (2012).
[CrossRef]

Bredtmann, T.

S. Chelkowski, T. Bredtmann, and A. D. Bandrauk, “High-order-harmonic generation from coherent electron wave packets in atoms and molecules as a tool for monitoring attosecond electrons,” Phys. Rev. A85,033404 (2012).
[CrossRef]

Breger, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Burnett, K.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A45,3347 (2000).
[CrossRef]

Cao, W.

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B40,2321–2331 (2007).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A76,021801(R) (2007).
[CrossRef]

Carré, B.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Chan, H.

H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
[CrossRef] [PubMed]

Chang, Z.

Z. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A71,023813(2005).
[CrossRef]

Chelkowski, S.

S. Chelkowski, T. Bredtmann, and A. D. Bandrauk, “High-order-harmonic generation from coherent electron wave packets in atoms and molecules as a tool for monitoring attosecond electrons,” Phys. Rev. A85,033404 (2012).
[CrossRef]

Chen, G.

Chen, W.

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]

Chu, Shih-I

P. Li, I. Liu, and Shih-I Chu, “Optimization of three-color laser field for the generation of single ultrashort attosecond pulse,” Opt. Express19,23857–23866(2011).

X. M. Tong and Shih-I Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A61,021802 (2000).
[CrossRef]

Cooper, J.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A45,3347 (2000).
[CrossRef]

Corkum, P. B.

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

de Bohan, A.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Dinu, L. C.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Frasinski, L. J.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Gaarde, M. B.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. LHuillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett.97,013001 (2006).
[CrossRef] [PubMed]

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Gagnon, J.

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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Gavrila, M.

M. Gavrila, Atoms in Intense Laser Fields (Academic, New York, 1992).

Goulielmakis, E.

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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Gullikson, E. 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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Gustafsson, E.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. LHuillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett.97,013001 (2006).
[CrossRef] [PubMed]

Hartree, D. R.

D. R. Hartree, The Calculation of Atomic Structures (Wiley, New York, 1957).

Hofstetter, 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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Hong, W.

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B40,2321–2331 (2007).
[CrossRef]

Hsieh, Z.

H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
[CrossRef] [PubMed]

Ivanov, M.

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

Johnsson, P.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. LHuillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett.97,013001 (2006).
[CrossRef] [PubMed]

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Kazamias, S.

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Kienberger, R.

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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Kim, D.

Kleineberg, U.

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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Knight, P. L.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A45,3347 (2000).
[CrossRef]

Kovacev, M.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Krausz, F.

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

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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Kung, A. H.

H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
[CrossRef] [PubMed]

Lai, C.

H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
[CrossRef] [PubMed]

Lan, P.

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A76,021801(R) (2007).
[CrossRef]

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B40,2321–2331 (2007).
[CrossRef]

Lee, C.

H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
[CrossRef] [PubMed]

LHuillier, A.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. LHuillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett.97,013001 (2006).
[CrossRef] [PubMed]

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Li, P.

Li, R.

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]

Li, Y.

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A76,021801(R) (2007).
[CrossRef]

Liang, W.

H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
[CrossRef] [PubMed]

Liu, I.

Lopez-Martens, R.

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Lu, P.

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A76,021801(R) (2007).
[CrossRef]

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B40,2321–2331 (2007).
[CrossRef]

Mairesse, Y.

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Mauritsson, J.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. LHuillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett.97,013001 (2006).
[CrossRef] [PubMed]

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Merdji, H.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Monchicourt, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Muller, H. G.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Pan, R.

H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
[CrossRef] [PubMed]

Peng, L.

H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
[CrossRef] [PubMed]

Reed, V. C.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A45,3347 (2000).
[CrossRef]

Remetter, T.

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Salie‘res, P.

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Salières, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Schafer, K. J.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. LHuillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett.97,013001 (2006).
[CrossRef] [PubMed]

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Schultze, 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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Song, X.

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]

Taïeb, R.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

Tong, X. M.

X. M. Tong and Shih-I Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A61,021802 (2000).
[CrossRef]

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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Valentin, C.

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Varju, K.

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Wabnitz, H.

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

Wang, X.

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B40,2321–2331 (2007).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A76,021801(R) (2007).
[CrossRef]

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).
[CrossRef] [PubMed]

Yakovlev, V. S.

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,” Science320,1614–1617(2008).
[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]

J. Phys. B (1)

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B40,2321–2331 (2007).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (5)

Z. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A71,023813(2005).
[CrossRef]

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A45,3347 (2000).
[CrossRef]

X. M. Tong and Shih-I Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A61,021802 (2000).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A76,021801(R) (2007).
[CrossRef]

S. Chelkowski, T. Bredtmann, and A. D. Bandrauk, “High-order-harmonic generation from coherent electron wave packets in atoms and molecules as a tool for monitoring attosecond electrons,” Phys. Rev. A85,033404 (2012).
[CrossRef]

Phys. Rev. Lett. (4)

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

J. Mauritsson, P. Johnsson, E. Gustafsson, A. LHuillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett.97,013001 (2006).
[CrossRef] [PubMed]

P. Johnsson, R. Lopez-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varju, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salie‘res, Ph. Balcou, K. J. Schafer, and A. LHuillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett.95,013001 (2005).
[CrossRef] [PubMed]

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]

Rev. Mod. Phys. (1)

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

Science (3)

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,” Science320,1614–1617(2008).
[CrossRef] [PubMed]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science302,1540–1543 (2003).
[CrossRef] [PubMed]

H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science331,1165–1168 (2011).
[CrossRef] [PubMed]

Other (2)

D. R. Hartree, The Calculation of Atomic Structures (Wiley, New York, 1957).

M. Gavrila, Atoms in Intense Laser Fields (Academic, New York, 1992).

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Figures (5)

Fig. 1
Fig. 1

The comparison between the electric field of Es(α, t) and Ef(α, t).

Fig. 2
Fig. 2

The HHG spectra driven by the laser fields with different sawtooth shape parameter α.

Fig. 3
Fig. 3

The attosecond pulse trains generated by selecting the harmonics between the 20th-and 40th-order of the HHG spectra in Fig. 2. (a)α = 0.25; (b)α = 0.35; (c)α = 0.5.

Fig. 4
Fig. 4

The time-frequency analysis of the HHG spectra in Fig. 2. (a)α = 0.25; (b)α = 0.35; (c)α = 0.5.

Fig. 5
Fig. 5

The attosecond pulse trains generated from the HHG spectrum driven by the laser field with α = 0.5. The harmonic orders used are: (a)20∼ 40; (b)25∼45; (c)30∼50.

Equations (6)

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i ψ ( r , t ) t = [ 1 2 2 + V c ( r ) z E ( t ) ] ψ ( r , t ) ,
P ( ω ) = | z ¨ e j ω t d t | 2 ,
z ¨ = ψ ( r , t ) | V c ( r ) z E ( t ) | ψ ( r , t ) .
E s ( α , t ) = { E 0 t α T 0 t < α T E 0 ( T 2 t ) ( 1 2 α ) T α T t < ( 1 α ) T E 0 ( t T ) α T ( 1 α ) T t < T E s ( α , t k T ) otherwise , ( k = ± 1 , ± 2 , ± 3 , ) .
E s ( α , t ) E f ( α , t ) = k = 1 5 c k ( α ) sin ( k ω t ) ,
c k ( α ) = { 2 k π α = 0 , sin ( 2 k π α ) α ( 1 2 α ) k 2 π 2 0 < α < 0.5 , 2 cos ( k π ) k π α = 0.5 ,

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