Abstract

We theoretically study infrared (IR)-driven high-order harmonic generation (HHG) assisted by attosecond pulses with a central energy above the atomic ionization threshold. We provide a clear physical picture for controlling HHG using the time delay between the attosecond pulses and the IR laser reported by Faria et al. [Phys. Rev. A 74, 053416 (2006)]. This physical picture also indicates that the combined attosecond pulses and IR laser can help resolve the dynamics of ionized electrons from time-dependent harmonic spectra. We present the quantum effect on HHG as an example. While leaving parent ions, ionized electrons can still emit harmonics in the semi-classically forbidden situation. The two-color excitation provides a practical method to observe the quantum effect experimentally. Furthermore, in our work, attosecond pulses and an IR field are considered with a realistic pulse shape, which shows a quantitatively important effect in controlling harmonic spectra. Accordingly, a guide to optimize the control capability for HHG is presented, and a method to determine the IR carrier-envelope phase based on the pulse-shape effect on the HHG is also proposed.

© 2013 Optical Society of America

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  18. K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004).
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    [CrossRef]
  25. K. L. Ishikawa, “Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003).
    [CrossRef]
  26. H. C. Lee, and T. F. Jiang, “Control mechanism of atomic ionization and high-order harmonic generation assisted by attosecond pulses,” Appl. Phys. B 109, 621–630 (2012).
    [CrossRef]
  27. E. J. Takahashi, P. Lan, Oliver D. Mücke, Y. Nabekawa, and K. Midorikawa, “Infrared two-color multicycle laser field synthesis for generating an intense attosecond pulse,” Phys. Rev. Lett. 104, 233901 (2010).
    [CrossRef]
  28. E. Mansten, J. M. Dahlström, P. Johnsson, M. Swoboda, A. L’Huillier, and J. Mauritsson, “Spectral shaping of attosecond pulses using two-colour laser fields,” New J. Phys. 10, 083041 (2008).
    [CrossRef]
  29. J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A 74, 023404 (2006).
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  32. J. A. Pérez-Hernández and L. Plaja, “Quantum description of the high-order harmonic generation in multiphoton and tunneling regimes,” Phys. Rev. A 76, 023829 (2007).
    [CrossRef]
  33. H. C. Lee, S. D. Jheng, and T. F. Jiang, “Theory of infrared-dressed atomic photoionization by extremely ultraviolet attosecond pulse trains,” J. Opt. Soc. Am. B 29, 286–293 (2012).
    [CrossRef]
  34. X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime, ” J. Phys. B 38, 2593–2600 (2005).
    [CrossRef]
  35. O. Smirnova, M. Spanner, and M. Ivanov, “Coulomb and polarization effects in sub-cycle dynamics of strong-field ionization,” J. Phys. B 39, S307–S321 (2006).
    [CrossRef]
  36. O. Smirnova, M. Spanner, and M. Y. Ivanov, “Coulomb and polarization effects in laser-assisted XUV ionization,” J. Phys. B 39, S323–S339 (2006).
    [CrossRef]
  37. O. Smirnova, M. Spanner, and M. Y. Ivanov, “Analytical solutions for strong field-driven atomic and molecular one- and two-electron continua and applications to strong-field problems,” Phys. Rev. A 77, 033407 (2008).
    [CrossRef]
  38. M. Ivanov and O. Smirnova, “How accurate is the attosecond streak camera?,” Phys. Rev. Lett. 107, 213605 (2011).
    [CrossRef]
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  40. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
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    [CrossRef]
  42. S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
    [CrossRef]
  43. J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
    [CrossRef]
  44. T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
    [CrossRef]
  45. G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett. 91, 253004 (2003).
    [CrossRef]
  46. P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25, 16–18 (2000).
    [CrossRef]
  47. E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
    [CrossRef]
  48. T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier–envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
    [CrossRef]

2012 (3)

H. C. Lee, and T. F. Jiang, “Control mechanism of atomic ionization and high-order harmonic generation assisted by attosecond pulses,” Appl. Phys. B 109, 621–630 (2012).
[CrossRef]

J. M. Dahlström, A. L’Huillier, and A. Maquet, “Introduction to attoseond delays in photoionization,” J. Phys. B 45, 183001 (2012).
[CrossRef]

H. C. Lee, S. D. Jheng, and T. F. Jiang, “Theory of infrared-dressed atomic photoionization by extremely ultraviolet attosecond pulse trains,” J. Opt. Soc. Am. B 29, 286–293 (2012).
[CrossRef]

2011 (3)

M. Ivanov and O. Smirnova, “How accurate is the attosecond streak camera?,” Phys. Rev. Lett. 107, 213605 (2011).
[CrossRef]

K. Klünder, J. M. Dahlström, M. Gisselbrecht, T. Fordell, M. Swoboda, D. Guénot, P. Johnsson, J. Caillat, J. Mauritsson, A. Maquet, R. Taïeb, and A. L. Huillier, “Probing single-photon ionization on the attosecond time scale,” Phys. Rev. Lett. 106, 143002 (2011).
[CrossRef]

F. Kelkensberg, W. Siu, J. F. Pérez-Torres, F. Morales, G. Gademann, A. Rouzée, P. Johnsson, M. Lucchini, F. Calegari, J. L. Sanz-Vicario, F. Martín, and M. J. J. Vrakking, “Attosecond control in photoionization of hydrogen molecules,” Phys. Rev. Lett. 107, 043002 (2011).
[CrossRef]

2010 (4)

F. He, and U. Thumm, “Dissociative ionization of H2 in an attosecond pulse train and delayed laser pulse,” Phys. Rev. A 81, 053413 (2010).
[CrossRef]

E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
[CrossRef]

E. J. Takahashi, P. Lan, Oliver D. Mücke, Y. Nabekawa, and K. Midorikawa, “Infrared two-color multicycle laser field synthesis for generating an intense attosecond pulse,” Phys. Rev. Lett. 104, 233901 (2010).
[CrossRef]

X. M. Tong, P. Ranitovic, C. L. Cocke, and N. Toshima, “Mechanisms of infrared-laser-assisted atomic ionization by attosecond pulses,” Phys. Rev. A 81, 021404(R) (2010).

2009 (3)

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. Quantum Electron. 33, 17–59 (2009).
[CrossRef]

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier–envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

2008 (4)

L. Y. Peng, E. A. Pronin, and A. F. Starace, “Attosecond pulse carrier-envelope phase effects on ionized electron momentum and energy distributions: roles of frequency, intensity and additional IR pulse,” New J. Phys. 10, 025030 (2008).
[CrossRef]

E. Mansten, J. M. Dahlström, P. Johnsson, M. Swoboda, A. L’Huillier, and J. Mauritsson, “Spectral shaping of attosecond pulses using two-colour laser fields,” New J. Phys. 10, 083041 (2008).
[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,” Science 320, 1614–1617 (2008).
[CrossRef]

O. Smirnova, M. Spanner, and M. Y. Ivanov, “Analytical solutions for strong field-driven atomic and molecular one- and two-electron continua and applications to strong-field problems,” Phys. Rev. A 77, 033407 (2008).
[CrossRef]

2007 (6)

J. A. Pérez-Hernández and L. Plaja, “Quantum description of the high-order harmonic generation in multiphoton and tunneling regimes,” Phys. Rev. A 76, 023829 (2007).
[CrossRef]

P. Johnsson, J. Mauritsson, T. Remetter, A. L’Huillier, and K. J. Schafer, “Attosecond control of ionization by wave-packet interference,” Phys. Rev. Lett. 99, 233001 (2007).
[CrossRef]

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446, 627–632 (2007).
[CrossRef]

T. Morishita, S. Watanabe, and C. D. Lin, “Attosecond light pulses for probing two-electron dynamics of helium in the time domain,” Phys. Rev. Lett. 98, 083003 (2007).
[CrossRef]

C. F. de M. Faria, and P. Salières, “High-order harmonic generation with a strong laser field and an attosecond-pulse train: the Dirac-Delta comb and monochromatic limits,” Laser Phys. 17, 390–400 (2007).
[CrossRef]

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Dramatic enhancement of high-order harmonic generation,” Phys. Rev. Lett. 99, 053904 (2007).
[CrossRef]

2006 (8)

C. F. de M. Faria, P. Salières, P. Villain, and M. Lewenstein, “Controlling high-order harmonic generation and above-threshold ionization with an attosecond-pulse train,” Phys. Rev. A 74, 053416 (2006).
[CrossRef]

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L. Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
[CrossRef]

J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A 74, 023404 (2006).
[CrossRef]

O. Smirnova, M. Spanner, and M. Ivanov, “Coulomb and polarization effects in sub-cycle dynamics of strong-field ionization,” J. Phys. B 39, S307–S321 (2006).
[CrossRef]

O. Smirnova, M. Spanner, and M. Y. Ivanov, “Coulomb and polarization effects in laser-assisted XUV ionization,” J. Phys. B 39, S323–S339 (2006).
[CrossRef]

D. B. Milošević, “Theoretical analysis of high-order harmonic generation from a coherent superposition of states,” J. Opt. Soc. Am. B 23, 308–317 (2006).
[CrossRef]

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
[CrossRef]

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[CrossRef]

2005 (5)

X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime, ” J. Phys. B 38, 2593–2600 (2005).
[CrossRef]

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L. Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

M. Wickenhauser, J. Burgdöfer, F. Krausz, and M. Drescher, “Time resolved Fano resonances,” Phys. Rev. Lett. 94, 023002 (2005).
[CrossRef]

Z. X. Zhao and C. D. Lin, “Theory of laser-assisted autoionization by attosecond light pulses,” Phys. Rev. A 71, 060702 (2005).
[CrossRef]

J. Biegert, A. Heinrich, C. P. Hauri, W. Kornelis, P. Schlup, M. Anscombe, K. J. Schafer, M. B. Gaarde, and U. Keller, “Enhancement of high-order harmonic emission using attosecond pulse trains,” Laser Phys. 15, 899–902 (2005).

2004 (2)

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004).
[CrossRef]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

2003 (3)

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[CrossRef]

K. L. Ishikawa, “Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003).
[CrossRef]

2002 (1)

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
[CrossRef]

2000 (3)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef]

X. M. Tong, and S. I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61, 021802 (2000).
[CrossRef]

P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25, 16–18 (2000).
[CrossRef]

1994 (1)

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

1993 (1)

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

Anscombe, M.

J. Biegert, A. Heinrich, C. P. Hauri, W. Kornelis, P. Schlup, M. Anscombe, K. J. Schafer, M. B. Gaarde, and U. Keller, “Enhancement of high-order harmonic emission using attosecond pulse trains,” Laser Phys. 15, 899–902 (2005).

Aquila, A. L.

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

Attwood, D. T.

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

Azzeer, A. M.

E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
[CrossRef]

Balcou, P.

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L. Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

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

Baltuska, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

Baltuška, A.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Biegert, J.

J. Biegert, A. Heinrich, C. P. Hauri, W. Kornelis, P. Schlup, M. Anscombe, K. J. Schafer, M. B. Gaarde, and U. Keller, “Enhancement of high-order harmonic emission using attosecond pulse trains,” Laser Phys. 15, 899–902 (2005).

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004).
[CrossRef]

Burgdöfer, J.

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P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L. Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
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J. Biegert, A. Heinrich, C. P. Hauri, W. Kornelis, P. Schlup, M. Anscombe, K. J. Schafer, M. B. Gaarde, and U. Keller, “Enhancement of high-order harmonic emission using attosecond pulse trains,” Laser Phys. 15, 899–902 (2005).

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004).
[CrossRef]

Schätzel, M. G.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier–envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Schlup, P.

J. Biegert, A. Heinrich, C. P. Hauri, W. Kornelis, P. Schlup, M. Anscombe, K. J. Schafer, M. B. Gaarde, and U. Keller, “Enhancement of high-order harmonic emission using attosecond pulse trains,” Laser Phys. 15, 899–902 (2005).

Schröder, H.

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446, 627–632 (2007).
[CrossRef]

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,” Science 320, 1614–1617 (2008).
[CrossRef]

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446, 627–632 (2007).
[CrossRef]

Scrinzi, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
[CrossRef]

Siu, W.

F. Kelkensberg, W. Siu, J. F. Pérez-Torres, F. Morales, G. Gademann, A. Rouzée, P. Johnsson, M. Lucchini, F. Calegari, J. L. Sanz-Vicario, F. Martín, and M. J. J. Vrakking, “Attosecond control in photoionization of hydrogen molecules,” Phys. Rev. Lett. 107, 043002 (2011).
[CrossRef]

Smirnova, O.

M. Ivanov and O. Smirnova, “How accurate is the attosecond streak camera?,” Phys. Rev. Lett. 107, 213605 (2011).
[CrossRef]

O. Smirnova, M. Spanner, and M. Y. Ivanov, “Analytical solutions for strong field-driven atomic and molecular one- and two-electron continua and applications to strong-field problems,” Phys. Rev. A 77, 033407 (2008).
[CrossRef]

O. Smirnova, M. Spanner, and M. Y. Ivanov, “Coulomb and polarization effects in laser-assisted XUV ionization,” J. Phys. B 39, S323–S339 (2006).
[CrossRef]

O. Smirnova, M. Spanner, and M. Ivanov, “Coulomb and polarization effects in sub-cycle dynamics of strong-field ionization,” J. Phys. B 39, S307–S321 (2006).
[CrossRef]

Spanner, M.

O. Smirnova, M. Spanner, and M. Y. Ivanov, “Analytical solutions for strong field-driven atomic and molecular one- and two-electron continua and applications to strong-field problems,” Phys. Rev. A 77, 033407 (2008).
[CrossRef]

O. Smirnova, M. Spanner, and M. Y. Ivanov, “Coulomb and polarization effects in laser-assisted XUV ionization,” J. Phys. B 39, S323–S339 (2006).
[CrossRef]

O. Smirnova, M. Spanner, and M. Ivanov, “Coulomb and polarization effects in sub-cycle dynamics of strong-field ionization,” J. Phys. B 39, S307–S321 (2006).
[CrossRef]

Starace, A. F.

L. Y. Peng, E. A. Pronin, and A. F. Starace, “Attosecond pulse carrier-envelope phase effects on ionized electron momentum and energy distributions: roles of frequency, intensity and additional IR pulse,” New J. Phys. 10, 025030 (2008).
[CrossRef]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef]

Swoboda, M.

K. Klünder, J. M. Dahlström, M. Gisselbrecht, T. Fordell, M. Swoboda, D. Guénot, P. Johnsson, J. Caillat, J. Mauritsson, A. Maquet, R. Taïeb, and A. L. Huillier, “Probing single-photon ionization on the attosecond time scale,” Phys. Rev. Lett. 106, 143002 (2011).
[CrossRef]

E. Mansten, J. M. Dahlström, P. Johnsson, M. Swoboda, A. L’Huillier, and J. Mauritsson, “Spectral shaping of attosecond pulses using two-colour laser fields,” New J. Phys. 10, 083041 (2008).
[CrossRef]

Taïeb, R.

K. Klünder, J. M. Dahlström, M. Gisselbrecht, T. Fordell, M. Swoboda, D. Guénot, P. Johnsson, J. Caillat, J. Mauritsson, A. Maquet, R. Taïeb, and A. L. Huillier, “Probing single-photon ionization on the attosecond time scale,” Phys. Rev. Lett. 106, 143002 (2011).
[CrossRef]

Takahashi, E. J.

E. J. Takahashi, P. Lan, Oliver D. Mücke, Y. Nabekawa, and K. Midorikawa, “Infrared two-color multicycle laser field synthesis for generating an intense attosecond pulse,” Phys. Rev. Lett. 104, 233901 (2010).
[CrossRef]

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Dramatic enhancement of high-order harmonic generation,” Phys. Rev. Lett. 99, 053904 (2007).
[CrossRef]

Thumm, U.

F. He, and U. Thumm, “Dissociative ionization of H2 in an attosecond pulse train and delayed laser pulse,” Phys. Rev. A 81, 053413 (2010).
[CrossRef]

Tong, X. M.

X. M. Tong, P. Ranitovic, C. L. Cocke, and N. Toshima, “Mechanisms of infrared-laser-assisted atomic ionization by attosecond pulses,” Phys. Rev. A 81, 021404(R) (2010).

J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A 74, 023404 (2006).
[CrossRef]

X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime, ” J. Phys. B 38, 2593–2600 (2005).
[CrossRef]

X. M. Tong, and S. I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61, 021802 (2000).
[CrossRef]

Toshima, N.

X. M. Tong, P. Ranitovic, C. L. Cocke, and N. Toshima, “Mechanisms of infrared-laser-assisted atomic ionization by attosecond pulses,” Phys. Rev. A 81, 021404(R) (2010).

Uiberacker, M.

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

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446, 627–632 (2007).
[CrossRef]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
[CrossRef]

Uphues, T.

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446, 627–632 (2007).
[CrossRef]

Valentin, C.

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L. Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

Varjú, K.

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L. Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
[CrossRef]

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L. Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

Verhoef, A. J.

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446, 627–632 (2007).
[CrossRef]

Villain, P.

C. F. de M. Faria, P. Salières, P. Villain, and M. Lewenstein, “Controlling high-order harmonic generation and above-threshold ionization with an attosecond-pulse train,” Phys. Rev. A 74, 053416 (2006).
[CrossRef]

Vrakking, M. J. J.

F. Kelkensberg, W. Siu, J. F. Pérez-Torres, F. Morales, G. Gademann, A. Rouzée, P. Johnsson, M. Lucchini, F. Calegari, J. L. Sanz-Vicario, F. Martín, and M. J. J. Vrakking, “Attosecond control in photoionization of hydrogen molecules,” Phys. Rev. Lett. 107, 043002 (2011).
[CrossRef]

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446, 627–632 (2007).
[CrossRef]

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L. Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
[CrossRef]

Wabnitz, H.

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L. Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

Walther, H.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Watanabe, S.

T. Morishita, S. Watanabe, and C. D. Lin, “Attosecond light pulses for probing two-electron dynamics of helium in the time domain,” Phys. Rev. Lett. 98, 083003 (2007).
[CrossRef]

Westerwalbesloh, T.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
[CrossRef]

Wickenhauser, M.

M. Wickenhauser, J. Burgdöfer, F. Krausz, and M. Drescher, “Time resolved Fano resonances,” Phys. Rev. Lett. 94, 023002 (2005).
[CrossRef]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef]

Wirth, A.

E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
[CrossRef]

Wittmann, T.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier–envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Yakovlev, V.

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446, 627–632 (2007).
[CrossRef]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
[CrossRef]

Yakovlev, V. S.

E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
[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,” Science 320, 1614–1617 (2008).
[CrossRef]

Ye, J.

S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[CrossRef]

Zhao, Z. X.

Z. X. Zhao and C. D. Lin, “Theory of laser-assisted autoionization by attosecond light pulses,” Phys. Rev. A 71, 060702 (2005).
[CrossRef]

Zherebtsov, S.

E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
[CrossRef]

Appl. Phys. B (1)

H. C. Lee, and T. F. Jiang, “Control mechanism of atomic ionization and high-order harmonic generation assisted by attosecond pulses,” Appl. Phys. B 109, 621–630 (2012).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (4)

X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime, ” J. Phys. B 38, 2593–2600 (2005).
[CrossRef]

O. Smirnova, M. Spanner, and M. Ivanov, “Coulomb and polarization effects in sub-cycle dynamics of strong-field ionization,” J. Phys. B 39, S307–S321 (2006).
[CrossRef]

O. Smirnova, M. Spanner, and M. Y. Ivanov, “Coulomb and polarization effects in laser-assisted XUV ionization,” J. Phys. B 39, S323–S339 (2006).
[CrossRef]

J. M. Dahlström, A. L’Huillier, and A. Maquet, “Introduction to attoseond delays in photoionization,” J. Phys. B 45, 183001 (2012).
[CrossRef]

Laser Phys. (2)

J. Biegert, A. Heinrich, C. P. Hauri, W. Kornelis, P. Schlup, M. Anscombe, K. J. Schafer, M. B. Gaarde, and U. Keller, “Enhancement of high-order harmonic emission using attosecond pulse trains,” Laser Phys. 15, 899–902 (2005).

C. F. de M. Faria, and P. Salières, “High-order harmonic generation with a strong laser field and an attosecond-pulse train: the Dirac-Delta comb and monochromatic limits,” Laser Phys. 17, 390–400 (2007).
[CrossRef]

Nat. Phys. (2)

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L. Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
[CrossRef]

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier–envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Nature (3)

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
[CrossRef]

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446, 627–632 (2007).
[CrossRef]

E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
[CrossRef]

New J. Phys. (2)

L. Y. Peng, E. A. Pronin, and A. F. Starace, “Attosecond pulse carrier-envelope phase effects on ionized electron momentum and energy distributions: roles of frequency, intensity and additional IR pulse,” New J. Phys. 10, 025030 (2008).
[CrossRef]

E. Mansten, J. M. Dahlström, P. Johnsson, M. Swoboda, A. L’Huillier, and J. Mauritsson, “Spectral shaping of attosecond pulses using two-colour laser fields,” New J. Phys. 10, 083041 (2008).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (9)

X. M. Tong, P. Ranitovic, C. L. Cocke, and N. Toshima, “Mechanisms of infrared-laser-assisted atomic ionization by attosecond pulses,” Phys. Rev. A 81, 021404(R) (2010).

J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A 74, 023404 (2006).
[CrossRef]

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

X. M. Tong, and S. I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61, 021802 (2000).
[CrossRef]

J. A. Pérez-Hernández and L. Plaja, “Quantum description of the high-order harmonic generation in multiphoton and tunneling regimes,” Phys. Rev. A 76, 023829 (2007).
[CrossRef]

O. Smirnova, M. Spanner, and M. Y. Ivanov, “Analytical solutions for strong field-driven atomic and molecular one- and two-electron continua and applications to strong-field problems,” Phys. Rev. A 77, 033407 (2008).
[CrossRef]

F. He, and U. Thumm, “Dissociative ionization of H2 in an attosecond pulse train and delayed laser pulse,” Phys. Rev. A 81, 053413 (2010).
[CrossRef]

C. F. de M. Faria, P. Salières, P. Villain, and M. Lewenstein, “Controlling high-order harmonic generation and above-threshold ionization with an attosecond-pulse train,” Phys. Rev. A 74, 053416 (2006).
[CrossRef]

Z. X. Zhao and C. D. Lin, “Theory of laser-assisted autoionization by attosecond light pulses,” Phys. Rev. A 71, 060702 (2005).
[CrossRef]

Phys. Rev. Lett. (13)

T. Morishita, S. Watanabe, and C. D. Lin, “Attosecond light pulses for probing two-electron dynamics of helium in the time domain,” Phys. Rev. Lett. 98, 083003 (2007).
[CrossRef]

K. Klünder, J. M. Dahlström, M. Gisselbrecht, T. Fordell, M. Swoboda, D. Guénot, P. Johnsson, J. Caillat, J. Mauritsson, A. Maquet, R. Taïeb, and A. L. Huillier, “Probing single-photon ionization on the attosecond time scale,” Phys. Rev. Lett. 106, 143002 (2011).
[CrossRef]

M. Wickenhauser, J. Burgdöfer, F. Krausz, and M. Drescher, “Time resolved Fano resonances,” Phys. Rev. Lett. 94, 023002 (2005).
[CrossRef]

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004).
[CrossRef]

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Dramatic enhancement of high-order harmonic generation,” Phys. Rev. Lett. 99, 053904 (2007).
[CrossRef]

F. Kelkensberg, W. Siu, J. F. Pérez-Torres, F. Morales, G. Gademann, A. Rouzée, P. Johnsson, M. Lucchini, F. Calegari, J. L. Sanz-Vicario, F. Martín, and M. J. J. Vrakking, “Attosecond control in photoionization of hydrogen molecules,” Phys. Rev. Lett. 107, 043002 (2011).
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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram for the SAP and IR vector potentials for (a) ϕd=0.5π and (b) ϕd=0. Timing HHG’s dipole moment for (c) ϕd=0.5π and (d) ϕd=0. HHG’s wavelet spectrum for (e) ϕd=0.5π and (f) ϕd=0. The horizontal axis denotes the emission time in units of the IR o.c. The peak intensities of the SAP and the IR field are 5×1013W/cm2 and 5×1014W/cm2, respectively, where τX=0.3fs, ωX=35eV, and ωIR=1.55eV.

Fig. 2.
Fig. 2.

Attopulse shape effect on the SAP+IR harmonic spectra at distinct attopulse widths (a) τX=80as, (b) τX=300as, (c) τX=600as, and (d) τX=1300as, where ωX=35eV. Red-solid and black-dashed lines denote the results of ϕd=0.5π and ϕd=0, respectively. Insets of (c) and (d) show the schematic diagram for the SAP and IR vector potentials at τX=600as and τX=1300as, respectively, where the horizontal axis is in units of the IR o.c.

Fig. 3.
Fig. 3.

SAP+IR harmonic spectra for (a) τX=80as and (b) τX=300as, where ωX=50eV. APT+IR harmonic spectra for (c) τX=80as and (d) τX=300as, where ωX=50eV and τT=5fs. Red-solid and black-dashed lines denote the results of ϕd=0.5π and ϕd=0, respectively.

Fig. 4.
Fig. 4.

IR pulse-shape effect on the harmonic spectra. Schematic diagram for the SAP and IR vector potentials with distinct SAP trigger times for (a) ϕd=0.5π and (b) ϕd=0, where the horizontal axis is in units of the IR o.c. SAP+IR harmonic spectra with distinct SAP’s trigger times for (c) ϕd=0.5π and (d) ϕd=0. Red-solid, green-dashed, and blue-dash-dotted lines denote the SAP triggered at t=0.5o.c. (ξ=1), t=0(ξ=0), and t=0.5o.c. (ξ=1), respectively. τX=0.3fs and ωX=35eV.

Fig. 5.
Fig. 5.

SAP+IR harmonic spectra as a function of the SAP’s trigger time for (a) ϕd=0.5π and (b) ϕd=0, where τX=80as, ωX=35eV, and the horizontal axis is in units of the IR o.c.

Equations (9)

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T(t)=itdt1ψkCV(r,t1)|VXUV(t1)|ψg(r,t1),
Eatto(t)=ξ[(1)ξEs(tξTh)]exp[2ln2(tτT)2],
Es(t)=z^EXsin(ωXt)exp[2ln2(tτX)2],
ψkCV(r,t1)=φk(r)exp[it1Ek(t)dt],
AIR(t)=z^cEIRωIRexp[2ln2(tτIR)2]cos(ωIRt+ϕd),
Ψ(r,t)=ψg(r,t)+d3kT(t)ψkCV(r,t).
d(t)Ψ(t)|z|Ψ(t)=itdt1d3kψg(t)|z|φkφk|VXUV(t1)|ψg(t1)exp[it1tEk(t)dt]+c.c.,
P(ω)=|d(t)exp(iωt)dt|2.
PW(t,ω)=|d(t)ωW[ω(tt)]dt|2,

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