Abstract

Angle-resolved energy spectra of high-order above-threshold ionization are calculated in the direction of the laser polarization for a linearly polarized four-cycle laser pulse (two cycles FWHM) as a function of the carrier-envelope relative phase (absolute phase). The spectra exhibit a characteristic left-right (backward-forward) asymmetry, which should allow one to determine the value of the absolute phase in a given experiment by comparison with the theoretical spectra. A classical analysis of the spectra calculated is presented. High-energy electron emission is found to occur in one or two ultrashort (≲0.7 fs) bursts. In the latter case, the spectra display a peak structure whose analysis reveals a time-domain image of electron emission.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
    [CrossRef]
  2. 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] [PubMed]
  3. A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
    [CrossRef] [PubMed]
  4. M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihira, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436–1438 (2001).
    [CrossRef]
  5. A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (1–4) (2002).
    [CrossRef]
  6. S.T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Phys. D 35, R43–R59 (2002).
    [CrossRef]
  7. D.W. Schumacher and P.H. Bucksbaum, “Phase dependence of intense-field ionization,” Phys. Rev. A 54, 4271–4278 (1996).
    [CrossRef] [PubMed]
  8. G.G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
    [CrossRef] [PubMed]
  9. F. Ehlotzky, “Atomic phenomena in bichromatic laser fields,” Phys. Rep. 345, 175–264 (2001).
    [CrossRef]
  10. A. de Bohan, Ph. Antoine, D.B. Miloševi?, and B. Piraux, “Phase-dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
    [CrossRef]
  11. A. de Bohan, Ph. Antoine, D.B. Miloševi?, G.L. Kamta, and B. Piraux, “Phase sensitivity of harmonic emission with ultrashort laser pulses,” Laser Phys. 9, 175–183 (1999).
  12. F. Krausz, T. Brabec, M. Schnürer, and C. Spielmann, “Extreme nonlinear optics: Exploring matter to a few periods of light,” Opt. Photon. News 9, 46–51 (1998).
    [CrossRef]
  13. G. Tempea, M. Geissler, and T. Brabec, “Phase sensitivity of high-order harmonic generation with few-cycle laser pulses,” J. Opt. Soc. Am. B 16, 669–673 (1999).
    [CrossRef]
  14. Z. Zeng, R. Li, W. Yu, and Z. Xu, “Effect of the carrier-envelope phase of the driving laser field on the high-order harmonic attosecond pulse,” Phys. Rev. A 67, 013815 (1–6) (2003).
    [CrossRef]
  15. A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
    [CrossRef]
  16. E. Cormier and P. Lambropoulos, “Effect of the initial phase of the field in ionization by ultrashort laser pulses,” Eur. Phys. J. D 2, 15–20 (1998).
    [CrossRef]
  17. I.P. Christov, “Phase-dependent loss due to nonadiabatic ionization by sub-10-fs pulses,” Opt. Lett. 24, 425–1427 (1999).
    [CrossRef]
  18. 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]
  19. S. Chelkowski and A.D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65, 061802(R) (1–4) (2002).
    [CrossRef]
  20. M. Kakehata, Y. Kobayashi, H. Takada, and K. Torizuka, “Single-shot measurement of a carrier-envelope phase by use of a time-dependent polarization pulse,” Opt. Lett. 27, 1247–1249 (2002).
    [CrossRef]
  21. G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
    [CrossRef] [PubMed]
  22. D.B. Miloševi?, G.G. Paulus, and W. Becker, “Phase-dependent effects of a few-cycle laser pulse,” Phys. Rev. Lett. 89, 153001 (1–4) (2002).
  23. D.B. Miloševi?, G.G. Paulus, and W. Becker, “Above-threshold ionization with few-cycle laser pulses and the relevance of the absolute phase,” Laser Phys. 13, xxx (2003).
  24. A.D. Bandrauk, S. Chelkowski, and N.H. Shon, “Measuring the electric field of few-cycle laser pulses by attosecond cross correlation,” Phys. Rev. Lett. 89, 283903 (1–4) (2002).
    [CrossRef]
  25. A. Scrinzi, M. Geissler, and T. Brabec, “Attosecond cross correlation technique,” Phys. Rev. Lett. 86, 412–415 (2001).
    [CrossRef] [PubMed]
  26. P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
    [CrossRef] [PubMed]
  27. M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
    [CrossRef] [PubMed]
  28. M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
    [CrossRef] [PubMed]
  29. A.D. Bandrauk and S. Chelkowski, “Dynamic imaging of nuclear wave functions with ultrashort UV laser pulses,” Phys. Rev. Lett. 87, 273004 (1–4) (2002).
  30. H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
    [CrossRef] [PubMed]
  31. W. Becker, F. Grasbon, R. Kopold, D.B. Miloševi?, G.G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At., Mol., Opt. Phys. 48, 35–98 (2002).
    [CrossRef]
  32. L.V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Zh. Eksp. Teor. Fiz. 47, 1945–1956 (1964) [Sov. Phys. JETP 20, 1307–1314 (1965).
  33. F.H.M. Faisal, “Multiple absorption of laser photons by atoms,” J. Phys. B 6, L89–92 (1973).
    [CrossRef]
  34. H.R. Reiss, “Effect of an intense electromagnetic field on weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
    [CrossRef]
  35. G.G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
    [CrossRef]
  36. D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
    [CrossRef]
  37. D.B. Miloševi? and F. Ehlotzky, “S-matrix theory of above-threshold ionization in a bichromatic laser field,” J. Phys. B 32, 1585–1596 (1999).
    [CrossRef]
  38. D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Laser Phys. 9, 149–154 (1999).
  39. D.B. Miloševi? and F. Ehlotzky, “Coulomb corrections in above-threshold ionization in a bichromatic laser field,” J. Phys. B 31, 4149–4161 (1998).
    [CrossRef]

2003 (3)

Z. Zeng, R. Li, W. Yu, and Z. Xu, “Effect of the carrier-envelope phase of the driving laser field on the high-order harmonic attosecond pulse,” Phys. Rev. A 67, 013815 (1–6) (2003).
[CrossRef]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Above-threshold ionization with few-cycle laser pulses and the relevance of the absolute phase,” Laser Phys. 13, xxx (2003).

2002 (9)

A.D. Bandrauk, S. Chelkowski, and N.H. Shon, “Measuring the electric field of few-cycle laser pulses by attosecond cross correlation,” Phys. Rev. Lett. 89, 283903 (1–4) (2002).
[CrossRef]

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (1–4) (2002).
[CrossRef]

S.T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Phys. D 35, R43–R59 (2002).
[CrossRef]

A.D. Bandrauk and S. Chelkowski, “Dynamic imaging of nuclear wave functions with ultrashort UV laser pulses,” Phys. Rev. Lett. 87, 273004 (1–4) (2002).

H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
[CrossRef] [PubMed]

W. Becker, F. Grasbon, R. Kopold, D.B. Miloševi?, G.G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At., Mol., Opt. Phys. 48, 35–98 (2002).
[CrossRef]

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Phase-dependent effects of a few-cycle laser pulse,” Phys. Rev. Lett. 89, 153001 (1–4) (2002).

S. Chelkowski and A.D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65, 061802(R) (1–4) (2002).
[CrossRef]

M. Kakehata, Y. Kobayashi, H. Takada, and K. Torizuka, “Single-shot measurement of a carrier-envelope phase by use of a time-dependent polarization pulse,” Opt. Lett. 27, 1247–1249 (2002).
[CrossRef]

2001 (7)

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihira, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436–1438 (2001).
[CrossRef]

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

F. Ehlotzky, “Atomic phenomena in bichromatic laser fields,” Phys. Rep. 345, 175–264 (2001).
[CrossRef]

A. Scrinzi, M. Geissler, and T. Brabec, “Attosecond cross correlation technique,” Phys. Rev. Lett. 86, 412–415 (2001).
[CrossRef] [PubMed]

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

2000 (4)

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

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] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

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]

1999 (5)

G. Tempea, M. Geissler, and T. Brabec, “Phase sensitivity of high-order harmonic generation with few-cycle laser pulses,” J. Opt. Soc. Am. B 16, 669–673 (1999).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “S-matrix theory of above-threshold ionization in a bichromatic laser field,” J. Phys. B 32, 1585–1596 (1999).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Laser Phys. 9, 149–154 (1999).

I.P. Christov, “Phase-dependent loss due to nonadiabatic ionization by sub-10-fs pulses,” Opt. Lett. 24, 425–1427 (1999).
[CrossRef]

A. de Bohan, Ph. Antoine, D.B. Miloševi?, G.L. Kamta, and B. Piraux, “Phase sensitivity of harmonic emission with ultrashort laser pulses,” Laser Phys. 9, 175–183 (1999).

1998 (5)

F. Krausz, T. Brabec, M. Schnürer, and C. Spielmann, “Extreme nonlinear optics: Exploring matter to a few periods of light,” Opt. Photon. News 9, 46–51 (1998).
[CrossRef]

A. de Bohan, Ph. Antoine, D.B. Miloševi?, and B. Piraux, “Phase-dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

E. Cormier and P. Lambropoulos, “Effect of the initial phase of the field in ionization by ultrashort laser pulses,” Eur. Phys. J. D 2, 15–20 (1998).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “Coulomb corrections in above-threshold ionization in a bichromatic laser field,” J. Phys. B 31, 4149–4161 (1998).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
[CrossRef]

1996 (1)

D.W. Schumacher and P.H. Bucksbaum, “Phase dependence of intense-field ionization,” Phys. Rev. A 54, 4271–4278 (1996).
[CrossRef] [PubMed]

1995 (1)

G.G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
[CrossRef] [PubMed]

1994 (1)

G.G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

1980 (1)

H.R. Reiss, “Effect of an intense electromagnetic field on weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
[CrossRef]

1973 (1)

F.H.M. Faisal, “Multiple absorption of laser photons by atoms,” J. Phys. B 6, L89–92 (1973).
[CrossRef]

1964 (1)

L.V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Zh. Eksp. Teor. Fiz. 47, 1945–1956 (1964) [Sov. Phys. JETP 20, 1307–1314 (1965).

Agostini, P.

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Antoine, Ph.

A. de Bohan, Ph. Antoine, D.B. Miloševi?, G.L. Kamta, and B. Piraux, “Phase sensitivity of harmonic emission with ultrashort laser pulses,” Laser Phys. 9, 175–183 (1999).

A. de Bohan, Ph. Antoine, D.B. Miloševi?, and B. Piraux, “Phase-dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

Apolonski, A.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

Augé, F.

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Balcou, Ph.

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Baltuška, A.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (1–4) (2002).
[CrossRef]

Bandrauk, A.D.

S. Chelkowski and A.D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65, 061802(R) (1–4) (2002).
[CrossRef]

A.D. Bandrauk and S. Chelkowski, “Dynamic imaging of nuclear wave functions with ultrashort UV laser pulses,” Phys. Rev. Lett. 87, 273004 (1–4) (2002).

H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
[CrossRef] [PubMed]

A.D. Bandrauk, S. Chelkowski, and N.H. Shon, “Measuring the electric field of few-cycle laser pulses by attosecond cross correlation,” Phys. Rev. Lett. 89, 283903 (1–4) (2002).
[CrossRef]

Becker, W.

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Above-threshold ionization with few-cycle laser pulses and the relevance of the absolute phase,” Laser Phys. 13, xxx (2003).

W. Becker, F. Grasbon, R. Kopold, D.B. Miloševi?, G.G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At., Mol., Opt. Phys. 48, 35–98 (2002).
[CrossRef]

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Phase-dependent effects of a few-cycle laser pulse,” Phys. Rev. Lett. 89, 153001 (1–4) (2002).

G.G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
[CrossRef] [PubMed]

G.G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

Brabec, T.

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

A. Scrinzi, M. Geissler, and T. Brabec, “Attosecond cross correlation technique,” Phys. Rev. Lett. 86, 412–415 (2001).
[CrossRef] [PubMed]

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

G. Tempea, M. Geissler, and T. Brabec, “Phase sensitivity of high-order harmonic generation with few-cycle laser pulses,” J. Opt. Soc. Am. B 16, 669–673 (1999).
[CrossRef]

F. Krausz, T. Brabec, M. Schnürer, and C. Spielmann, “Extreme nonlinear optics: Exploring matter to a few periods of light,” Opt. Photon. News 9, 46–51 (1998).
[CrossRef]

Breger, P.

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Bucksbaum, P.H.

D.W. Schumacher and P.H. Bucksbaum, “Phase dependence of intense-field ionization,” Phys. Rev. A 54, 4271–4278 (1996).
[CrossRef] [PubMed]

Chelkowski, S.

S. Chelkowski and A.D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65, 061802(R) (1–4) (2002).
[CrossRef]

A.D. Bandrauk and S. Chelkowski, “Dynamic imaging of nuclear wave functions with ultrashort UV laser pulses,” Phys. Rev. Lett. 87, 273004 (1–4) (2002).

A.D. Bandrauk, S. Chelkowski, and N.H. Shon, “Measuring the electric field of few-cycle laser pulses by attosecond cross correlation,” Phys. Rev. Lett. 89, 283903 (1–4) (2002).
[CrossRef]

Christov, I.P.

I.P. Christov, “Phase-dependent loss due to nonadiabatic ionization by sub-10-fs pulses,” Opt. Lett. 24, 425–1427 (1999).
[CrossRef]

Corkum, P.

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

Corkum, P.B.

H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

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]

Cormier, E.

E. Cormier and P. Lambropoulos, “Effect of the initial phase of the field in ionization by ultrashort laser pulses,” Eur. Phys. J. D 2, 15–20 (1998).
[CrossRef]

Cundiff, S.T.

S.T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Phys. D 35, R43–R59 (2002).
[CrossRef]

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] [PubMed]

de Bohan, A.

A. de Bohan, Ph. Antoine, D.B. Miloševi?, G.L. Kamta, and B. Piraux, “Phase sensitivity of harmonic emission with ultrashort laser pulses,” Laser Phys. 9, 175–183 (1999).

A. de Bohan, Ph. Antoine, D.B. Miloševi?, and B. Piraux, “Phase-dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

De Silvestri, S.

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

Diddams, S.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] [PubMed]

Dietrich, P.

Drescher, M.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

Ehlotzky, F.

F. Ehlotzky, “Atomic phenomena in bichromatic laser fields,” Phys. Rep. 345, 175–264 (2001).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “S-matrix theory of above-threshold ionization in a bichromatic laser field,” J. Phys. B 32, 1585–1596 (1999).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Laser Phys. 9, 149–154 (1999).

D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “Coulomb corrections in above-threshold ionization in a bichromatic laser field,” J. Phys. B 31, 4149–4161 (1998).
[CrossRef]

Faisal, F.H.M.

F.H.M. Faisal, “Multiple absorption of laser photons by atoms,” J. Phys. B 6, L89–92 (1973).
[CrossRef]

Fuji, T.

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (1–4) (2002).
[CrossRef]

Fujihira, Y.

Geissler, M.

Gohle, C.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

Goulielmakis, E.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

Grasbon, F.

W. Becker, F. Grasbon, R. Kopold, D.B. Miloševi?, G.G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At., Mol., Opt. Phys. 48, 35–98 (2002).
[CrossRef]

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

Hall, J.L.

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] [PubMed]

Hänsch, T.W.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

Hasbani, R.

H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
[CrossRef] [PubMed]

Heinzmann, U.

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

Hentschel, M.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

Holzwarth, R.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

Homma, T.

Ivanov, M.Yu.

H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
[CrossRef] [PubMed]

Jones, D.J.

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] [PubMed]

Kakehata, M.

Kamta, G.L.

A. de Bohan, Ph. Antoine, D.B. Miloševi?, G.L. Kamta, and B. Piraux, “Phase sensitivity of harmonic emission with ultrashort laser pulses,” Laser Phys. 9, 175–183 (1999).

Keldysh, L.V.

L.V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Zh. Eksp. Teor. Fiz. 47, 1945–1956 (1964) [Sov. Phys. JETP 20, 1307–1314 (1965).

Kienberger, R.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

Kobayashi, T.

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (1–4) (2002).
[CrossRef]

Kobayashi, Y.

Kopold, R.

W. Becker, F. Grasbon, R. Kopold, D.B. Miloševi?, G.G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At., Mol., Opt. Phys. 48, 35–98 (2002).
[CrossRef]

Krausz, F.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

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

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

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]

F. Krausz, T. Brabec, M. Schnürer, and C. Spielmann, “Extreme nonlinear optics: Exploring matter to a few periods of light,” Opt. Photon. News 9, 46–51 (1998).
[CrossRef]

Lambropoulos, P.

E. Cormier and P. Lambropoulos, “Effect of the initial phase of the field in ionization by ultrashort laser pulses,” Eur. Phys. J. D 2, 15–20 (1998).
[CrossRef]

Légaré, F.

H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
[CrossRef] [PubMed]

Li, R.

Z. Zeng, R. Li, W. Yu, and Z. Xu, “Effect of the carrier-envelope phase of the driving laser field on the high-order harmonic attosecond pulse,” Phys. Rev. A 67, 013815 (1–6) (2003).
[CrossRef]

Milosevic, N.

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

Miloševic, D.B.

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Above-threshold ionization with few-cycle laser pulses and the relevance of the absolute phase,” Laser Phys. 13, xxx (2003).

W. Becker, F. Grasbon, R. Kopold, D.B. Miloševi?, G.G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At., Mol., Opt. Phys. 48, 35–98 (2002).
[CrossRef]

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Phase-dependent effects of a few-cycle laser pulse,” Phys. Rev. Lett. 89, 153001 (1–4) (2002).

D.B. Miloševi? and F. Ehlotzky, “S-matrix theory of above-threshold ionization in a bichromatic laser field,” J. Phys. B 32, 1585–1596 (1999).
[CrossRef]

A. de Bohan, Ph. Antoine, D.B. Miloševi?, G.L. Kamta, and B. Piraux, “Phase sensitivity of harmonic emission with ultrashort laser pulses,” Laser Phys. 9, 175–183 (1999).

D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Laser Phys. 9, 149–154 (1999).

D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
[CrossRef]

A. de Bohan, Ph. Antoine, D.B. Miloševi?, and B. Piraux, “Phase-dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “Coulomb corrections in above-threshold ionization in a bichromatic laser field,” J. Phys. B 31, 4149–4161 (1998).
[CrossRef]

Muller, H.G.

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Mullot, G.

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Nicklich, W.

G.G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

Niikura, H.

H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
[CrossRef] [PubMed]

Nisoli, M.

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

Paul, P.M.

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Paulus, G.G.

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Above-threshold ionization with few-cycle laser pulses and the relevance of the absolute phase,” Laser Phys. 13, xxx (2003).

W. Becker, F. Grasbon, R. Kopold, D.B. Miloševi?, G.G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At., Mol., Opt. Phys. 48, 35–98 (2002).
[CrossRef]

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Phase-dependent effects of a few-cycle laser pulse,” Phys. Rev. Lett. 89, 153001 (1–4) (2002).

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

G.G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
[CrossRef] [PubMed]

G.G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

Piraux, B.

A. de Bohan, Ph. Antoine, D.B. Miloševi?, G.L. Kamta, and B. Piraux, “Phase sensitivity of harmonic emission with ultrashort laser pulses,” Laser Phys. 9, 175–183 (1999).

A. de Bohan, Ph. Antoine, D.B. Miloševi?, and B. Piraux, “Phase-dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

Poppe, A.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

Priori, E.

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

Ranka, J.K.

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] [PubMed]

Reider, G.A.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

Reiss, H.R.

H.R. Reiss, “Effect of an intense electromagnetic field on weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
[CrossRef]

Schnürer, M.

F. Krausz, T. Brabec, M. Schnürer, and C. Spielmann, “Extreme nonlinear optics: Exploring matter to a few periods of light,” Opt. Photon. News 9, 46–51 (1998).
[CrossRef]

Schumacher, D.W.

D.W. Schumacher and P.H. Bucksbaum, “Phase dependence of intense-field ionization,” Phys. Rev. A 54, 4271–4278 (1996).
[CrossRef] [PubMed]

Scrinzi, A.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

A. Scrinzi, M. Geissler, and T. Brabec, “Attosecond cross correlation technique,” Phys. Rev. Lett. 86, 412–415 (2001).
[CrossRef] [PubMed]

Shon, N.H.

A.D. Bandrauk, S. Chelkowski, and N.H. Shon, “Measuring the electric field of few-cycle laser pulses by attosecond cross correlation,” Phys. Rev. Lett. 89, 283903 (1–4) (2002).
[CrossRef]

Spielmann, C.

F. Krausz, T. Brabec, M. Schnürer, and C. Spielmann, “Extreme nonlinear optics: Exploring matter to a few periods of light,” Opt. Photon. News 9, 46–51 (1998).
[CrossRef]

Spielmann, Ch.

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

Stagira, S.

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

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] [PubMed]

Takada, H.

Takahashi, H.

Tempea, G.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

G. Tempea, M. Geissler, and T. Brabec, “Phase sensitivity of high-order harmonic generation with few-cycle laser pulses,” J. Opt. Soc. Am. B 16, 669–673 (1999).
[CrossRef]

Toma, E.S.

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Torizuka, K.

Udem, T.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

Udem, Th.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

Uiberacker, M.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

Villeneuve, D.M.

H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
[CrossRef] [PubMed]

Villoresi, P.

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

Walther, H.

W. Becker, F. Grasbon, R. Kopold, D.B. Miloševi?, G.G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At., Mol., Opt. Phys. 48, 35–98 (2002).
[CrossRef]

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

G.G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
[CrossRef] [PubMed]

G.G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[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] [PubMed]

Xu, Z.

Z. Zeng, R. Li, W. Yu, and Z. Xu, “Effect of the carrier-envelope phase of the driving laser field on the high-order harmonic attosecond pulse,” Phys. Rev. A 67, 013815 (1–6) (2003).
[CrossRef]

Yakovlev, V.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

Yu, W.

Z. Zeng, R. Li, W. Yu, and Z. Xu, “Effect of the carrier-envelope phase of the driving laser field on the high-order harmonic attosecond pulse,” Phys. Rev. A 67, 013815 (1–6) (2003).
[CrossRef]

Zeng, Z.

Z. Zeng, R. Li, W. Yu, and Z. Xu, “Effect of the carrier-envelope phase of the driving laser field on the high-order harmonic attosecond pulse,” Phys. Rev. A 67, 013815 (1–6) (2003).
[CrossRef]

Adv. At., Mol., Opt. Phys. (1)

W. Becker, F. Grasbon, R. Kopold, D.B. Miloševi?, G.G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At., Mol., Opt. Phys. 48, 35–98 (2002).
[CrossRef]

Eur. Phys. J. D (1)

E. Cormier and P. Lambropoulos, “Effect of the initial phase of the field in ionization by ultrashort laser pulses,” Eur. Phys. J. D 2, 15–20 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B (4)

F.H.M. Faisal, “Multiple absorption of laser photons by atoms,” J. Phys. B 6, L89–92 (1973).
[CrossRef]

G.G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “S-matrix theory of above-threshold ionization in a bichromatic laser field,” J. Phys. B 32, 1585–1596 (1999).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “Coulomb corrections in above-threshold ionization in a bichromatic laser field,” J. Phys. B 31, 4149–4161 (1998).
[CrossRef]

J. Phys. D (1)

S.T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Phys. D 35, R43–R59 (2002).
[CrossRef]

Laser Phys. (3)

A. de Bohan, Ph. Antoine, D.B. Miloševi?, G.L. Kamta, and B. Piraux, “Phase sensitivity of harmonic emission with ultrashort laser pulses,” Laser Phys. 9, 175–183 (1999).

D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Laser Phys. 9, 149–154 (1999).

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Above-threshold ionization with few-cycle laser pulses and the relevance of the absolute phase,” Laser Phys. 13, xxx (2003).

Nature (4)

M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef] [PubMed]

G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena” in photoionization with few-cycle laser pulses,” Nature 414 (London), 182–185 (2001).
[CrossRef] [PubMed]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. Yakovlev, A. Scrinzi, T.W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003).
[CrossRef]

H. Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, M.Yu. Ivanov, D.M. Villeneuve, and P.B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature (London) 417, 917–922 (2002).
[CrossRef] [PubMed]

Opt. Lett. (4)

Opt. Photon. News (1)

F. Krausz, T. Brabec, M. Schnürer, and C. Spielmann, “Extreme nonlinear optics: Exploring matter to a few periods of light,” Opt. Photon. News 9, 46–51 (1998).
[CrossRef]

Phys. Rep. (1)

F. Ehlotzky, “Atomic phenomena in bichromatic laser fields,” Phys. Rep. 345, 175–264 (2001).
[CrossRef]

Phys. Rev. A (6)

D.W. Schumacher and P.H. Bucksbaum, “Phase dependence of intense-field ionization,” Phys. Rev. A 54, 4271–4278 (1996).
[CrossRef] [PubMed]

G.G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
[CrossRef] [PubMed]

Z. Zeng, R. Li, W. Yu, and Z. Xu, “Effect of the carrier-envelope phase of the driving laser field on the high-order harmonic attosecond pulse,” Phys. Rev. A 67, 013815 (1–6) (2003).
[CrossRef]

S. Chelkowski and A.D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65, 061802(R) (1–4) (2002).
[CrossRef]

D.B. Miloševi? and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
[CrossRef]

H.R. Reiss, “Effect of an intense electromagnetic field on weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
[CrossRef]

Phys. Rev. Lett. (7)

A.D. Bandrauk and S. Chelkowski, “Dynamic imaging of nuclear wave functions with ultrashort UV laser pulses,” Phys. Rev. Lett. 87, 273004 (1–4) (2002).

A.D. Bandrauk, S. Chelkowski, and N.H. Shon, “Measuring the electric field of few-cycle laser pulses by attosecond cross correlation,” Phys. Rev. Lett. 89, 283903 (1–4) (2002).
[CrossRef]

A. Scrinzi, M. Geissler, and T. Brabec, “Attosecond cross correlation technique,” Phys. Rev. Lett. 86, 412–415 (2001).
[CrossRef] [PubMed]

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (1–4) (2002).
[CrossRef]

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T.W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740–743 (2000).
[CrossRef] [PubMed]

D.B. Miloševi?, G.G. Paulus, and W. Becker, “Phase-dependent effects of a few-cycle laser pulse,” Phys. Rev. Lett. 89, 153001 (1–4) (2002).

A. de Bohan, Ph. Antoine, D.B. Miloševi?, and B. Piraux, “Phase-dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

Rev. Mod. Phys. (1)

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

Science (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] [PubMed]

P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H.G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, Ch. Spielmann, G.A. Reider, P.B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

L.V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Zh. Eksp. Teor. Fiz. 47, 1945–1956 (1964) [Sov. Phys. JETP 20, 1307–1314 (1965).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Angle-resolved ATI energy spectrum generated by the 4-cycle pulse (11) with intensity I=E02=6×1013 Wcm-2 and λ=800 nm in krypton (IP =14 eV) for an absolute phase ϕ=0°, for the two opposite detector positions θ=0° and θ=180° along the laser-field polarization. For comparison, the envelope of the ATI spectrum for the same atomic and laser parameters but for an infinitely long pulse with flat envelope (amplitude E 0) is also shown (green dashed line with circles). For this case, the high-energy cutoff is at 10UP =35.9 eV. The high-energy part of the 4-cycle spectrum for θ=0° virtually agrees with the envelope of the infinitely-long-pulse spectrum. The explanation will be found in the classical model considered below.

Fig. 2.
Fig. 2.

The same as Fig. 1, but for nine different absolute phases between ϕ=0° and ϕ=180°. The uppermost left panel with ϕ=0° shows the same spectra as Fig. 1. The spectra for θ=0° are designated by black lines, those for θ=180° by thin red (gray) lines.

Fig. 3.
Fig. 3.

Solutions of the classical rescattering model formulated in Eqs. (16)–(18) for the parameters of Fig. 1, absolute phase ϕ=0°, and θ=0° (upper panel) and θ=180° (lower panel). The various black curves specify the energy E p at the detector as a function of the ionization time t. The dashed magenta curve represents the electric field given by Eq. (11) with the scale given on the right-hand ordinate. The solid blue curves that are identical in both panels, being symmetric with respect to t=2 o.c. and having two maxima at E p =7.1 eV refer to direct ionization. They are trivial solutions of Eq. (16) for t=t′.

Fig. 4.
Fig. 4.

Rescattering times t′ as a function of the ionization time t for the solutions of the classical model, given by Eqs. (16)–(18). The parameters are those of Fig. 1 and the absolute phase is ϕ=0°. Rescattering times that give rise to E p >10 eV, E p >20 eV, and E p >30 eV, are marked in red (medium gray), blue (dark gray), and cyan (light gray), respectively.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

M p = i lim t 0 t d t ψ p ( t ) U ( t , t ) r · E ( t ) ψ 0 ( t ) .
H ( t ) = 2 2 + r · E ( t ) + V ( r ) ,
U ( t , t ) = U F ( t , t ) i t t d t U F ( t , t ) V U ( t , t ) ,
χ p ( t ) = p + A ( t ) exp [ i S p ( t ) ]
S p ( t ) = 1 2 t d t [ p + A ( t ) ] 2 .
U F ( t , t ) = d 3 k χ k ( t ) χ k ( t ) .
p ~ = p A ( T p )
M p SFA = M p ( 0 ) + M p ( 1 ) ,
M p ( 0 ) = i 0 T p d t χ p ~ ( t ) r · E ( t ) ψ 0 ( t ) ,
M p ( 1 ) = 0 T p d t t d t χ p ~ ( t ) V U F ( t , t ) r · E ( t ) ψ 0 ( t ) .
E ( t ) = e ̂ E 0 sin 2 ω p t 2 cos ( ω t + ϕ ) = e ̂ i = 0 , 1 , 2 i cos ( ω i t + ϕ )
A ( t ) = t d t E ( t ) = e ̂ i = 0,1,2 i ω i sin ( ω i t + ϕ ) .
w ( θ , ϕ ) = M p 2 d 3 p d Ω p ̂ d E p = p M p 2 ,
k r · E ( t ) ψ 0 = i 2 7 2 ( 2 I p ) 5 4 k · E ( t ) π ( k 2 + 2 I p ) 3 .
v ( t 1 ) = A ( t 1 ) A ( t ) .
r ( t ) = α ( t ) α ( t ) A ( t ) ( t t ) = 0 ,
E p = v 2 ( T p ) 2 ,
v ( T p ) = A ( T p ) A ( t ) + A ( t ) A ( t ) v ̂ ( t + ) p ,

Metrics