Abstract

We report on calculations of the above threshold detachment of F- by a few-cycle circularly polarized laser field, discussing the effects of both the carrier-envelope relative phase and the number of the cycle contained in a pulse on the angular distribution of ejected photoelectron. The results are analyzed in terms of a two-step semiclassical model: after the electrons are detached through tunnelling their motion is determined by the electric field pulse according to the classical dynamics laws. Anisotropies in the angular distributions of the electrons ejected on the plane perpendicular to the laser propagation direction are found that depend on the number of cycle of the laser pulse.

© 2006 Optical Society of America

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  1. Sometimes the acronym ATD is used to indicate Above Threshold Dissociation; in the present paper, however, ATD is meant for indicating Above Threshold Detachment.
  2. P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman “Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
    [CrossRef]
  3. H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
    [CrossRef] [PubMed]
  4. Rainer Reichle, Hanspeter Helm, and Igor Yu. Kiyan, “Photodetachment of H- in a Strong Infrared Laser Field,” Phys. Rev. Lett. 87, 243001, (2001).
    [CrossRef] [PubMed]
  5. Igor Yu. Kiyan and Hanspeter Helm, “Production of Energetic Electrons in the Process of Photodetachment of F-,” Phys. Rev. Lett. 90, 183001, (2003).
    [CrossRef] [PubMed]
  6. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JEPT 20, 1307–1314 (1965).
  7. G. F. Gribakin and M. Yu. Kuchiev,“Multiphoton detachment of electrons from negative ions,” Phys. Rev. A 55, 3760–3771 (1997).
    [CrossRef]
  8. R. Kopold and W. Becker, “Interference in high-order above-threshold ionization,” J. Phys.B: At. Mol. Opt. Phys. 32, L419–L424 (1999).
    [CrossRef]
  9. D. B. Milosevic, A. Gazibegovic-Busuladzic, and W. Becker,“Direct and rescattered electrons in above-threshold detachment from negative ions,” Phys. Rev. A 68, 050702(R) (2003).
    [CrossRef]
  10. M. V. Frolov, N. L. Manakov, E. A. Pronin, and Anthony F. Starace, “Strong field detachment of a negative ion with non-zero angular momentum: application to F-,” J. Phys. B: A. Mol. Opt. Phys. 36, L419–L426 (2003).
    [CrossRef]
  11. Boris Bergues, Yongfeng Ni, Hanspeter Helm, and Igor Yu. Kiyan, “Experimental Study of Photodetachment in a Strong Laser Field of Circular Polarization,” Phys. Rev. Lett. 95, 263002 (2005).
    [CrossRef]
  12. Svea Beiser, Michael Klaiber, and Igor Yu. Kiyan , “Photodetachment in a strong circularly polarized laser field,” Phys. Rev. A 70, 011402 (2004).
    [CrossRef]
  13. D. B. Milosevic, G. G. Paulus, and W. Becker, “ Phase-Dependent Effects of a Few-Cycle Laser Pulse,” Phys. Rev. Lett. 89, 153001 (2002).
    [CrossRef] [PubMed]
  14. S. X. Hu and Anthony F. Starace, “Controlling H- detachment with few-cycle pulses,” Phys. Rev. A 68, 043407 (2003).
    [CrossRef]
  15. 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, 182–184 (2001).
    [CrossRef] [PubMed]
  16. A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
    [CrossRef] [PubMed]
  17. M. Nisoli, G. Sansone, S. Stagire, and S. De Silvestri, “Effects of Carrier-Envelope Phase Differences of Few-Optical-Cycle Light Pulses in Single-Shot High-Order-Harmonic Spectra,” Phys. Rev. Lett. 91, 213905 (2003).
    [CrossRef] [PubMed]
  18. G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
    [CrossRef]
  19. G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
    [CrossRef] [PubMed]
  20. G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long pulse,” Phys. Rev. A 70, 013411 (2004).
    [CrossRef]
  21. 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) (2002).
    [CrossRef]
  22. P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [CrossRef] [PubMed]
  23. P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-Threshold Ionization in the Long-Wavelength Limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
    [CrossRef] [PubMed]
  24. A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B: At. Mol. Opt. Phys. 39, R1–R37 (2006) and reference therein.
    [CrossRef]

2006 (1)

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B: At. Mol. Opt. Phys. 39, R1–R37 (2006) and reference therein.
[CrossRef]

2005 (1)

Boris Bergues, Yongfeng Ni, Hanspeter Helm, and Igor Yu. Kiyan, “Experimental Study of Photodetachment in a Strong Laser Field of Circular Polarization,” Phys. Rev. Lett. 95, 263002 (2005).
[CrossRef]

2004 (3)

Svea Beiser, Michael Klaiber, and Igor Yu. Kiyan , “Photodetachment in a strong circularly polarized laser field,” Phys. Rev. A 70, 011402 (2004).
[CrossRef]

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[CrossRef] [PubMed]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long pulse,” Phys. Rev. A 70, 013411 (2004).
[CrossRef]

2003 (7)

S. X. Hu and Anthony F. Starace, “Controlling H- detachment with few-cycle pulses,” Phys. Rev. A 68, 043407 (2003).
[CrossRef]

Igor Yu. Kiyan and Hanspeter Helm, “Production of Energetic Electrons in the Process of Photodetachment of F-,” Phys. Rev. Lett. 90, 183001, (2003).
[CrossRef] [PubMed]

D. B. Milosevic, A. Gazibegovic-Busuladzic, and W. Becker,“Direct and rescattered electrons in above-threshold detachment from negative ions,” Phys. Rev. A 68, 050702(R) (2003).
[CrossRef]

M. V. Frolov, N. L. Manakov, E. A. Pronin, and Anthony F. Starace, “Strong field detachment of a negative ion with non-zero angular momentum: application to F-,” J. Phys. B: A. Mol. Opt. Phys. 36, L419–L426 (2003).
[CrossRef]

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

M. Nisoli, G. Sansone, S. Stagire, and S. De Silvestri, “Effects of Carrier-Envelope Phase Differences of Few-Optical-Cycle Light Pulses in Single-Shot High-Order-Harmonic Spectra,” Phys. Rev. Lett. 91, 213905 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

2002 (2)

D. B. Milosevic, G. G. Paulus, and W. Becker, “ Phase-Dependent Effects of a Few-Cycle Laser Pulse,” Phys. Rev. Lett. 89, 153001 (2002).
[CrossRef] [PubMed]

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) (2002).
[CrossRef]

2001 (2)

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, 182–184 (2001).
[CrossRef] [PubMed]

Rainer Reichle, Hanspeter Helm, and Igor Yu. Kiyan, “Photodetachment of H- in a Strong Infrared Laser Field,” Phys. Rev. Lett. 87, 243001, (2001).
[CrossRef] [PubMed]

1999 (1)

R. Kopold and W. Becker, “Interference in high-order above-threshold ionization,” J. Phys.B: At. Mol. Opt. Phys. 32, L419–L424 (1999).
[CrossRef]

1997 (1)

G. F. Gribakin and M. Yu. Kuchiev,“Multiphoton detachment of electrons from negative ions,” Phys. Rev. A 55, 3760–3771 (1997).
[CrossRef]

1993 (1)

P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

1989 (1)

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-Threshold Ionization in the Long-Wavelength Limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[CrossRef] [PubMed]

1987 (1)

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

1979 (1)

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman “Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JEPT 20, 1307–1314 (1965).

Agostini, P.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman “Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Baltuska, A.

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

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[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) (2002).
[CrossRef]

Becker, W.

D. B. Milosevic, A. Gazibegovic-Busuladzic, and W. Becker,“Direct and rescattered electrons in above-threshold detachment from negative ions,” Phys. Rev. A 68, 050702(R) (2003).
[CrossRef]

D. B. Milosevic, G. G. Paulus, and W. Becker, “ Phase-Dependent Effects of a Few-Cycle Laser Pulse,” Phys. Rev. Lett. 89, 153001 (2002).
[CrossRef] [PubMed]

R. Kopold and W. Becker, “Interference in high-order above-threshold ionization,” J. Phys.B: At. Mol. Opt. Phys. 32, L419–L424 (1999).
[CrossRef]

Beiser, Svea

Svea Beiser, Michael Klaiber, and Igor Yu. Kiyan , “Photodetachment in a strong circularly polarized laser field,” Phys. Rev. A 70, 011402 (2004).
[CrossRef]

Bergues, Boris

Boris Bergues, Yongfeng Ni, Hanspeter Helm, and Igor Yu. Kiyan, “Experimental Study of Photodetachment in a Strong Laser Field of Circular Polarization,” Phys. Rev. Lett. 95, 263002 (2005).
[CrossRef]

Brunel, F.

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-Threshold Ionization in the Long-Wavelength Limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[CrossRef] [PubMed]

Bryant, H. C.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Burnett, N. H.

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-Threshold Ionization in the Long-Wavelength Limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[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) (2002).
[CrossRef]

Cohen, S.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Corkum, P. B.

P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-Threshold Ionization in the Long-Wavelength Limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[CrossRef] [PubMed]

De Silvestri, S.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[CrossRef] [PubMed]

M. Nisoli, G. Sansone, S. Stagire, and S. De Silvestri, “Effects of Carrier-Envelope Phase Differences of Few-Optical-Cycle Light Pulses in Single-Shot High-Order-Harmonic Spectra,” Phys. Rev. Lett. 91, 213905 (2003).
[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, 182–184 (2001).
[CrossRef] [PubMed]

Donahue, J. B.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Fabre, F.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman “Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Frolov, M. V.

M. V. Frolov, N. L. Manakov, E. A. Pronin, and Anthony F. Starace, “Strong field detachment of a negative ion with non-zero angular momentum: application to F-,” J. Phys. B: A. Mol. Opt. Phys. 36, L419–L426 (2003).
[CrossRef]

Gazibegovic-Busuladzic, A.

D. B. Milosevic, A. Gazibegovic-Busuladzic, and W. Becker,“Direct and rescattered electrons in above-threshold detachment from negative ions,” Phys. Rev. A 68, 050702(R) (2003).
[CrossRef]

Gohle, C.

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

Goulielmakis, E.

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

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Grasbon, F.

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, 182–184 (2001).
[CrossRef] [PubMed]

Gribakin, G. F.

G. F. Gribakin and M. Yu. Kuchiev,“Multiphoton detachment of electrons from negative ions,” Phys. Rev. A 55, 3760–3771 (1997).
[CrossRef]

Hansch, T. W.

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

Helm, Hanspeter

Boris Bergues, Yongfeng Ni, Hanspeter Helm, and Igor Yu. Kiyan, “Experimental Study of Photodetachment in a Strong Laser Field of Circular Polarization,” Phys. Rev. Lett. 95, 263002 (2005).
[CrossRef]

Igor Yu. Kiyan and Hanspeter Helm, “Production of Energetic Electrons in the Process of Photodetachment of F-,” Phys. Rev. Lett. 90, 183001, (2003).
[CrossRef] [PubMed]

Rainer Reichle, Hanspeter Helm, and Igor Yu. Kiyan, “Photodetachment of H- in a Strong Infrared Laser Field,” Phys. Rev. Lett. 87, 243001, (2001).
[CrossRef] [PubMed]

Hentschel, M.

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

Holzwarth, R.

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

Hu, S. X.

S. X. Hu and Anthony F. Starace, “Controlling H- detachment with few-cycle pulses,” Phys. Rev. A 68, 043407 (2003).
[CrossRef]

Hummer, C. R.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Ivanov, M. Yu

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B: At. Mol. Opt. Phys. 39, R1–R37 (2006) and reference therein.
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JEPT 20, 1307–1314 (1965).

Kienberger, R.

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B: At. Mol. Opt. Phys. 39, R1–R37 (2006) and reference therein.
[CrossRef]

Kiyan, Igor Yu.

Boris Bergues, Yongfeng Ni, Hanspeter Helm, and Igor Yu. Kiyan, “Experimental Study of Photodetachment in a Strong Laser Field of Circular Polarization,” Phys. Rev. Lett. 95, 263002 (2005).
[CrossRef]

Svea Beiser, Michael Klaiber, and Igor Yu. Kiyan , “Photodetachment in a strong circularly polarized laser field,” Phys. Rev. A 70, 011402 (2004).
[CrossRef]

Igor Yu. Kiyan and Hanspeter Helm, “Production of Energetic Electrons in the Process of Photodetachment of F-,” Phys. Rev. Lett. 90, 183001, (2003).
[CrossRef] [PubMed]

Rainer Reichle, Hanspeter Helm, and Igor Yu. Kiyan, “Photodetachment of H- in a Strong Infrared Laser Field,” Phys. Rev. Lett. 87, 243001, (2001).
[CrossRef] [PubMed]

Klaiber, Michael

Svea Beiser, Michael Klaiber, and Igor Yu. Kiyan , “Photodetachment in a strong circularly polarized laser field,” Phys. Rev. A 70, 011402 (2004).
[CrossRef]

Kopold, R.

R. Kopold and W. Becker, “Interference in high-order above-threshold ionization,” J. Phys.B: At. Mol. Opt. Phys. 32, L419–L424 (1999).
[CrossRef]

Krausz, F.

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

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Kuchiev, M. Yu.

G. F. Gribakin and M. Yu. Kuchiev,“Multiphoton detachment of electrons from negative ions,” Phys. Rev. A 55, 3760–3771 (1997).
[CrossRef]

Lezius, M.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Lindner, F.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Mainfray, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman “Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Manakov, N. L.

M. V. Frolov, N. L. Manakov, E. A. Pronin, and Anthony F. Starace, “Strong field detachment of a negative ion with non-zero angular momentum: application to F-,” J. Phys. B: A. Mol. Opt. Phys. 36, L419–L426 (2003).
[CrossRef]

Milosevic, D. B.

D. B. Milosevic, A. Gazibegovic-Busuladzic, and W. Becker,“Direct and rescattered electrons in above-threshold detachment from negative ions,” Phys. Rev. A 68, 050702(R) (2003).
[CrossRef]

D. B. Milosevic, G. G. Paulus, and W. Becker, “ Phase-Dependent Effects of a Few-Cycle Laser Pulse,” Phys. Rev. Lett. 89, 153001 (2002).
[CrossRef] [PubMed]

Mohagheghi, A.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Ni, Yongfeng

Boris Bergues, Yongfeng Ni, Hanspeter Helm, and Igor Yu. Kiyan, “Experimental Study of Photodetachment in a Strong Laser Field of Circular Polarization,” Phys. Rev. Lett. 95, 263002 (2005).
[CrossRef]

Nisoli, M.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[CrossRef] [PubMed]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long pulse,” Phys. Rev. A 70, 013411 (2004).
[CrossRef]

M. Nisoli, G. Sansone, S. Stagire, and S. De Silvestri, “Effects of Carrier-Envelope Phase Differences of Few-Optical-Cycle Light Pulses in Single-Shot High-Order-Harmonic Spectra,” Phys. Rev. Lett. 91, 213905 (2003).
[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, 182–184 (2001).
[CrossRef] [PubMed]

Overman, L.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Pascolini, M.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[CrossRef] [PubMed]

Paulus, G. G.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

D. B. Milosevic, G. G. Paulus, and W. Becker, “ Phase-Dependent Effects of a Few-Cycle Laser Pulse,” Phys. Rev. Lett. 89, 153001 (2002).
[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, 182–184 (2001).
[CrossRef] [PubMed]

Petite, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman “Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Poletto, L.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[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, 182–184 (2001).
[CrossRef] [PubMed]

Pronin, E. A.

M. V. Frolov, N. L. Manakov, E. A. Pronin, and Anthony F. Starace, “Strong field detachment of a negative ion with non-zero angular momentum: application to F-,” J. Phys. B: A. Mol. Opt. Phys. 36, L419–L426 (2003).
[CrossRef]

Quick, C. R.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Rahman, N. K.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman “Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Reeder, R. A.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Reichle, Rainer

Rainer Reichle, Hanspeter Helm, and Igor Yu. Kiyan, “Photodetachment of H- in a Strong Infrared Laser Field,” Phys. Rev. Lett. 87, 243001, (2001).
[CrossRef] [PubMed]

Reinhardt, W. P.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Sansone, G.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[CrossRef] [PubMed]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long pulse,” Phys. Rev. A 70, 013411 (2004).
[CrossRef]

M. Nisoli, G. Sansone, S. Stagire, and S. De Silvestri, “Effects of Carrier-Envelope Phase Differences of Few-Optical-Cycle Light Pulses in Single-Shot High-Order-Harmonic Spectra,” Phys. Rev. Lett. 91, 213905 (2003).
[CrossRef] [PubMed]

Scrinzi, A.

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B: At. Mol. Opt. Phys. 39, R1–R37 (2006) and reference therein.
[CrossRef]

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

Smith, W. W.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Stagira, S.

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long pulse,” Phys. Rev. A 70, 013411 (2004).
[CrossRef]

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[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, 182–184 (2001).
[CrossRef] [PubMed]

Stagire, S.

M. Nisoli, G. Sansone, S. Stagire, and S. De Silvestri, “Effects of Carrier-Envelope Phase Differences of Few-Optical-Cycle Light Pulses in Single-Shot High-Order-Harmonic Spectra,” Phys. Rev. Lett. 91, 213905 (2003).
[CrossRef] [PubMed]

Starace, Anthony F.

S. X. Hu and Anthony F. Starace, “Controlling H- detachment with few-cycle pulses,” Phys. Rev. A 68, 043407 (2003).
[CrossRef]

M. V. Frolov, N. L. Manakov, E. A. Pronin, and Anthony F. Starace, “Strong field detachment of a negative ion with non-zero angular momentum: application to F-,” J. Phys. B: A. Mol. Opt. Phys. 36, L419–L426 (2003).
[CrossRef]

Tondello, G.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[CrossRef] [PubMed]

Udem, T.

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

Uiberacker, M.

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

Villeneuve, D. M.

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B: At. Mol. Opt. Phys. 39, R1–R37 (2006) and reference therein.
[CrossRef]

Villoresi, P.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[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, 182–184 (2001).
[CrossRef] [PubMed]

Vozzi, C.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[CrossRef] [PubMed]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long pulse,” Phys. Rev. A 70, 013411 (2004).
[CrossRef]

Walther, H.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[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, 182–184 (2001).
[CrossRef] [PubMed]

Yakoviev, V. S.

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

Yuan, V.

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

J. Phys. B: A. Mol. Opt. Phys. (1)

M. V. Frolov, N. L. Manakov, E. A. Pronin, and Anthony F. Starace, “Strong field detachment of a negative ion with non-zero angular momentum: application to F-,” J. Phys. B: A. Mol. Opt. Phys. 36, L419–L426 (2003).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (1)

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B: At. Mol. Opt. Phys. 39, R1–R37 (2006) and reference therein.
[CrossRef]

J. Phys.B: At. Mol. Opt. Phys. (1)

R. Kopold and W. Becker, “Interference in high-order above-threshold ionization,” J. Phys.B: At. Mol. Opt. Phys. 32, L419–L424 (1999).
[CrossRef]

Nature (2)

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, 182–184 (2001).
[CrossRef] [PubMed]

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

Phys. Rev. A (6)

Svea Beiser, Michael Klaiber, and Igor Yu. Kiyan , “Photodetachment in a strong circularly polarized laser field,” Phys. Rev. A 70, 011402 (2004).
[CrossRef]

D. B. Milosevic, A. Gazibegovic-Busuladzic, and W. Becker,“Direct and rescattered electrons in above-threshold detachment from negative ions,” Phys. Rev. A 68, 050702(R) (2003).
[CrossRef]

G. F. Gribakin and M. Yu. Kuchiev,“Multiphoton detachment of electrons from negative ions,” Phys. Rev. A 55, 3760–3771 (1997).
[CrossRef]

S. X. Hu and Anthony F. Starace, “Controlling H- detachment with few-cycle pulses,” Phys. Rev. A 68, 043407 (2003).
[CrossRef]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long pulse,” Phys. Rev. A 70, 013411 (2004).
[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) (2002).
[CrossRef]

Phys. Rev. Lett. (11)

P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-Threshold Ionization in the Long-Wavelength Limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[CrossRef] [PubMed]

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman “Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

H. C. Bryant, A. Mohagheghi, J. B. Donahue, C. R. Quick, R. A. Reeder, V. Yuan, C. R. Hummer, W. W. Smith, S. Cohen, W. P. Reinhardt, and L. Overman, “Obervation of motional-field-induced ripples in the photodetachment cross section of H-,” Phys. Rev. Lett. 58, 2412–2415 (1987).
[CrossRef] [PubMed]

Rainer Reichle, Hanspeter Helm, and Igor Yu. Kiyan, “Photodetachment of H- in a Strong Infrared Laser Field,” Phys. Rev. Lett. 87, 243001, (2001).
[CrossRef] [PubMed]

Igor Yu. Kiyan and Hanspeter Helm, “Production of Energetic Electrons in the Process of Photodetachment of F-,” Phys. Rev. Lett. 90, 183001, (2003).
[CrossRef] [PubMed]

D. B. Milosevic, G. G. Paulus, and W. Becker, “ Phase-Dependent Effects of a Few-Cycle Laser Pulse,” Phys. Rev. Lett. 89, 153001 (2002).
[CrossRef] [PubMed]

Boris Bergues, Yongfeng Ni, Hanspeter Helm, and Igor Yu. Kiyan, “Experimental Study of Photodetachment in a Strong Laser Field of Circular Polarization,” Phys. Rev. Lett. 95, 263002 (2005).
[CrossRef]

M. Nisoli, G. Sansone, S. Stagire, and S. De Silvestri, “Effects of Carrier-Envelope Phase Differences of Few-Optical-Cycle Light Pulses in Single-Shot High-Order-Harmonic Spectra,” Phys. Rev. Lett. 91, 213905 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of Carrir-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,” Phys. Rev. Lett. 92, 113904 (2004).
[CrossRef] [PubMed]

Sov. Phys. JEPT (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JEPT 20, 1307–1314 (1965).

Other (1)

Sometimes the acronym ATD is used to indicate Above Threshold Dissociation; in the present paper, however, ATD is meant for indicating Above Threshold Detachment.

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Figures (4)

Fig. 1.
Fig. 1.

Averaged electron momentum distribution in the (x,y) polarization plane of the laser pulse for different values of the cycle numbers (nc =2, 3, 4, 20). The photoelectron distribution are averaged over a Gaussian spatial intensity with the focal parameters near to those estimated in [11] with E02/2 the peak intensity. E0 =0.0292 a.u., ω=0.030 a.u. and δ=0.

Fig. 2.
Fig. 2.

The left panel curves show the time-dependent electric field E (t, 0) for nc =2, 3. The corresponding curves for the momentum k L (t, 0) imparted to the electron by the laser pulse are reported in the right panel. In the left curves the symbols mark the time interval extrema where the electric field is more intense. The same symbols are also marked in the corresponding curves for k L (t, 0). The laser parameters as in Fig. 1.

Fig. 3.
Fig. 3.

Averaged electron momentum distribution in the (x,y) polarization plane of the laser pulse for two values of δ with nc =2. The values of E0 and ω are the same as in Fig.1.

Fig.4
Fig.4

Averaged electron momentum distribution in the (x,z) plane, perpendicular to the polarization plane of the laser pulse, for different values of the cycle number (nc =2, 3, 4, 20). The laser parameters as in Fig.1

Equations (15)

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

E ( t , δ ) = { E 0 2 sin 2 ( π t τ ) [ x ̂ cos ( ω t + δ ) + y ̂ sin ( ω t + δ ) ] t [ 0 , τ ] 0 otherwise
A ( t , δ ) = c 0 t d t E ( t , δ )
T fi ( δ ) = i 0 τ d t ψ f ( r , t ) E ( t , δ ) · r ψ i ( r , t )
ψ i ( r , t ) = ψ i ( r ) exp ( i I 0 t )
ψ i ( r ) = A r 1 exp ( k r ) Y l , m ( r ̂ )
T fi ( δ ) = i 0 τ ψ f ( r ) r · E ( t , δ ) ψ i ( r ) exp { i S q ( t , δ ) } d t
ψ f ( r ) = exp { i [ q + k L ( t , δ ) ] · r }
S q ( t , δ ) = t d t { [ q + k L ( t , δ ) ] 2 2 + I 0 }
d 2 P fi ( δ ) d q x d q y = + T fi ( δ ) 2 d q z
π ( τ , δ ) π ( t d , δ ) = t d τ E ( t , δ ) d t
π ( τ , δ ) = t d τ E ( t , δ ) d t = 0 τ E ( t , δ ) d t + 0 t d E ( t , δ ) d t
0 t E(t',δ)dt'=1/cA( t d ,δ)= k L ( t d ,δ)
T fi ( δ ) = i 0 τ d t ψ f ( r , t ) E ( t , δ ) · r ψ i ( r , t )
= i 0 τ d t ψ f ( r , t ) T + ( δ ) T ( δ ) E ( t , δ ) · r T + ( δ ) T ( δ ) ψ i ( r , t )
= i 0 τ d t ψ f ( r , t ) E ( t , 0 ) · r ψ i ( r , t )

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