Abstract

The scaling law of photoionization in few-cycle laser pulses is verified in this paper. By means of numerical solution of time-dependent Schrödinger equation, the photoionization and the asymmetry degree of photoionization of atoms with different binding potential irradiated by various laser pulses are studied. We find that the effect of increasing pulse intensity is compensated by deepening the atomic binding potential. In order to keep the asymmetric photoionization unchanged, if the central frequency of the pulse is enlarged by k times, the atomic binding potential should also be enlarged by k times, and the laser intensity should be enlarged by k3 times.

© 2005 Optical Society of America

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  1. D.-S. Guo, Jingtao Zhang, Zhizhan Xu, Xiaofeng Li, Panming Fu, and R. R. Freeman, �??Practical scaling law for photoionization angular distributions,�?? Phys. Rev. A 68, 043404 (1-5) (2003).
    [CrossRef]
  2. A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V.S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, �??Attosecond control of electronic processes by intense light fields,�?? Nature 421, 611-615 (2003).
    [CrossRef] [PubMed]
  3. 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, 182-185 (2001).
    [CrossRef] [PubMed]
  4. A. de Bohan, Ph. Antonie, D. B. Miloševi�?, and B. Piraux, �??Phase-dependent harmonic emission with ultrashort laser pulses,�?? Phys. Rev. Lett. 81, 1837-1840 (1998).
    [CrossRef]
  5. Zhinan Zeng, Ruxin Li, Wei Yu, and ZhiZhan Xu, �??Effect of the carrier-envelope phase of driving laser field on the high-order harmonic attosecond pulse,�?? Phys. Rev. A 67, 013815 (1-6) (2003).
    [CrossRef]
  6. C. Lemell, X. M. Tong, F. Krausz, and J. Burgdörfer, �??Electron emission from metal surfaces by ultrashort pulses: determination of carrier-envelope phase,�?? Phys. Rev. Lett. 90, 076403 (1-4) (2003).
    [CrossRef] [PubMed]
  7. A. Brown and W. J. Meath, �??On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules,�?? J. Chem. Phys. 109, 9351-9365 (1998).
    [CrossRef]
  8. 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).
    [CrossRef] [PubMed]
  9. G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, �??Measurement of the phase of few-cycle laser pulses,�?? Phys. Rev. Lett. 91, 253004 (1-4) (2003).
    [CrossRef]
  10. S. Chelkowski, A. D. Bandrauk, and A. Apolonski, �??Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses,�?? Phys. Rev. A 70, 013815 (1-9) (2004).
    [CrossRef]
  11. Jingtao Zhang and Zhizhan Xu, �??Above-threshold ionization of Kr atoms in an infinite sequence of circular polarized few-cycle pulses,�?? Phys. Rev. A 68, 013402 (1-6) (2003
    [CrossRef]
  12. Jingtao Zhang, Xunli Feng, D.-S. Guo, and Zhizhan Xu, �??Phase-dependent angular distributions of photoelectrons in an infinite sequence of linearly polarized few-cycle pulses,�?? Phys. Rev. A 69, 043409 (1-6) (2004).
    [CrossRef]
  13. Jingtao Zhang, Shaohui Li, and Zhizhan Xu, �??Above-threshold ionization of xenon atoms in a bichromatic phase-controlled laser field of linear and circular polarizations,�?? Phys. Rev. A 69, 053410 (1-6) (2004).
    [CrossRef]
  14. A. Gürtler, E. Robicheaux, W. J. van der Zande, and L. D. Noordam, �??Asymmetry in the strong-field ionization of Rydberg atoms by few-cycle pulses,�?? Phys. Rev. Lett. 92, 033002 (1-4) (2004).
    [CrossRef] [PubMed]
  15. Xiaoming Zhang, State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100087, China and Jingtao Zhang are preparing a manuscript to be called �??Photoionization of H atoms in few-cycle laser pulses.�??
  16. Jingtao Zhang, State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China is preparing a manuscript to be called �??A scaling law of photoionization in few-cycle regime.�??
  17. D.-S. Guo, T. �?berg and B. Crasemann, �??Scattering theory of multiphoton ionization in strong fields,�?? Phys. Rev. A 40, 4997-5005 (1989).
    [CrossRef] [PubMed]
  18. Q. Su and J. H. Eberly, �??Suppression of ionization and atomic electron localization by short intense laser pulses,�?? Phys. Rev. A 43, 2474-2479 (1991).
    [CrossRef] [PubMed]
  19. P. H. Bucksbaum, M. Bashkansky, and D. W. Schumacher, �??Above-threshold ionization in helium,�?? Phys. Rev. A 37, 3615-3618 (1988).
    [CrossRef] [PubMed]
  20. S. Chelkowski and A. D. Bandrauk, �??Asymmetries in strong-field photoionization by few-cycle laser pulses:Kinetic-energy spectra and semiclassical explanation of the asymmetries of fast and slow electrons,�?? Phys. Rev. A 71, 053815 (2005).
    [CrossRef]

J. Chem. Phys.

A. Brown and W. J. Meath, �??On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules,�?? J. Chem. Phys. 109, 9351-9365 (1998).
[CrossRef]

Nature

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V.S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, �??Attosecond control of electronic processes by intense light fields,�?? Nature 421, 611-615 (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, 182-185 (2001).
[CrossRef] [PubMed]

Phys. Rev. A

Zhinan Zeng, Ruxin Li, Wei Yu, and ZhiZhan Xu, �??Effect of the carrier-envelope phase of driving laser field on the high-order harmonic attosecond pulse,�?? Phys. Rev. A 67, 013815 (1-6) (2003).
[CrossRef]

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, �??Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses,�?? Phys. Rev. A 70, 013815 (1-9) (2004).
[CrossRef]

Jingtao Zhang and Zhizhan Xu, �??Above-threshold ionization of Kr atoms in an infinite sequence of circular polarized few-cycle pulses,�?? Phys. Rev. A 68, 013402 (1-6) (2003
[CrossRef]

Jingtao Zhang, Xunli Feng, D.-S. Guo, and Zhizhan Xu, �??Phase-dependent angular distributions of photoelectrons in an infinite sequence of linearly polarized few-cycle pulses,�?? Phys. Rev. A 69, 043409 (1-6) (2004).
[CrossRef]

Jingtao Zhang, Shaohui Li, and Zhizhan Xu, �??Above-threshold ionization of xenon atoms in a bichromatic phase-controlled laser field of linear and circular polarizations,�?? Phys. Rev. A 69, 053410 (1-6) (2004).
[CrossRef]

D.-S. Guo, Jingtao Zhang, Zhizhan Xu, Xiaofeng Li, Panming Fu, and R. R. Freeman, �??Practical scaling law for photoionization angular distributions,�?? Phys. Rev. A 68, 043404 (1-5) (2003).
[CrossRef]

D.-S. Guo, T. �?berg and B. Crasemann, �??Scattering theory of multiphoton ionization in strong fields,�?? Phys. Rev. A 40, 4997-5005 (1989).
[CrossRef] [PubMed]

Q. Su and J. H. Eberly, �??Suppression of ionization and atomic electron localization by short intense laser pulses,�?? Phys. Rev. A 43, 2474-2479 (1991).
[CrossRef] [PubMed]

P. H. Bucksbaum, M. Bashkansky, and D. W. Schumacher, �??Above-threshold ionization in helium,�?? Phys. Rev. A 37, 3615-3618 (1988).
[CrossRef] [PubMed]

S. Chelkowski and A. D. Bandrauk, �??Asymmetries in strong-field photoionization by few-cycle laser pulses:Kinetic-energy spectra and semiclassical explanation of the asymmetries of fast and slow electrons,�?? Phys. Rev. A 71, 053815 (2005).
[CrossRef]

Phys. Rev. Lett.

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).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, �??Measurement of the phase of few-cycle laser pulses,�?? Phys. Rev. Lett. 91, 253004 (1-4) (2003).
[CrossRef]

A. Gürtler, E. Robicheaux, W. J. van der Zande, and L. D. Noordam, �??Asymmetry in the strong-field ionization of Rydberg atoms by few-cycle pulses,�?? Phys. Rev. Lett. 92, 033002 (1-4) (2004).
[CrossRef] [PubMed]

C. Lemell, X. M. Tong, F. Krausz, and J. Burgdörfer, �??Electron emission from metal surfaces by ultrashort pulses: determination of carrier-envelope phase,�?? Phys. Rev. Lett. 90, 076403 (1-4) (2003).
[CrossRef] [PubMed]

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

Other

Xiaoming Zhang, State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100087, China and Jingtao Zhang are preparing a manuscript to be called �??Photoionization of H atoms in few-cycle laser pulses.�??

Jingtao Zhang, State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China is preparing a manuscript to be called �??A scaling law of photoionization in few-cycle regime.�??

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Figures (4)

Fig. 1.
Fig. 1.

Variation of photoionization probabilities with the CE phase at different laser intensities: (a) I=2.25×1014W/cm2; (b) I=3.51×1014W/cm2. Line with black squares is for P+ and that with red circles for P-. Curves in (c) show the variation of the asymmetry degree with CE phase. Line with real circles is for (a), and that with open circles is for (b). The atomic binding energy is set as 13.6eV, and the laser pulses are of five-cycle duration and of wavelength 800nm.

Fig. 2.
Fig. 2.

(a) Variation of photoionization probabilities with the CE phase at a deeper binding potential: Eb=18.2eV. Line with black squares is for P+, and that with red circles is for P-. A comparison can be made with Fig. 1(b); (b) Variation of the asymmetry degree with CE phase. Line with real circles is for (a), and that with open circles is for Fig. 1(b). The laser pulses are of five-cycle duration, wavelength 800nm, and peak intensity 3.51×1014W/cm2.

Fig. 3.
Fig. 3.

The dependence on the CE phase of the asymmetric degree in five-cycle pulses. (O) is for Eb=13.6eV, λ=800nm, I=3.51×l014W/cm2; (A)-(D) are for Eb'=k Eb, λ'=λ/k, but for different intensities: (A) I1=kI; (B)I2=k2I; (C) I3=k3I; and (D) I4=k4I. In plot (a), λ'=616nm, thus k=1.3; in plot (b) λ'=400nm, thus k=2.0. The similarity in (O) and (C) verifies the scaling law.

Fig. 4.
Fig. 4.

Comparison of the asymmetry degree as a function of the CE phase in several pulse durations: (a) n=3; (b) n=5; (c) n=7.

Equations (6)

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

i t Ψ ( r , t ) = ( 2 2 + V ( r ) + r · E ( t ) ) Ψ ( r , t ) ,
i t Ψ ( x , t ) = ( 1 2 2 x 2 + V ( x ) + x E ( t ) ) ψ ( x , t ) ,
V ( x ) = α 1 + x 2 .
A ( t ) = ( E 0 c ω ) sin 2 ( π t T p ) sin ( ω t + φ ) , 0 t T p = n p T ,
a = P + P P + + P ,
u p U p ħ ω = 2 π e 2 I m e ω 3 ,

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