Abstract

Electronic wave function movies obtained by numerically solving the time-dependent Schrödinger equation are used to elucidate the mechanism responsible for enhancements in the ATI spectrum of argon between 30 and 40 TW/cm 2.

© 2001 Optical Society of America

Full Article  |  PDF Article
Related Articles
Classical and quantal nonperturbative treatments of multiphoton and above-threshold ionization

Shih-I Chu and R. Y. Yin
J. Opt. Soc. Am. B 4(5) 720-725 (1987)

High-order harmonic production in multiphoton ionization

J. H. Eberly, Q. Su, and J. Javanainen
J. Opt. Soc. Am. B 6(7) 1289-1298 (1989)

Nonperturbative treatments of level shifts of excited states and high-order harmonic generation in strong fields

Shih-I Chu, Kwanghsi Wang, and Eric Layton
J. Opt. Soc. Am. B 7(4) 425-432 (1990)

References

  • View by:
  • |
  • |
  • |

  1. M.P. Hertlein, P.H. Bucksbaum, and H.G. Muller, “Evidence for resonant effects in high-order ATI spectra,” J. Phys. B 30 (1997) L197.
    [Crossref]
  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 (1979) 1127.
    [Crossref]
  3. H.G. Muller, A. Tip, and M.J. van der Wiel, “Ponderomotive force and AC Stark shift in multiphoton ionization,” J. Phys. B 16 (1983) L679.
    [Crossref]
  4. K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, (Academic Press, 1992, Boston) p.247.
  5. K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A 42 (1990) 5794.
    [Crossref] [PubMed]
  6. H.G. Muller, “An Efficient propagation scheme for the time-dependent Schrodinger equation in the velocity gauge,” Laser Phys. 9 (1999) 138.
  7. H.G. Muller and F.C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81 (1998) 1207.
    [Crossref]
  8. H. G. Muller, “Numerical simulation of high-order above-threshold-ionization enhancement in argon,” Phys. Rev. A 60, 1341 (1999).
    [Crossref]
  9. M. J. Nandor, M. A. Walker, L. D. Van Woerkom, and H. G. Muller, “Detailed comparison of above-threshold-ionization spectra from accurate numerical integration and high-resolution measurements,” Phys. Rev. A 60, R1771 (1999).
    [Crossref]
  10. H.B. van Linden van den Heuvell and H.G. Muller, “Limiting cases of excess-photon ionization,” Studies in Modern Optics No. 8, Multiphoton processes, S.J. Smith and P.L. Knighteds., (Cambridge University Press, 1988, Cambridge) p. 25.
  11. G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
    [Crossref] [PubMed]
  12. P. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71 (1993) 199
    [Crossref]

1999 (3)

H. G. Muller, “Numerical simulation of high-order above-threshold-ionization enhancement in argon,” Phys. Rev. A 60, 1341 (1999).
[Crossref]

M. J. Nandor, M. A. Walker, L. D. Van Woerkom, and H. G. Muller, “Detailed comparison of above-threshold-ionization spectra from accurate numerical integration and high-resolution measurements,” Phys. Rev. A 60, R1771 (1999).
[Crossref]

H.G. Muller, “An Efficient propagation scheme for the time-dependent Schrodinger equation in the velocity gauge,” Laser Phys. 9 (1999) 138.

1998 (1)

H.G. Muller and F.C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81 (1998) 1207.
[Crossref]

1997 (1)

M.P. Hertlein, P.H. Bucksbaum, and H.G. Muller, “Evidence for resonant effects in high-order ATI spectra,” J. Phys. B 30 (1997) L197.
[Crossref]

1994 (1)

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

1993 (1)

P. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71 (1993) 199
[Crossref]

1990 (1)

K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A 42 (1990) 5794.
[Crossref] [PubMed]

1983 (1)

H.G. Muller, A. Tip, and M.J. van der Wiel, “Ponderomotive force and AC Stark shift in multiphoton ionization,” J. Phys. B 16 (1983) L679.
[Crossref]

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 (1979) 1127.
[Crossref]

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 (1979) 1127.
[Crossref]

Bucksbaum, P.H.

M.P. Hertlein, P.H. Bucksbaum, and H.G. Muller, “Evidence for resonant effects in high-order ATI spectra,” J. Phys. B 30 (1997) L197.
[Crossref]

Corkum, P.

P. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71 (1993) 199
[Crossref]

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 (1979) 1127.
[Crossref]

Hertlein, M.P.

M.P. Hertlein, P.H. Bucksbaum, and H.G. Muller, “Evidence for resonant effects in high-order ATI spectra,” J. Phys. B 30 (1997) L197.
[Crossref]

Kooiman, F.C.

H.G. Muller and F.C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81 (1998) 1207.
[Crossref]

Krause, J.L.

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, (Academic Press, 1992, Boston) p.247.

Kulander, K. C.

K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A 42 (1990) 5794.
[Crossref] [PubMed]

Kulander, K.C.

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, (Academic Press, 1992, Boston) p.247.

Lambropoulos, P.

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

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 (1979) 1127.
[Crossref]

Muller, H. G.

H. G. Muller, “Numerical simulation of high-order above-threshold-ionization enhancement in argon,” Phys. Rev. A 60, 1341 (1999).
[Crossref]

M. J. Nandor, M. A. Walker, L. D. Van Woerkom, and H. G. Muller, “Detailed comparison of above-threshold-ionization spectra from accurate numerical integration and high-resolution measurements,” Phys. Rev. A 60, R1771 (1999).
[Crossref]

Muller, H.G.

H.G. Muller, “An Efficient propagation scheme for the time-dependent Schrodinger equation in the velocity gauge,” Laser Phys. 9 (1999) 138.

H.G. Muller and F.C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81 (1998) 1207.
[Crossref]

M.P. Hertlein, P.H. Bucksbaum, and H.G. Muller, “Evidence for resonant effects in high-order ATI spectra,” J. Phys. B 30 (1997) L197.
[Crossref]

H.G. Muller, A. Tip, and M.J. van der Wiel, “Ponderomotive force and AC Stark shift in multiphoton ionization,” J. Phys. B 16 (1983) L679.
[Crossref]

H.B. van Linden van den Heuvell and H.G. Muller, “Limiting cases of excess-photon ionization,” Studies in Modern Optics No. 8, Multiphoton processes, S.J. Smith and P.L. Knighteds., (Cambridge University Press, 1988, Cambridge) p. 25.

Nandor, M. J.

M. J. Nandor, M. A. Walker, L. D. Van Woerkom, and H. G. Muller, “Detailed comparison of above-threshold-ionization spectra from accurate numerical integration and high-resolution measurements,” Phys. Rev. A 60, R1771 (1999).
[Crossref]

Nicklich, W.

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

Paulus, G.G.

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[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 (1979) 1127.
[Crossref]

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 (1979) 1127.
[Crossref]

Schafer, K. J.

K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A 42 (1990) 5794.
[Crossref] [PubMed]

Schafer, K.J.

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, (Academic Press, 1992, Boston) p.247.

Tip, A.

H.G. Muller, A. Tip, and M.J. van der Wiel, “Ponderomotive force and AC Stark shift in multiphoton ionization,” J. Phys. B 16 (1983) L679.
[Crossref]

van der Wiel, M.J.

H.G. Muller, A. Tip, and M.J. van der Wiel, “Ponderomotive force and AC Stark shift in multiphoton ionization,” J. Phys. B 16 (1983) L679.
[Crossref]

van Linden van den Heuvell, H.B.

H.B. van Linden van den Heuvell and H.G. Muller, “Limiting cases of excess-photon ionization,” Studies in Modern Optics No. 8, Multiphoton processes, S.J. Smith and P.L. Knighteds., (Cambridge University Press, 1988, Cambridge) p. 25.

Van Woerkom, L. D.

M. J. Nandor, M. A. Walker, L. D. Van Woerkom, and H. G. Muller, “Detailed comparison of above-threshold-ionization spectra from accurate numerical integration and high-resolution measurements,” Phys. Rev. A 60, R1771 (1999).
[Crossref]

Walker, M. A.

M. J. Nandor, M. A. Walker, L. D. Van Woerkom, and H. G. Muller, “Detailed comparison of above-threshold-ionization spectra from accurate numerical integration and high-resolution measurements,” Phys. Rev. A 60, R1771 (1999).
[Crossref]

Walther, H.

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

Xu, Huale

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

J. Phys. B (2)

M.P. Hertlein, P.H. Bucksbaum, and H.G. Muller, “Evidence for resonant effects in high-order ATI spectra,” J. Phys. B 30 (1997) L197.
[Crossref]

H.G. Muller, A. Tip, and M.J. van der Wiel, “Ponderomotive force and AC Stark shift in multiphoton ionization,” J. Phys. B 16 (1983) L679.
[Crossref]

Laser Phys. (1)

H.G. Muller, “An Efficient propagation scheme for the time-dependent Schrodinger equation in the velocity gauge,” Laser Phys. 9 (1999) 138.

Phys. Rev. A (3)

H. G. Muller, “Numerical simulation of high-order above-threshold-ionization enhancement in argon,” Phys. Rev. A 60, 1341 (1999).
[Crossref]

M. J. Nandor, M. A. Walker, L. D. Van Woerkom, and H. G. Muller, “Detailed comparison of above-threshold-ionization spectra from accurate numerical integration and high-resolution measurements,” Phys. Rev. A 60, R1771 (1999).
[Crossref]

K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A 42 (1990) 5794.
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

P. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71 (1993) 199
[Crossref]

H.G. Muller and F.C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81 (1998) 1207.
[Crossref]

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 (1979) 1127.
[Crossref]

Other (2)

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, (Academic Press, 1992, Boston) p.247.

H.B. van Linden van den Heuvell and H.G. Muller, “Limiting cases of excess-photon ionization,” Studies in Modern Optics No. 8, Multiphoton processes, S.J. Smith and P.L. Knighteds., (Cambridge University Press, 1988, Cambridge) p. 25.

Supplementary Material (6)

» Media 1: MOV (1356 KB)     
» Media 2: MOV (1567 KB)     
» Media 3: MOV (1581 KB)     
» Media 4: MOV (1612 KB)     
» Media 5: MOV (1753 KB)     
» Media 6: MOV (1609 KB)     

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 (6)

Fig. 1.
Fig. 1.

Calculated partial yield of the individual ATI channels (in the polarization direction) as a function of the field amplitude E 0, divided by e 220 E 0 to supress the huge increase with intensity, and thus make representation on a linear scale possible. The curves are offset from each other for clarity. The upper seven curves represent (top to bottom) ionization by 12 to 18 photons. The lowest curve represents 28-photon ionization, and is multiplied by 10 compared to the others. The intensity range shows resonances with the g Rydberg series (left), the f and h series (middle) and again the g series (right) with 11, 12 and 13 photons, respectively. The dashed lines indicate intensities where movies are available.

Fig. 2.
Fig. 2.

One-cycle movie (1.5 MB) of the wavefunction at E 0=0.0315 a.u., where the 5g state is shifted in 11-photon resonance with the ground state. At this intensity the quiver amplitude is 9.5 Bohr, which brings the wave function (radius 25 Bohr) very close to the point where an electron tunneling out of the atomic ground state would appear with zero kinetic energy (16.5 Bohr).

Fig. 3.
Fig. 3.

One-cycle movie (1.6 MB) at E 0=0.0410 a.u., where the n=6 Rydberg manifold is shifted into 12-photon resonance with the ground state. By its number of angular nodes, the wavefunction can be identified as a nearly pure 6h state.

Fig. 4.
Fig. 4.

Again a resonance with the 5g state, this time by a 13-photon transition at E 0=0.0505 a.u.. At this intensity the quiver amplitude is large enough to make the state hit the nucleus, and cause some backscattering products (the short wavelength ripples that move out fast when the remainder of the wave function is at rest). (Movie size 1.5 MB)

Fig. 5.
Fig. 5.

One-cycle movie (1.6MB) at E 0=0.0440 a.u., where maximum enhancement occurs in the 28th order ATI peak. A burst of high-energy electrons can be seen to move out when most of the charge is on the other side of the atom.

Fig. 6.
Fig. 6.

One-cycle movies at E 0=0.0433 a.u. (top, 1.6 MB) and E 0=0.0444 a.u., (1.8 MB) two intensities in the opposite wings of the strong high-order enhancement. The cover frame of both movies is taken at the same phase of the laser. Note the strong off-axis lobe in the upper movie, as compared to the lower one.

Equations (1)

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

V ( r ) = ( 1 + 5.4 e r + 11.6 e 3.682 r ) / r .

Metrics