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.

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References

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  1. M.P. Hertlein, P.H. Bucksbaum and H.G. Muller, "Evidence for resonant effects in high-order ATI spectra," J. Phys. B 30 L197 (1997).
    [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 1127 (1979).
    [CrossRef]
  3. H.G. Muller, A. Tip and M.J. van der Wiel, "Ponderomotive force and AC Stark shift in multi-photon ionization," J. Phys. B 16, L679 (1983).
    [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 5794 (1990).
    [CrossRef] [PubMed]
  6. H.G. Muller, "An Efficient propagation scheme for the time-dependent Schrodinger equation in the velocity gauge," Laser Phys. 9 138 (1999).
  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, 1207 (1998).
    [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. Knight eds., (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, 2851 (1994).
    [CrossRef] [PubMed]
  12. P. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 199 (1993).
    [CrossRef]

Other (12)

M.P. Hertlein, P.H. Bucksbaum and H.G. Muller, "Evidence for resonant effects in high-order ATI spectra," J. Phys. B 30 L197 (1997).
[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 1127 (1979).
[CrossRef]

H.G. Muller, A. Tip and M.J. van der Wiel, "Ponderomotive force and AC Stark shift in multi-photon ionization," J. Phys. B 16, L679 (1983).
[CrossRef]

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.

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

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

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, 1207 (1998).
[CrossRef]

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.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. Knight eds., (Cambridge University Press, 1988, Cambridge) p. 25.

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

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

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)     

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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)

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

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