Abstract

We report the production of high-order optical harmonics in computer experiments on multiphoton ionization at high laser intensity. We correlate features of the scattered light spectra with above-threshold-ionization electron spectra from the same laser pulse in a number of experiments at different wavelengths and laser intensities.

© 1989 Optical Society of America

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  1. For early ATI experiments see P. Agostini, F. Fabre, G. Main-fray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979); P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983).
    [Crossref]
  2. Recent ATI experimental work has been reported, for example by U. Johann, T. S. Luk, H. Egger, and C. K. Rhodes, Phys. Rev. A 34, 1084 (1986); P. H. Bucksbaum, M. Bashkansky, R. R. Freeman, T. J. McIlrath, and L. F. DiMauro, Phys. Rev. Lett. 56, 2590 (1986); G. Petite, P. Agostini, and F. Yergeau, J. Opt. Soc. Am B 4, 765 (1987).
    [Crossref] [PubMed]
  3. Several reviews of above-threshold ionization are available: P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988); J. H. Eberly and J. Javanainen, Eur. J. Phys. 9, 265 (1988), P. W. Milonni, in Atoms in Strong Fields, M. H. Nayfeh, ed. (Springer-Verlag, Berlin, 1989).
    [Crossref]
  4. The first discussion of light scattering motivated by above-threshold ionization processes appears to be Y. Gontier and M. Trahin, IEEE J. Quantum Electron. QE-18, 1137 (1982). A nonperturbative treatment based on the “essential states” formalism has been given by B. W. Shore and P. L. Knight, J. Phys. B 20, 413 (1987).
    [Crossref]
  5. C. K. Rhodes, Phys. Scr. T17, 193 (1987); A. McPherson, G. Gibson, H. Jara, U. Johann, I. A. McIntyre, K. Boyer, and C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
    [Crossref]
  6. M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
    [Crossref]
  7. See, for example, J. E. Bayfield, Comments At. Mol. Phys. 20, 245 (1987) for an overview and J. E. Bayfield and D. W. Sokol, Phys. Rev. Lett. 61, 2007 (1988) for recent results on hydrogen. Alkali atom studies have been reported by P. Pillet, C. H. Mahon, and T. W. Gallagher, Phys. Rev. Lett. 60, 21 (1988).
    [Crossref] [PubMed]
  8. J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
    [Crossref] [PubMed]
  9. We use the notational conventions in, for example, P. W. Mim lonni and J. H. Eberly, Lasers (Wiley, New York, 1988). See also J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984); Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).
  10. See, for example, S. E. Harris, Phys. Rev. Lett. 31, 341 (1973); Y. Gontier, M. Poirier, and M. Trahin, J. Phys. B 13, 1381 (1980); M. Aymar and M. Crance, J. Phys. B 14, 3585 (1981); L. Pan, K. T. Taylor, and C. W. Clark, Phys. Rev. Lett. 61, 2673 (1988).
    [Crossref] [PubMed]
  11. J. Javanainen and J. H. Eberly, in Multiphoton Processes, S. J. Smith and P. L. Knight, eds. (Cambridge U. Press, Cambridge, 1988), p. 88; J. H. Eberly, J. Javanainen, and Q. Su, Kvantovaya Elektron. (Moscow) 15, 1157 (1988); J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346C (1988); J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988); J. Javanainen, Q. C. Su, and J. H. Eberly, in Atomic and Molecular Processes with Short Intense Laser Pulses, A. D. Bandrauk, ed. (Plenum, New York, 1988), p. 243; J. Javanainen and J. H. Eberly, Phys. Rev. A 39, 458 (1989).
    [Crossref] [PubMed]
  12. C. Cerjan and R. Kosloff, J. Phys. B 20, 4441 (1987); L. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988); B. Sundaram and L. Armstrong, Phys. Rev. A 38, 152 (1988); R. V. Jensen and S. M. Susskind, Phys. Rev. A 38, 711 (1988); J. N. Bardsley, M. J. Comella, and A. Szöke, J. Phys. B 21, 3899 (1989).
    [Crossref] [PubMed]
  13. See, for example, J. Bokor, P. H. Bucksbaum, and R. R. Freeman, Opt. Lett. 8, 217 (1983).
    [Crossref] [PubMed]
  14. K. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
    [Crossref] [PubMed]
  15. J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
    [Crossref] [PubMed]
  16. J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346C (1988); J. H. Eberly, J. Javanainen, and Q. Su, Kvantovaya Elektron. (Moscow) 15, 1157 (1988).
    [Crossref]

1989 (2)

K. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
[Crossref] [PubMed]

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

1988 (4)

J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346C (1988); J. H. Eberly, J. Javanainen, and Q. Su, Kvantovaya Elektron. (Moscow) 15, 1157 (1988).
[Crossref]

Several reviews of above-threshold ionization are available: P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988); J. H. Eberly and J. Javanainen, Eur. J. Phys. 9, 265 (1988), P. W. Milonni, in Atoms in Strong Fields, M. H. Nayfeh, ed. (Springer-Verlag, Berlin, 1989).
[Crossref]

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

1987 (3)

See, for example, J. E. Bayfield, Comments At. Mol. Phys. 20, 245 (1987) for an overview and J. E. Bayfield and D. W. Sokol, Phys. Rev. Lett. 61, 2007 (1988) for recent results on hydrogen. Alkali atom studies have been reported by P. Pillet, C. H. Mahon, and T. W. Gallagher, Phys. Rev. Lett. 60, 21 (1988).
[Crossref] [PubMed]

C. Cerjan and R. Kosloff, J. Phys. B 20, 4441 (1987); L. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988); B. Sundaram and L. Armstrong, Phys. Rev. A 38, 152 (1988); R. V. Jensen and S. M. Susskind, Phys. Rev. A 38, 711 (1988); J. N. Bardsley, M. J. Comella, and A. Szöke, J. Phys. B 21, 3899 (1989).
[Crossref] [PubMed]

C. K. Rhodes, Phys. Scr. T17, 193 (1987); A. McPherson, G. Gibson, H. Jara, U. Johann, I. A. McIntyre, K. Boyer, and C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
[Crossref]

1986 (1)

Recent ATI experimental work has been reported, for example by U. Johann, T. S. Luk, H. Egger, and C. K. Rhodes, Phys. Rev. A 34, 1084 (1986); P. H. Bucksbaum, M. Bashkansky, R. R. Freeman, T. J. McIlrath, and L. F. DiMauro, Phys. Rev. Lett. 56, 2590 (1986); G. Petite, P. Agostini, and F. Yergeau, J. Opt. Soc. Am B 4, 765 (1987).
[Crossref] [PubMed]

1983 (1)

1982 (1)

The first discussion of light scattering motivated by above-threshold ionization processes appears to be Y. Gontier and M. Trahin, IEEE J. Quantum Electron. QE-18, 1137 (1982). A nonperturbative treatment based on the “essential states” formalism has been given by B. W. Shore and P. L. Knight, J. Phys. B 20, 413 (1987).
[Crossref]

1979 (1)

For early ATI experiments see P. Agostini, F. Fabre, G. Main-fray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979); P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983).
[Crossref]

1973 (1)

See, for example, S. E. Harris, Phys. Rev. Lett. 31, 341 (1973); Y. Gontier, M. Poirier, and M. Trahin, J. Phys. B 13, 1381 (1980); M. Aymar and M. Crance, J. Phys. B 14, 3585 (1981); L. Pan, K. T. Taylor, and C. W. Clark, Phys. Rev. Lett. 61, 2673 (1988).
[Crossref] [PubMed]

Agostini, P.

Several reviews of above-threshold ionization are available: P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988); J. H. Eberly and J. Javanainen, Eur. J. Phys. 9, 265 (1988), P. W. Milonni, in Atoms in Strong Fields, M. H. Nayfeh, ed. (Springer-Verlag, Berlin, 1989).
[Crossref]

For early ATI experiments see P. Agostini, F. Fabre, G. Main-fray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979); P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983).
[Crossref]

Bayfield, J. E.

See, for example, J. E. Bayfield, Comments At. Mol. Phys. 20, 245 (1987) for an overview and J. E. Bayfield and D. W. Sokol, Phys. Rev. Lett. 61, 2007 (1988) for recent results on hydrogen. Alkali atom studies have been reported by P. Pillet, C. H. Mahon, and T. W. Gallagher, Phys. Rev. Lett. 60, 21 (1988).
[Crossref] [PubMed]

Bokor, J.

Bucksbaum, P. H.

Cerjan, C.

C. Cerjan and R. Kosloff, J. Phys. B 20, 4441 (1987); L. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988); B. Sundaram and L. Armstrong, Phys. Rev. A 38, 152 (1988); R. V. Jensen and S. M. Susskind, Phys. Rev. A 38, 711 (1988); J. N. Bardsley, M. J. Comella, and A. Szöke, J. Phys. B 21, 3899 (1989).
[Crossref] [PubMed]

Eberly, J. H.

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346C (1988); J. H. Eberly, J. Javanainen, and Q. Su, Kvantovaya Elektron. (Moscow) 15, 1157 (1988).
[Crossref]

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

We use the notational conventions in, for example, P. W. Mim lonni and J. H. Eberly, Lasers (Wiley, New York, 1988). See also J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984); Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

J. Javanainen and J. H. Eberly, in Multiphoton Processes, S. J. Smith and P. L. Knight, eds. (Cambridge U. Press, Cambridge, 1988), p. 88; J. H. Eberly, J. Javanainen, and Q. Su, Kvantovaya Elektron. (Moscow) 15, 1157 (1988); J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346C (1988); J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988); J. Javanainen, Q. C. Su, and J. H. Eberly, in Atomic and Molecular Processes with Short Intense Laser Pulses, A. D. Bandrauk, ed. (Plenum, New York, 1988), p. 243; J. Javanainen and J. H. Eberly, Phys. Rev. A 39, 458 (1989).
[Crossref] [PubMed]

Egger, H.

Recent ATI experimental work has been reported, for example by U. Johann, T. S. Luk, H. Egger, and C. K. Rhodes, Phys. Rev. A 34, 1084 (1986); P. H. Bucksbaum, M. Bashkansky, R. R. Freeman, T. J. McIlrath, and L. F. DiMauro, Phys. Rev. Lett. 56, 2590 (1986); G. Petite, P. Agostini, and F. Yergeau, J. Opt. Soc. Am B 4, 765 (1987).
[Crossref] [PubMed]

Fabre, F.

For early ATI experiments see P. Agostini, F. Fabre, G. Main-fray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979); P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983).
[Crossref]

Ferray, M.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Freeman, R. R.

Gontier, Y.

The first discussion of light scattering motivated by above-threshold ionization processes appears to be Y. Gontier and M. Trahin, IEEE J. Quantum Electron. QE-18, 1137 (1982). A nonperturbative treatment based on the “essential states” formalism has been given by B. W. Shore and P. L. Knight, J. Phys. B 20, 413 (1987).
[Crossref]

Harris, S. E.

See, for example, S. E. Harris, Phys. Rev. Lett. 31, 341 (1973); Y. Gontier, M. Poirier, and M. Trahin, J. Phys. B 13, 1381 (1980); M. Aymar and M. Crance, J. Phys. B 14, 3585 (1981); L. Pan, K. T. Taylor, and C. W. Clark, Phys. Rev. Lett. 61, 2673 (1988).
[Crossref] [PubMed]

Javanainen, J.

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346C (1988); J. H. Eberly, J. Javanainen, and Q. Su, Kvantovaya Elektron. (Moscow) 15, 1157 (1988).
[Crossref]

J. Javanainen and J. H. Eberly, in Multiphoton Processes, S. J. Smith and P. L. Knight, eds. (Cambridge U. Press, Cambridge, 1988), p. 88; J. H. Eberly, J. Javanainen, and Q. Su, Kvantovaya Elektron. (Moscow) 15, 1157 (1988); J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346C (1988); J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988); J. Javanainen, Q. C. Su, and J. H. Eberly, in Atomic and Molecular Processes with Short Intense Laser Pulses, A. D. Bandrauk, ed. (Plenum, New York, 1988), p. 243; J. Javanainen and J. H. Eberly, Phys. Rev. A 39, 458 (1989).
[Crossref] [PubMed]

Johann, U.

Recent ATI experimental work has been reported, for example by U. Johann, T. S. Luk, H. Egger, and C. K. Rhodes, Phys. Rev. A 34, 1084 (1986); P. H. Bucksbaum, M. Bashkansky, R. R. Freeman, T. J. McIlrath, and L. F. DiMauro, Phys. Rev. Lett. 56, 2590 (1986); G. Petite, P. Agostini, and F. Yergeau, J. Opt. Soc. Am B 4, 765 (1987).
[Crossref] [PubMed]

Kosloff, R.

C. Cerjan and R. Kosloff, J. Phys. B 20, 4441 (1987); L. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988); B. Sundaram and L. Armstrong, Phys. Rev. A 38, 152 (1988); R. V. Jensen and S. M. Susskind, Phys. Rev. A 38, 711 (1988); J. N. Bardsley, M. J. Comella, and A. Szöke, J. Phys. B 21, 3899 (1989).
[Crossref] [PubMed]

Kulander, K.

K. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
[Crossref] [PubMed]

L’Huillier, A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Li, X. F.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Lompre, L. A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Luk, T. S.

Recent ATI experimental work has been reported, for example by U. Johann, T. S. Luk, H. Egger, and C. K. Rhodes, Phys. Rev. A 34, 1084 (1986); P. H. Bucksbaum, M. Bashkansky, R. R. Freeman, T. J. McIlrath, and L. F. DiMauro, Phys. Rev. Lett. 56, 2590 (1986); G. Petite, P. Agostini, and F. Yergeau, J. Opt. Soc. Am B 4, 765 (1987).
[Crossref] [PubMed]

Mainfray, G.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Main-fray, G.

For early ATI experiments see P. Agostini, F. Fabre, G. Main-fray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979); P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983).
[Crossref]

Manus, C.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Mim lonni, P. W.

We use the notational conventions in, for example, P. W. Mim lonni and J. H. Eberly, Lasers (Wiley, New York, 1988). See also J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984); Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

Petite, G.

Several reviews of above-threshold ionization are available: P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988); J. H. Eberly and J. Javanainen, Eur. J. Phys. 9, 265 (1988), P. W. Milonni, in Atoms in Strong Fields, M. H. Nayfeh, ed. (Springer-Verlag, Berlin, 1989).
[Crossref]

For early ATI experiments see P. Agostini, F. Fabre, G. Main-fray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979); P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983).
[Crossref]

Rahman, N. K.

For early ATI experiments see P. Agostini, F. Fabre, G. Main-fray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979); P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983).
[Crossref]

Rhodes, C. K.

C. K. Rhodes, Phys. Scr. T17, 193 (1987); A. McPherson, G. Gibson, H. Jara, U. Johann, I. A. McIntyre, K. Boyer, and C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
[Crossref]

Recent ATI experimental work has been reported, for example by U. Johann, T. S. Luk, H. Egger, and C. K. Rhodes, Phys. Rev. A 34, 1084 (1986); P. H. Bucksbaum, M. Bashkansky, R. R. Freeman, T. J. McIlrath, and L. F. DiMauro, Phys. Rev. Lett. 56, 2590 (1986); G. Petite, P. Agostini, and F. Yergeau, J. Opt. Soc. Am B 4, 765 (1987).
[Crossref] [PubMed]

Shore, B. W.

K. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
[Crossref] [PubMed]

Su, Q.

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

Trahin, M.

The first discussion of light scattering motivated by above-threshold ionization processes appears to be Y. Gontier and M. Trahin, IEEE J. Quantum Electron. QE-18, 1137 (1982). A nonperturbative treatment based on the “essential states” formalism has been given by B. W. Shore and P. L. Knight, J. Phys. B 20, 413 (1987).
[Crossref]

Comments At. Mol. Phys. (1)

See, for example, J. E. Bayfield, Comments At. Mol. Phys. 20, 245 (1987) for an overview and J. E. Bayfield and D. W. Sokol, Phys. Rev. Lett. 61, 2007 (1988) for recent results on hydrogen. Alkali atom studies have been reported by P. Pillet, C. H. Mahon, and T. W. Gallagher, Phys. Rev. Lett. 60, 21 (1988).
[Crossref] [PubMed]

Contemp. Phys. (1)

Several reviews of above-threshold ionization are available: P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988); J. H. Eberly and J. Javanainen, Eur. J. Phys. 9, 265 (1988), P. W. Milonni, in Atoms in Strong Fields, M. H. Nayfeh, ed. (Springer-Verlag, Berlin, 1989).
[Crossref]

IEEE J. Quantum Electron. (1)

The first discussion of light scattering motivated by above-threshold ionization processes appears to be Y. Gontier and M. Trahin, IEEE J. Quantum Electron. QE-18, 1137 (1982). A nonperturbative treatment based on the “essential states” formalism has been given by B. W. Shore and P. L. Knight, J. Phys. B 20, 413 (1987).
[Crossref]

J. Phys. B (2)

C. Cerjan and R. Kosloff, J. Phys. B 20, 4441 (1987); L. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988); B. Sundaram and L. Armstrong, Phys. Rev. A 38, 152 (1988); R. V. Jensen and S. M. Susskind, Phys. Rev. A 38, 711 (1988); J. N. Bardsley, M. J. Comella, and A. Szöke, J. Phys. B 21, 3899 (1989).
[Crossref] [PubMed]

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (2)

Recent ATI experimental work has been reported, for example by U. Johann, T. S. Luk, H. Egger, and C. K. Rhodes, Phys. Rev. A 34, 1084 (1986); P. H. Bucksbaum, M. Bashkansky, R. R. Freeman, T. J. McIlrath, and L. F. DiMauro, Phys. Rev. Lett. 56, 2590 (1986); G. Petite, P. Agostini, and F. Yergeau, J. Opt. Soc. Am B 4, 765 (1987).
[Crossref] [PubMed]

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

See, for example, S. E. Harris, Phys. Rev. Lett. 31, 341 (1973); Y. Gontier, M. Poirier, and M. Trahin, J. Phys. B 13, 1381 (1980); M. Aymar and M. Crance, J. Phys. B 14, 3585 (1981); L. Pan, K. T. Taylor, and C. W. Clark, Phys. Rev. Lett. 61, 2673 (1988).
[Crossref] [PubMed]

For early ATI experiments see P. Agostini, F. Fabre, G. Main-fray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979); P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983).
[Crossref]

K. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
[Crossref] [PubMed]

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346C (1988); J. H. Eberly, J. Javanainen, and Q. Su, Kvantovaya Elektron. (Moscow) 15, 1157 (1988).
[Crossref]

Phys. Scr. (1)

C. K. Rhodes, Phys. Scr. T17, 193 (1987); A. McPherson, G. Gibson, H. Jara, U. Johann, I. A. McIntyre, K. Boyer, and C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
[Crossref]

Other (2)

J. Javanainen and J. H. Eberly, in Multiphoton Processes, S. J. Smith and P. L. Knight, eds. (Cambridge U. Press, Cambridge, 1988), p. 88; J. H. Eberly, J. Javanainen, and Q. Su, Kvantovaya Elektron. (Moscow) 15, 1157 (1988); J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346C (1988); J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988); J. Javanainen, Q. C. Su, and J. H. Eberly, in Atomic and Molecular Processes with Short Intense Laser Pulses, A. D. Bandrauk, ed. (Plenum, New York, 1988), p. 243; J. Javanainen and J. H. Eberly, Phys. Rev. A 39, 458 (1989).
[Crossref] [PubMed]

We use the notational conventions in, for example, P. W. Mim lonni and J. H. Eberly, Lasers (Wiley, New York, 1988). See also J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984); Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (12)

Fig. 1
Fig. 1

Energy-level diagram for the model atom used in this paper. The high-lying Rydberg levels are not shown. The vertical arrows indicate (to scale) the two-photon and ten-photon ionization processes discussed in Sections 4 and 5.

Fig. 2
Fig. 2

Magnitude of dipole matrix elements x0m versus energy of level Em.

Fig. 3
Fig. 3

Three ATI spectra showing spectral shifting as a function of laser intensity in the case of five-photon ionization of the model atom, with a laser field strength having the following values, in atomic units: (a) 0 = 0.05, (b) 0 = 0.07071, (c) 0 = 0.85. The horizontal axis is photoelectron kinetic energy, labeled in units of photon energy. There is one smooth photoelectron peak below threshold because the highest-lying Rydberg levels are not separately resolved in the short time of the square laser pulse (here 4.25 cycles).

Fig. 4
Fig. 4

Scattered light spectrum accompanying five-photon ionization of the model atom. The incident (32.25-cycle) pulse had a square envelope, and 0 = 0.05 a.u. The vertical axis is logarithmic, normalized to the intensity of the third harmonic, and the horizontal axis is labeled in units of the incident photon energy. Note the appearance of odd harmonics up to the seventh as well numerous other much weaker spectral peaks and a continuous background of scattered light.

Fig. 5
Fig. 5

(a) ATI spectrum and (b) light scattering spectrum computed for the same 16.25-cycle square laser pulse. The vertical axes are logarithmic (base 10), normalized to fit the graph window. Comparison of the graphs in this format is facilitated by giving the true value of the third-harmonic peak in (a) and one ATI peak height in (b). The horizontal axes measure photon energy and electron kinetic energy, respectively, in units of the incident laser photon energy. Various peaks are labeled with their k numbers, as defined in Subsection 3.C. Here 0 = 0.03 a.u., and the ATI peak 13 height = 0.00145 and the third-harmonic peak height = 1.12, in arbitrary units that are held the same in all figures below.

Fig. 6
Fig. 6

Same as Fig. 5, except that 0 = 0.04 a.u., the ATI peak 13 height = 0.077, and the third-harmonic peak height = 7.70.

Fig. 7
Fig. 7

Same as Fig. 5, except that 0 = 0.05 a.u., the ATI peak 13 height = 0.116, and the third-harmonic peak height = 54.2.

Fig. 8
Fig. 8

Same as Fig. 5, except that 0 = 0.06 a.u., ATI peak 13 height = 1.11, and third-harmonic peak height = 282.

Fig. 9
Fig. 9

Same as Fig. 5, with 0 = 0.05, except that the pulse duration is 32.25 cycles, the ATI peak 13 height = 0.00248, and the third-harmonic peak height = 4.75.

Fig. 10
Fig. 10

Same as Fig. 5, except that 0 = 0.05, the pulse is 32 cycles and smooth, the ATI peak 13 height = 0.038, and the third-harmonic peak height = 15.1.

Fig. 11
Fig. 11

(a) Scattered light spectrum and (b) ATI spectrum accompanying two-photon ionization of model atom with a 64.25-cycle square pulse and 0 = 0.05. The axis and labeling conventions are the same as in Fig. 5. The scattered light spectrum shows fundamental, line radiation, and wave-mixing peaks as well as poorly resolved second- and third-harmonic peaks. The ATI spectrum includes bound level replicas in each ATI peak. The notation (n, m) indicates a photon energy equal to the transition energy EnEm. The ATI two-photon peak height = 0.199; the first-harmonic (fundamental) peak height = 96,300.

Fig. 12
Fig. 12

Same as Fig. 11, except that the pulse is 96 cycles and smooth. The light scattering spectrum shows fewer fundamental and line radiation peaks but a well-resolved third-harmonic peak. Note that the background is much lower than in Fig. 11(a), and the fifth harmonic is absent. ATI two-photon peak height = 0.0675; first-harmonic peak height = 15,200.

Tables (1)

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Table 1 Model Atom Lowest Bound Energiesa

Equations (21)

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χ ( - 3 ω L , ω L , ω L , ω L ) = ( N / 0 3 ) l , m , n μ g l μ l m μ m n μ n g A l m n .
A l m n = ( ω l g - 3 ω L ) - 1 ( ω m g - 2 ω L ) - 1 ( ω n g - ω L ) - 1 + ( ) ,
P ( 3 ) ( 3 ω L ) = ( 1 / 4 ) 0 χ ( 3 ) ( - 3 ω L , ω L , ω L , ω L ) E 3 ( ω L ) .
P ( 3 ) N μ ( κ ) 3 ,
κ = ( μ E / Δ E ) .
κ = 100 E / E at ,
D ( t ) = Ψ ( t ) e x Ψ ( t )
H 0 = - ( 2 / 2 m ) 2 / x 2 + V ( x ) ,
V ( x ) = - e 2 / ( a 0 2 + x 2 ) 1 / 2 .
H = - e x E ( t ) = e x E 0 ( t ) sin ω L t ,
E 0 ( t ) = E 0 = const .             ( square pulse )
E 0 ( t ) = E 0 sin 2 ( π t / T )             ( smooth pulse ) .
H = - ( 1 / 2 ) 2 / x 2 - 1 / ( 1 + x 2 ) 1 / 2 - x E 0 ( t ) sin ω L t .
c m ( t ) = m Ψ ( t ) ,
P ( W ) d W = W Ψ ( t ) 2 d W
Δ E = e 2 E 0 2 / 4 m ω L 2 ,
Ψ ( t ) = m a m ( t ) exp ( - i E m t ) m ,
D ( t ) = n , m x n m a n * a m exp [ i ( E n - E m ) t ] .
D ( t ) = d E x 0 E a 0 * a ( E ) e - i E t + c . c .
I k = I 0 a ( k ω L ) 2 ,
P ( W k ) = a ( k ω L ) 2 .

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