Abstract

The degenerate four-wave-mixing process in the vicinity of an autoionizing state is studied theoretically in the context of perturbation theory. The autoionizing state is represented either by an isolated Fano profile or by the appropriate expression of the multichannel quantum-defect theory for the corresponding Rydberg series of autoionizing states. Analytic expressions for the third-order susceptibility are given together with realistic numerical estimates based on atomic parameters extracted from accurate spectroscopic data. It is demonstrated that the observation of the effect is feasible in extensively studied atomic systems (e.g., alkaline earths) with existing coherent light sources. Constraints on the atomic parameters that will facilitate the experimental observation of the effect are identified and shown to be frequently met in real atomic systems.

© 1998 Optical Society of America

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References

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  1. M. Aymar, C. H. Greene, and E. Luc-Koening, “Multichannel Rydberg spectroscopy of complex atoms,” Rev. Mod. Phys. 68, 1015–1122 (1996).
    [CrossRef]
  2. R. D. Verma and A. Chanda, “Technique to study Rydberg states by multiphoton ionization spectroscopy,” J. Opt. Soc. Am. B 5, 86–90 (1988).
    [CrossRef]
  3. R. T. Hodgson, P. P. Sorokin, and J. J. Wynne, “Tunable coherent vacuum-ultraviolet generation in atomic vapors,” Phys. Rev. Lett. 32, 343–246 (1974).
    [CrossRef]
  4. D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, Heidelberg, 1979).
  5. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
  6. R. A. Fisher, ed., Optical Phase Conjugation (Academic, Orlando, Fla., 1983).
  7. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. A 124, 1866–1878 (1961).
    [CrossRef]
  8. X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
    [CrossRef] [PubMed]
  9. P. Balcou, P. Salieres, K. S. Budil, T. Ditmire, M. D. Perry, and A. L’Huillier, “High harmonic generation in rare gases: a new source in photoionization spectroscopy,” Z. Phys. D 34, 107–110 (1995).
    [CrossRef]
  10. P. Ljungberg and P. Axner, “Degenerate four wave mixing from laser populated excited states,” Appl. Opt. 34, 527–536 (1995).
    [CrossRef] [PubMed]
  11. P. Camus, “Production of alkaline earth metastable states by a discharge in a heat pipe,” J. Phys. B 7, 1154–1160 (1973); A. Jimoyannis, A. Bolovinos, and P. Tsekeris, “Detection of the even-parity J=0–3, autoionizing 4dnl Rydberg states of strontium by two-step laser optogalvanic spectroscopy,” Z. Phys. D 22, 577–589 (1992); W. Richardson, L. Maleki, and E. Garmire, “Degenerate four-wave mixing in a mercury-argon discharge,” Opt. Lett. OPLEDP 11, 572–574 (1986).
    [CrossRef] [PubMed]
  12. L. Armstrong, Jr. and B. L. Beers, “Comment concerning the study of autoionizing states using parametric generation,” Phys. Rev. Lett. 34, 1290–1291 (1975).
    [CrossRef]
  13. N. L. Manakov, V. D. Ovsianikov, and L. P. Rapoport, “Atoms in a laser field,” Phys. Rep. 141, 319–433 (1986).
    [CrossRef]
  14. P. Schlagheck, P. Maragakis, and P. Lambropoulos, “Theory of laser-induced two-step electron-ion recombination,” Z. Phys. D 37, 19–27 (1996).
    [CrossRef]
  15. C. Jungen, in Fundamental Processes of Atomic Dynamics, J. Briggs, H. Kleinpoppen, and H. Lutz, eds. (Plenum, New York, 1988), p. 79.
  16. A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of the two-channel coupling,” J. Phys. B 17, 215–229 (1984).
    [CrossRef]
  17. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge University, Cambridge, UK, 1992).
  18. K. Ueda, “Spectral line shapes of autoionizing Rydberg series,” Phys. Rev. A 35, 2484–2492 (1987).
    [CrossRef] [PubMed]
  19. J. Landais, M. Huet, H. Kucal, and T. Dohnalik, “High resolution spectroscopy of the ns autoionizing resonances in Ar,” J. Phys. B 28, 2395–2406 (1995).
    [CrossRef]
  20. H. Hieronymus, J. Neukammer, and H. Rinneberg, “Line narrowing and reversal in profile symmetry caused by intrachannel mixing of [5dnd]J=0 autoionizing Ba Rydberg states,” J. Phys. B 25, 3463–3474 (1992).
    [CrossRef]
  21. A. Gusti-Suzor and H. Lefebvre-Brion, “Theoretical study of complex resonances near ionization thresholds: application to the N2 photoionization spectrum,” Phys. Rev. A 30, 3057–3065 (1984).
    [CrossRef]
  22. D. Wintgen and H. Friedrich, “Perturbed Rydberg series of autoionizing resonances,” Phys. Rev. A 35, 1628–1633 (1987).
    [CrossRef] [PubMed]
  23. B. Willke and M. Kock, “Measurement of photoionization cross sections from the laser-excited Ba I (6s6p) 11P10 state,” J. Phys. B 26, 1129–1140 (1993).
    [CrossRef]
  24. D. M. Bloom, P. F. Liao, and N. P. Economou, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” Opt. Lett. 2, 58–60 (1978).
    [CrossRef] [PubMed]
  25. S. Le Boiteux, P. Simoneau, D. Bloch, F. A. M. De Oliveira, and M. Dycloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low-pressure Ne discharge,” IEEE J. Quantum Electron. 22, 1229–1247 (1986).
    [CrossRef]

1996 (2)

P. Schlagheck, P. Maragakis, and P. Lambropoulos, “Theory of laser-induced two-step electron-ion recombination,” Z. Phys. D 37, 19–27 (1996).
[CrossRef]

M. Aymar, C. H. Greene, and E. Luc-Koening, “Multichannel Rydberg spectroscopy of complex atoms,” Rev. Mod. Phys. 68, 1015–1122 (1996).
[CrossRef]

1995 (3)

P. Balcou, P. Salieres, K. S. Budil, T. Ditmire, M. D. Perry, and A. L’Huillier, “High harmonic generation in rare gases: a new source in photoionization spectroscopy,” Z. Phys. D 34, 107–110 (1995).
[CrossRef]

J. Landais, M. Huet, H. Kucal, and T. Dohnalik, “High resolution spectroscopy of the ns autoionizing resonances in Ar,” J. Phys. B 28, 2395–2406 (1995).
[CrossRef]

P. Ljungberg and P. Axner, “Degenerate four wave mixing from laser populated excited states,” Appl. Opt. 34, 527–536 (1995).
[CrossRef] [PubMed]

1993 (1)

B. Willke and M. Kock, “Measurement of photoionization cross sections from the laser-excited Ba I (6s6p) 11P10 state,” J. Phys. B 26, 1129–1140 (1993).
[CrossRef]

1992 (1)

H. Hieronymus, J. Neukammer, and H. Rinneberg, “Line narrowing and reversal in profile symmetry caused by intrachannel mixing of [5dnd]J=0 autoionizing Ba Rydberg states,” J. Phys. B 25, 3463–3474 (1992).
[CrossRef]

1989 (1)

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (2)

K. Ueda, “Spectral line shapes of autoionizing Rydberg series,” Phys. Rev. A 35, 2484–2492 (1987).
[CrossRef] [PubMed]

D. Wintgen and H. Friedrich, “Perturbed Rydberg series of autoionizing resonances,” Phys. Rev. A 35, 1628–1633 (1987).
[CrossRef] [PubMed]

1986 (2)

N. L. Manakov, V. D. Ovsianikov, and L. P. Rapoport, “Atoms in a laser field,” Phys. Rep. 141, 319–433 (1986).
[CrossRef]

S. Le Boiteux, P. Simoneau, D. Bloch, F. A. M. De Oliveira, and M. Dycloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low-pressure Ne discharge,” IEEE J. Quantum Electron. 22, 1229–1247 (1986).
[CrossRef]

1984 (2)

A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of the two-channel coupling,” J. Phys. B 17, 215–229 (1984).
[CrossRef]

A. Gusti-Suzor and H. Lefebvre-Brion, “Theoretical study of complex resonances near ionization thresholds: application to the N2 photoionization spectrum,” Phys. Rev. A 30, 3057–3065 (1984).
[CrossRef]

1978 (1)

1975 (1)

L. Armstrong, Jr. and B. L. Beers, “Comment concerning the study of autoionizing states using parametric generation,” Phys. Rev. Lett. 34, 1290–1291 (1975).
[CrossRef]

1974 (1)

R. T. Hodgson, P. P. Sorokin, and J. J. Wynne, “Tunable coherent vacuum-ultraviolet generation in atomic vapors,” Phys. Rev. Lett. 32, 343–246 (1974).
[CrossRef]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. A 124, 1866–1878 (1961).
[CrossRef]

Armstrong Jr., L.

L. Armstrong, Jr. and B. L. Beers, “Comment concerning the study of autoionizing states using parametric generation,” Phys. Rev. Lett. 34, 1290–1291 (1975).
[CrossRef]

Axner, P.

Aymar, M.

M. Aymar, C. H. Greene, and E. Luc-Koening, “Multichannel Rydberg spectroscopy of complex atoms,” Rev. Mod. Phys. 68, 1015–1122 (1996).
[CrossRef]

Balcou, P.

P. Balcou, P. Salieres, K. S. Budil, T. Ditmire, M. D. Perry, and A. L’Huillier, “High harmonic generation in rare gases: a new source in photoionization spectroscopy,” Z. Phys. D 34, 107–110 (1995).
[CrossRef]

Beers, B. L.

L. Armstrong, Jr. and B. L. Beers, “Comment concerning the study of autoionizing states using parametric generation,” Phys. Rev. Lett. 34, 1290–1291 (1975).
[CrossRef]

Bloch, D.

S. Le Boiteux, P. Simoneau, D. Bloch, F. A. M. De Oliveira, and M. Dycloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low-pressure Ne discharge,” IEEE J. Quantum Electron. 22, 1229–1247 (1986).
[CrossRef]

Bloom, D. M.

Budil, K. S.

P. Balcou, P. Salieres, K. S. Budil, T. Ditmire, M. D. Perry, and A. L’Huillier, “High harmonic generation in rare gases: a new source in photoionization spectroscopy,” Z. Phys. D 34, 107–110 (1995).
[CrossRef]

Chanda, A.

De Oliveira, F. A. M.

S. Le Boiteux, P. Simoneau, D. Bloch, F. A. M. De Oliveira, and M. Dycloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low-pressure Ne discharge,” IEEE J. Quantum Electron. 22, 1229–1247 (1986).
[CrossRef]

Ditmire, T.

P. Balcou, P. Salieres, K. S. Budil, T. Ditmire, M. D. Perry, and A. L’Huillier, “High harmonic generation in rare gases: a new source in photoionization spectroscopy,” Z. Phys. D 34, 107–110 (1995).
[CrossRef]

Dohnalik, T.

J. Landais, M. Huet, H. Kucal, and T. Dohnalik, “High resolution spectroscopy of the ns autoionizing resonances in Ar,” J. Phys. B 28, 2395–2406 (1995).
[CrossRef]

Dycloy, M.

S. Le Boiteux, P. Simoneau, D. Bloch, F. A. M. De Oliveira, and M. Dycloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low-pressure Ne discharge,” IEEE J. Quantum Electron. 22, 1229–1247 (1986).
[CrossRef]

Economou, N. P.

Fano, U.

A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of the two-channel coupling,” J. Phys. B 17, 215–229 (1984).
[CrossRef]

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. A 124, 1866–1878 (1961).
[CrossRef]

Ferray, M.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Friedrich, H.

D. Wintgen and H. Friedrich, “Perturbed Rydberg series of autoionizing resonances,” Phys. Rev. A 35, 1628–1633 (1987).
[CrossRef] [PubMed]

Giusti-Suzor, A.

A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of the two-channel coupling,” J. Phys. B 17, 215–229 (1984).
[CrossRef]

Greene, C. H.

M. Aymar, C. H. Greene, and E. Luc-Koening, “Multichannel Rydberg spectroscopy of complex atoms,” Rev. Mod. Phys. 68, 1015–1122 (1996).
[CrossRef]

Gusti-Suzor, A.

A. Gusti-Suzor and H. Lefebvre-Brion, “Theoretical study of complex resonances near ionization thresholds: application to the N2 photoionization spectrum,” Phys. Rev. A 30, 3057–3065 (1984).
[CrossRef]

Hieronymus, H.

H. Hieronymus, J. Neukammer, and H. Rinneberg, “Line narrowing and reversal in profile symmetry caused by intrachannel mixing of [5dnd]J=0 autoionizing Ba Rydberg states,” J. Phys. B 25, 3463–3474 (1992).
[CrossRef]

Hodgson, R. T.

R. T. Hodgson, P. P. Sorokin, and J. J. Wynne, “Tunable coherent vacuum-ultraviolet generation in atomic vapors,” Phys. Rev. Lett. 32, 343–246 (1974).
[CrossRef]

Huet, M.

J. Landais, M. Huet, H. Kucal, and T. Dohnalik, “High resolution spectroscopy of the ns autoionizing resonances in Ar,” J. Phys. B 28, 2395–2406 (1995).
[CrossRef]

Kock, M.

B. Willke and M. Kock, “Measurement of photoionization cross sections from the laser-excited Ba I (6s6p) 11P10 state,” J. Phys. B 26, 1129–1140 (1993).
[CrossRef]

Kucal, H.

J. Landais, M. Huet, H. Kucal, and T. Dohnalik, “High resolution spectroscopy of the ns autoionizing resonances in Ar,” J. Phys. B 28, 2395–2406 (1995).
[CrossRef]

L’Huillier, A.

P. Balcou, P. Salieres, K. S. Budil, T. Ditmire, M. D. Perry, and A. L’Huillier, “High harmonic generation in rare gases: a new source in photoionization spectroscopy,” Z. Phys. D 34, 107–110 (1995).
[CrossRef]

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Lambropoulos, P.

P. Schlagheck, P. Maragakis, and P. Lambropoulos, “Theory of laser-induced two-step electron-ion recombination,” Z. Phys. D 37, 19–27 (1996).
[CrossRef]

Landais, J.

J. Landais, M. Huet, H. Kucal, and T. Dohnalik, “High resolution spectroscopy of the ns autoionizing resonances in Ar,” J. Phys. B 28, 2395–2406 (1995).
[CrossRef]

Le Boiteux, S.

S. Le Boiteux, P. Simoneau, D. Bloch, F. A. M. De Oliveira, and M. Dycloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low-pressure Ne discharge,” IEEE J. Quantum Electron. 22, 1229–1247 (1986).
[CrossRef]

Lefebvre-Brion, H.

A. Gusti-Suzor and H. Lefebvre-Brion, “Theoretical study of complex resonances near ionization thresholds: application to the N2 photoionization spectrum,” Phys. Rev. A 30, 3057–3065 (1984).
[CrossRef]

Li, X. F.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Liao, P. F.

Ljungberg, P.

Lompre, L. A.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Luc-Koening, E.

M. Aymar, C. H. Greene, and E. Luc-Koening, “Multichannel Rydberg spectroscopy of complex atoms,” Rev. Mod. Phys. 68, 1015–1122 (1996).
[CrossRef]

Mainfray, G.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Manakov, N. L.

N. L. Manakov, V. D. Ovsianikov, and L. P. Rapoport, “Atoms in a laser field,” Phys. Rep. 141, 319–433 (1986).
[CrossRef]

Maragakis, P.

P. Schlagheck, P. Maragakis, and P. Lambropoulos, “Theory of laser-induced two-step electron-ion recombination,” Z. Phys. D 37, 19–27 (1996).
[CrossRef]

Neukammer, J.

H. Hieronymus, J. Neukammer, and H. Rinneberg, “Line narrowing and reversal in profile symmetry caused by intrachannel mixing of [5dnd]J=0 autoionizing Ba Rydberg states,” J. Phys. B 25, 3463–3474 (1992).
[CrossRef]

Ovsianikov, V. D.

N. L. Manakov, V. D. Ovsianikov, and L. P. Rapoport, “Atoms in a laser field,” Phys. Rep. 141, 319–433 (1986).
[CrossRef]

Perry, M. D.

P. Balcou, P. Salieres, K. S. Budil, T. Ditmire, M. D. Perry, and A. L’Huillier, “High harmonic generation in rare gases: a new source in photoionization spectroscopy,” Z. Phys. D 34, 107–110 (1995).
[CrossRef]

Rapoport, L. P.

N. L. Manakov, V. D. Ovsianikov, and L. P. Rapoport, “Atoms in a laser field,” Phys. Rep. 141, 319–433 (1986).
[CrossRef]

Rinneberg, H.

H. Hieronymus, J. Neukammer, and H. Rinneberg, “Line narrowing and reversal in profile symmetry caused by intrachannel mixing of [5dnd]J=0 autoionizing Ba Rydberg states,” J. Phys. B 25, 3463–3474 (1992).
[CrossRef]

Salieres, P.

P. Balcou, P. Salieres, K. S. Budil, T. Ditmire, M. D. Perry, and A. L’Huillier, “High harmonic generation in rare gases: a new source in photoionization spectroscopy,” Z. Phys. D 34, 107–110 (1995).
[CrossRef]

Schlagheck, P.

P. Schlagheck, P. Maragakis, and P. Lambropoulos, “Theory of laser-induced two-step electron-ion recombination,” Z. Phys. D 37, 19–27 (1996).
[CrossRef]

Simoneau, P.

S. Le Boiteux, P. Simoneau, D. Bloch, F. A. M. De Oliveira, and M. Dycloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low-pressure Ne discharge,” IEEE J. Quantum Electron. 22, 1229–1247 (1986).
[CrossRef]

Sorokin, P. P.

R. T. Hodgson, P. P. Sorokin, and J. J. Wynne, “Tunable coherent vacuum-ultraviolet generation in atomic vapors,” Phys. Rev. Lett. 32, 343–246 (1974).
[CrossRef]

Ueda, K.

K. Ueda, “Spectral line shapes of autoionizing Rydberg series,” Phys. Rev. A 35, 2484–2492 (1987).
[CrossRef] [PubMed]

Verma, R. D.

Willke, B.

B. Willke and M. Kock, “Measurement of photoionization cross sections from the laser-excited Ba I (6s6p) 11P10 state,” J. Phys. B 26, 1129–1140 (1993).
[CrossRef]

Wintgen, D.

D. Wintgen and H. Friedrich, “Perturbed Rydberg series of autoionizing resonances,” Phys. Rev. A 35, 1628–1633 (1987).
[CrossRef] [PubMed]

Wynne, J. J.

R. T. Hodgson, P. P. Sorokin, and J. J. Wynne, “Tunable coherent vacuum-ultraviolet generation in atomic vapors,” Phys. Rev. Lett. 32, 343–246 (1974).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

S. Le Boiteux, P. Simoneau, D. Bloch, F. A. M. De Oliveira, and M. Dycloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low-pressure Ne discharge,” IEEE J. Quantum Electron. 22, 1229–1247 (1986).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B (4)

B. Willke and M. Kock, “Measurement of photoionization cross sections from the laser-excited Ba I (6s6p) 11P10 state,” J. Phys. B 26, 1129–1140 (1993).
[CrossRef]

A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of the two-channel coupling,” J. Phys. B 17, 215–229 (1984).
[CrossRef]

J. Landais, M. Huet, H. Kucal, and T. Dohnalik, “High resolution spectroscopy of the ns autoionizing resonances in Ar,” J. Phys. B 28, 2395–2406 (1995).
[CrossRef]

H. Hieronymus, J. Neukammer, and H. Rinneberg, “Line narrowing and reversal in profile symmetry caused by intrachannel mixing of [5dnd]J=0 autoionizing Ba Rydberg states,” J. Phys. B 25, 3463–3474 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

N. L. Manakov, V. D. Ovsianikov, and L. P. Rapoport, “Atoms in a laser field,” Phys. Rep. 141, 319–433 (1986).
[CrossRef]

Phys. Rev. A (5)

A. Gusti-Suzor and H. Lefebvre-Brion, “Theoretical study of complex resonances near ionization thresholds: application to the N2 photoionization spectrum,” Phys. Rev. A 30, 3057–3065 (1984).
[CrossRef]

D. Wintgen and H. Friedrich, “Perturbed Rydberg series of autoionizing resonances,” Phys. Rev. A 35, 1628–1633 (1987).
[CrossRef] [PubMed]

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. A 124, 1866–1878 (1961).
[CrossRef]

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

K. Ueda, “Spectral line shapes of autoionizing Rydberg series,” Phys. Rev. A 35, 2484–2492 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

L. Armstrong, Jr. and B. L. Beers, “Comment concerning the study of autoionizing states using parametric generation,” Phys. Rev. Lett. 34, 1290–1291 (1975).
[CrossRef]

R. T. Hodgson, P. P. Sorokin, and J. J. Wynne, “Tunable coherent vacuum-ultraviolet generation in atomic vapors,” Phys. Rev. Lett. 32, 343–246 (1974).
[CrossRef]

Rev. Mod. Phys. (1)

M. Aymar, C. H. Greene, and E. Luc-Koening, “Multichannel Rydberg spectroscopy of complex atoms,” Rev. Mod. Phys. 68, 1015–1122 (1996).
[CrossRef]

Z. Phys. D (2)

P. Balcou, P. Salieres, K. S. Budil, T. Ditmire, M. D. Perry, and A. L’Huillier, “High harmonic generation in rare gases: a new source in photoionization spectroscopy,” Z. Phys. D 34, 107–110 (1995).
[CrossRef]

P. Schlagheck, P. Maragakis, and P. Lambropoulos, “Theory of laser-induced two-step electron-ion recombination,” Z. Phys. D 37, 19–27 (1996).
[CrossRef]

Other (6)

C. Jungen, in Fundamental Processes of Atomic Dynamics, J. Briggs, H. Kleinpoppen, and H. Lutz, eds. (Plenum, New York, 1988), p. 79.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge University, Cambridge, UK, 1992).

P. Camus, “Production of alkaline earth metastable states by a discharge in a heat pipe,” J. Phys. B 7, 1154–1160 (1973); A. Jimoyannis, A. Bolovinos, and P. Tsekeris, “Detection of the even-parity J=0–3, autoionizing 4dnl Rydberg states of strontium by two-step laser optogalvanic spectroscopy,” Z. Phys. D 22, 577–589 (1992); W. Richardson, L. Maleki, and E. Garmire, “Degenerate four-wave mixing in a mercury-argon discharge,” Opt. Lett. OPLEDP 11, 572–574 (1986).
[CrossRef] [PubMed]

D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, Heidelberg, 1979).

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

R. A. Fisher, ed., Optical Phase Conjugation (Academic, Orlando, Fla., 1983).

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Figures (5)

Fig. 1
Fig. 1

(a) Typical DFWM geometry leading to generation of a PC wave. It involves two counterpropagating pump beams, crossed at a small angle by a probe beam. The produced PC wave is counterpropagating to the probe beam. All the four interacting waves have the same frequency ω, and the phase-matching condition is automatically satisfied. (b) Simplified energy-level diagram and possible one-photon resonant DFWM scheme through an autoionizing upper state |f. The latter is a linear combination of the discrete component |o and the continuum components |c. (c) The same as for (b) but for the two-photon resonant DFWM case. The intermediate states |l and |m are assumed not to be in resonance with one photon from the initial state |i.

Fig. 2
Fig. 2

One-photon resonant absorption (dotted curve) and PC (solid curve) spectra for four selected values of the Fano parameter q. Both spectra are scaled to unity.  

Fig. 3
Fig. 3

Two-photon resonant absorption (dotted curve) and PC (solid curve) spectra for two selected values of the effective two-photon Fano parameter q(2). Both spectra are scaled to unity.

Fig. 4
Fig. 4

(a) Spectral dependence of the one-photon resonant absorption (solid curve) and (b) PC signal (solid curve) for the Xe [5p1/25nd3/2]J=1, n=1112 and [5p1/25ns1/2]J=1, n=1314 Rydberg states. The initial state is the Xe ground state. The vertical solid line shows the shift of the absorption and DFWM maxima for the low-q, [5p1/2512d3/2]J=1 state. The dashed curve in (a) shows the absorption profile of the [5p1/2511d3/2]J=1 state as predicted by the Fano formula (2) for an isolated resonance. The inset in (b) shows in an expanded scale the PC profiles calculated by the analytical expression (10) and the numerical computation with the MQDT absorption spectrum.

Fig. 5
Fig. 5

(a) Spectral dependence of the one-photon resonant absorption and (b) the PC signal for the [5dnd]J=0 spectrum of Ba from the excited 5d6p 1P1 initial state and in the neighborhood of the stabilized [5d3/226d]J=0 level around 46 710 cm-1. The energy scale refers to the Ba ground state. The arrows indicate that both absorption and PC signals become quasi infinite. In practice the calculated intensity of the stabilized line on the DFWM spectrum is about five orders of magnitude higher than the intensity of the other lines.

Tables (2)

Tables Icon

Table 1 MQDT Parameters18 Employed in the Calculation of the Absorption and PC Spectra of Xe, Shown in Fig. 4 a

Tables Icon

Table 2 MQDT Parameters20 Inserted in Eq. (24) for the Calculation of the Absorption and PC Spectra of Ba, Shown in Fig. 5 a

Equations (26)

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χ1(3)(ω, ω, -ω, ω)=-2N3εo3 f |μfi|2(ωfi-ω)×f |μfi|2(ωfi-ω)2.
μfi(ε)=μci ε+q(ε2+1)1/2,
χ1(3)=-2N|μci|43εo(Γ/2)3 I1I2,
I1=- (ε+q)2(ε2+1)(ε-x+iγ) dε,
I2=- (ε+q)2(ε2+1)(ε-x+iγ)2 dε.
1ε-x+iγ=P 1ε-x-iπδ(ε-x),
I1=π x(1-q2)+2qx2+1+iπ (x+q)2x2+1,
I2=I1x,
|χ1(3)|=2N|μci|43εo(Γ/2)3 π2(1+q2)(x+2q)2+q4(x2+1)3,
S1PC|χ1(3)|2 (2q+x)2+q4(x2+1)3.
χ2(3)(ω, ω, -ω, ω)=2N3εo3
×f,m,lμimμmfμflμli(ωmi-ω)(ωfi-2ω)(ωli-ω),
χ2(3)=2N3εo f 1(ωfi-2ω) l μflμli(ωli-ω)×m μimμmf(ωmi-ω),
|f=1[π(Γ/2)(ε2+1)]1/2|o+ε[π(Γ/2)(ε2+1)]1/2|c,
l μflμli(ωli-ω)=1[π(Γ/2)(ε2+1)]1/2 l μolμli(ωli-ω)+l μclμli(ωli-ω) ε=μci(2) ε+q(2)(ε2+1)1/2,
μab(2)=k μakμkb(ωkb-ω),
q(2)=μoi(2)(πΓ/2)1/2μci(2),
χ2(3)=2N|μci(2)|23εo(Γ/2) - (ε+q(2))2(ε2+1)(ε-x+iγ) dε.
|χ2(3)|=2N|μci(2)|23εo(Γ/2) π[x+2q(2)]2+[q(2)]4x2+1.
|μfi(Ec)|2 (T-λR)2T2+R4,
I2=- [|μfi(Ec)|2]Ec 1(Ec-Eω+iγ) dEc.
S1PC4νω4P1P2-νω3|μfi(νω)|2[|μfi(ν)|2]ν |ν=νω2+4νω5P1 [|μfi(ν)|2]ν |ν=νω+νω2P2|μfi(νω)|22,
P1=Pνthr-νω |μfi(y)|2y(y+νω)(y+2νω) dy,
y=ν-νω,
P2=Pνthr-νω [|μfi(y)|2]y (y+νω)2y(y+2νω) dy,
|μfi(Ec)|2[(T2T3-R232)λ1+(R13R23-R12T3)λ2+(R12R23-R13T2)λ3]2(T2T3-R232)2+(2R12R13R23-R122T3-R132T2)2,

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