Abstract

We investigate theoretically high-order harmonic generation in gases and show that, if the target thickness is high, off-axial phase matching is of importance. Results of a numerical study of harmonic generation that takes into account the self-action of the laser pulse are presented. We show that self-guiding of the laser pulse in a noble gas makes possible off-axially phase-matched high harmonic generation if some easily ionizable gas is added to the main generating gas. In calculations for such mixtures we obtained conversion efficiencies as great as approximately 10-310-2 for the 33rd harmonic of a Ti:sapphire laser and approximately 10-4 for the 121st harmonic.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
    [CrossRef]
  2. Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1425 (1999).
    [CrossRef]
  3. K. Midorikawa, Y. Tamaki, J. Itatani, and M. Obara, “Efficient phase-matched high-order-harmonic generation by guided femtosecond Ti:sapphire laser pulses,” presented at the 8th International Laser Physics Workshop, Budapest, July 2–6, 1999.
  4. H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtoseconds pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
    [CrossRef]
  5. V. T. Platonenko and V. V. Strelkov, “Generation of high-order harmonics in a high-intensity laser radiation field (review),” Quantum Electron. 28, 564–583 (1998).
    [CrossRef]
  6. P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
    [CrossRef] [PubMed]
  7. R. A. Smith, J. W. G. Tisch, M. Ciarrocca, S. Augst, and M. H. R. Hutchinson, “Angularly resolved ultra high harmonic generation experiments with picosecond laser pulses,” in Super-Intense Laser–Atom Physics, B. Piraux, A. L’Huillier, and K. Rzazewski, eds. (Plenum, New York, 1993), pp. 31–41.
  8. W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540–1560 (1994).
    [CrossRef] [PubMed]
  9. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
    [CrossRef] [PubMed]
  10. C. Kan, C. E. Capjack, R. Rankin, and N. R. Burnett, “Spectral and temporal structure in high harmonic emission from ionizing atomic gases,” Phys. Rev. A 52, R4336–R4339 (1995).
    [CrossRef] [PubMed]
  11. V. T. Platonenko and V. V. Strelkov, “Phase-matching and spectrum of high-order harmonics generated in an extended medium,” Quantum Electron. 30, 236–242 (2000).
    [CrossRef]
  12. Ph. Balcou, P. Salie’res, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
    [CrossRef]
  13. V. T. Platonenko and V. V. Strelkov, “Spatiotemporal structure of the combined field of high-order harmonics and generation of attosecond pulses,” Quantum Electron. 27, 779–784 (1997).
    [CrossRef]
  14. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power laser pulses in air,” Opt. Lett. 20, 73–75 (1995).
    [CrossRef] [PubMed]
  15. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  16. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).
  17. R. J. Pressley, ed., Handbook of Lasers (Chemical Rubber Company, Cleveland, Ohio, 1971).
  18. M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986)[Zh. Eksp. Teor. Fiz. 91, 2008–2011 (1986)].
  19. L. A. Lompre, G. Mainfray, C. Manus, S. Repoux, and J. Thebault, “Multiphoton ionization of rare gases at very high laser intensity 1015 W/cm2 by a 30-psec laser pulse at 1.06 μm,” Phys. Rev. Lett. 36, 949–952 (1976).
    [CrossRef]
  20. A. L’Huillier, X. F. Li, and L. A. Lompre, “Propagation effects in high-order harmonic generation in rare gases,” J. Opt. Soc. Am. B 7, 527–536 (1990).
    [CrossRef]
  21. V. B. Berestetskii, Ev. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics, Vol. IV of Course of Theoretical Physics (Pergamon, Oxford, 1977).

2000 (1)

V. T. Platonenko and V. V. Strelkov, “Phase-matching and spectrum of high-order harmonics generated in an extended medium,” Quantum Electron. 30, 236–242 (2000).
[CrossRef]

1999 (1)

Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1425 (1999).
[CrossRef]

1998 (2)

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtoseconds pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

V. T. Platonenko and V. V. Strelkov, “Generation of high-order harmonics in a high-intensity laser radiation field (review),” Quantum Electron. 28, 564–583 (1998).
[CrossRef]

1997 (2)

Ph. Balcou, P. Salie’res, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

V. T. Platonenko and V. V. Strelkov, “Spatiotemporal structure of the combined field of high-order harmonics and generation of attosecond pulses,” Quantum Electron. 27, 779–784 (1997).
[CrossRef]

1995 (3)

P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[CrossRef] [PubMed]

C. Kan, C. E. Capjack, R. Rankin, and N. R. Burnett, “Spectral and temporal structure in high harmonic emission from ionizing atomic gases,” Phys. Rev. A 52, R4336–R4339 (1995).
[CrossRef] [PubMed]

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power laser pulses in air,” Opt. Lett. 20, 73–75 (1995).
[CrossRef] [PubMed]

1994 (2)

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540–1560 (1994).
[CrossRef] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

1993 (1)

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
[CrossRef]

1990 (1)

1976 (1)

L. A. Lompre, G. Mainfray, C. Manus, S. Repoux, and J. Thebault, “Multiphoton ionization of rare gases at very high laser intensity 1015 W/cm2 by a 30-psec laser pulse at 1.06 μm,” Phys. Rev. Lett. 36, 949–952 (1976).
[CrossRef]

Agostini, P.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtoseconds pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Balcou, P.

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
[CrossRef]

Balcou, Ph.

Ph. Balcou, P. Salie’res, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Becker, W.

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540–1560 (1994).
[CrossRef] [PubMed]

Braun, A.

Breger, P.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtoseconds pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Burnett, N. R.

C. Kan, C. E. Capjack, R. Rankin, and N. R. Burnett, “Spectral and temporal structure in high harmonic emission from ionizing atomic gases,” Phys. Rev. A 52, R4336–R4339 (1995).
[CrossRef] [PubMed]

Capjack, C. E.

C. Kan, C. E. Capjack, R. Rankin, and N. R. Burnett, “Spectral and temporal structure in high harmonic emission from ionizing atomic gases,” Phys. Rev. A 52, R4336–R4339 (1995).
[CrossRef] [PubMed]

Chiron, A.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtoseconds pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Corkum, P. B.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Du, D.

Itatani, J.

Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1425 (1999).
[CrossRef]

Ivanov, M. Yu.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Kan, C.

C. Kan, C. E. Capjack, R. Rankin, and N. R. Burnett, “Spectral and temporal structure in high harmonic emission from ionizing atomic gases,” Phys. Rev. A 52, R4336–R4339 (1995).
[CrossRef] [PubMed]

Korn, G.

L’Huillier, A.

Ph. Balcou, P. Salie’res, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[CrossRef] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
[CrossRef]

A. L’Huillier, X. F. Li, and L. A. Lompre, “Propagation effects in high-order harmonic generation in rare gases,” J. Opt. Soc. Am. B 7, 527–536 (1990).
[CrossRef]

Lange, H. R.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtoseconds pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Lewenstein, M.

Ph. Balcou, P. Salie’res, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[CrossRef] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Li, X. F.

Liu, X.

Lompre, L. A.

A. L’Huillier, X. F. Li, and L. A. Lompre, “Propagation effects in high-order harmonic generation in rare gases,” J. Opt. Soc. Am. B 7, 527–536 (1990).
[CrossRef]

L. A. Lompre, G. Mainfray, C. Manus, S. Repoux, and J. Thebault, “Multiphoton ionization of rare gases at very high laser intensity 1015 W/cm2 by a 30-psec laser pulse at 1.06 μm,” Phys. Rev. Lett. 36, 949–952 (1976).
[CrossRef]

Long, S.

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540–1560 (1994).
[CrossRef] [PubMed]

Mainfray, G.

L. A. Lompre, G. Mainfray, C. Manus, S. Repoux, and J. Thebault, “Multiphoton ionization of rare gases at very high laser intensity 1015 W/cm2 by a 30-psec laser pulse at 1.06 μm,” Phys. Rev. Lett. 36, 949–952 (1976).
[CrossRef]

Manus, C.

L. A. Lompre, G. Mainfray, C. Manus, S. Repoux, and J. Thebault, “Multiphoton ionization of rare gases at very high laser intensity 1015 W/cm2 by a 30-psec laser pulse at 1.06 μm,” Phys. Rev. Lett. 36, 949–952 (1976).
[CrossRef]

McIver, J. K.

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540–1560 (1994).
[CrossRef] [PubMed]

Midorikawa, K.

Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1425 (1999).
[CrossRef]

Mourou, G.

Mysyrowicz, A.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtoseconds pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Nagata, Y.

Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1425 (1999).
[CrossRef]

Obara, M.

Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1425 (1999).
[CrossRef]

Platonenko, V. T.

V. T. Platonenko and V. V. Strelkov, “Phase-matching and spectrum of high-order harmonics generated in an extended medium,” Quantum Electron. 30, 236–242 (2000).
[CrossRef]

V. T. Platonenko and V. V. Strelkov, “Generation of high-order harmonics in a high-intensity laser radiation field (review),” Quantum Electron. 28, 564–583 (1998).
[CrossRef]

V. T. Platonenko and V. V. Strelkov, “Spatiotemporal structure of the combined field of high-order harmonics and generation of attosecond pulses,” Quantum Electron. 27, 779–784 (1997).
[CrossRef]

Rankin, R.

C. Kan, C. E. Capjack, R. Rankin, and N. R. Burnett, “Spectral and temporal structure in high harmonic emission from ionizing atomic gases,” Phys. Rev. A 52, R4336–R4339 (1995).
[CrossRef] [PubMed]

Repoux, S.

L. A. Lompre, G. Mainfray, C. Manus, S. Repoux, and J. Thebault, “Multiphoton ionization of rare gases at very high laser intensity 1015 W/cm2 by a 30-psec laser pulse at 1.06 μm,” Phys. Rev. Lett. 36, 949–952 (1976).
[CrossRef]

Ripoche, J.-F.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtoseconds pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Salie’res, P.

Ph. Balcou, P. Salie’res, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

Salieres, P.

P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[CrossRef] [PubMed]

Squier, J.

Strelkov, V. V.

V. T. Platonenko and V. V. Strelkov, “Phase-matching and spectrum of high-order harmonics generated in an extended medium,” Quantum Electron. 30, 236–242 (2000).
[CrossRef]

V. T. Platonenko and V. V. Strelkov, “Generation of high-order harmonics in a high-intensity laser radiation field (review),” Quantum Electron. 28, 564–583 (1998).
[CrossRef]

V. T. Platonenko and V. V. Strelkov, “Spatiotemporal structure of the combined field of high-order harmonics and generation of attosecond pulses,” Quantum Electron. 27, 779–784 (1997).
[CrossRef]

Tamaki, Y.

Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1425 (1999).
[CrossRef]

Thebault, J.

L. A. Lompre, G. Mainfray, C. Manus, S. Repoux, and J. Thebault, “Multiphoton ionization of rare gases at very high laser intensity 1015 W/cm2 by a 30-psec laser pulse at 1.06 μm,” Phys. Rev. Lett. 36, 949–952 (1976).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. A (4)

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540–1560 (1994).
[CrossRef] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

C. Kan, C. E. Capjack, R. Rankin, and N. R. Burnett, “Spectral and temporal structure in high harmonic emission from ionizing atomic gases,” Phys. Rev. A 52, R4336–R4339 (1995).
[CrossRef] [PubMed]

Ph. Balcou, P. Salie’res, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

Phys. Rev. Lett. (5)

P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[CrossRef] [PubMed]

L. A. Lompre, G. Mainfray, C. Manus, S. Repoux, and J. Thebault, “Multiphoton ionization of rare gases at very high laser intensity 1015 W/cm2 by a 30-psec laser pulse at 1.06 μm,” Phys. Rev. Lett. 36, 949–952 (1976).
[CrossRef]

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
[CrossRef]

Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1425 (1999).
[CrossRef]

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtoseconds pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Quantum Electron. (3)

V. T. Platonenko and V. V. Strelkov, “Generation of high-order harmonics in a high-intensity laser radiation field (review),” Quantum Electron. 28, 564–583 (1998).
[CrossRef]

V. T. Platonenko and V. V. Strelkov, “Phase-matching and spectrum of high-order harmonics generated in an extended medium,” Quantum Electron. 30, 236–242 (2000).
[CrossRef]

V. T. Platonenko and V. V. Strelkov, “Spatiotemporal structure of the combined field of high-order harmonics and generation of attosecond pulses,” Quantum Electron. 27, 779–784 (1997).
[CrossRef]

Other (7)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

R. J. Pressley, ed., Handbook of Lasers (Chemical Rubber Company, Cleveland, Ohio, 1971).

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986)[Zh. Eksp. Teor. Fiz. 91, 2008–2011 (1986)].

V. B. Berestetskii, Ev. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics, Vol. IV of Course of Theoretical Physics (Pergamon, Oxford, 1977).

R. A. Smith, J. W. G. Tisch, M. Ciarrocca, S. Augst, and M. H. R. Hutchinson, “Angularly resolved ultra high harmonic generation experiments with picosecond laser pulses,” in Super-Intense Laser–Atom Physics, B. Piraux, A. L’Huillier, and K. Rzazewski, eds. (Plenum, New York, 1993), pp. 31–41.

K. Midorikawa, Y. Tamaki, J. Itatani, and M. Obara, “Efficient phase-matched high-order-harmonic generation by guided femtosecond Ti:sapphire laser pulses,” presented at the 8th International Laser Physics Workshop, Budapest, July 2–6, 1999.

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 (9)

Fig. 1
Fig. 1

Dependence of the single-atom responses on distance from the beam axes calculated for the 41st, 53rd, and 67th harmonics produced in neon with an intensity of the laser beam on the axis of 4×1014 W/cm2 for λ=0.8 µm. Here and below, rel. un. means relative units.

Fig. 2
Fig. 2

Far-field angular spectra of the 41st, 53rd, and 67th harmonics generated by a thin gas layer under the same conditions as for Fig. 1.

Fig. 3
Fig. 3

Harmonic spectra generated with a Gaussian laser beam in an extended target with (1) zero dispersion of the medium and with (2) positive and (3) negative dispersions (a) that are equal in magnitude to half of the geometric dispersion and (b) with positive dispersion on a logarithmic scale.

Fig. 4
Fig. 4

Spatial structure of the laser field propagating in a mixture of xenon and cesium (i.e., dependence of laser field intensity on running time t-ν/zg and on distance r from the beam axis). Xenon number density, N0a=3×1018 cm-3; cesium number density N0b=3×1017 cm-3; laser wavelength, 0.8 µm; pulse power, 25 GW. The laser field initially has Gaussian spatial and temporal structure, the beam is focused on the front boundary of the target, and the initial pulse duration is 15 fs and its peak intensity is 1.7×1014 W/cm2. The pulse has propagated 1 cm.

Fig. 5
Fig. 5

Dependence of detuning κ on coordinate z on the beam’s axis (r=0) and at a distance r=0.5a0 from the axis.

Fig. 6
Fig. 6

Conversion efficiency (in energy) for generation of various harmonics in a 1.5-cm-thick target consisting of a mixture of xenon and cesium. The medium and the pulse parameters are the same as for Fig. 4.

Fig. 7
Fig. 7

Conversion efficiency (in energy) for generation of various harmonics in a 2.5-cm-thick target consisting of a mixture of neon (with number density N0a=2.7×1019 cm-3) and xenon (with number density N0b=2.3×1017 cm-3). Laser wavelength, 0.8 µm; pulse power, 800 GW; initial peak intensity, 8×1014 W/cm2; pulse duration, 100 fs.

Fig. 8
Fig. 8

Conversion efficiency for generation of several harmonics as a function of target thickness. The medium and the pulse parameters are the same as for Fig. 4.

Fig. 9
Fig. 9

Conversion efficiency for generation of the 33rd harmonic as a function of laser pulse power (at a fixed initial peak laser intensity of 2.3×1014 W/cm2) for three pulse durations.

Equations (28)

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

κn(z, t)=n(k1+δk1)-(kn+δkn)+αn(I/z)
n(k1+δk1)kn cos θ.
0kn-n(k1+δk1)θn22kn,
En(Z, r)i2πωnc2 exp(iknZ2+r2)j˜˜n(z, ρ)Z×expiznk1-kn+knr22Z2×J0knρrZρdρdz,
j˜˜n(z, ρ)=jn[I(z, ρ)]N(z, ρ)×expink1z-φ(z)+k1ρ22R(z),
Pn= pn(θ)θdθ,
pn(θ)=1c3 expiznk1-knz+knθ22-inφ(z)gn(θ, z)dz2,
gn(θ, z)=2π  ωnjn[I(z, ρ)]N(z, ρ)×expink1ρ22R(z)J0(knρθ)ρdρ.
1R(z)=4z/b21+4z2/b2;
Pn=b3λ3N2P˜n/2π,
P˜n= p˜n(θ˜)θ˜dθ˜,
p˜n(θ˜)=1c32z1/b2z2/bexpiz˜b2(nk1-kn)+i2nθ˜22-in arctan z˜g˜n(θ˜, z˜)dz˜2.
g˜n(θ˜, z˜)=(1+z˜2) ωnjnI0 exp(-2x2)1+z˜2×exp(inz˜x2)J0(2nx1+z˜2θ˜)xdx.
pn(θ)=λ2b4N24p˜n(θ/θ0).
i2k1z+2E=-2k12Δnat-Δnen1E,
Na=N0a exp--twa[E(r, z, t-z/νg)]dt,
Nb=N0b exp--twb[E(r, z, t-z/νg)]dt,
Δnat=3π2n1[χa(3)Na+χb(3)Nb]|E|2,
Δne=-2πe2n1mω2[(N0a-Na)+(N0b-Nb)].
Pn=2π pn(θ)θdθ,
pn(θ)=1c3z1z2expi(z-z2)×nk1-kn+knθ22gn(θ, z)dz2,
gn(θ, z)=2π ωnjn[I(z, ρ)]N(z, ρ)×exp[inϕ(z, ρ)]J0(knρθ)dρdρ,
ϕ(z, ρ)=arg(E).
κ=k1+δk1-ω/c,
δk1=ϕ/z.
-2πNeadde2n1mωc:
κ(r, z, t)=k1+δk1(r, z, t)-ωc-2πNeadde2n1mωc.
κ(r, z, t)<0.

Metrics