Abstract

The results of a study of fifth-harmonic production in neon and argon irradiated with 248-nm picosecond laser pulses are presented. Focused intensities range from 1013 to 1015 W/cm2. Data for fifth-harmonic intensity as a function of both target density and focused laser intensity are presented and compared with theory. For the laser intensities and medium densities studied, estimates for the linear and nonlinear components of Δk, the wave-vector mismatch between the fundamental and harmonic waves, indicate that the nonlinear component is much greater than the linear component.

© 1988 Optical Society of America

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Corrections

R. Rosman, G. Gibson, K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, J. C. Solem, and C. K. Rhodes, "Fifth-harmonic production in neon and argon with picosecond 248-nm radiation: errata," J. Opt. Soc. Am. B 5, 1948_1-1948 (1988)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-5-9-1948_1

References

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  1. J. Reintjes, C. Y. She, R. E. Eckardt, IEEE J. Quantum Electron. QE-14, 581 (1978).
    [CrossRef]
  2. J. Reintjes, R. C. Eckardt, C. Y. She, N. E. Karangelen, R. C. Elton, R. A. Andrews, Phys. Rev. Lett. 37, 1540 (1976).
    [CrossRef]
  3. J. Reintjes, C. Y. She, R. C. Eckardt, N. E. Karangelen, R. A. Andrews, R. C. Elton, Appl. Phys. Lett. 30, 480 (1977).
    [CrossRef]
  4. D. P. Shelton, A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
    [CrossRef]
  5. H. J. Lehmeier, W. Leupacher, A. Penzkofer, Opt. Commun. 56, 67 (1985).
    [CrossRef]
  6. M. P. Bogaard, B. J. Orr, in International Review of Science, Molecular Structure and Properties, Vol. 2 of Physical Chemistry Series 2 (Butterworth, London, 1975), p. 149.
  7. J. F. Ward, G. H. C. New, Phys. Rev. 185, 57 (1969).
    [CrossRef]
  8. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
    [CrossRef]
  9. G. Bjorklund, IEEE J. Quantum Electron. QE-11, 287 (1975).
    [CrossRef]
  10. J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984).
  11. The index of refraction is related to density by n2(ω) = 1 + 4πNe2/mΣjfj(ωj2− ω2− iωγ)−1. For n≈ 1, n(5ω) − n(ω) ∝ N.See J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 285.
  12. A. P. Schwarzenbach, T. S. Luk, I. A. McIntyre, U. Johann, A. McPherson, K. Boyer, C. K. Rhodes, Opt. Lett. 11, 499 (1986).
    [CrossRef] [PubMed]
  13. M. H. R. Hutchinson, I. A. McIntyre, G. N. Gibson, C. K. Rhodes, Opt. Lett. 12, 102 (1987).
    [CrossRef] [PubMed]
  14. The axial intensity is given by I(u)/I0= [4 sin(u/4)/u]2, where u= πz/2λF2. At I(u)/I0= ½, u≈ 5.6, and b= 2z≈ 7F2λ.See M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 441.
  15. U. Johann, T. S. Luk, I. A. McIntyre, A. McPherson, A. P. Schwarzenbach, K. Boyer, C. K. Rhodes, AIP Conf. Proc. 147, 202 (1986).
    [CrossRef]
  16. K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).
  17. R. D. Hudson, L. J. Kieffer, Atomic Data 2, 205 (1971).
    [CrossRef]
  18. L. J. Zych, J. F. Young, IEEE J. Quantum Electron. QE-14, 147 (1978).
    [CrossRef]
  19. D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
    [CrossRef]

1987 (2)

1986 (2)

U. Johann, T. S. Luk, I. A. McIntyre, A. McPherson, A. P. Schwarzenbach, K. Boyer, C. K. Rhodes, AIP Conf. Proc. 147, 202 (1986).
[CrossRef]

A. P. Schwarzenbach, T. S. Luk, I. A. McIntyre, U. Johann, A. McPherson, K. Boyer, C. K. Rhodes, Opt. Lett. 11, 499 (1986).
[CrossRef] [PubMed]

1985 (1)

H. J. Lehmeier, W. Leupacher, A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

1982 (1)

D. P. Shelton, A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
[CrossRef]

1978 (2)

J. Reintjes, C. Y. She, R. E. Eckardt, IEEE J. Quantum Electron. QE-14, 581 (1978).
[CrossRef]

L. J. Zych, J. F. Young, IEEE J. Quantum Electron. QE-14, 147 (1978).
[CrossRef]

1977 (1)

J. Reintjes, C. Y. She, R. C. Eckardt, N. E. Karangelen, R. A. Andrews, R. C. Elton, Appl. Phys. Lett. 30, 480 (1977).
[CrossRef]

1976 (1)

J. Reintjes, R. C. Eckardt, C. Y. She, N. E. Karangelen, R. C. Elton, R. A. Andrews, Phys. Rev. Lett. 37, 1540 (1976).
[CrossRef]

1975 (1)

G. Bjorklund, IEEE J. Quantum Electron. QE-11, 287 (1975).
[CrossRef]

1971 (1)

R. D. Hudson, L. J. Kieffer, Atomic Data 2, 205 (1971).
[CrossRef]

1969 (1)

J. F. Ward, G. H. C. New, Phys. Rev. 185, 57 (1969).
[CrossRef]

Andrews, R. A.

J. Reintjes, C. Y. She, R. C. Eckardt, N. E. Karangelen, R. A. Andrews, R. C. Elton, Appl. Phys. Lett. 30, 480 (1977).
[CrossRef]

J. Reintjes, R. C. Eckardt, C. Y. She, N. E. Karangelen, R. C. Elton, R. A. Andrews, Phys. Rev. Lett. 37, 1540 (1976).
[CrossRef]

Bjorklund, G.

G. Bjorklund, IEEE J. Quantum Electron. QE-11, 287 (1975).
[CrossRef]

Bogaard, M. P.

M. P. Bogaard, B. J. Orr, in International Review of Science, Molecular Structure and Properties, Vol. 2 of Physical Chemistry Series 2 (Butterworth, London, 1975), p. 149.

Born, M.

The axial intensity is given by I(u)/I0= [4 sin(u/4)/u]2, where u= πz/2λF2. At I(u)/I0= ½, u≈ 5.6, and b= 2z≈ 7F2λ.See M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 441.

Boyer, K.

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
[CrossRef]

A. P. Schwarzenbach, T. S. Luk, I. A. McIntyre, U. Johann, A. McPherson, K. Boyer, C. K. Rhodes, Opt. Lett. 11, 499 (1986).
[CrossRef] [PubMed]

U. Johann, T. S. Luk, I. A. McIntyre, A. McPherson, A. P. Schwarzenbach, K. Boyer, C. K. Rhodes, AIP Conf. Proc. 147, 202 (1986).
[CrossRef]

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

Buckingham, A. D.

D. P. Shelton, A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
[CrossRef]

Cotter, D.

D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
[CrossRef]

Eckardt, R. C.

J. Reintjes, C. Y. She, R. C. Eckardt, N. E. Karangelen, R. A. Andrews, R. C. Elton, Appl. Phys. Lett. 30, 480 (1977).
[CrossRef]

J. Reintjes, R. C. Eckardt, C. Y. She, N. E. Karangelen, R. C. Elton, R. A. Andrews, Phys. Rev. Lett. 37, 1540 (1976).
[CrossRef]

Eckardt, R. E.

J. Reintjes, C. Y. She, R. E. Eckardt, IEEE J. Quantum Electron. QE-14, 581 (1978).
[CrossRef]

Elton, R. C.

J. Reintjes, C. Y. She, R. C. Eckardt, N. E. Karangelen, R. A. Andrews, R. C. Elton, Appl. Phys. Lett. 30, 480 (1977).
[CrossRef]

J. Reintjes, R. C. Eckardt, C. Y. She, N. E. Karangelen, R. C. Elton, R. A. Andrews, Phys. Rev. Lett. 37, 1540 (1976).
[CrossRef]

Gibson, G.

Gibson, G. N.

Hanna, D. C.

D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
[CrossRef]

Hudson, R. D.

R. D. Hudson, L. J. Kieffer, Atomic Data 2, 205 (1971).
[CrossRef]

Hutchinson, M. H. R.

Jackson, J. D.

The index of refraction is related to density by n2(ω) = 1 + 4πNe2/mΣjfj(ωj2− ω2− iωγ)−1. For n≈ 1, n(5ω) − n(ω) ∝ N.See J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 285.

Jara, H.

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
[CrossRef]

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

Johann, U.

Karangelen, N. E.

J. Reintjes, C. Y. She, R. C. Eckardt, N. E. Karangelen, R. A. Andrews, R. C. Elton, Appl. Phys. Lett. 30, 480 (1977).
[CrossRef]

J. Reintjes, R. C. Eckardt, C. Y. She, N. E. Karangelen, R. C. Elton, R. A. Andrews, Phys. Rev. Lett. 37, 1540 (1976).
[CrossRef]

Kieffer, L. J.

R. D. Hudson, L. J. Kieffer, Atomic Data 2, 205 (1971).
[CrossRef]

Lehmeier, H. J.

H. J. Lehmeier, W. Leupacher, A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

Leupacher, W.

H. J. Lehmeier, W. Leupacher, A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

Luk, T. S.

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
[CrossRef]

U. Johann, T. S. Luk, I. A. McIntyre, A. McPherson, A. P. Schwarzenbach, K. Boyer, C. K. Rhodes, AIP Conf. Proc. 147, 202 (1986).
[CrossRef]

A. P. Schwarzenbach, T. S. Luk, I. A. McIntyre, U. Johann, A. McPherson, K. Boyer, C. K. Rhodes, Opt. Lett. 11, 499 (1986).
[CrossRef] [PubMed]

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

McIntyre, I. A.

M. H. R. Hutchinson, I. A. McIntyre, G. N. Gibson, C. K. Rhodes, Opt. Lett. 12, 102 (1987).
[CrossRef] [PubMed]

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
[CrossRef]

A. P. Schwarzenbach, T. S. Luk, I. A. McIntyre, U. Johann, A. McPherson, K. Boyer, C. K. Rhodes, Opt. Lett. 11, 499 (1986).
[CrossRef] [PubMed]

U. Johann, T. S. Luk, I. A. McIntyre, A. McPherson, A. P. Schwarzenbach, K. Boyer, C. K. Rhodes, AIP Conf. Proc. 147, 202 (1986).
[CrossRef]

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

McPherson, A.

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
[CrossRef]

U. Johann, T. S. Luk, I. A. McIntyre, A. McPherson, A. P. Schwarzenbach, K. Boyer, C. K. Rhodes, AIP Conf. Proc. 147, 202 (1986).
[CrossRef]

A. P. Schwarzenbach, T. S. Luk, I. A. McIntyre, U. Johann, A. McPherson, K. Boyer, C. K. Rhodes, Opt. Lett. 11, 499 (1986).
[CrossRef] [PubMed]

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

New, G. H. C.

J. F. Ward, G. H. C. New, Phys. Rev. 185, 57 (1969).
[CrossRef]

Orr, B. J.

M. P. Bogaard, B. J. Orr, in International Review of Science, Molecular Structure and Properties, Vol. 2 of Physical Chemistry Series 2 (Butterworth, London, 1975), p. 149.

Penzkofer, A.

H. J. Lehmeier, W. Leupacher, A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

Reintjes, J.

J. Reintjes, C. Y. She, R. E. Eckardt, IEEE J. Quantum Electron. QE-14, 581 (1978).
[CrossRef]

J. Reintjes, C. Y. She, R. C. Eckardt, N. E. Karangelen, R. A. Andrews, R. C. Elton, Appl. Phys. Lett. 30, 480 (1977).
[CrossRef]

J. Reintjes, R. C. Eckardt, C. Y. She, N. E. Karangelen, R. C. Elton, R. A. Andrews, Phys. Rev. Lett. 37, 1540 (1976).
[CrossRef]

Reintjes, J. F.

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984).

Rhodes, C. K.

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, C. K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987).
[CrossRef]

M. H. R. Hutchinson, I. A. McIntyre, G. N. Gibson, C. K. Rhodes, Opt. Lett. 12, 102 (1987).
[CrossRef] [PubMed]

A. P. Schwarzenbach, T. S. Luk, I. A. McIntyre, U. Johann, A. McPherson, K. Boyer, C. K. Rhodes, Opt. Lett. 11, 499 (1986).
[CrossRef] [PubMed]

U. Johann, T. S. Luk, I. A. McIntyre, A. McPherson, A. P. Schwarzenbach, K. Boyer, C. K. Rhodes, AIP Conf. Proc. 147, 202 (1986).
[CrossRef]

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

Rosman, R.

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

Schwarzenbach, A. P.

U. Johann, T. S. Luk, I. A. McIntyre, A. McPherson, A. P. Schwarzenbach, K. Boyer, C. K. Rhodes, AIP Conf. Proc. 147, 202 (1986).
[CrossRef]

A. P. Schwarzenbach, T. S. Luk, I. A. McIntyre, U. Johann, A. McPherson, K. Boyer, C. K. Rhodes, Opt. Lett. 11, 499 (1986).
[CrossRef] [PubMed]

She, C. Y.

J. Reintjes, C. Y. She, R. E. Eckardt, IEEE J. Quantum Electron. QE-14, 581 (1978).
[CrossRef]

J. Reintjes, C. Y. She, R. C. Eckardt, N. E. Karangelen, R. A. Andrews, R. C. Elton, Appl. Phys. Lett. 30, 480 (1977).
[CrossRef]

J. Reintjes, R. C. Eckardt, C. Y. She, N. E. Karangelen, R. C. Elton, R. A. Andrews, Phys. Rev. Lett. 37, 1540 (1976).
[CrossRef]

Shelton, D. P.

D. P. Shelton, A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
[CrossRef]

Solem, J. C.

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

Szöke, A.

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

Ward, J. F.

J. F. Ward, G. H. C. New, Phys. Rev. 185, 57 (1969).
[CrossRef]

Wolf, E.

The axial intensity is given by I(u)/I0= [4 sin(u/4)/u]2, where u= πz/2λF2. At I(u)/I0= ½, u≈ 5.6, and b= 2z≈ 7F2λ.See M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 441.

Young, J. F.

L. J. Zych, J. F. Young, IEEE J. Quantum Electron. QE-14, 147 (1978).
[CrossRef]

Yuratich, M. A.

D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
[CrossRef]

Zych, L. J.

L. J. Zych, J. F. Young, IEEE J. Quantum Electron. QE-14, 147 (1978).
[CrossRef]

AIP Conf. Proc. (1)

U. Johann, T. S. Luk, I. A. McIntyre, A. McPherson, A. P. Schwarzenbach, K. Boyer, C. K. Rhodes, AIP Conf. Proc. 147, 202 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

J. Reintjes, C. Y. She, R. C. Eckardt, N. E. Karangelen, R. A. Andrews, R. C. Elton, Appl. Phys. Lett. 30, 480 (1977).
[CrossRef]

Atomic Data (1)

R. D. Hudson, L. J. Kieffer, Atomic Data 2, 205 (1971).
[CrossRef]

IEEE J. Quantum Electron. (3)

L. J. Zych, J. F. Young, IEEE J. Quantum Electron. QE-14, 147 (1978).
[CrossRef]

G. Bjorklund, IEEE J. Quantum Electron. QE-11, 287 (1975).
[CrossRef]

J. Reintjes, C. Y. She, R. E. Eckardt, IEEE J. Quantum Electron. QE-14, 581 (1978).
[CrossRef]

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

Opt. Commun. (1)

H. J. Lehmeier, W. Leupacher, A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

J. F. Ward, G. H. C. New, Phys. Rev. 185, 57 (1969).
[CrossRef]

Phys. Rev. A (1)

D. P. Shelton, A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
[CrossRef]

Phys. Rev. Lett. (1)

J. Reintjes, R. C. Eckardt, C. Y. She, N. E. Karangelen, R. C. Elton, R. A. Andrews, Phys. Rev. Lett. 37, 1540 (1976).
[CrossRef]

Other (6)

M. P. Bogaard, B. J. Orr, in International Review of Science, Molecular Structure and Properties, Vol. 2 of Physical Chemistry Series 2 (Butterworth, London, 1975), p. 149.

The axial intensity is given by I(u)/I0= [4 sin(u/4)/u]2, where u= πz/2λF2. At I(u)/I0= ½, u≈ 5.6, and b= 2z≈ 7F2λ.See M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 441.

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984).

The index of refraction is related to density by n2(ω) = 1 + 4πNe2/mΣjfj(ωj2− ω2− iωγ)−1. For n≈ 1, n(5ω) − n(ω) ∝ N.See J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 285.

D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
[CrossRef]

K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, R. Rosman, J. C. Solem, C. K. Rhodes, A. Szöke, “Discussion of the role of many-electron motions in multiphoton ionization and excitation,” in Proceedings of the International Conference on Multiphoton Processes IV (Cambridge U. Press, Cambridge, to be published).

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Figures (7)

Fig. 1
Fig. 1

Schematic of pulsed gas valve and spectrometer-detector assembly. The lens focuses 1-psec 248-nm laser pulses with 0.1–10 mJ/pulse into neon and argon. Typical background pressures are indicated.

Fig. 2
Fig. 2

Fifth-harmonic production in neutral neon as a function of target density. The focused 248-nm laser intensity is approximately 8 × 1013 W/cm2. The fifth-harmonic intensity dependence of the lowest pressure data points is roughly between N2 and N3. The scatter in the data in Figs. 26 gives an estimate of the statistical errors.

Fig. 3
Fig. 3

Fifth-harmonic production in the neutral argon as a function of target density. The focused 248-nm laser intensity is approximately 4 × 1013 W/cm2. The fifth-harmonic intensity dependence of the lowest pressure data points is roughly between N2 and N3.

Fig. 4
Fig. 4

Fifth-harmonic production in neon as a function of focused laser intensity. Arrows indicate first and second ionization thresholds, Note the change in slopes at the ionization thresholds. The target density, ≈2 × 1017 cm−3, is well below the maximum shown in Fig. 2. Repeated experiments at this density show that the fifth-harmonic intensity varies approximately as I16.5I19.3 below the first ionization threshold and as I11.5I12.3 above it.

Fig. 5
Fig. 5

Fifth-harmonic production in argon as a function of focused laser intensity. Arrows indicate first and second ionization thresholds. Note the change in slopes at the ionization thresholds. The fifth-harmonic intensity varies approximately as I12.5 below the first ionization threshold. The target density is ≈2 × 1017 cm−3.

Fig. 6
Fig. 6

Fifth-harmonic production in neon as a function of focused laser intensity. Arrows indicate first and second ionization thresholds. The fifth-harmonic intensity varies approximately as I13,9 below the first ionization threshold. The target density, ≈4 × 1017 cm−3, is twice that shown in Fig. 4. This target density corresponds to the peak of the density curve shown in Fig. 2.

Fig. 7
Fig. 7

Computer-generated data based on relation (22) with a least-squares power-law fit. (a) N = 2 × 1017 cm−3, b = 0.16 cm, I5I17.1; (b) N = 4 × 1017 cm−3, b = 0.16 cm, I5I14.1.

Equations (24)

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P ( r , z ) = N [ χ ( 1 ) E ( r , z ) + ( ¼ ) χ ( 3 ) E ( 3 ) ( r , z ) + ( 1 / 16 ) χ ( 5 ) E 5 ( r , z ) + ] ,
E ( r , z , t ) = ( ½ ) { E ( r , z ) exp [ i ( ω t k z ) ] + c . c . } ,
× × E 5 ( r , z , t ) + 1 c 2 2 t 2 E 5 ( r , z , t ) = 4 π c 2 2 t 2 P 5 ( r , z , t ) ,
I 5 I 1 5 | χ ( 5 ) | 2 N 2 ( 1 / b 2 ) | F 5 ( b Δ k ) | 2 .
Δ k k 5 5 k 1 = ( 2 π / λ ) 5 ( n 5 n 1 ) .
F 5 ( b Δ k ) { ( b Δ k / 2 ) 3 exp ( b Δ k / 2 ) , Δ k < 0 0 , Δ k > 0 .
I 5 I 1 5 | χ ( 5 ) | 2 N 2 b 4 ( Δ k ) 6 e b Δ k .
I 5 I 1 5 | χ ( 5 ) | 2 N 8 b 4 exp ( bCN σ l N ) ,
N ( b C + σ l ) = 8 .
w 0 = 1.22 F λ ,
I 1 = E / t π w 0 2 ,
b 7 F 2 λ .
Δ k = [ ( 6 ± 1 ) × 10 17 cm 2 ] N for neon , Δ k = [ ( 2 ± 1 ) × 10 16 cm 2 ] N for argon ,
P NL ( ω ) = ( ¾ ) N χ ( 3 ) ( ω ; ω , ω , ω ) E 1 E 1 * E 1
P NL ( 5 ω ) = ( 3 / 2 ) N χ ( 3 ) ( 5 ω ; ω , ω , 5 ω ) E 1 E 1 * E 5 .
total E = E + 4 π P L ( ω ) + 4 π P NL ( ω ) .
n total 2 ( ω ) = [ n L ( ω ) + ( ½ ) n NL ( ω ) E 1 2 + ] 2 ,
n NL ( ω ) = 3 π N χ ( 3 ) ( ω ; ω , ω , ω ) n L ( ω ) .
n NL ( 5 ω ) = 6 π N χ ( 3 ) ( 5 ω ; ω , ω , 5 ω ) n L ( 5 ω ) .
Δ k NL = 30 π 2 N E 1 2 λ [ χ ( 3 ) ( 5 ω ; ω , ω , 5 ω ) ( ½ ) χ ( 3 ) ( ω ; ω , ω , ω ) ] ,
Δ k NL = ( 2 π / λ ) 5 γ ( 3 ) I 1 N .
I 5 I 1 5 ( 1 + A I 1 ) 6 exp ( b Δ k L A I 1 ) ,
γ ( 3 ) ( 5 ω ; ω , ω , 5 ω ) ( ½ ) γ ( 3 ) ( ω ; ω , ω , ω ) { ( 6 ± 1 ) × 10 37 cm 5 / W for neon ( 3 ± 1 ) × 10 36 cm 5 / W for argon .
γ Ne ( 3 ) ( 2 ω ; ω , ω , 0 ) = 4.5 × 10 40 cm 5 / W , γ Xe ( 3 ) ( 2 ω ; ω , ω , 0 ) = 3.4 × 10 38 cm 5 / W .

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