Abstract

The nonlinear interaction of neutral krypton atoms with picosecond 193-nm radiation with intensities ≤1013 W/cm2 has been studied. Because of the relatively high intensity of the applied radiation field and the two-photon resonance of the 4p–6p transition, several competing nonlinear processes were observed that result in the generation of coherent radiation. Amplified spontaneous emission (ASE) from the two-photon-resonant level was observed in the IR frequency at ~2 μm. Additionally, a tunable IR wave, in the same frequency range, was generated by stimulated hyper-Raman scattering of the incident laser. The observed self-generated IR waves induced other nonlinear interactions, which resulted in the generation of extreme-ultraviolet (XUV) radiation in the same medium. Tunable XUV frequency was shown to be generated by four-wave sum mixing of the laser and the hyper-Raman wave. Vacuum-ultraviolet frequency was shown to be generated by four-wave oscillation, and other nontunable XUV frequencies resulted from anti-Stokes Raman scattering of the ASE IR waves.

© 1988 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. D. Bonin, T. J. McIlrath, J. Opt. Soc. Am. B 2, 527 (1985).
    [CrossRef]
  2. R. Hilbig, R. Wallenstein, IEEE J. Quantum Electron. QE-19, 194 (1983).
    [CrossRef]
  3. F. S. Tomkins, R. Mahon, Opt. Lett. 6, 179 (1981).
    [CrossRef] [PubMed]
  4. J. Bokor, R. R. Freeman, R. L. Panock, J. C. White, Opt. Lett. 6, 182 (1981).
    [CrossRef] [PubMed]
  5. K. W. Ludewigt, W. Pfingsten, C. Mohlmann, B. Wallegehausen, Opt. Lett. 11, 39 (1987).
    [CrossRef]
  6. T. S. Luk, H. Egger, W. Müller, H. Pummer, C. K. Rhodes, J. Chem. Phys. 82, 4497 (1985).
    [CrossRef]
  7. T. Srinivasan, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, IEEE J. Quantum Electron. QE-19, 1874 (1983).
    [CrossRef]
  8. H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
    [CrossRef]
  9. R. L. Kelly, L. J. Palumbo, Atomic and Ionic Emission Lines Below 2000 Angstroms, (U.S. Government Printing Office, Washington, D.C., 1973).
  10. K. Boyer, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, J. Opt. Soc. Am. B 1, 3 (1984).
    [CrossRef]
  11. K. Codling, R. P. Madden, Phys. Rev. A 4, 2261 (1971); J. Res. Natl. Bur. Stand. Sec. A 76, 1 (1972).
    [CrossRef]
  12. H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
    [CrossRef]
  13. J. Bokor, J. Zavelovich, C. K. Rhodes, Phys. Rev. A 21, 1453 (1980).
    [CrossRef]
  14. H. Pummer, H. Egger, T. S. Luk, T. Srinivasan, C. K. Rhodes, Phys. Rev. A 28, 795 (1983).
    [CrossRef]
  15. P. Avon, C. Cohen-Taunondji, J. Dupont-Roc, C. Fabre, J. Phys. (Paris) 9, 993 (1976).
  16. G. C. Bjorklund, IEEE J. Quantum Electron. QE-11, 287 (1975).
    [CrossRef]
  17. J. Geiger, Z. Phys. A 282, 129 (1977).
    [CrossRef]
  18. D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, Berlin, 1979), Vol. 17.
    [CrossRef]
  19. J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984), p. 121.
  20. H. Scheingraber, H. Puell, C. R. Vidal, Phys. Rev. A 18, 2585 (1978).
    [CrossRef]
  21. W. K. Bischel, J. Bokor, D. J. Kligler, C. K. Rhodes, IEEE J. Quantum Electron. QE-15, 380 (1979).
    [CrossRef]
  22. M. Malcuit, J. Gauthier, R. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
    [CrossRef] [PubMed]
  23. R. Boyd, M. Malcuit, D. Gauthier, Phys. Rev. A 35, 1648 (1987).
    [CrossRef] [PubMed]

1987

1985

M. Malcuit, J. Gauthier, R. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

T. S. Luk, H. Egger, W. Müller, H. Pummer, C. K. Rhodes, J. Chem. Phys. 82, 4497 (1985).
[CrossRef]

K. D. Bonin, T. J. McIlrath, J. Opt. Soc. Am. B 2, 527 (1985).
[CrossRef]

1984

1983

H. Pummer, H. Egger, T. S. Luk, T. Srinivasan, C. K. Rhodes, Phys. Rev. A 28, 795 (1983).
[CrossRef]

R. Hilbig, R. Wallenstein, IEEE J. Quantum Electron. QE-19, 194 (1983).
[CrossRef]

T. Srinivasan, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, IEEE J. Quantum Electron. QE-19, 1874 (1983).
[CrossRef]

1982

H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
[CrossRef]

1981

F. S. Tomkins, R. Mahon, Opt. Lett. 6, 179 (1981).
[CrossRef] [PubMed]

J. Bokor, R. R. Freeman, R. L. Panock, J. C. White, Opt. Lett. 6, 182 (1981).
[CrossRef] [PubMed]

H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
[CrossRef]

1980

J. Bokor, J. Zavelovich, C. K. Rhodes, Phys. Rev. A 21, 1453 (1980).
[CrossRef]

1979

W. K. Bischel, J. Bokor, D. J. Kligler, C. K. Rhodes, IEEE J. Quantum Electron. QE-15, 380 (1979).
[CrossRef]

1978

H. Scheingraber, H. Puell, C. R. Vidal, Phys. Rev. A 18, 2585 (1978).
[CrossRef]

1977

J. Geiger, Z. Phys. A 282, 129 (1977).
[CrossRef]

1976

P. Avon, C. Cohen-Taunondji, J. Dupont-Roc, C. Fabre, J. Phys. (Paris) 9, 993 (1976).

1975

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

1971

K. Codling, R. P. Madden, Phys. Rev. A 4, 2261 (1971); J. Res. Natl. Bur. Stand. Sec. A 76, 1 (1972).
[CrossRef]

Avon, P.

P. Avon, C. Cohen-Taunondji, J. Dupont-Roc, C. Fabre, J. Phys. (Paris) 9, 993 (1976).

Bischel, W. K.

W. K. Bischel, J. Bokor, D. J. Kligler, C. K. Rhodes, IEEE J. Quantum Electron. QE-15, 380 (1979).
[CrossRef]

Bjorklund, G. C.

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

Bokor, J.

J. Bokor, R. R. Freeman, R. L. Panock, J. C. White, Opt. Lett. 6, 182 (1981).
[CrossRef] [PubMed]

J. Bokor, J. Zavelovich, C. K. Rhodes, Phys. Rev. A 21, 1453 (1980).
[CrossRef]

W. K. Bischel, J. Bokor, D. J. Kligler, C. K. Rhodes, IEEE J. Quantum Electron. QE-15, 380 (1979).
[CrossRef]

Bonin, K. D.

Boyd, R.

R. Boyd, M. Malcuit, D. Gauthier, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

M. Malcuit, J. Gauthier, R. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

Boyer, K.

K. Boyer, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, J. Opt. Soc. Am. B 1, 3 (1984).
[CrossRef]

H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
[CrossRef]

Codling, K.

K. Codling, R. P. Madden, Phys. Rev. A 4, 2261 (1971); J. Res. Natl. Bur. Stand. Sec. A 76, 1 (1972).
[CrossRef]

Cohen-Taunondji, C.

P. Avon, C. Cohen-Taunondji, J. Dupont-Roc, C. Fabre, J. Phys. (Paris) 9, 993 (1976).

Cotter, D.

D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, Berlin, 1979), Vol. 17.
[CrossRef]

Dupont-Roc, J.

P. Avon, C. Cohen-Taunondji, J. Dupont-Roc, C. Fabre, J. Phys. (Paris) 9, 993 (1976).

Egger, H.

T. S. Luk, H. Egger, W. Müller, H. Pummer, C. K. Rhodes, J. Chem. Phys. 82, 4497 (1985).
[CrossRef]

K. Boyer, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, J. Opt. Soc. Am. B 1, 3 (1984).
[CrossRef]

H. Pummer, H. Egger, T. S. Luk, T. Srinivasan, C. K. Rhodes, Phys. Rev. A 28, 795 (1983).
[CrossRef]

T. Srinivasan, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, IEEE J. Quantum Electron. QE-19, 1874 (1983).
[CrossRef]

H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
[CrossRef]

H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
[CrossRef]

Fabre, C.

P. Avon, C. Cohen-Taunondji, J. Dupont-Roc, C. Fabre, J. Phys. (Paris) 9, 993 (1976).

Freeman, R. R.

Gauthier, D.

R. Boyd, M. Malcuit, D. Gauthier, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

Gauthier, J.

M. Malcuit, J. Gauthier, R. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

Geiger, J.

J. Geiger, Z. Phys. A 282, 129 (1977).
[CrossRef]

Hanna, D. C.

D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, Berlin, 1979), Vol. 17.
[CrossRef]

Hilbig, R.

R. Hilbig, R. Wallenstein, IEEE J. Quantum Electron. QE-19, 194 (1983).
[CrossRef]

Hohla, K.

H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
[CrossRef]

Kelly, R. L.

R. L. Kelly, L. J. Palumbo, Atomic and Ionic Emission Lines Below 2000 Angstroms, (U.S. Government Printing Office, Washington, D.C., 1973).

Kligler, D. J.

W. K. Bischel, J. Bokor, D. J. Kligler, C. K. Rhodes, IEEE J. Quantum Electron. QE-15, 380 (1979).
[CrossRef]

Ludewigt, K. W.

Luk, T. S.

T. S. Luk, H. Egger, W. Müller, H. Pummer, C. K. Rhodes, J. Chem. Phys. 82, 4497 (1985).
[CrossRef]

K. Boyer, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, J. Opt. Soc. Am. B 1, 3 (1984).
[CrossRef]

H. Pummer, H. Egger, T. S. Luk, T. Srinivasan, C. K. Rhodes, Phys. Rev. A 28, 795 (1983).
[CrossRef]

T. Srinivasan, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, IEEE J. Quantum Electron. QE-19, 1874 (1983).
[CrossRef]

H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
[CrossRef]

Madden, R. P.

K. Codling, R. P. Madden, Phys. Rev. A 4, 2261 (1971); J. Res. Natl. Bur. Stand. Sec. A 76, 1 (1972).
[CrossRef]

Mahon, R.

Malcuit, M.

R. Boyd, M. Malcuit, D. Gauthier, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

M. Malcuit, J. Gauthier, R. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

McIlrath, T. J.

Mohlmann, C.

Muller, D. F.

H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
[CrossRef]

Müller, W.

T. S. Luk, H. Egger, W. Müller, H. Pummer, C. K. Rhodes, J. Chem. Phys. 82, 4497 (1985).
[CrossRef]

Palumbo, L. J.

R. L. Kelly, L. J. Palumbo, Atomic and Ionic Emission Lines Below 2000 Angstroms, (U.S. Government Printing Office, Washington, D.C., 1973).

Panock, R. L.

Pfingsten, W.

Puell, H.

H. Scheingraber, H. Puell, C. R. Vidal, Phys. Rev. A 18, 2585 (1978).
[CrossRef]

Pummer, H.

T. S. Luk, H. Egger, W. Müller, H. Pummer, C. K. Rhodes, J. Chem. Phys. 82, 4497 (1985).
[CrossRef]

K. Boyer, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, J. Opt. Soc. Am. B 1, 3 (1984).
[CrossRef]

H. Pummer, H. Egger, T. S. Luk, T. Srinivasan, C. K. Rhodes, Phys. Rev. A 28, 795 (1983).
[CrossRef]

T. Srinivasan, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, IEEE J. Quantum Electron. QE-19, 1874 (1983).
[CrossRef]

H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
[CrossRef]

H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
[CrossRef]

Reintjes, J. F.

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984), p. 121.

Rhodes, C. K.

T. S. Luk, H. Egger, W. Müller, H. Pummer, C. K. Rhodes, J. Chem. Phys. 82, 4497 (1985).
[CrossRef]

K. Boyer, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, J. Opt. Soc. Am. B 1, 3 (1984).
[CrossRef]

T. Srinivasan, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, IEEE J. Quantum Electron. QE-19, 1874 (1983).
[CrossRef]

H. Pummer, H. Egger, T. S. Luk, T. Srinivasan, C. K. Rhodes, Phys. Rev. A 28, 795 (1983).
[CrossRef]

H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
[CrossRef]

H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
[CrossRef]

J. Bokor, J. Zavelovich, C. K. Rhodes, Phys. Rev. A 21, 1453 (1980).
[CrossRef]

W. K. Bischel, J. Bokor, D. J. Kligler, C. K. Rhodes, IEEE J. Quantum Electron. QE-15, 380 (1979).
[CrossRef]

Scheingraber, H.

H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
[CrossRef]

H. Scheingraber, H. Puell, C. R. Vidal, Phys. Rev. A 18, 2585 (1978).
[CrossRef]

Srinivasan, T.

H. Pummer, H. Egger, T. S. Luk, T. Srinivasan, C. K. Rhodes, Phys. Rev. A 28, 795 (1983).
[CrossRef]

T. Srinivasan, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, IEEE J. Quantum Electron. QE-19, 1874 (1983).
[CrossRef]

H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
[CrossRef]

H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
[CrossRef]

Tomkins, F. S.

Vidal, C. R.

H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
[CrossRef]

H. Scheingraber, H. Puell, C. R. Vidal, Phys. Rev. A 18, 2585 (1978).
[CrossRef]

Wallegehausen, B.

Wallenstein, R.

R. Hilbig, R. Wallenstein, IEEE J. Quantum Electron. QE-19, 194 (1983).
[CrossRef]

White, J. C.

Yuratich, M. A.

D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, Berlin, 1979), Vol. 17.
[CrossRef]

Zavelovich, J.

J. Bokor, J. Zavelovich, C. K. Rhodes, Phys. Rev. A 21, 1453 (1980).
[CrossRef]

Appl. Phys. Lett.

H. Egger, T. S. Luk, K. Boyer, D. F. Muller, H. Pummer, T. Srinivasan, C. K. Rhodes, Appl. Phys. Lett. 41, 1032 (1982).
[CrossRef]

H. Egger, T. Srinivasan, K. Hohla, H. Scheingraber, C. R. Vidal, H. Pummer, C. K. Rhodes, Appl. Phys. Lett. 39, 37 (1981).
[CrossRef]

IEEE J. Quantum Electron.

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

R. Hilbig, R. Wallenstein, IEEE J. Quantum Electron. QE-19, 194 (1983).
[CrossRef]

T. Srinivasan, H. Egger, T. S. Luk, H. Pummer, C. K. Rhodes, IEEE J. Quantum Electron. QE-19, 1874 (1983).
[CrossRef]

W. K. Bischel, J. Bokor, D. J. Kligler, C. K. Rhodes, IEEE J. Quantum Electron. QE-15, 380 (1979).
[CrossRef]

J. Chem. Phys.

T. S. Luk, H. Egger, W. Müller, H. Pummer, C. K. Rhodes, J. Chem. Phys. 82, 4497 (1985).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. (Paris)

P. Avon, C. Cohen-Taunondji, J. Dupont-Roc, C. Fabre, J. Phys. (Paris) 9, 993 (1976).

Opt. Lett.

Phys. Rev. A

K. Codling, R. P. Madden, Phys. Rev. A 4, 2261 (1971); J. Res. Natl. Bur. Stand. Sec. A 76, 1 (1972).
[CrossRef]

J. Bokor, J. Zavelovich, C. K. Rhodes, Phys. Rev. A 21, 1453 (1980).
[CrossRef]

H. Pummer, H. Egger, T. S. Luk, T. Srinivasan, C. K. Rhodes, Phys. Rev. A 28, 795 (1983).
[CrossRef]

H. Scheingraber, H. Puell, C. R. Vidal, Phys. Rev. A 18, 2585 (1978).
[CrossRef]

R. Boyd, M. Malcuit, D. Gauthier, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett.

M. Malcuit, J. Gauthier, R. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

Z. Phys. A

J. Geiger, Z. Phys. A 282, 129 (1977).
[CrossRef]

Other

D. C. Hanna, M. A. Yuratich, D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, Berlin, 1979), Vol. 17.
[CrossRef]

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984), p. 121.

R. L. Kelly, L. J. Palumbo, Atomic and Ionic Emission Lines Below 2000 Angstroms, (U.S. Government Printing Office, Washington, D.C., 1973).

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 (7)

Fig. 1
Fig. 1

Schematic of the experimental apparatus for the detection of the XUV radiation. OMA, optical multichannel analyzer.

Fig. 2
Fig. 2

Schematic energy-level diagram of krypton showing the different nonlinear interactions: a, two-photon absorption/ASE b, anti-Stokes stimulated Raman scattering; c, four-wave oscillation; d, SHRS/four-wave mixing.

Fig. 3
Fig. 3

Frequency-tuning behavior of the HR wave as a function of laser frequency. The dashed line corresponds to ω = 2ωL − Ωs.

Fig. 4
Fig. 4

Frequency-tuning behavior of the 93-nm emission as a function of the laser frequency measured for single laser shots. The dashed line corresponds to ω = 4ωL − Ωs.

Fig. 5
Fig. 5

Pressure dependence of the 93-nm radiation determined experimentally. The dashed curve is the calculated pressure behavior for the FWM process, in the inset (Fig. 12 of Ref. 16) multiplied by a factor of 5 to match optimum pressure of the two curves.

Fig. 6
Fig. 6

a, Calculated phase mismatch per atom. The arrows point to frequencies at which the phase mismatch is zero. b, Absorption cross section as a function of frequency.

Fig. 7
Fig. 7

Calculated relative intensity of a wave generated in four-wave difference frequency mixing, including absorption, as a function of the generated VUV frequency (cm−1) and NL (cm−2). Comparison with experimentally observed frequency, ω0 (top).

Tables (2)

Tables Icon

Table 1 Estimates for Gain Coefficients

Tables Icon

Table 2 Estimates for Anti-Stokes Raman Scattering Cross Sectionsa

Equations (14)

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

6 p ( 3 / 2 ) 2 4 d ( 3 / 2 ) 1 6 s ( 3 / 2 ) 2 + γ 2.68 μ m , 6 p ( 3 / 2 ) 2 6 p ( 5 / 2 ) 2 4 d ( 5 / 2 ) 3 4 d ( 5 / 2 ) 2 + γ 2.34 μ m , 6 p ( 3 / 2 ) 1 4 d ( 3 / 2 ) 1 6 s ( 3 / 2 ) 2 + γ 2.73 μ m .
G p = 3 ( ω 3 ω 4 ) 1 / 2 χ ( 3 ) N 0 I L / 0 c 2 ,
χ ( 3 ) ~ 2 μ g j μ j f μ f m μ m g / 6 3 0 Γ Δ j Δ m ,
Δ k = k 4 - 2 k L + k 3 ,
k ω = n ω ω / c = [ 1 + χ ω ( 1 ) / 2 ] ω / c , ω 4 - 2 ω L + ω 3 = 0 , ( n 4 - 1 ) ω 4 - 2 ( n L - 1 ) ω L + ( n 3 - 1 ) ω 3 ,
Δ k ~ N 0 ω 4 μ m g 2 / 2 c 0 Δ m .
G p Δ k ~ ( ω 4 ω 3 ) 1 / 2 ω 4 2 μ g j μ j f μ f m μ m g μ m g 2 I L 2 c 0 Δ j Γ .
G p Δ k ~ 5 × 10 - 12 I L ( W / cm 2 ) .
E 4 z = 3 i ω 8 c χ ( 3 ) N E L 2 E 3 * exp ( i Δ k z ) - σ N E 4 / 2 ,
I 4 ( L , ω , N ) = 9 8 0 2 c 4 I L 2 ω 2 χ ( ω ) 2 G ( L , ω , N ) ,
G ( L , ω , N ) = 1 - 2 cos ( α N L ) exp ( - σ N L / 2 ) + exp ( - σ N L ) ( α ) 2 + ( σ / 2 ) 2
Δ k / N α = α ( ω ) ,             σ = σ ( ω ) .
G = 3 ω Im [ χ ( 3 ) ] N I / 0 c 2 ,
G HR = 15 ω HR Im [ χ ( 5 ) ] N I 2 / 2 0 2 c 3 .

Metrics