Abstract

We present recent measurements of refractive indices, nonlinear susceptibilities, and isotope shifts important for sum- and difference-frequency mixing through the 71,3S two-photon resonances of Hg. These data are presented in a form that makes it possible to make quick and accurate calculations of index-matching and mixing efficiencies in the low-intensity limit.

© 1987 Optical Society of America

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References

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  1. J. Bokor, R. R. Freeman, R. L. Panock, and J. C. White, “Generation of high-brightness coherent radiation in the vacuum ultraviolet by four-wave parametric oscillation in mercury vapor,” Opt. Lett. 6, 182–184 (1981).
    [CrossRef] [PubMed]
  2. F. S. Tomkins and R. Mahon, “High-efficiency four-wave sum and difference mixing in Hg vapor,” Opt. Lett. 6, 179–181 (1981); R. Mahon and F. S. Tomkins, “Frequency up-conversion to the VUV in Hg vapor,” IEEE J. Quantum Electron. QE-18, 913–920 (1982); F. S. Tomkins and R. Mahon, “Generation of continuously tunable narrow-band radiation from 1220 to 1174 Å in Hg vapor,” Opt. Lett. 7, 304–306 (1982).
    [CrossRef] [PubMed]
  3. R. Hilbig and R. Wallenstein, “Resonant sum and difference frequency mixing in Hg,” IEEE J. Quantum Electron. QE-19, 1759–1770 (1983).
    [CrossRef]
  4. P. R. Herman and B. P. Stoicheff, “Tunable extreme-ultraviolet radiation from 105 to 87.5 nm using Hg vapor,” Opt. Lett. 10, 502–504 (1985).
    [CrossRef] [PubMed]
  5. A. V. Smith and W. J. Alford, “Vacuum ultraviolet oscillator strengths of Hg measured by sum-frequency mixing,” Phys. Rev. A 33, 3172–3180 (1986).
    [CrossRef] [PubMed]
  6. W. J. Alford and A. V. Smith, “Measured third-order susceptibilities and excited state oscillator strengths for atomic mercury,” Phys. Rev. A 36, 641–648 (1987).
    [CrossRef] [PubMed]
  7. A. V. Smith, G. R. Hadley, P. Esherick, and W. J. Alford, “Efficient two-photon resonant frequency conversion in Hg: the effects of amplified spontaneous emission,” submitted to J. Opt. Soc. Am. B.
  8. K. Watanabe and M. Zelikoff, “Absorption coefficients of water vapor in the vacuum ultraviolet,” J. Opt. Soc. Am. 43, 753–755 (1953).
    [CrossRef]
  9. J. F. Rientjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984).
  10. J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
    [CrossRef]
  11. G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
    [CrossRef]
  12. R. Mahon, T. J. McIlrath, V. P. Myerscough, and D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
    [CrossRef]
  13. B. D. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).
  14. S. Gerstenkorn, J. J. Labarthe, and J. Vergès, “Fine and hyperfine structures and isotope shifts in the arc spectrum of mercury,” Phys. Scr. 15, 167–172 (1977).
    [CrossRef]
  15. See Chap. 4 of Ref. 9 for a discussion of efficiency-limiting processes.

1987 (1)

W. J. Alford and A. V. Smith, “Measured third-order susceptibilities and excited state oscillator strengths for atomic mercury,” Phys. Rev. A 36, 641–648 (1987).
[CrossRef] [PubMed]

1986 (1)

A. V. Smith and W. J. Alford, “Vacuum ultraviolet oscillator strengths of Hg measured by sum-frequency mixing,” Phys. Rev. A 33, 3172–3180 (1986).
[CrossRef] [PubMed]

1985 (1)

1983 (1)

R. Hilbig and R. Wallenstein, “Resonant sum and difference frequency mixing in Hg,” IEEE J. Quantum Electron. QE-19, 1759–1770 (1983).
[CrossRef]

1981 (2)

1979 (1)

R. Mahon, T. J. McIlrath, V. P. Myerscough, and D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

1977 (1)

S. Gerstenkorn, J. J. Labarthe, and J. Vergès, “Fine and hyperfine structures and isotope shifts in the arc spectrum of mercury,” Phys. Scr. 15, 167–172 (1977).
[CrossRef]

1975 (1)

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
[CrossRef]

1969 (1)

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

1953 (1)

Alford, W. J.

W. J. Alford and A. V. Smith, “Measured third-order susceptibilities and excited state oscillator strengths for atomic mercury,” Phys. Rev. A 36, 641–648 (1987).
[CrossRef] [PubMed]

A. V. Smith and W. J. Alford, “Vacuum ultraviolet oscillator strengths of Hg measured by sum-frequency mixing,” Phys. Rev. A 33, 3172–3180 (1986).
[CrossRef] [PubMed]

A. V. Smith, G. R. Hadley, P. Esherick, and W. J. Alford, “Efficient two-photon resonant frequency conversion in Hg: the effects of amplified spontaneous emission,” submitted to J. Opt. Soc. Am. B.

Bjorklund, G. C.

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
[CrossRef]

Bokor, J.

Conte, S. D.

B. D. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

Esherick, P.

A. V. Smith, G. R. Hadley, P. Esherick, and W. J. Alford, “Efficient two-photon resonant frequency conversion in Hg: the effects of amplified spontaneous emission,” submitted to J. Opt. Soc. Am. B.

Freeman, R. R.

Fried, B. D.

B. D. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

Gerstenkorn, S.

S. Gerstenkorn, J. J. Labarthe, and J. Vergès, “Fine and hyperfine structures and isotope shifts in the arc spectrum of mercury,” Phys. Scr. 15, 167–172 (1977).
[CrossRef]

Hadley, G. R.

A. V. Smith, G. R. Hadley, P. Esherick, and W. J. Alford, “Efficient two-photon resonant frequency conversion in Hg: the effects of amplified spontaneous emission,” submitted to J. Opt. Soc. Am. B.

Herman, P. R.

Hilbig, R.

R. Hilbig and R. Wallenstein, “Resonant sum and difference frequency mixing in Hg,” IEEE J. Quantum Electron. QE-19, 1759–1770 (1983).
[CrossRef]

Koopman, D. W.

R. Mahon, T. J. McIlrath, V. P. Myerscough, and D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

Labarthe, J. J.

S. Gerstenkorn, J. J. Labarthe, and J. Vergès, “Fine and hyperfine structures and isotope shifts in the arc spectrum of mercury,” Phys. Scr. 15, 167–172 (1977).
[CrossRef]

Mahon, R.

McIlrath, T. J.

R. Mahon, T. J. McIlrath, V. P. Myerscough, and D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

Myerscough, V. P.

R. Mahon, T. J. McIlrath, V. P. Myerscough, and D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

New, G. H. C.

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Panock, R. L.

Rientjes, J. F.

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

Smith, A. V.

W. J. Alford and A. V. Smith, “Measured third-order susceptibilities and excited state oscillator strengths for atomic mercury,” Phys. Rev. A 36, 641–648 (1987).
[CrossRef] [PubMed]

A. V. Smith and W. J. Alford, “Vacuum ultraviolet oscillator strengths of Hg measured by sum-frequency mixing,” Phys. Rev. A 33, 3172–3180 (1986).
[CrossRef] [PubMed]

A. V. Smith, G. R. Hadley, P. Esherick, and W. J. Alford, “Efficient two-photon resonant frequency conversion in Hg: the effects of amplified spontaneous emission,” submitted to J. Opt. Soc. Am. B.

Stoicheff, B. P.

Tomkins, F. S.

Vergès, J.

S. Gerstenkorn, J. J. Labarthe, and J. Vergès, “Fine and hyperfine structures and isotope shifts in the arc spectrum of mercury,” Phys. Scr. 15, 167–172 (1977).
[CrossRef]

Wallenstein, R.

R. Hilbig and R. Wallenstein, “Resonant sum and difference frequency mixing in Hg,” IEEE J. Quantum Electron. QE-19, 1759–1770 (1983).
[CrossRef]

Ward, J. F.

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Watanabe, K.

White, J. C.

Zelikoff, M.

IEEE J. Quantum Electron. (3)

R. Hilbig and R. Wallenstein, “Resonant sum and difference frequency mixing in Hg,” IEEE J. Quantum Electron. QE-19, 1759–1770 (1983).
[CrossRef]

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
[CrossRef]

R. Mahon, T. J. McIlrath, V. P. Myerscough, and D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (3)

Phys. Rev. (1)

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Phys. Rev. A (2)

A. V. Smith and W. J. Alford, “Vacuum ultraviolet oscillator strengths of Hg measured by sum-frequency mixing,” Phys. Rev. A 33, 3172–3180 (1986).
[CrossRef] [PubMed]

W. J. Alford and A. V. Smith, “Measured third-order susceptibilities and excited state oscillator strengths for atomic mercury,” Phys. Rev. A 36, 641–648 (1987).
[CrossRef] [PubMed]

Phys. Scr. (1)

S. Gerstenkorn, J. J. Labarthe, and J. Vergès, “Fine and hyperfine structures and isotope shifts in the arc spectrum of mercury,” Phys. Scr. 15, 167–172 (1977).
[CrossRef]

Other (4)

See Chap. 4 of Ref. 9 for a discussion of efficiency-limiting processes.

B. D. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

A. V. Smith, G. R. Hadley, P. Esherick, and W. J. Alford, “Efficient two-photon resonant frequency conversion in Hg: the effects of amplified spontaneous emission,” submitted to J. Opt. Soc. Am. B.

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

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Figures (5)

Fig. 1
Fig. 1

Energy-level diagram of Hg and typical mixing scheme with notation indicated.

Fig. 2
Fig. 2

Equilibrium vapor pressure of atomic Hg as a function of temperature.

Fig. 3
Fig. 3

Partial Δk (as defined in the text) as a function of frequency. Three energy ranges are given: (a) 30 000–75 000 cm−1, (b) 75 000–80 500 cm−1, (c) 80 500–83 000 cm−1. Hatching indicates regions of negative dispersion for Xe and Kr buffer gases.

Fig. 4
Fig. 4

Partial susceptibilities χp (as defined in the text) as a function of frequency. Solid lines are for 71S resonance; dotted lines are for 73S resonance. Three energy ranges are given: (a) 30 000–75 000 cm−1, (b) 75 000–80 500 cm−1, (c) 80 500–83 000 cm−1.

Fig. 5
Fig. 5

The two-photon resonance line-shape function |S(ω1 + ω2)|2 for (b) the 71S and (a) the 73S resonances. The solid lines in (a) indicate calculated positions and strengths of the various Hg isotopes with unknown constant frequency offset. The solid line is a Doppler-free fluorescence spectrum of the 71S resonance for a natural Hg isotopic mixture. Line positions are accurate to <0.01 cm−1.

Equations (15)

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P 4 = 1.9 × 10 - 49 K P 1 P 2 P 3 × | χ p ( ω 1 ) χ p ( ω 4 ) ω 4 N L S ( ω 1 + ω 2 ) sin ( N L Δ k / 2 ) A ( N L Δ k / 2 ) | 2
P 4 = 7.8 × 10 - 49 K ω 1 ω 2 ω 3 ω 4 P 1 P 2 P 3 × χ p ( ω 1 ) χ p ( ω 4 ) N F S ( ω 1 + ω 2 ) 2 ,
K = { 1             for ω 1 ω 2 1 / 4             for ω 1 = ω 2 ,
Δ k = [ k ( ω 4 ) - k ( ω 1 ) - k ( ω 2 ) ± k ( ω 3 ) ] / N ,
b = 16 / k ( ω ) δ 2 ,
F 2 = { π 2 ( b Δ k N ) 2 exp ( b Δ k N ) , Δ k < 0 0 , Δ k 0
Δ k p ( ω ) = [ k ( ω ) + k ( E 7 S - ω ) ] / N ,
k ( - ω ) = - k ( ω ) ,
Δ k = Δ k p ( ω 4 ) - Δ k p ( ω 1 ) .
Δ k cross = ± k 1 k 3 2 k 1 + k 3 θ 2 ,
χ p ( ω ) = f ( i d · e ^ ω f f d · e ^ ω g ω f - ω + i d · e ^ ω f f d · e ^ ω g ω f - ω ) ,
χ ( 3 ) ( - ω 4 ; ω 1 , ω 2 , ω 3 ) = ( e a 0 ) 4 6 ( h c ) 3 S ( ω 1 + ω 2 ) χ 1 χ p ( ω 4 ) = 8.87 × 10 - 25 S ( ω 1 + ω 2 ) χ 1 χ p ( ω 4 ) ,
S ( ω 1 + ω 2 ) = 1 w π 1 / 2 exp ( - x 2 ) x - ζ d x = Z ( ζ ) / w ,
ζ = ( ω 1 + ω 2 - ω 7 S + i Γ ) / w ,
w = ω 7 S ( 2 k T / m c 2 ) 1 / 2 = Δ ω D / 2 ( ln 2 ) 1 / 2 ,

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