Abstract

We have investigated degenerate four-wave mixing (DFWM) in a strongly absorbing molecular gas. A theory taking into account saturable absorption of the interacting beams is used to explain the dependence of the DFWM reflectivity on laser intensity and on the molecular number density. These parameters have a great influence on the observed spectra, owing to linear absorption that suppresses the DFWM signal in the line center of the molecular transitions. The great sensitivity of the spectra to the experimental conditions limits the applicability of DFWM for spectroscopic studies in absorbing media.

© 1992 Optical Society of America

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References

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  1. R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
  2. J. M. Andrews, K. M. Weed, M. G. Tong, Appl. Spectrosc. 45, 697 (1991).
    [CrossRef]
  3. D. G. Steel, J. F. Lam, Opt. Commun. 40, 77 (1981).
    [CrossRef]
  4. P. Ewart, P. Snowdown, I. Magnusson, Opt. Lett. 14, 563 (1989).
    [CrossRef] [PubMed]
  5. T. Dreier, D. J. Rakestraw, Opt. Lett. 15, 72 (1990).
    [CrossRef] [PubMed]
  6. D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).
    [CrossRef]
  7. M. T. Gruneisen, A. L. Gaeta, R. W. Boyd, J. Opt. Soc. Am. B 2, 1117 (1985).
    [CrossRef]
  8. A. L. Gaeta, M. T. Gruneisen, R. W. Boyd, IEEE J. Quantum Electron. QE-22, 1095 (1986).
    [CrossRef]
  9. R. L. Abrams, R. C. Lind, Opt. Lett. 2, 94 (1978).
    [CrossRef]
  10. R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, Ref. 1, p. 211.
  11. J. Gumbel, W. Kiefer, Chem. Phys. Lett. 189, 231 (1992).
    [CrossRef]
  12. P. Ewart, A. I. Ferguson, S. V. O’Leary, Opt. Commun. 40, 147 (1981).
    [CrossRef]
  13. A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [CrossRef]
  14. B. Kleinmann, F. Trehin, M. Pinard, G. Grynberg, J. Opt. Soc. Am. B 2, 704 (1985).
    [CrossRef]

1992 (1)

J. Gumbel, W. Kiefer, Chem. Phys. Lett. 189, 231 (1992).
[CrossRef]

1991 (1)

1990 (1)

1989 (1)

1986 (1)

A. L. Gaeta, M. T. Gruneisen, R. W. Boyd, IEEE J. Quantum Electron. QE-22, 1095 (1986).
[CrossRef]

1985 (2)

1981 (2)

D. G. Steel, J. F. Lam, Opt. Commun. 40, 77 (1981).
[CrossRef]

P. Ewart, A. I. Ferguson, S. V. O’Leary, Opt. Commun. 40, 147 (1981).
[CrossRef]

1978 (2)

1977 (1)

Abrams, R. L.

R. L. Abrams, R. C. Lind, Opt. Lett. 2, 94 (1978).
[CrossRef]

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, Ref. 1, p. 211.

Andrews, J. M.

Bloom, D. M.

Boyd, R. W.

A. L. Gaeta, M. T. Gruneisen, R. W. Boyd, IEEE J. Quantum Electron. QE-22, 1095 (1986).
[CrossRef]

M. T. Gruneisen, A. L. Gaeta, R. W. Boyd, J. Opt. Soc. Am. B 2, 1117 (1985).
[CrossRef]

Dreier, T.

Economou, N. P.

Ewart, P.

P. Ewart, P. Snowdown, I. Magnusson, Opt. Lett. 14, 563 (1989).
[CrossRef] [PubMed]

P. Ewart, A. I. Ferguson, S. V. O’Leary, Opt. Commun. 40, 147 (1981).
[CrossRef]

Ferguson, A. I.

P. Ewart, A. I. Ferguson, S. V. O’Leary, Opt. Commun. 40, 147 (1981).
[CrossRef]

Gaeta, A. L.

A. L. Gaeta, M. T. Gruneisen, R. W. Boyd, IEEE J. Quantum Electron. QE-22, 1095 (1986).
[CrossRef]

M. T. Gruneisen, A. L. Gaeta, R. W. Boyd, J. Opt. Soc. Am. B 2, 1117 (1985).
[CrossRef]

Gruneisen, M. T.

A. L. Gaeta, M. T. Gruneisen, R. W. Boyd, IEEE J. Quantum Electron. QE-22, 1095 (1986).
[CrossRef]

M. T. Gruneisen, A. L. Gaeta, R. W. Boyd, J. Opt. Soc. Am. B 2, 1117 (1985).
[CrossRef]

Grynberg, G.

Gumbel, J.

J. Gumbel, W. Kiefer, Chem. Phys. Lett. 189, 231 (1992).
[CrossRef]

Kiefer, W.

J. Gumbel, W. Kiefer, Chem. Phys. Lett. 189, 231 (1992).
[CrossRef]

Kleinmann, B.

Lam, J. F.

D. G. Steel, J. F. Lam, Opt. Commun. 40, 77 (1981).
[CrossRef]

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, Ref. 1, p. 211.

Liao, P. F.

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).
[CrossRef]

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, Ref. 1, p. 211.

Lind, R. C.

R. L. Abrams, R. C. Lind, Opt. Lett. 2, 94 (1978).
[CrossRef]

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, Ref. 1, p. 211.

Magnusson, I.

O’Leary, S. V.

P. Ewart, A. I. Ferguson, S. V. O’Leary, Opt. Commun. 40, 147 (1981).
[CrossRef]

Pepper, D. M.

Pinard, M.

Rakestraw, D. J.

Snowdown, P.

Steel, D. G.

D. G. Steel, J. F. Lam, Opt. Commun. 40, 77 (1981).
[CrossRef]

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, Ref. 1, p. 211.

Tong, M. G.

Trehin, F.

Weed, K. M.

Yariv, A.

Appl. Spectrosc. (1)

Chem. Phys. Lett. (1)

J. Gumbel, W. Kiefer, Chem. Phys. Lett. 189, 231 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. L. Gaeta, M. T. Gruneisen, R. W. Boyd, IEEE J. Quantum Electron. QE-22, 1095 (1986).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

D. G. Steel, J. F. Lam, Opt. Commun. 40, 77 (1981).
[CrossRef]

P. Ewart, A. I. Ferguson, S. V. O’Leary, Opt. Commun. 40, 147 (1981).
[CrossRef]

Opt. Lett. (5)

Other (2)

R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, Ref. 1, p. 211.

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Figures (4)

Fig. 1
Fig. 1

DFWM reflectivity versus pump intensity for an iodine B(30+u) ← X(1g+) transition at 585 nm. The experimental points have been measured at a vapor temperature of 47°C in the center of a strong iodine transition.

Fig. 2
Fig. 2

DFWM reflectivity versus number density for two BX iodine transitions. The measurements were carried out for two wavelengths near 585 nm coinciding with the centers of two iodine lines. The crosses represent the transition that possesses the larger dipole transition moment |μ12|.

Fig. 3
Fig. 3

DFWM spectra of iodine vapor for various pump intensities. The vapor temperature was 47°C. Important transitions are assigned in the form υ′,J′υ″,J″. The changes in the spectra are due to absorption.

Fig. 4
Fig. 4

Calculated dependence of the homogeneous DFWM line shape: a, on linear absorption and b, on laser intensity. In a, the pump intensity is fixed at If0/Isat = 1; and in b, the absorption is α0L = 1.

Equations (8)

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d s d z = α s + i β p * ,
d p d z = α p i β s * .
α = α 0 1 1 + Δ 2 / γ 12 2 1 + I f + I b I sat [ ( 1 + I f + I b I sat ) 2 4 I f I b I sat 2 ] 3 / 2 ,
β = α 0 i + Δ / γ 12 1 + Δ 2 / γ 12 2 2 ( I f I b ) 1 / 2 I sat [ ( 1 + I f + I b I sat ) 2 4 I f I b I sat 2 ] 3 / 2 ,
I f ( z ) = I f 0 exp ( 2 z ) ,
I b ( z ) = I f 0 exp [ 2 ( 2 L z ) ] ,
I s = ( 1 + Δ 2 γ 12 2 ) [ 1 exp ( 2 L ) ] 2 × I 10 2 I sat 2 exp ( 4 L ) [ 1 + I f 0 I sat 1 exp ( 4 L ) 2 L ] 2 I p 0 ,
R = I s / I p 0 .

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