Abstract

Doubly resonant four-wave mixing has been used with two lasers set for resonance with the two Na D-line transitions to perform elemental analysis with a Na-seeded flame. The method is analogous to phase-conjugation methods where all lasers have the same frequency. Strong saturation effects and dynamic Stark splittings are observed and used to optimize the mixing efficiency. A nonperturbative theory is presented and shown to describe the experimental results.

© 1988 Optical Society of America

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References

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  1. J. Pender, L. Hesselink, Opt. Lett. 10, 264 (1985).
    [Crossref] [PubMed]
  2. J. M. Ramsey, W. B. Whitten, Anal. Chem. 59, 167 (1987).
    [Crossref]
  3. W. G. Tong, D. A. Chen, Appl. Spectrosc. 41, 586 (1987).
    [Crossref]
  4. M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982).
  5. B. K. Winker, Ph.D. dissertation (University of Wisconsin, 1987) (University Microfilms, Ann Arbor, Mich., order no. DA 8723364).
  6. S. Chandra, A. Compaan, E. Wiener-Avnear, Appl. Phys. Lett. 33, 867 (1978).
    [Crossref]
  7. N. Bloembergen, Y. R. Shen, Phys. Rev. 133, A37 (1964).
    [Crossref]
  8. F. Ouellette, M. M. Denariez-Roberge, Can. J. Phys. 60, 877 (1982).
    [Crossref]
  9. Y. Prior, A. R. Bogdan, M. Dagenais, N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981).
    [Crossref]
  10. N. Bloembergen, H. Lotem, R. T. Lynch, Indian J. Pure Appl. Phys. 16, 151 (1978).
  11. B. K. Winker, J. C. Wright, Anal. Chem. (to be published).

1987 (2)

J. M. Ramsey, W. B. Whitten, Anal. Chem. 59, 167 (1987).
[Crossref]

W. G. Tong, D. A. Chen, Appl. Spectrosc. 41, 586 (1987).
[Crossref]

1985 (1)

1982 (1)

F. Ouellette, M. M. Denariez-Roberge, Can. J. Phys. 60, 877 (1982).
[Crossref]

1981 (1)

Y. Prior, A. R. Bogdan, M. Dagenais, N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981).
[Crossref]

1978 (2)

N. Bloembergen, H. Lotem, R. T. Lynch, Indian J. Pure Appl. Phys. 16, 151 (1978).

S. Chandra, A. Compaan, E. Wiener-Avnear, Appl. Phys. Lett. 33, 867 (1978).
[Crossref]

1964 (1)

N. Bloembergen, Y. R. Shen, Phys. Rev. 133, A37 (1964).
[Crossref]

Bloembergen, N.

Y. Prior, A. R. Bogdan, M. Dagenais, N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981).
[Crossref]

N. Bloembergen, H. Lotem, R. T. Lynch, Indian J. Pure Appl. Phys. 16, 151 (1978).

N. Bloembergen, Y. R. Shen, Phys. Rev. 133, A37 (1964).
[Crossref]

Bogdan, A. R.

Y. Prior, A. R. Bogdan, M. Dagenais, N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981).
[Crossref]

Chandra, S.

S. Chandra, A. Compaan, E. Wiener-Avnear, Appl. Phys. Lett. 33, 867 (1978).
[Crossref]

Chen, D. A.

Compaan, A.

S. Chandra, A. Compaan, E. Wiener-Avnear, Appl. Phys. Lett. 33, 867 (1978).
[Crossref]

Dagenais, M.

Y. Prior, A. R. Bogdan, M. Dagenais, N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981).
[Crossref]

Denariez-Roberge, M. M.

F. Ouellette, M. M. Denariez-Roberge, Can. J. Phys. 60, 877 (1982).
[Crossref]

Hesselink, L.

Levenson, M. D.

M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982).

Lotem, H.

N. Bloembergen, H. Lotem, R. T. Lynch, Indian J. Pure Appl. Phys. 16, 151 (1978).

Lynch, R. T.

N. Bloembergen, H. Lotem, R. T. Lynch, Indian J. Pure Appl. Phys. 16, 151 (1978).

Ouellette, F.

F. Ouellette, M. M. Denariez-Roberge, Can. J. Phys. 60, 877 (1982).
[Crossref]

Pender, J.

Prior, Y.

Y. Prior, A. R. Bogdan, M. Dagenais, N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981).
[Crossref]

Ramsey, J. M.

J. M. Ramsey, W. B. Whitten, Anal. Chem. 59, 167 (1987).
[Crossref]

Shen, Y. R.

N. Bloembergen, Y. R. Shen, Phys. Rev. 133, A37 (1964).
[Crossref]

Tong, W. G.

Whitten, W. B.

J. M. Ramsey, W. B. Whitten, Anal. Chem. 59, 167 (1987).
[Crossref]

Wiener-Avnear, E.

S. Chandra, A. Compaan, E. Wiener-Avnear, Appl. Phys. Lett. 33, 867 (1978).
[Crossref]

Winker, B. K.

B. K. Winker, Ph.D. dissertation (University of Wisconsin, 1987) (University Microfilms, Ann Arbor, Mich., order no. DA 8723364).

B. K. Winker, J. C. Wright, Anal. Chem. (to be published).

Wright, J. C.

B. K. Winker, J. C. Wright, Anal. Chem. (to be published).

Anal. Chem. (1)

J. M. Ramsey, W. B. Whitten, Anal. Chem. 59, 167 (1987).
[Crossref]

Appl. Phys. Lett. (1)

S. Chandra, A. Compaan, E. Wiener-Avnear, Appl. Phys. Lett. 33, 867 (1978).
[Crossref]

Appl. Spectrosc. (1)

Can. J. Phys. (1)

F. Ouellette, M. M. Denariez-Roberge, Can. J. Phys. 60, 877 (1982).
[Crossref]

Indian J. Pure Appl. Phys. (1)

N. Bloembergen, H. Lotem, R. T. Lynch, Indian J. Pure Appl. Phys. 16, 151 (1978).

Opt. Lett. (1)

Phys. Rev. (1)

N. Bloembergen, Y. R. Shen, Phys. Rev. 133, A37 (1964).
[Crossref]

Phys. Rev. Lett. (1)

Y. Prior, A. R. Bogdan, M. Dagenais, N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981).
[Crossref]

Other (3)

M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982).

B. K. Winker, Ph.D. dissertation (University of Wisconsin, 1987) (University Microfilms, Ann Arbor, Mich., order no. DA 8723364).

B. K. Winker, J. C. Wright, Anal. Chem. (to be published).

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Figures (3)

Fig. 1
Fig. 1

Resonance scheme used for doubly degenerate fully resonant four-wave mixing showing labels used for the lasers and levels for the experimental and theoretical discussions. The polarizations of each beam are indicated.

Fig. 2
Fig. 2

Four-wave-mixing spectra as a function of ω1 frequency for a series of different ω1 laser intensities. The ω2 laser intensity was 35 W/cm2. The scale expansions and laser intensities are indicated by each trace.

Fig. 3
Fig. 3

The left side shows simulations of the four-wave-mixing intensity for ω1 resonant with the D1 transition and ω2 scanned across the D2 resonance. The right side shows simulations for ω2 resonant with the D2 transition and ω1 scanned across the D1 transition. The scale expansions and Rabi frequencies induced by the ω1 laser are shown.

Equations (3)

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ρ 31 L - S + P = Ω L Ω S * Ω P ρ 11 8 δ 31 L - S + P A 11 A 31 L - S + P 1 δ 32 P - S A 32 P - S × ( 1 δ 31 P A 31 P + B δ 12 - S ) + B δ 11 L - S A 11 L - S × ( 1 δ 12 - S + 1 δ 21 L ) ( 1 + B L - S Ω L 2 4 δ 12 - S δ 32 P - S A 32 P - S ) ,
δ i j A + B + C = ω i j - ω A - ω B - ω C - i Γ i j , A 31 P = 1 - Ω L 2 4 δ 31 P δ 32 P - L , A 11 = 1 - ( 1 δ 11 + 1 δ 22 ) [ Ω L 2 ( 1 δ 21 L + 1 δ 12 - L ) + Ω S 2 ( 1 δ 21 S + 1 δ 12 - S ) + Ω L 2 Ω S 2 B L - S ( 1 δ 21 L + 1 δ 12 - S ) 2 ] / δ 11 L - S A 11 L - S , A 11 L - S = 1 - Ω L 2 B L - S 4 δ 11 L - S ( 1 δ 12 - S + 1 δ 21 2 L - S ) - Ω S 2 B L - S 4 δ 11 L - S × ( 1 δ 21 L + 1 δ 12 L - 2 S ) . A 32 P - S = 1 - Ω S 2 4 δ 32 P - S δ 31 P A 31 P , A 31 L - S + P = 1 - Ω L 2 4 δ 31 L - S + P δ 32 P - S A 32 P - S - Ω S 2 4 δ 31 L - S + P δ 32 L - 2 S + P , B = ρ 11 + ρ 22 ρ 11 , B L - S = δ 11 L - S + δ 22 L - S δ 22 L - S ,
Ω A = μ i j E A ,

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