Abstract

We report a simple theoretical model for the calculation of the dependence of filter quantum efficiency versus laser pump power in an atomic Rb vapor laser-excited optical filter. We present the calculations for a 532.4-nm Rb filter that can be used to detect the practical and important frequency-doubled Nd:YAG laser. The results of these calculations show that the filter’s quantum efficiency is relatively insensitive to the laser pump power. The laser powers required to pump the filter range from 3.6 to 226 mW per square centimeter of filter aperture.

© 1988 Optical Society of America

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References

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  1. J. A. Gelbwachs, C. F. Klein, J. E. Wessel, IEEE J. Quantum Electron. QE-14, 77 (1978).
    [CrossRef]
  2. J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
    [CrossRef]
  3. Y. C. Chung, J. D. Dobbins, T. M. Shay, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), p. 64.
  4. Y. C. Chung, T. M. Shay, IEEE J. Quantum Electron. (to be published).
  5. A. Lingard, S. E. Nielsen, At. Data Nucl. Data Tables 19, 533 (1977).
    [CrossRef]
  6. H. Kopferman, W. Tietze, Z. Phys. 56, 604 (1929).
    [CrossRef]
  7. T. Holstein, Phys. Rev. 72, 1212 (1947).
    [CrossRef]
  8. T. Holstein, Phys. Rev. 83, 1159 (1951).
    [CrossRef]
  9. L. M. Bieberman, J. Exp. Theor. Phys. (USSR) 17, 416 (1947).
  10. Holstein’s formula was derived under the approximation that σ(λp)n5sr ≫ 1. However, comparisons with experimental data show that Holstein’s formula underestimates the resonance trapping by only <25% for σ(λp)n5sr = 3, and the accuracy improves rapidly as σ(λp)n5sr increases. Therefore we used this relation.
  11. The collisional deactivation rates for the Rb(10s) atoms have not yet been measured. Therefore, to be conservative, we have used the largest measured collisional quenching cross section for Rb. The quenching rate for Rb(13d) atoms in collisions with Rb(5s) atoms was measured by Hugon et al.12
  12. M. Hugon, F. Gounand, P. R. Fournier, J. Phys. B 13, L109 (1980).
    [CrossRef]
  13. In spite of the strong resonance trapping, the cell can easily be uniformly excited by detuning the pump laser from line center.

1980

M. Hugon, F. Gounand, P. R. Fournier, J. Phys. B 13, L109 (1980).
[CrossRef]

1979

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

1978

J. A. Gelbwachs, C. F. Klein, J. E. Wessel, IEEE J. Quantum Electron. QE-14, 77 (1978).
[CrossRef]

1977

A. Lingard, S. E. Nielsen, At. Data Nucl. Data Tables 19, 533 (1977).
[CrossRef]

1951

T. Holstein, Phys. Rev. 83, 1159 (1951).
[CrossRef]

1947

L. M. Bieberman, J. Exp. Theor. Phys. (USSR) 17, 416 (1947).

T. Holstein, Phys. Rev. 72, 1212 (1947).
[CrossRef]

1929

H. Kopferman, W. Tietze, Z. Phys. 56, 604 (1929).
[CrossRef]

Bieberman, L. M.

L. M. Bieberman, J. Exp. Theor. Phys. (USSR) 17, 416 (1947).

Chung, Y. C.

Y. C. Chung, J. D. Dobbins, T. M. Shay, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), p. 64.

Y. C. Chung, T. M. Shay, IEEE J. Quantum Electron. (to be published).

Dobbins, J. D.

Y. C. Chung, J. D. Dobbins, T. M. Shay, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), p. 64.

Fournier, P. R.

M. Hugon, F. Gounand, P. R. Fournier, J. Phys. B 13, L109 (1980).
[CrossRef]

Gelbwachs, J. A.

J. A. Gelbwachs, C. F. Klein, J. E. Wessel, IEEE J. Quantum Electron. QE-14, 77 (1978).
[CrossRef]

Gounand, F.

M. Hugon, F. Gounand, P. R. Fournier, J. Phys. B 13, L109 (1980).
[CrossRef]

Holstein, T.

T. Holstein, Phys. Rev. 83, 1159 (1951).
[CrossRef]

T. Holstein, Phys. Rev. 72, 1212 (1947).
[CrossRef]

Hugon, M.

M. Hugon, F. Gounand, P. R. Fournier, J. Phys. B 13, L109 (1980).
[CrossRef]

Klein, C. F.

J. A. Gelbwachs, C. F. Klein, J. E. Wessel, IEEE J. Quantum Electron. QE-14, 77 (1978).
[CrossRef]

Kopferman, H.

H. Kopferman, W. Tietze, Z. Phys. 56, 604 (1929).
[CrossRef]

Lingard, A.

A. Lingard, S. E. Nielsen, At. Data Nucl. Data Tables 19, 533 (1977).
[CrossRef]

Marling, J. B.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

Nielsen, S. E.

A. Lingard, S. E. Nielsen, At. Data Nucl. Data Tables 19, 533 (1977).
[CrossRef]

Nilsen, J.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

Shay, T. M.

Y. C. Chung, J. D. Dobbins, T. M. Shay, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), p. 64.

Y. C. Chung, T. M. Shay, IEEE J. Quantum Electron. (to be published).

Tietze, W.

H. Kopferman, W. Tietze, Z. Phys. 56, 604 (1929).
[CrossRef]

Wessel, J. E.

J. A. Gelbwachs, C. F. Klein, J. E. Wessel, IEEE J. Quantum Electron. QE-14, 77 (1978).
[CrossRef]

West, L. C.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

Wood, L. L.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

At. Data Nucl. Data Tables

A. Lingard, S. E. Nielsen, At. Data Nucl. Data Tables 19, 533 (1977).
[CrossRef]

IEEE J. Quantum Electron.

J. A. Gelbwachs, C. F. Klein, J. E. Wessel, IEEE J. Quantum Electron. QE-14, 77 (1978).
[CrossRef]

J. Appl. Phys.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

J. Exp. Theor. Phys. (USSR)

L. M. Bieberman, J. Exp. Theor. Phys. (USSR) 17, 416 (1947).

J. Phys. B

M. Hugon, F. Gounand, P. R. Fournier, J. Phys. B 13, L109 (1980).
[CrossRef]

Phys. Rev.

T. Holstein, Phys. Rev. 72, 1212 (1947).
[CrossRef]

T. Holstein, Phys. Rev. 83, 1159 (1951).
[CrossRef]

Z. Phys.

H. Kopferman, W. Tietze, Z. Phys. 56, 604 (1929).
[CrossRef]

Other

Y. C. Chung, J. D. Dobbins, T. M. Shay, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), p. 64.

Y. C. Chung, T. M. Shay, IEEE J. Quantum Electron. (to be published).

In spite of the strong resonance trapping, the cell can easily be uniformly excited by detuning the pump laser from line center.

Holstein’s formula was derived under the approximation that σ(λp)n5sr ≫ 1. However, comparisons with experimental data show that Holstein’s formula underestimates the resonance trapping by only <25% for σ(λp)n5sr = 3, and the accuracy improves rapidly as σ(λp)n5sr increases. Therefore we used this relation.

The collisional deactivation rates for the Rb(10s) atoms have not yet been measured. Therefore, to be conservative, we have used the largest measured collisional quenching cross section for Rb. The quenching rate for Rb(13d) atoms in collisions with Rb(5s) atoms was measured by Hugon et al.12

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Figures (2)

Fig. 1
Fig. 1

Partial energy diagram of Rb indicating the two dominant processes when 532-nm photons are absorbed in an actively pumped Rb. The numbers in parentheses are the quantum efficiency for generation of the associated violet photons following the absorption of a blue-green photon.

Fig. 2
Fig. 2

RQE versus laser pump power for the 532-nm transition when the cell signal transmission probability, P(λ0), is 0.1 and the reflectivity of the cell walls at the pump wavelength, R, is 0.96.

Equations (8)

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IQE = Total Quantum Efficiency 1 BR ( 532 nm ) = 0 . 28 ,
RQE = [ 1 P ( λ 0 ) ] j = 1 4 IQE j P ( λ j ) ,
P ( λ 0 ) = exp [ n 5 p σ ( λ 0 ) d ] ,
RQE = [ 1 P ( λ 0 ) ] j = 1 4 IQE j { 1 k = 1 a k ( 1 ) k + 1 [ σ ( λ j ) n 5 s r ] k m = 0 b m ( 1 ) m [ σ ( λ j ) n 5 s r ] m } ,
a k = 2 k + 1 2 ( k + 1 ) ! ( k + 1 ) 1 / 2 ,
b m = 1 ( m + 1 ) ! ( m + 1 ) 1 / 2 ,
P L = ( 1 R p ) n 5 p L π r 2 h ν p A eff ,
P L π r 2 = ( 1 R p ) h ν p A rad × 1 . 6 { ln [ P ( λ 0 ) ] } 2 ( σ ( λ p ) n 5 s r { π ln [ σ ( λ p ) n 5 s r ] } 1 / 2 ) σ ( λ 0 ) ,

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