Abstract

We propose a new approach to the analysis of stochastic processes (such as fluctuating laser fields) with super-Gaussian statistics: the expansion of stochastic processes in terms of first and higher powers of Gaussian components, which are used like a basis set. This approach is applied to treat the super-Gaussian correlation effects observed in coherent anti-Stokes Raman scattering experiments using frequency-doubled pump laser fields. Our results give much better agreement with experimental data than previous theories do.

© 1989 Optical Society of America

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References

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  1. L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
    [CrossRef]
  2. A. A. Grutter, H. P. Weber, R. Dandliker, Phys. Rev. 185, 629 (1969).
    [CrossRef]
  3. M. A. Duguay, J. W. Hansen, S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
    [CrossRef]
  4. L. A. Rahn, R. L. Farrow, R. P. Lucht, Opt. Lett. 9, 223 (1984).
    [CrossRef] [PubMed]
  5. R. L. Farrow, L. A. Rahn, J. Opt. Soc. Am. B 2, 903 (1985).
    [CrossRef]
  6. R. J. Hall, Opt. Commun. 56, 127 (1985).
    [CrossRef]
  7. R. J. Hall, Opt. Quantum Electron. 18, 319 (1986).
    [CrossRef]
  8. G. S. Agarwal, R. L. Farrow, J. Opt. Soc. Am. B 3, 1596 (1986).
    [CrossRef]
  9. W. M. Huo, K. P. Gross, R. L. McKenzie, Phys. Rev. Lett. 54, 1012 (1985). Both the Gaussian and the non-Gaussian (the time-dependent and spatially variant models) cases were treated here.
    [CrossRef] [PubMed]
  10. M. Aldén, D. A. Greenhalgh, R. J. Hall, Department of Physics, Lund Institute of Technology, Lund, Sweden (personal communication).
  11. If needed, one may add an independent zeroth-order term G0 to account for sub-Gaussian statistics. In some application this G0 term may be a coherent field [J. H. Churnside, Opt. Commun. 51, 207 (1984)].
    [CrossRef]
  12. C. Radzewicz, Z. W. Li, M. G. Raymer, Phys. Rev. A 37, 2039 (1988); Opt. Lett. 13, 491 (1988).
    [CrossRef] [PubMed]
  13. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, New York, 1981).
  14. R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford U. Press, Oxford, 1983), p. 83.

1988 (1)

C. Radzewicz, Z. W. Li, M. G. Raymer, Phys. Rev. A 37, 2039 (1988); Opt. Lett. 13, 491 (1988).
[CrossRef] [PubMed]

1986 (2)

1985 (3)

W. M. Huo, K. P. Gross, R. L. McKenzie, Phys. Rev. Lett. 54, 1012 (1985). Both the Gaussian and the non-Gaussian (the time-dependent and spatially variant models) cases were treated here.
[CrossRef] [PubMed]

R. L. Farrow, L. A. Rahn, J. Opt. Soc. Am. B 2, 903 (1985).
[CrossRef]

R. J. Hall, Opt. Commun. 56, 127 (1985).
[CrossRef]

1984 (2)

If needed, one may add an independent zeroth-order term G0 to account for sub-Gaussian statistics. In some application this G0 term may be a coherent field [J. H. Churnside, Opt. Commun. 51, 207 (1984)].
[CrossRef]

L. A. Rahn, R. L. Farrow, R. P. Lucht, Opt. Lett. 9, 223 (1984).
[CrossRef] [PubMed]

1970 (1)

M. A. Duguay, J. W. Hansen, S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
[CrossRef]

1969 (1)

A. A. Grutter, H. P. Weber, R. Dandliker, Phys. Rev. 185, 629 (1969).
[CrossRef]

1965 (1)

L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

Agarwal, G. S.

Aldén, M.

M. Aldén, D. A. Greenhalgh, R. J. Hall, Department of Physics, Lund Institute of Technology, Lund, Sweden (personal communication).

Churnside, J. H.

If needed, one may add an independent zeroth-order term G0 to account for sub-Gaussian statistics. In some application this G0 term may be a coherent field [J. H. Churnside, Opt. Commun. 51, 207 (1984)].
[CrossRef]

Dandliker, R.

A. A. Grutter, H. P. Weber, R. Dandliker, Phys. Rev. 185, 629 (1969).
[CrossRef]

Duguay, M. A.

M. A. Duguay, J. W. Hansen, S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
[CrossRef]

Farrow, R. L.

Greenhalgh, D. A.

M. Aldén, D. A. Greenhalgh, R. J. Hall, Department of Physics, Lund Institute of Technology, Lund, Sweden (personal communication).

Gross, K. P.

W. M. Huo, K. P. Gross, R. L. McKenzie, Phys. Rev. Lett. 54, 1012 (1985). Both the Gaussian and the non-Gaussian (the time-dependent and spatially variant models) cases were treated here.
[CrossRef] [PubMed]

Grutter, A. A.

A. A. Grutter, H. P. Weber, R. Dandliker, Phys. Rev. 185, 629 (1969).
[CrossRef]

Hall, R. J.

R. J. Hall, Opt. Quantum Electron. 18, 319 (1986).
[CrossRef]

R. J. Hall, Opt. Commun. 56, 127 (1985).
[CrossRef]

M. Aldén, D. A. Greenhalgh, R. J. Hall, Department of Physics, Lund Institute of Technology, Lund, Sweden (personal communication).

Hansen, J. W.

M. A. Duguay, J. W. Hansen, S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
[CrossRef]

Huo, W. M.

W. M. Huo, K. P. Gross, R. L. McKenzie, Phys. Rev. Lett. 54, 1012 (1985). Both the Gaussian and the non-Gaussian (the time-dependent and spatially variant models) cases were treated here.
[CrossRef] [PubMed]

Li, Z. W.

C. Radzewicz, Z. W. Li, M. G. Raymer, Phys. Rev. A 37, 2039 (1988); Opt. Lett. 13, 491 (1988).
[CrossRef] [PubMed]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford U. Press, Oxford, 1983), p. 83.

Lucht, R. P.

Mandel, L.

L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

McKenzie, R. L.

W. M. Huo, K. P. Gross, R. L. McKenzie, Phys. Rev. Lett. 54, 1012 (1985). Both the Gaussian and the non-Gaussian (the time-dependent and spatially variant models) cases were treated here.
[CrossRef] [PubMed]

Radzewicz, C.

C. Radzewicz, Z. W. Li, M. G. Raymer, Phys. Rev. A 37, 2039 (1988); Opt. Lett. 13, 491 (1988).
[CrossRef] [PubMed]

Rahn, L. A.

Raymer, M. G.

C. Radzewicz, Z. W. Li, M. G. Raymer, Phys. Rev. A 37, 2039 (1988); Opt. Lett. 13, 491 (1988).
[CrossRef] [PubMed]

Shapiro, S. L.

M. A. Duguay, J. W. Hansen, S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
[CrossRef]

Van Kampen, N. G.

N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, New York, 1981).

Weber, H. P.

A. A. Grutter, H. P. Weber, R. Dandliker, Phys. Rev. 185, 629 (1969).
[CrossRef]

Wolf, E.

L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. A. Duguay, J. W. Hansen, S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
[CrossRef]

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

Opt. Commun. (2)

R. J. Hall, Opt. Commun. 56, 127 (1985).
[CrossRef]

If needed, one may add an independent zeroth-order term G0 to account for sub-Gaussian statistics. In some application this G0 term may be a coherent field [J. H. Churnside, Opt. Commun. 51, 207 (1984)].
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

R. J. Hall, Opt. Quantum Electron. 18, 319 (1986).
[CrossRef]

Phys. Rev. (1)

A. A. Grutter, H. P. Weber, R. Dandliker, Phys. Rev. 185, 629 (1969).
[CrossRef]

Phys. Rev. A (1)

C. Radzewicz, Z. W. Li, M. G. Raymer, Phys. Rev. A 37, 2039 (1988); Opt. Lett. 13, 491 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

W. M. Huo, K. P. Gross, R. L. McKenzie, Phys. Rev. Lett. 54, 1012 (1985). Both the Gaussian and the non-Gaussian (the time-dependent and spatially variant models) cases were treated here.
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

Other (3)

M. Aldén, D. A. Greenhalgh, R. J. Hall, Department of Physics, Lund Institute of Technology, Lund, Sweden (personal communication).

N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, New York, 1981).

R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford U. Press, Oxford, 1983), p. 83.

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Figures (2)

Fig. 1
Fig. 1

Comparison of experimental (filled dots) resonant and nonresonant CARS intensities and their ratios [measured on the O(18) transition of nitrogen at 500 Torr and 296 K] with theoretical results using the present theory (solid curves) and the Gaussian (dashed curves) and the squared-Gaussian (dotted curves) statistics to model the fluctuations in the pump laser fields.

Fig. 2
Fig. 2

Comparison of experimental (filled dots) resonant and nonresonant CARS intensities and their ratios [measured on the O(18) transition of nitrogen at 4500 Torr and 296 K] with theoretical results using the present theory (solid curves) with the same field statistics determined from the 500-Torr data. The results of the Gaussian (dashed curves) and the squared-Gaussian (dotted curves) models are also presented for comparison.

Equations (3)

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E ( t ) = m = 1 n [ G m ( t ) ] m ,
I d = E d * ( t ) E d ( t ) = I 1 + 2 ( I 2 ) 2 ,
I aS ( δ ) = 4 I d 2 I S ( χ nr 2 [ 1 + γ 2 2 ( δ ) γ 2 2 ( - δ ) + 4 α 2 γ 2 ( δ ) γ 2 ( - δ ) ] + { i χ r χ nr 2 T 2 0 d τ exp [ - ( 1 T 2 + i Δ ) τ ] γ S ( - τ ) × [ γ 2 2 ( τ ) + γ 2 2 ( τ + δ ) γ 2 2 ( - δ ) + 4 α 2 γ 2 ( τ ) × γ 2 ( - δ ) γ 2 ( δ + τ ) + ( δ - δ ) ] + c . c . } + χ r 2 4 T 2 2 { 0 d η exp [ - ( 1 T 2 + i Δ ) η ] × 0 n d τ exp [ - ( 1 T 2 - i Δ ) τ ] γ S ( τ - η ) [ γ 2 2 ( η - τ ) + γ 2 2 ( η + δ ) γ 2 2 ( - τ - δ ) + 4 α 2 γ 2 ( η + δ ) × γ 2 ( η - τ ) γ 2 ( - τ - δ ) + γ 2 2 ( - δ ) γ 2 2 ( η + δ - τ ) + γ 2 2 ( η ) γ 2 2 ( - τ ) + 4 α 2 γ 2 ( - τ ) γ 2 ( η + δ - τ ) × γ 2 ( - δ ) γ 2 ( η ) + ( δ - δ ) ] + c . c . } ) ,

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