Abstract

We evaluate the average intensity and contrast of the output of a laser amplifier in which stochastic gain distributions exist. This situation occurs when turbulence flows are developed in a gas- or liquid-laser amplifier. The gain medium is assumed to be partially homogeneously broadened and slightly saturated and to consist of two-level atoms. In our computations, a plane wave is propagated through the gain medium with weak turbulences, under the assumption that the size of the first Fresnel zone is much smaller than the characteristic length of turbulences.

© 1988 Optical Society of America

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References

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  1. F. J. Duarte, J. A. Piper, Appl. Opt. 23, 1391 (1984).
    [CrossRef] [PubMed]
  2. T. H. Chyba, E. C. Gage, R. Ghosh, P. Lett, L. Mandel, Opt. Lett. 12, 422 (1987).
    [CrossRef] [PubMed]
  3. M. Duchet, J.-P. Crancon, J. Solmon, in Gas Flow and Chemical Lasers, M. Onorato, ed. (Plenum, New York, 1982), p. 227.
  4. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (U.S. Department of Commerce, Washington, D.C., 1971), Chap. 3.
  5. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), p. 169.
  6. H. Gamo, H. Sato, Jpn. J. Appl. Phys. 20, 139 (1981).
    [CrossRef]
  7. S. Y. Lee, C. H. Liu, K. C. Yeh, in Research Topics in Electromagnetic Wave Theory, J. A. Kong, ed. (Wiley, New York, 1981), Chap. 2.
  8. W. H. Munk, F. Zachariasen, J. Acoust. Soc. Am. 59, 818 (1976).
    [CrossRef]
  9. C. C. Yang, J. H. Tarng, Opt. Lett. 12, 380 (1987).
    [CrossRef] [PubMed]

1987 (2)

1984 (1)

1981 (1)

H. Gamo, H. Sato, Jpn. J. Appl. Phys. 20, 139 (1981).
[CrossRef]

1976 (1)

W. H. Munk, F. Zachariasen, J. Acoust. Soc. Am. 59, 818 (1976).
[CrossRef]

Chyba, T. H.

Crancon, J.-P.

M. Duchet, J.-P. Crancon, J. Solmon, in Gas Flow and Chemical Lasers, M. Onorato, ed. (Plenum, New York, 1982), p. 227.

Duarte, F. J.

Duchet, M.

M. Duchet, J.-P. Crancon, J. Solmon, in Gas Flow and Chemical Lasers, M. Onorato, ed. (Plenum, New York, 1982), p. 227.

Gage, E. C.

Gamo, H.

H. Gamo, H. Sato, Jpn. J. Appl. Phys. 20, 139 (1981).
[CrossRef]

Ghosh, R.

Lee, S. Y.

S. Y. Lee, C. H. Liu, K. C. Yeh, in Research Topics in Electromagnetic Wave Theory, J. A. Kong, ed. (Wiley, New York, 1981), Chap. 2.

Lett, P.

Liu, C. H.

S. Y. Lee, C. H. Liu, K. C. Yeh, in Research Topics in Electromagnetic Wave Theory, J. A. Kong, ed. (Wiley, New York, 1981), Chap. 2.

Mandel, L.

Munk, W. H.

W. H. Munk, F. Zachariasen, J. Acoust. Soc. Am. 59, 818 (1976).
[CrossRef]

Piper, J. A.

Sato, H.

H. Gamo, H. Sato, Jpn. J. Appl. Phys. 20, 139 (1981).
[CrossRef]

Solmon, J.

M. Duchet, J.-P. Crancon, J. Solmon, in Gas Flow and Chemical Lasers, M. Onorato, ed. (Plenum, New York, 1982), p. 227.

Tarng, J. H.

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (U.S. Department of Commerce, Washington, D.C., 1971), Chap. 3.

Yang, C. C.

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), p. 169.

Yeh, K. C.

S. Y. Lee, C. H. Liu, K. C. Yeh, in Research Topics in Electromagnetic Wave Theory, J. A. Kong, ed. (Wiley, New York, 1981), Chap. 2.

Zachariasen, F.

W. H. Munk, F. Zachariasen, J. Acoust. Soc. Am. 59, 818 (1976).
[CrossRef]

Appl. Opt. (1)

J. Acoust. Soc. Am. (1)

W. H. Munk, F. Zachariasen, J. Acoust. Soc. Am. 59, 818 (1976).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Gamo, H. Sato, Jpn. J. Appl. Phys. 20, 139 (1981).
[CrossRef]

Opt. Lett. (2)

Other (4)

S. Y. Lee, C. H. Liu, K. C. Yeh, in Research Topics in Electromagnetic Wave Theory, J. A. Kong, ed. (Wiley, New York, 1981), Chap. 2.

M. Duchet, J.-P. Crancon, J. Solmon, in Gas Flow and Chemical Lasers, M. Onorato, ed. (Plenum, New York, 1982), p. 227.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (U.S. Department of Commerce, Washington, D.C., 1971), Chap. 3.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), p. 169.

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Figures (2)

Fig. 1
Fig. 1

Normalized average intensity η as a function of Δ, the ratio of the input intensity over the saturation intensity, for three 〈N12〉 values: 0, 0.05, and 0.15. The value of η is increased when the turbulence becomes stronger; however, η is decreased when the saturation becomes more prominent.

Fig. 2
Fig. 2

Contrast C as a function of Δ for two 〈N12〉 values: 0.05 and 0.15. The value of C is increased when the turbulence becomes stronger; however, C is decreased when the saturation becomes more prominent.

Equations (27)

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2 E + k 0 2 ( 1 + + χ ) E = 0 .
χ ( ν ) = χ ˜ ( ν , ν ) p ( ν ) d ν ,
χ ( ν ) = χ ˜ ( ν , ν ) p ( ν ) d ν .
χ ( ν ) = G N Ψ ( x , y , I / I s ) ,
χ ( ν ) = G N ϕ ( x , y , I / I s ) .
Ψ ( x , y , I / I s ) = 1 π y exp ( ξ 2 ) ( x ξ ) 2 + y 2 ( 1 + I / I s ) d ξ ,
ϕ ( x , y , I / I s ) = 1 π ( x ξ ) exp ( ξ 2 ) ( x ξ ) 2 + y 2 ( 1 + I / I s ) d ξ .
I s = h 2 / ( 16 π 2 μ 2 T 2 τ ) ,
2 E + k 2 E + N χ ˜ ( I / I s ) E = 0 ,
χ ˜ ( I / I s ) = G [ Ψ ( x , y , I / I s ) i ϕ ( x , y , I / I s ) ] .
G = ( ln 2 ) 1 / 2 λ 0 ( ρ 22 ρ 11 ) 0 2 π 1 / 2 n t s Δ ν D ,
χ ˜ ( I / I s ) = χ ˜ 0 + χ ˜ 1 I / I s + χ ˜ 2 ( I / I s ) 2 + ,
E ( r ) = E 0 U ( r ) exp ( γ 0 z ) ,
γ 0 2 = k 2 N χ ˜ 0 ,
δ = ( E 0 2 / I s ) exp [ ( γ 0 + γ 0 * ) L ]
U ( r ) = U 0 ( r ) + δ U 1 ( r ) + δ 2 U 2 ( r ) + .
U U * U 0 U 0 * + 2 δ Re U 0 * U 1 ,
U 2 U * 2 U 0 2 U 0 * 2 + 4 δ Re U 0 U 1 U 0 * 2 ,
U 0 U 0 * = exp [ ζ 2 A ˜ N ( L ) ] ,
U 0 2 U 0 * 2 = exp [ 4 ζ 2 A ˜ N ( L ) ] ,
U 0 * U 1 = χ ˜ 1 N / ( 2 γ 0 ) 0 L d z exp [ 2 α ( z L ) ] × { 1 + ζ [ 2 B ˜ N ( z ) + B ˜ N ( L z ) ] } × exp { ζ 2 [ 2 A ˜ N ( z ) + 2 A ˜ N ( L ) A ˜ N ( L z ) ] } ,
U 0 U 1 U 0 * 2 = χ ˜ 1 N / ( 2 γ 0 ) 0 L d z exp [ 2 α ( z L ) ] × { 1 + ζ [ 3 B ˜ N ( z ) + 2 B ˜ N ( L z ) ] } × exp { ζ 2 [ 3 A ˜ N ( z ) + 6 A ˜ N ( L ) 2 A ˜ N ( L z ) ] } .
A ˜ N ( z ) = 0 z B ˜ N ( z ) d z ,
B ˜ N ( z ) = 0 z B N ( z ) d z ,
B N ( z ) = N 1 2 exp ( z 2 / l 2 ) ,
η = I / [ E 0 2 exp ( 2 α L ) ]
C = [ ( I 2 I 2 ) / I 2 ] 1 / 2 .

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