Abstract

The pressure dependence of the integrated power of coherent anti-Stokes Raman scattering (CARS) has been investigated experimentally as well as theoretically. The integrated CARS power has been found to be inversely proportional to linewidth, in contrast to the spontaneous Raman scattering for which the integrated power is independent of linewidth. Because of the pressure broadening of the Raman lines and the interference among them, the integrated power deviates from a simple square-law dependence, the degree of deviation being a function of molecular species. Experimental results are presented for CH4, CO, N2, and H2, with collisional narrowing being demonstrated for H2.

© 1978 Optical Society of America

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References

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  1. P. R. Regnier, J. P. E. Taran, Appl. Phys. Lett. 23, 240 (1973).
    [CrossRef]
  2. P. R. Regnier, J. P. E. Taran, in Laser Raman Gas Diagnostics, M. Lapp, C. M. Penney, Eds. (Plenum, New York, 1974).
  3. F. Moya, S. A. J. Druet, J. P. E. Taran, Opt. Commun. 13, 169 (1975).
    [CrossRef]
  4. J. W. Nibler, J. R. McDonald, A. B. Harvey, Opt. Commun. 18, 371 (1976).
    [CrossRef]
  5. W. B. Roh, P. W. Schreiber, J. P. E. Taran, Appl. Phys. Lett. 29, 174 (1976).
    [CrossRef]
  6. P. N. Butcher, Nonlinear Optical Phenomena, Engineering Experiment Station Bulletin 200 (Ohio State U., Columbus, 1965).
  7. F. Moya, S. Druet, M. Pealat, J. P. E. Taran, AIAA Paper 76-29, Presented at 14th AIAA Conference on Aerospace Science, Washington, D.C., 26–28 January 1976.
  8. W. B. Roh, Coherent Anti-Stokes Raman Scattering of Molecular Gases, AFAPL-TR-77-47, Air Force Aero Propulsion Laboratory, Wright-Patterson AFB, Ohio (August1977).
  9. P. Lallemand, P. Simova, J. Mol. Spectrosc. 26, 262 (1968).
    [CrossRef]
  10. R. F. Begley, A. B. Harvey, R. L. Byer, Appl. Phys. Lett. 25, 387 (1974).
    [CrossRef]
  11. R. H. Dicke, Phys. Rev. 89, 472 (1953).
    [CrossRef]
  12. J. R. Murray, A. Javan, J. Mol. Spectrosc. 42, 1 (1972).
    [CrossRef]
  13. M. A. Henesian, L. Kulevskii, R. L. Byer, R. L. Herbst, Opt. Commun. 18, 225 (1976).
    [CrossRef]

1976 (3)

J. W. Nibler, J. R. McDonald, A. B. Harvey, Opt. Commun. 18, 371 (1976).
[CrossRef]

W. B. Roh, P. W. Schreiber, J. P. E. Taran, Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

M. A. Henesian, L. Kulevskii, R. L. Byer, R. L. Herbst, Opt. Commun. 18, 225 (1976).
[CrossRef]

1975 (1)

F. Moya, S. A. J. Druet, J. P. E. Taran, Opt. Commun. 13, 169 (1975).
[CrossRef]

1974 (1)

R. F. Begley, A. B. Harvey, R. L. Byer, Appl. Phys. Lett. 25, 387 (1974).
[CrossRef]

1973 (1)

P. R. Regnier, J. P. E. Taran, Appl. Phys. Lett. 23, 240 (1973).
[CrossRef]

1972 (1)

J. R. Murray, A. Javan, J. Mol. Spectrosc. 42, 1 (1972).
[CrossRef]

1968 (1)

P. Lallemand, P. Simova, J. Mol. Spectrosc. 26, 262 (1968).
[CrossRef]

1953 (1)

R. H. Dicke, Phys. Rev. 89, 472 (1953).
[CrossRef]

Begley, R. F.

R. F. Begley, A. B. Harvey, R. L. Byer, Appl. Phys. Lett. 25, 387 (1974).
[CrossRef]

Butcher, P. N.

P. N. Butcher, Nonlinear Optical Phenomena, Engineering Experiment Station Bulletin 200 (Ohio State U., Columbus, 1965).

Byer, R. L.

M. A. Henesian, L. Kulevskii, R. L. Byer, R. L. Herbst, Opt. Commun. 18, 225 (1976).
[CrossRef]

R. F. Begley, A. B. Harvey, R. L. Byer, Appl. Phys. Lett. 25, 387 (1974).
[CrossRef]

Dicke, R. H.

R. H. Dicke, Phys. Rev. 89, 472 (1953).
[CrossRef]

Druet, S.

F. Moya, S. Druet, M. Pealat, J. P. E. Taran, AIAA Paper 76-29, Presented at 14th AIAA Conference on Aerospace Science, Washington, D.C., 26–28 January 1976.

Druet, S. A. J.

F. Moya, S. A. J. Druet, J. P. E. Taran, Opt. Commun. 13, 169 (1975).
[CrossRef]

Harvey, A. B.

J. W. Nibler, J. R. McDonald, A. B. Harvey, Opt. Commun. 18, 371 (1976).
[CrossRef]

R. F. Begley, A. B. Harvey, R. L. Byer, Appl. Phys. Lett. 25, 387 (1974).
[CrossRef]

Henesian, M. A.

M. A. Henesian, L. Kulevskii, R. L. Byer, R. L. Herbst, Opt. Commun. 18, 225 (1976).
[CrossRef]

Herbst, R. L.

M. A. Henesian, L. Kulevskii, R. L. Byer, R. L. Herbst, Opt. Commun. 18, 225 (1976).
[CrossRef]

Javan, A.

J. R. Murray, A. Javan, J. Mol. Spectrosc. 42, 1 (1972).
[CrossRef]

Kulevskii, L.

M. A. Henesian, L. Kulevskii, R. L. Byer, R. L. Herbst, Opt. Commun. 18, 225 (1976).
[CrossRef]

Lallemand, P.

P. Lallemand, P. Simova, J. Mol. Spectrosc. 26, 262 (1968).
[CrossRef]

McDonald, J. R.

J. W. Nibler, J. R. McDonald, A. B. Harvey, Opt. Commun. 18, 371 (1976).
[CrossRef]

Moya, F.

F. Moya, S. A. J. Druet, J. P. E. Taran, Opt. Commun. 13, 169 (1975).
[CrossRef]

F. Moya, S. Druet, M. Pealat, J. P. E. Taran, AIAA Paper 76-29, Presented at 14th AIAA Conference on Aerospace Science, Washington, D.C., 26–28 January 1976.

Murray, J. R.

J. R. Murray, A. Javan, J. Mol. Spectrosc. 42, 1 (1972).
[CrossRef]

Nibler, J. W.

J. W. Nibler, J. R. McDonald, A. B. Harvey, Opt. Commun. 18, 371 (1976).
[CrossRef]

Pealat, M.

F. Moya, S. Druet, M. Pealat, J. P. E. Taran, AIAA Paper 76-29, Presented at 14th AIAA Conference on Aerospace Science, Washington, D.C., 26–28 January 1976.

Regnier, P. R.

P. R. Regnier, J. P. E. Taran, Appl. Phys. Lett. 23, 240 (1973).
[CrossRef]

P. R. Regnier, J. P. E. Taran, in Laser Raman Gas Diagnostics, M. Lapp, C. M. Penney, Eds. (Plenum, New York, 1974).

Roh, W. B.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

W. B. Roh, Coherent Anti-Stokes Raman Scattering of Molecular Gases, AFAPL-TR-77-47, Air Force Aero Propulsion Laboratory, Wright-Patterson AFB, Ohio (August1977).

Schreiber, P. W.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

Simova, P.

P. Lallemand, P. Simova, J. Mol. Spectrosc. 26, 262 (1968).
[CrossRef]

Taran, J. P. E.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

F. Moya, S. A. J. Druet, J. P. E. Taran, Opt. Commun. 13, 169 (1975).
[CrossRef]

P. R. Regnier, J. P. E. Taran, Appl. Phys. Lett. 23, 240 (1973).
[CrossRef]

P. R. Regnier, J. P. E. Taran, in Laser Raman Gas Diagnostics, M. Lapp, C. M. Penney, Eds. (Plenum, New York, 1974).

F. Moya, S. Druet, M. Pealat, J. P. E. Taran, AIAA Paper 76-29, Presented at 14th AIAA Conference on Aerospace Science, Washington, D.C., 26–28 January 1976.

Appl. Phys. Lett. (3)

P. R. Regnier, J. P. E. Taran, Appl. Phys. Lett. 23, 240 (1973).
[CrossRef]

W. B. Roh, P. W. Schreiber, J. P. E. Taran, Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

R. F. Begley, A. B. Harvey, R. L. Byer, Appl. Phys. Lett. 25, 387 (1974).
[CrossRef]

J. Mol. Spectrosc. (2)

J. R. Murray, A. Javan, J. Mol. Spectrosc. 42, 1 (1972).
[CrossRef]

P. Lallemand, P. Simova, J. Mol. Spectrosc. 26, 262 (1968).
[CrossRef]

Opt. Commun. (3)

M. A. Henesian, L. Kulevskii, R. L. Byer, R. L. Herbst, Opt. Commun. 18, 225 (1976).
[CrossRef]

F. Moya, S. A. J. Druet, J. P. E. Taran, Opt. Commun. 13, 169 (1975).
[CrossRef]

J. W. Nibler, J. R. McDonald, A. B. Harvey, Opt. Commun. 18, 371 (1976).
[CrossRef]

Phys. Rev. (1)

R. H. Dicke, Phys. Rev. 89, 472 (1953).
[CrossRef]

Other (4)

P. R. Regnier, J. P. E. Taran, in Laser Raman Gas Diagnostics, M. Lapp, C. M. Penney, Eds. (Plenum, New York, 1974).

P. N. Butcher, Nonlinear Optical Phenomena, Engineering Experiment Station Bulletin 200 (Ohio State U., Columbus, 1965).

F. Moya, S. Druet, M. Pealat, J. P. E. Taran, AIAA Paper 76-29, Presented at 14th AIAA Conference on Aerospace Science, Washington, D.C., 26–28 January 1976.

W. B. Roh, Coherent Anti-Stokes Raman Scattering of Molecular Gases, AFAPL-TR-77-47, Air Force Aero Propulsion Laboratory, Wright-Patterson AFB, Ohio (August1977).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental system. The components are as follows: mirrors M1–M4; achromatic lenses L1–L3; simple lenses L4–L7; filters F1–F4; dichroic mirrors DM1–DM3; beam splitter BS1; prism P1; Q-switch Q1; output etalon E1; monochromators MC1– MC2; and photomultipliers PM1–PM2.

Fig. 2
Fig. 2

Partial pressure dependence of integrated anti-Stokes power of methane gas: upper line for pure methane; lower line for a mixture with nitrogen under a fixed total pressure.

Fig. 3
Fig. 3

Partial pressure dependence of integrated anti-Stokes power of carbon-monoxide gas.

Fig. 4
Fig. 4

Pressure dependence of integrated anti-Stokes power of Q(1) line of hydrogen molecule. (Error bars represent ±1 standard deviation in the data.)

Fig. 5
Fig. 5

Integrated anti-Stokes power of Q(1) line of the hydrogen molecule as a function of total gas pressure. (Pressure was varied by adding helium gas while maintaining the hydrogen partial pressure constant at 20 Torr.)

Equations (22)

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P ( 3 ) ( ω ) = χ ( 3 ) ( ω , ω , ω ω ω ) × E ( ω ) E ( ω ) E ( ω ω ω ) d ω d ω ,
E ( ω ) = E p ( ω ) + E s ( ω )
P a ( 3 ) ( ω ) = E p ( ω ) d ω 3 χ ( 3 ) ( ω , ω , ω ω ω ) × E p ( ω ) E s * ( ω + ω ω ) d ω ,
P a ( 3 ) ( ω ) = 3 χ ( 3 ) ( ω p , ω p , ω 2 ω p ) | E p o | 2 E s * ( 2 ω p ω ) ,
P a ( 3 ) ( ω a + δ ) = 3 χ ( 3 ) ( ω p , ω p , ω s + δ ) | E p o | 2 E s * ( ω s δ ) ,
P a ( ω a + δ ) = ( 4 π ω p ω a n a 2 c ) 2 | 3 χ ( 3 ) ( ω p , ω p , ω s + δ ) | 2 P p 2 P s ( ω s + δ ) ,
P INT = ( 4 π ω p ω a n a 2 c ) 2 0 | 3 χ ( 3 ) ( ω ) | 2 P p 2 P s ( ω ω p ) d ω ,
P INT = ( 12 π ω p ω a n a 2 c ) 2 P p 2 P s 0 | χ ( 3 ) ( ω ) | 2 d ω .
χ ( 3 ) = χ R R + χ O R + χ E ,
χ R R = J χ J R R = J K J 1 ω J ω i Γ
χ O R = K χ K O R = K K K 1 ω K ω i Γ ,
K J = N Δ J c 4 3 ω s 4 ( d σ d Ω ) o ,
0 | χ ( 3 ) | 2 d ω = 0 { J | χ J R R | 2 + 2 Re [ J J ( χ J R R ) * χ J R R + J K ( χ J R R ) * χ K O R + J χ J R R χ E ] + | K χ K O R + χ E | 2 } d ω .
0 | χ ( 3 ) | 2 d ω = J [ K J 2 π Γ + J J K J K J 8 π Γ ( ω J ω J ) 2 + 4 Γ 2 + K K J K K 8 π Γ ( ω J ω K ) 2 ] + K .
P INT = K 1 { p r 2 [ F ( T ) Γ + J J Γ G J J ( T ) ( ω J ω J ) 2 + 4 Γ 2 ] + p r p o r [ J K Γ H J K ( T ) ( ω J ω K ) 2 ] + K 2 } ,
P INT = K 1 p r 2 F ( T ) Γ eff ,
Γ eff = Γ 1 + 1 F ( T ) J J Γ G J J ( T ) ( ω J ω J ) 2 + 4 Γ 2 .
P INT = K 1 F ( T ) p t 2 Γ eff ( p t ) ,
log P INT = a 1 log p t + log a o ,
Γ eff ( p t ) = K 2 p t 2 a 1 K 2 p t η ,
P INT = a o ( T ) p t η ( T ) p r 2 .
P INT = K 1 { p r 2 F ( T ) Γ eff + p r p o r [ J K Γ H J K ( T ) ( ω J ω K ) 2 ] + K 2 } .

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