Abstract

An analytic investigation of the role of multimode pump laser intensity fluctuations in single-pulse coherent anti-Stokes Raman spectroscopy is presented. The results show that, given statistically independent sources with Gaussian statistics for the Stokes, the noise performance of multimode pump lasers, in principle, should be comparable with that of coherent sources. Pulses that are long compared with intermode beat periods and a large number of Stokes modes per detector pixel are required to minimize noise addition. Certain conditions under which multimode pumps could add noise are identified and discussed.

© 1986 Optical Society of America

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References

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  1. D. A. Greenhalgh and S. T. Whittley, Appl. Opt. 24, 907 (1985).
    [Crossref]
  2. A. A. Grutter, H. P. Weber, and R. Dandliker, Phys. Rev. 135, 629 (1969).
    [Crossref]
  3. A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, and P. A. Tellex, Appl. Opt. 23, 1328 (1984).
    [Crossref]
  4. A. C. Eckbreth and J. H. Stufflebeam, Exp. Fluids 3, 301 (1985).
    [Crossref]
  5. D. R. Snelling, R. A. Sawchuk, and R. E. Mueller, Appl. Opt. 24, 2771 (1985).
    [Crossref] [PubMed]
  6. M. Pealat, P. Bouchardy, M. Lefebvre, and J. P. Taran, Appl. Opt. 24, 1012 (1985).
    [Crossref]
  7. A. C. Eckbreth, in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), p. 84.
  8. D. A. Greenhalgh and F. M. Porter, presented at the First International Laser Sciences Conference, Dallas, Texas, November 1985; F. M. Porter, “A study of temperature measurements using CARS,” Ph.D. dissertation (Surrey University, U.K., 1985).
  9. J. Ducuing and N. Bloembergen, Phys. Rev. A 133, 1493 (1964).
  10. R. Dandliker, A. A. Grutter, and H. P. Weber, IEEE J. Quantum Electron. QE-6, 687 (1970).
    [Crossref]
  11. L. A. Rahn, R. L. Farrow, and R. P. Lucht, Opt. Lett. 9, 223 (1984).
    [Crossref] [PubMed]
  12. L. A. Westling, M. G. Raymer, and J. J. Snyder, J. Opt. Soc. Am. B 1, 150 (1984); L. A. Westling, M. G. Raymer, M. G. Sceats, and D. F. Cokes, Opt. Commun. 47, 212 (1983).
    [Crossref]
  13. R. E. Teets, presented at the First International Laser Sciences Conference, Dallas, Texas, 1985.
  14. M. A. Yuratich, Mol. Phys. 38, 625 (1979).
    [Crossref]
  15. R. J. Hall, Opt. Commun. 56, 127 (1985).
    [Crossref]
  16. W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).
  17. W. Brunner and H. Paul, Opt. Quantum Electron. 12, 393 (1980).
    [Crossref]
  18. D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, and T. Parameswaran, in Advanced Instrumentation for Aero Engine Components, AGARD Conf. Proc. (to be published).
  19. S. Kröll and T. Berglind, submitted to Appl. Opt.

1985 (5)

1984 (3)

1980 (1)

W. Brunner and H. Paul, Opt. Quantum Electron. 12, 393 (1980).
[Crossref]

1979 (1)

M. A. Yuratich, Mol. Phys. 38, 625 (1979).
[Crossref]

1970 (1)

R. Dandliker, A. A. Grutter, and H. P. Weber, IEEE J. Quantum Electron. QE-6, 687 (1970).
[Crossref]

1969 (1)

A. A. Grutter, H. P. Weber, and R. Dandliker, Phys. Rev. 135, 629 (1969).
[Crossref]

1964 (1)

J. Ducuing and N. Bloembergen, Phys. Rev. A 133, 1493 (1964).

Berglind, T.

S. Kröll and T. Berglind, submitted to Appl. Opt.

Bloembergen, N.

J. Ducuing and N. Bloembergen, Phys. Rev. A 133, 1493 (1964).

Bouchardy, P.

Brunner, W.

W. Brunner and H. Paul, Opt. Quantum Electron. 12, 393 (1980).
[Crossref]

Dandliker, R.

R. Dandliker, A. A. Grutter, and H. P. Weber, IEEE J. Quantum Electron. QE-6, 687 (1970).
[Crossref]

A. A. Grutter, H. P. Weber, and R. Dandliker, Phys. Rev. 135, 629 (1969).
[Crossref]

Davenport, W. B.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Dobbs, G. M.

Ducuing, J.

J. Ducuing and N. Bloembergen, Phys. Rev. A 133, 1493 (1964).

Eckbreth, A. C.

A. C. Eckbreth and J. H. Stufflebeam, Exp. Fluids 3, 301 (1985).
[Crossref]

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, and P. A. Tellex, Appl. Opt. 23, 1328 (1984).
[Crossref]

A. C. Eckbreth, in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), p. 84.

Farrow, R. L.

Greenhalgh, D. A.

D. A. Greenhalgh and S. T. Whittley, Appl. Opt. 24, 907 (1985).
[Crossref]

D. A. Greenhalgh and F. M. Porter, presented at the First International Laser Sciences Conference, Dallas, Texas, November 1985; F. M. Porter, “A study of temperature measurements using CARS,” Ph.D. dissertation (Surrey University, U.K., 1985).

Grutter, A. A.

R. Dandliker, A. A. Grutter, and H. P. Weber, IEEE J. Quantum Electron. QE-6, 687 (1970).
[Crossref]

A. A. Grutter, H. P. Weber, and R. Dandliker, Phys. Rev. 135, 629 (1969).
[Crossref]

Hall, R. J.

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

Kröll, S.

S. Kröll and T. Berglind, submitted to Appl. Opt.

Lefebvre, M.

Lucht, R. P.

Mueller, R. E.

Parameswaran, T.

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, and T. Parameswaran, in Advanced Instrumentation for Aero Engine Components, AGARD Conf. Proc. (to be published).

Paul, H.

W. Brunner and H. Paul, Opt. Quantum Electron. 12, 393 (1980).
[Crossref]

Pealat, M.

Porter, F. M.

D. A. Greenhalgh and F. M. Porter, presented at the First International Laser Sciences Conference, Dallas, Texas, November 1985; F. M. Porter, “A study of temperature measurements using CARS,” Ph.D. dissertation (Surrey University, U.K., 1985).

Rahn, L. A.

Raymer, M. G.

Root, W. L.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Sawchuk, R. A.

D. R. Snelling, R. A. Sawchuk, and R. E. Mueller, Appl. Opt. 24, 2771 (1985).
[Crossref] [PubMed]

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, and T. Parameswaran, in Advanced Instrumentation for Aero Engine Components, AGARD Conf. Proc. (to be published).

Smallwood, G. J.

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, and T. Parameswaran, in Advanced Instrumentation for Aero Engine Components, AGARD Conf. Proc. (to be published).

Snelling, D. R.

D. R. Snelling, R. A. Sawchuk, and R. E. Mueller, Appl. Opt. 24, 2771 (1985).
[Crossref] [PubMed]

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, and T. Parameswaran, in Advanced Instrumentation for Aero Engine Components, AGARD Conf. Proc. (to be published).

Snyder, J. J.

Stufflebeam, J. H.

Taran, J. P.

Teets, R. E.

R. E. Teets, presented at the First International Laser Sciences Conference, Dallas, Texas, 1985.

Tellex, P. A.

Weber, H. P.

R. Dandliker, A. A. Grutter, and H. P. Weber, IEEE J. Quantum Electron. QE-6, 687 (1970).
[Crossref]

A. A. Grutter, H. P. Weber, and R. Dandliker, Phys. Rev. 135, 629 (1969).
[Crossref]

Westling, L. A.

Whittley, S. T.

Yuratich, M. A.

M. A. Yuratich, Mol. Phys. 38, 625 (1979).
[Crossref]

Appl. Opt. (4)

Exp. Fluids (1)

A. C. Eckbreth and J. H. Stufflebeam, Exp. Fluids 3, 301 (1985).
[Crossref]

IEEE J. Quantum Electron. (1)

R. Dandliker, A. A. Grutter, and H. P. Weber, IEEE J. Quantum Electron. QE-6, 687 (1970).
[Crossref]

J. Opt. Soc. Am. B (1)

Mol. Phys. (1)

M. A. Yuratich, Mol. Phys. 38, 625 (1979).
[Crossref]

Opt. Commun. (1)

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

Opt. Lett. (1)

Opt. Quantum Electron. (1)

W. Brunner and H. Paul, Opt. Quantum Electron. 12, 393 (1980).
[Crossref]

Phys. Rev. (1)

A. A. Grutter, H. P. Weber, and R. Dandliker, Phys. Rev. 135, 629 (1969).
[Crossref]

Phys. Rev. A (1)

J. Ducuing and N. Bloembergen, Phys. Rev. A 133, 1493 (1964).

Other (6)

A. C. Eckbreth, in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), p. 84.

D. A. Greenhalgh and F. M. Porter, presented at the First International Laser Sciences Conference, Dallas, Texas, November 1985; F. M. Porter, “A study of temperature measurements using CARS,” Ph.D. dissertation (Surrey University, U.K., 1985).

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, and T. Parameswaran, in Advanced Instrumentation for Aero Engine Components, AGARD Conf. Proc. (to be published).

S. Kröll and T. Berglind, submitted to Appl. Opt.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

R. E. Teets, presented at the First International Laser Sciences Conference, Dallas, Texas, 1985.

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Equations (19)

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[ N 1 1 N ( i j i j ) 2 ] 1 / 2 ,
1 T t T / 2 t + T / 2 exp ( i Δ ω t ) d t = δ ( Δ ω ) .
I a s ( ω a s ) ~ χ NR 2 d ω S ( ω a s ω a s ) d ω I p ( ω ) × d ω I p ( ω p ) I s ( ω + ω ω a s ) ,
I a s ( ω a s ) ~ χ NR 2 I ˆ p 2 d ω a s S ( ω a s ω a s ) I s ( 2 ω p ( 0 ) ω a s ) χ NR 2 I ˆ p 2 I s ( 2 ω p ( 0 ) ω a s ) ,
E p ( t ) = exp ( i ω p ( 0 ) t ) n a n exp [ i ( n Ω p t + ϕ n ) ] , E s ( t ) = exp ( i ω s ( 0 ) t ) n A n exp [ i ( n Ω s t + θ n ) ] ,
I a s ( t ) χ NR 2 I p 2 ( t ) I s ( t ) .
I a s ( t ) k , l , m , n a k a l a m a n exp [ i ( k l + m n ) Ω p t + i ( ϕ k ϕ l + ϕ m ϕ n ) ] r , s A r A s exp [ i ( r s ) Ω s t + i ( θ r θ s ) ] .
Q n ( P ) ( ϕ n ) = Q n ( S ) ( θ n ) = 1 2 π for all n
P n ( P ) ( a n ) , P n ( S ) ( A n )
P k l m n ( P ) ( a k a l a m a n ) = P k ( P ) ( a k ) P l ( P ) ( a l ) P m ( P ) ( a m ) P n ( P ) ( a n ) , P i j ( S ) ( A i A j ) = P i ( S ) ( A i ) P j ( S ) ( A j ) .
I a s ( t ) a , A , ϕ , θ = d ϕ k Q k ( ϕ k ) d ϕ n Q n ( ϕ n ) × d a k P k ( P ) ( a k ) d a n P n ( P ) ( a n ) × d θ r Q r ( θ r ) d A r P r ( S ) ( A r ) [ Eq . ( 7 ) ] = [ 2 n 0 a n 2 P n ( P ) ( a n ) d a n × m n 0 a m 2 P m ( P ) ( a m ) d a m + n 0 a n 4 P n ( P ) ( a n ) d a n ] × [ r 0 A r 2 P r ( S ) ( A r ) d A r ] = ( 2 n a n 2 m n a m 2 + n a n 4 ) × r A r 2 ,
I a s ( t ) 2 [ n i n ( P ) ] 2 r i r ( S ) ,
I a s ( t ) Δ ω i = 2 I ˆ p 2 r Δ ω i i r ( S ) ,
1 T t T / 2 t + T / 2 I a s ( t ) d t .
1 T t T / 2 t + T / 2 [ expression ( 7 ) ] d t = ( 2 n a n 2 m n a m 2 + n a n 4 ) r A r 2 + δ [ ( k l + m n ) Ω p + ( r s ) Ω s ] a k a l a m a n A r A s × exp [ i ( ϕ k ϕ l + ϕ m ϕ n + θ r θ s ) ] ,
{ δ ( k l + m n ) | a k a l a m a n exp [ i ( ϕ k ϕ l + ϕ m ϕ n ) ] } × r A r 2 , k 1 or n , m n or 1 , k l m n ,
2 [ n i n ( P ) ] 2 r i r ( S ) ,
n a n 2 m a m 2 r A r 2
n a n 2 m a m 2 r A r 2 .

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