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, S. T. Whittley, Appl. Opt. 24, 907 (1985).
    [CrossRef]
  2. A. A. Grutter, H. P. Weber, R. Dandliker, Phys. Rev. 135, 629 (1969).
    [CrossRef]
  3. A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, Appl. Opt. 23, 1328 (1984).
    [CrossRef]
  4. A. C. Eckbreth, J. H. Stufflebeam, Exp. Fluids 3, 301 (1985).
    [CrossRef]
  5. D. R. Snelling, R. A. Sawchuk, R. E. Mueller, Appl. Opt. 24, 2771 (1985).
    [CrossRef] [PubMed]
  6. M. Pealat, P. Bouchardy, M. Lefebvre, 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, 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, N. Bloembergen, Phys. Rev. A 133, 1493 (1964).
  10. R. Dandliker, A. A. Grutter, H. P. Weber, IEEE J. Quantum Electron. QE-6, 687 (1970).
    [CrossRef]
  11. L. A. Rahn, R. L. Farrow, R. P. Lucht, Opt. Lett. 9, 223 (1984).
    [CrossRef] [PubMed]
  12. L. A. Westling, M. G. Raymer, J. J. Snyder, J. Opt. Soc. Am. B 1, 150 (1984); L. A. Westling, M. G. Raymer, M. G. Sceats, 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, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).
  17. W. Brunner, H. Paul, Opt. Quantum Electron. 12, 393 (1980).
    [CrossRef]
  18. D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, in Advanced Instrumentation for Aero Engine Components, AGARD Conf. Proc. (to be published).
  19. S. Kröll, T. Berglind, submitted to Appl. Opt.

1985

1984

1980

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

1979

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

1970

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

1969

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

1964

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

Berglind, T.

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

Bloembergen, N.

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

Bouchardy, P.

Brunner, W.

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

Dandliker, R.

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

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

Davenport, W. B.

W. B. Davenport, 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, N. Bloembergen, Phys. Rev. A 133, 1493 (1964).

Eckbreth, A. C.

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

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, 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, S. T. Whittley, Appl. Opt. 24, 907 (1985).
[CrossRef]

D. A. Greenhalgh, 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, H. P. Weber, IEEE J. Quantum Electron. QE-6, 687 (1970).
[CrossRef]

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

Hall, R. J.

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

Kröll, S.

S. Kröll, 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, T. Parameswaran, in Advanced Instrumentation for Aero Engine Components, AGARD Conf. Proc. (to be published).

Paul, H.

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

Pealat, M.

Porter, F. M.

D. A. Greenhalgh, 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, 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, R. E. Mueller, Appl. Opt. 24, 2771 (1985).
[CrossRef] [PubMed]

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

Snelling, D. R.

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

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, 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, H. P. Weber, IEEE J. Quantum Electron. QE-6, 687 (1970).
[CrossRef]

A. A. Grutter, H. P. Weber, 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.

Exp. Fluids

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

IEEE J. Quantum Electron.

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

J. Opt. Soc. Am. B

Mol. Phys.

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

Opt. Commun.

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

Opt. Lett.

Opt. Quantum Electron.

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

Phys. Rev.

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

Phys. Rev. A

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

Other

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

D. A. Greenhalgh, 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).

W. B. Davenport, 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.

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

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

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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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