Abstract

Propagation of short, transient pulses undergoing stimulated Raman scattering over long length scales is considered. It is shown that under common experimental circumstances the evolution has two different regimes: an I regime, at short lengths, where the pump changes little and the Stokes rapidly grows, and a J regime, at long lengths, where the Stokes intensity is close to saturation and the pump intensity decreases slowly as the square root of distance. The distance at which the J regime is reached is determined numerically.

© 1989 Optical Society of America

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  1. R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, Phys. Rev. A 2, 60 (1970).
    [CrossRef]
  2. N. Tan-no, T. Shirahata, K. Yokoto, H. Inaba, Phys. Rev. A 12, 159 (1975).
    [CrossRef]
  3. G. I. Kachen, W. H. Lowdermilk, Phys. Rev. A 14, 1472 (1976).
    [CrossRef]
  4. J. N. Elgin, T. B. O’Hare, J. Phys. B 12, 159 (1979).
    [CrossRef]
  5. M. G. Raymer, J. Mostowski, J. L. Carlsten, Phys. Rev. A 19, 2304 (1979).
    [CrossRef]
  6. M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
    [CrossRef]
  7. F. Y. F. Chu, A. C. Scott, Phys. Rev. A 12, 2060 (1975).
    [CrossRef]
  8. K. Drühl, R. G. Wenzel, J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983).
    [CrossRef]
  9. D. J. Kaup, Physica 6D, 143 (1983).
  10. H. Steudel, Physica 6D, 155 (1983).
  11. M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, J. Opt. Soc. Am. B 5, 37 (1988).
    [CrossRef]
  12. M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Proc. Soc. Photo-Opt. Instrum. Eng. 784, 200 (1988).
  13. See, e.g., P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 434–443.
  14. C. S. Wang, Phys. Rev. 182, 482 (1969).
    [CrossRef]

1988

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, J. Opt. Soc. Am. B 5, 37 (1988).
[CrossRef]

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Proc. Soc. Photo-Opt. Instrum. Eng. 784, 200 (1988).

1983

K. Drühl, R. G. Wenzel, J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983).
[CrossRef]

D. J. Kaup, Physica 6D, 143 (1983).

H. Steudel, Physica 6D, 155 (1983).

1981

M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
[CrossRef]

1979

J. N. Elgin, T. B. O’Hare, J. Phys. B 12, 159 (1979).
[CrossRef]

M. G. Raymer, J. Mostowski, J. L. Carlsten, Phys. Rev. A 19, 2304 (1979).
[CrossRef]

1976

G. I. Kachen, W. H. Lowdermilk, Phys. Rev. A 14, 1472 (1976).
[CrossRef]

1975

N. Tan-no, T. Shirahata, K. Yokoto, H. Inaba, Phys. Rev. A 12, 159 (1975).
[CrossRef]

F. Y. F. Chu, A. C. Scott, Phys. Rev. A 12, 2060 (1975).
[CrossRef]

1970

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, Phys. Rev. A 2, 60 (1970).
[CrossRef]

1969

C. S. Wang, Phys. Rev. 182, 482 (1969).
[CrossRef]

Bloembergen, N.

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, Phys. Rev. A 2, 60 (1970).
[CrossRef]

Carlsten, J. L.

K. Drühl, R. G. Wenzel, J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983).
[CrossRef]

M. G. Raymer, J. Mostowski, J. L. Carlsten, Phys. Rev. A 19, 2304 (1979).
[CrossRef]

Carman, R. L.

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, Phys. Rev. A 2, 60 (1970).
[CrossRef]

Chu, F. Y. F.

F. Y. F. Chu, A. C. Scott, Phys. Rev. A 12, 2060 (1975).
[CrossRef]

Drühl, K.

K. Drühl, R. G. Wenzel, J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983).
[CrossRef]

Duncan, M. D.

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, J. Opt. Soc. Am. B 5, 37 (1988).
[CrossRef]

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Proc. Soc. Photo-Opt. Instrum. Eng. 784, 200 (1988).

Elgin, J. N.

J. N. Elgin, T. B. O’Hare, J. Phys. B 12, 159 (1979).
[CrossRef]

Feshbach, H.

See, e.g., P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 434–443.

Inaba, H.

N. Tan-no, T. Shirahata, K. Yokoto, H. Inaba, Phys. Rev. A 12, 159 (1975).
[CrossRef]

Kachen, G. I.

G. I. Kachen, W. H. Lowdermilk, Phys. Rev. A 14, 1472 (1976).
[CrossRef]

Kaup, D. J.

D. J. Kaup, Physica 6D, 143 (1983).

Lowdermilk, W. H.

G. I. Kachen, W. H. Lowdermilk, Phys. Rev. A 14, 1472 (1976).
[CrossRef]

Mahon, R.

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Proc. Soc. Photo-Opt. Instrum. Eng. 784, 200 (1988).

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, J. Opt. Soc. Am. B 5, 37 (1988).
[CrossRef]

Morse, P. M.

See, e.g., P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 434–443.

Mostowski, J.

M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
[CrossRef]

M. G. Raymer, J. Mostowski, J. L. Carlsten, Phys. Rev. A 19, 2304 (1979).
[CrossRef]

O’Hare, T. B.

J. N. Elgin, T. B. O’Hare, J. Phys. B 12, 159 (1979).
[CrossRef]

Raymer, M. G.

M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
[CrossRef]

M. G. Raymer, J. Mostowski, J. L. Carlsten, Phys. Rev. A 19, 2304 (1979).
[CrossRef]

Reintjes, J.

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, J. Opt. Soc. Am. B 5, 37 (1988).
[CrossRef]

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Proc. Soc. Photo-Opt. Instrum. Eng. 784, 200 (1988).

Scott, A. C.

F. Y. F. Chu, A. C. Scott, Phys. Rev. A 12, 2060 (1975).
[CrossRef]

Shimizu, F.

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, Phys. Rev. A 2, 60 (1970).
[CrossRef]

Shirahata, T.

N. Tan-no, T. Shirahata, K. Yokoto, H. Inaba, Phys. Rev. A 12, 159 (1975).
[CrossRef]

Steudel, H.

H. Steudel, Physica 6D, 155 (1983).

Tankersley, L. L.

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, J. Opt. Soc. Am. B 5, 37 (1988).
[CrossRef]

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Proc. Soc. Photo-Opt. Instrum. Eng. 784, 200 (1988).

Tan-no, N.

N. Tan-no, T. Shirahata, K. Yokoto, H. Inaba, Phys. Rev. A 12, 159 (1975).
[CrossRef]

Wang, C. S.

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, Phys. Rev. A 2, 60 (1970).
[CrossRef]

C. S. Wang, Phys. Rev. 182, 482 (1969).
[CrossRef]

Wenzel, R. G.

K. Drühl, R. G. Wenzel, J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983).
[CrossRef]

Yokoto, K.

N. Tan-no, T. Shirahata, K. Yokoto, H. Inaba, Phys. Rev. A 12, 159 (1975).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

J. N. Elgin, T. B. O’Hare, J. Phys. B 12, 159 (1979).
[CrossRef]

Phys. Rev.

C. S. Wang, Phys. Rev. 182, 482 (1969).
[CrossRef]

Phys. Rev. A

M. G. Raymer, J. Mostowski, J. L. Carlsten, Phys. Rev. A 19, 2304 (1979).
[CrossRef]

M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
[CrossRef]

F. Y. F. Chu, A. C. Scott, Phys. Rev. A 12, 2060 (1975).
[CrossRef]

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, Phys. Rev. A 2, 60 (1970).
[CrossRef]

N. Tan-no, T. Shirahata, K. Yokoto, H. Inaba, Phys. Rev. A 12, 159 (1975).
[CrossRef]

G. I. Kachen, W. H. Lowdermilk, Phys. Rev. A 14, 1472 (1976).
[CrossRef]

Phys. Rev. Lett.

K. Drühl, R. G. Wenzel, J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983).
[CrossRef]

Physica

D. J. Kaup, Physica 6D, 143 (1983).

H. Steudel, Physica 6D, 155 (1983).

Proc. Soc. Photo-Opt. Instrum. Eng.

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Proc. Soc. Photo-Opt. Instrum. Eng. 784, 200 (1988).

Other

See, e.g., P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 434–443.

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Figures (2)

Fig. 1
Fig. 1

Plots of R versus ζ for different pulse shapes, (a) Sech-squared amplitude, FWHM = 40 psec; (b) Lorentzian-squared amplitude, FWHM = 39 psec; (c) square pulse, FWHM = 43.8 psec.

Fig. 2
Fig. 2

Plots of N versus ζ; N is plotted on a parabolic axis. The shapes and parameters are the same as in Fig. 1.

Equations (13)

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E L z = i k L k S κ 2 Q E S , E S z = i κ 2 Q * E L , Q t + Γ Q = i κ 1 E S * E L ,
K ( t ) | E L ( z , t ) | 2 + k L k S | E S ( z , t ) | 2
E S ( z , t ) = E S ( 0 , t ) + ( κ 1 κ 2 z ) 1 / 2 E L ( t ) t exp [ Γ ( t t ) ] × E L * ( t ) E S ( 0 , t ) [ τ ( t ) τ ( t ) ] 1 / 2 × I 1 ( 2 { κ 1 κ 2 z [ τ ( t ) τ ( t ) ] } 1 / 2 ) d t ,
Q ( z , t ) = i κ 1 t exp [ Γ ( t t ) ] E L ( t ) E S * ( 0 , t ) × I 0 ( 2 { κ 1 κ 2 z [ τ ( t ) τ ( t ) ] } 1 / 2 ) d t ,
τ ( t ) = t K ( t ) d t .
s 4 κ 1 κ 2 z [ τ ( t ) τ ( t ) ] , s 4 κ 1 κ 2 z τ ( t ) ,
I 1 ( s 1 / 2 ) exp [ s 1 / 2 1 2 ln ( 2 π s 1 / 2 ) ] .
E L ( t ) = A L exp ( Γ w t ) exp [ i ϕ L ( t ) ] ,
t 0 = 1 2 Γ w ln [ 2 ( Γ w + Γ ) τ ( t ) / A L 2 s 1 / 2 3 / 2 ] .
E S ( z , t ) = 2 κ 1 κ 2 z [ π Γ w 2 ( 1 + Γ / Γ w ) ] 1 / 2 × E L ( t ) E S ( 0 , t 0 ) E L * ( t 0 ) × exp [ Γ ( t t 0 ) ] exp ( s 1 / 2 ) / ( 2 π s 3 / 2 ) 1 / 2 ,
E L ( z , t ) = E L ( z 0 , t ) [ κ 1 κ 2 ( z z 0 ) ] 1 / 2 × k L k S E S ( t ) t exp [ Γ ( t t ) ] × E S * ( t ) E L ( z 0 , t ) [ τ ( t ) τ ( t ) ] 1 / 2 × J 1 ( 2 { κ 1 κ 2 ( z z 0 ) [ τ ( t ) τ ( t ) ] } 1 / 2 ) d t ,
Q ( z , t ) = i κ 1 t exp [ Γ ( t t ) ] × E S * ( t ) E L ( z 0 , t ) × J 0 ( 2 { κ 1 κ 2 ( z z 0 ) [ τ ( t ) τ ( t ) ] } 1 / 2 ) d t ,
J n ( x ) = ( 2 π x ) 1 / 2 cos ( x 1 2 n π 1 4 π ) ,

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