Abstract

The quantum theory of forward Stokes generation by means of stimulated Raman scattering is extended to the case of a colored (finite-bandwidth) chaotic pump, which has both amplitude and phase fluctuations. In both transient and steady-state limits the mean Stokes intensity is found to be enhanced over that resulting from a coherent pump. In the limit that the chaotic-pump bandwidth becomes large, the mean Stokes intensity becomes identical with that resulting from a coherent pump of the same total power.

© 1984 Optical Society of America

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  1. R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, Phys. Rev. A 2, 60 (1970).
    [CrossRef]
  2. S. A. Akhamnov, Yu. E. Dyakov, and L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).
  3. G. P. Dzhotyan, Yu. E. Dyakov, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, Sov. Phys. JETP 46, 431 (1977).
  4. M. G. Raymer, J. Mostowski, and J. L. Carlsten, Phys. Rev. A 19, 2304 (1979).
    [CrossRef]
  5. W. R. Trutna, Y. K. Park, and R. L. Byer, IEEE J. Quantum Electron. QE-15, 648 (1979).
    [CrossRef]
  6. J. EgglestonandR and L. Byer, IEEE J. Quantum Electron. QE-16, 850 (1980).
    [CrossRef]
  7. G. S. Agarwal, Opt. Commun. 35, 267 (1980).
    [CrossRef]
  8. A. T. Georges, Opt. Commun. 41, 61 (1982).
    [CrossRef]
  9. M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); J. Mostowski and M. G. Raymer, Opt. Commun. 36, 237 (1981).
    [CrossRef]
  10. T. von Foerster and R. J. Glauber, Phys. Rev. A 3, 1484 (1971).
    [CrossRef]
  11. R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).
  12. P. Zoller and P. Lambropoulos, J. Phys. B 13, 69 (1980).
    [CrossRef]
  13. V. I. Krylov and N. S. Skoblya, Handbook of Numerical Inversion of Laplace Transforms (Israel Program for Scientific Translations, Jerusalem, 1969).
  14. I. S. Gradshteyn and I. M. Ryzik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965), Eqs. (6.615), (6.621-4), (8.486), and (6.681.3).
  15. C. Lecompte, G. Mainfray, C. Manus, and F. Sanchez, Phys. Rev. A 11, 1009 (1975).
    [CrossRef]
  16. A related result was found for stimulated thermal scattering with a broadband pump laser. See V. Bespalov, A. Kubarev, and G. Pasmanik, Phys. Rev. Lett. 24, 1274 (1970); A. O. Creaser and R. M. Herman, Phys. Rev. Lett. 29, 147 (1972).
    [CrossRef]
  17. R. Wyatt and D. Cotter, Appl. Phys. 21, 199 (1980).
    [CrossRef]
  18. M. Abramowitz and I. Stegun, eds., Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1964), Eqs. (9.6.16) and (11.3.12).

1982 (1)

A. T. Georges, Opt. Commun. 41, 61 (1982).
[CrossRef]

1981 (1)

M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); J. Mostowski and M. G. Raymer, Opt. Commun. 36, 237 (1981).
[CrossRef]

1980 (4)

J. EgglestonandR and L. Byer, IEEE J. Quantum Electron. QE-16, 850 (1980).
[CrossRef]

G. S. Agarwal, Opt. Commun. 35, 267 (1980).
[CrossRef]

P. Zoller and P. Lambropoulos, J. Phys. B 13, 69 (1980).
[CrossRef]

R. Wyatt and D. Cotter, Appl. Phys. 21, 199 (1980).
[CrossRef]

1979 (2)

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

W. R. Trutna, Y. K. Park, and R. L. Byer, IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

1977 (1)

G. P. Dzhotyan, Yu. E. Dyakov, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, Sov. Phys. JETP 46, 431 (1977).

1975 (1)

C. Lecompte, G. Mainfray, C. Manus, and F. Sanchez, Phys. Rev. A 11, 1009 (1975).
[CrossRef]

1974 (1)

S. A. Akhamnov, Yu. E. Dyakov, and L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

1971 (1)

T. von Foerster and R. J. Glauber, Phys. Rev. A 3, 1484 (1971).
[CrossRef]

1970 (2)

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

A related result was found for stimulated thermal scattering with a broadband pump laser. See V. Bespalov, A. Kubarev, and G. Pasmanik, Phys. Rev. Lett. 24, 1274 (1970); A. O. Creaser and R. M. Herman, Phys. Rev. Lett. 29, 147 (1972).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, Opt. Commun. 35, 267 (1980).
[CrossRef]

Akhamnov, S. A.

S. A. Akhamnov, Yu. E. Dyakov, and L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

Bespalov, V.

A related result was found for stimulated thermal scattering with a broadband pump laser. See V. Bespalov, A. Kubarev, and G. Pasmanik, Phys. Rev. Lett. 24, 1274 (1970); A. O. Creaser and R. M. Herman, Phys. Rev. Lett. 29, 147 (1972).
[CrossRef]

Bloembergen, N.

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

Byer, L.

J. EgglestonandR and L. Byer, IEEE J. Quantum Electron. QE-16, 850 (1980).
[CrossRef]

Byer, R. L.

W. R. Trutna, Y. K. Park, and R. L. Byer, IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

Carlsten, J. L.

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

Carman, R. L.

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

Cotter, D.

R. Wyatt and D. Cotter, Appl. Phys. 21, 199 (1980).
[CrossRef]

Dyakov, Yu. E.

G. P. Dzhotyan, Yu. E. Dyakov, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, Sov. Phys. JETP 46, 431 (1977).

S. A. Akhamnov, Yu. E. Dyakov, and L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

Dzhotyan, G. P.

G. P. Dzhotyan, Yu. E. Dyakov, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, Sov. Phys. JETP 46, 431 (1977).

EgglestonandR, J.

J. EgglestonandR and L. Byer, IEEE J. Quantum Electron. QE-16, 850 (1980).
[CrossRef]

Georges, A. T.

A. T. Georges, Opt. Commun. 41, 61 (1982).
[CrossRef]

Glauber, R. J.

T. von Foerster and R. J. Glauber, Phys. Rev. A 3, 1484 (1971).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965), Eqs. (6.615), (6.621-4), (8.486), and (6.681.3).

Krylov, V. I.

V. I. Krylov and N. S. Skoblya, Handbook of Numerical Inversion of Laplace Transforms (Israel Program for Scientific Translations, Jerusalem, 1969).

Kubarev, A.

A related result was found for stimulated thermal scattering with a broadband pump laser. See V. Bespalov, A. Kubarev, and G. Pasmanik, Phys. Rev. Lett. 24, 1274 (1970); A. O. Creaser and R. M. Herman, Phys. Rev. Lett. 29, 147 (1972).
[CrossRef]

Lambropoulos, P.

P. Zoller and P. Lambropoulos, J. Phys. B 13, 69 (1980).
[CrossRef]

Lecompte, C.

C. Lecompte, G. Mainfray, C. Manus, and F. Sanchez, Phys. Rev. A 11, 1009 (1975).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).

Mainfray, G.

C. Lecompte, G. Mainfray, C. Manus, and F. Sanchez, Phys. Rev. A 11, 1009 (1975).
[CrossRef]

Manus, C.

C. Lecompte, G. Mainfray, C. Manus, and F. Sanchez, Phys. Rev. A 11, 1009 (1975).
[CrossRef]

Mikhailov, S. I.

G. P. Dzhotyan, Yu. E. Dyakov, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, Sov. Phys. JETP 46, 431 (1977).

Mironov, A. B.

G. P. Dzhotyan, Yu. E. Dyakov, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, Sov. Phys. JETP 46, 431 (1977).

Mostowski, J.

M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); J. Mostowski and M. G. Raymer, Opt. Commun. 36, 237 (1981).
[CrossRef]

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

Park, Y. K.

W. R. Trutna, Y. K. Park, and R. L. Byer, IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

Pasmanik, G.

A related result was found for stimulated thermal scattering with a broadband pump laser. See V. Bespalov, A. Kubarev, and G. Pasmanik, Phys. Rev. Lett. 24, 1274 (1970); A. O. Creaser and R. M. Herman, Phys. Rev. Lett. 29, 147 (1972).
[CrossRef]

Pavlov, L. I.

S. A. Akhamnov, Yu. E. Dyakov, and L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

Raymer, M. G.

M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); J. Mostowski and M. G. Raymer, Opt. Commun. 36, 237 (1981).
[CrossRef]

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

Ryzik, I. M.

I. S. Gradshteyn and I. M. Ryzik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965), Eqs. (6.615), (6.621-4), (8.486), and (6.681.3).

Sanchez, F.

C. Lecompte, G. Mainfray, C. Manus, and F. Sanchez, Phys. Rev. A 11, 1009 (1975).
[CrossRef]

Shimizu, F.

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

Skoblya, N. S.

V. I. Krylov and N. S. Skoblya, Handbook of Numerical Inversion of Laplace Transforms (Israel Program for Scientific Translations, Jerusalem, 1969).

Trutna, W. R.

W. R. Trutna, Y. K. Park, and R. L. Byer, IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

von Foerster, T.

T. von Foerster and R. J. Glauber, Phys. Rev. A 3, 1484 (1971).
[CrossRef]

Wang, C. S.

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

Wyatt, R.

R. Wyatt and D. Cotter, Appl. Phys. 21, 199 (1980).
[CrossRef]

Zoller, P.

P. Zoller and P. Lambropoulos, J. Phys. B 13, 69 (1980).
[CrossRef]

Zubarev, I. G.

G. P. Dzhotyan, Yu. E. Dyakov, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, Sov. Phys. JETP 46, 431 (1977).

Appl. Phys. (1)

R. Wyatt and D. Cotter, Appl. Phys. 21, 199 (1980).
[CrossRef]

IEEE J. Quantum Electron. (2)

W. R. Trutna, Y. K. Park, and R. L. Byer, IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

J. EgglestonandR and L. Byer, IEEE J. Quantum Electron. QE-16, 850 (1980).
[CrossRef]

J. Phys. B (1)

P. Zoller and P. Lambropoulos, J. Phys. B 13, 69 (1980).
[CrossRef]

Opt. Commun. (2)

G. S. Agarwal, Opt. Commun. 35, 267 (1980).
[CrossRef]

A. T. Georges, Opt. Commun. 41, 61 (1982).
[CrossRef]

Phys. Rev. A (5)

M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); J. Mostowski and M. G. Raymer, Opt. Commun. 36, 237 (1981).
[CrossRef]

T. von Foerster and R. J. Glauber, Phys. Rev. A 3, 1484 (1971).
[CrossRef]

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

C. Lecompte, G. Mainfray, C. Manus, and F. Sanchez, Phys. Rev. A 11, 1009 (1975).
[CrossRef]

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

Phys. Rev. Lett. (1)

A related result was found for stimulated thermal scattering with a broadband pump laser. See V. Bespalov, A. Kubarev, and G. Pasmanik, Phys. Rev. Lett. 24, 1274 (1970); A. O. Creaser and R. M. Herman, Phys. Rev. Lett. 29, 147 (1972).
[CrossRef]

Sov. Phys. JETP (2)

S. A. Akhamnov, Yu. E. Dyakov, and L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

G. P. Dzhotyan, Yu. E. Dyakov, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, Sov. Phys. JETP 46, 431 (1977).

Other (4)

V. I. Krylov and N. S. Skoblya, Handbook of Numerical Inversion of Laplace Transforms (Israel Program for Scientific Translations, Jerusalem, 1969).

I. S. Gradshteyn and I. M. Ryzik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965), Eqs. (6.615), (6.621-4), (8.486), and (6.681.3).

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).

M. Abramowitz and I. Stegun, eds., Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1964), Eqs. (9.6.16) and (11.3.12).

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Figures (2)

Fig. 1
Fig. 1

Mean generated Stokes intensity in transient limit (Γτ = 0.01) versus g ¯z for different ratios of chaotic-pump bandwidth to Raman linewidth ΓL/Γ. The infinite-bandwidth chaotic result is identical with the result for a coherent pump.

Fig. 2
Fig. 2

Mean generated Stokes intensity in steady-state limit (Γτ → ∞) versus g ¯z for different values of ΓL/Γ.

Equations (33)

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E L * ( τ ) E L ( τ ) = E 0 2 exp ( - Γ L τ - τ )
I L ( τ ) I L ( τ ) = E 0 4 [ exp ( - 2 Γ L τ - τ ) + 1 ] ,
z E ^ S ( - ) = - i κ 2 E L Q ^ ,
τ Q ^ = - Γ Q ^ + i κ 1 E L * E ^ S ( - ) + F ^ ,
g ¯ = 2 κ 1 κ 2 E 0 2 / Γ .
I ( τ ) = A 2 π ω S E ^ S ( - ) ( z , τ ) E ^ S ( + ) ( z , τ ) Q M ,
Q ^ ( z , O ) Q ^ ( z , O ) = ( A N ) - 1 δ ( z - z ) ,
F ^ ( z , τ ) F ^ ( z , τ ) = 2 Γ ( A N ) - 1 δ ( z - z ) δ ( τ - τ ) ,
I ( τ ) = ½ Γ g ¯ z A ( τ ) 2 { e - 2 Γ τ ( I 0 2 { [ 2 Γ g ¯ z p ( τ ) ] 1 / 2 } - I 1 2 { 2 Γ g ¯ z p ( τ ) ] 1 / 2 } ) + 2 Γ 0 τ d τ e - 2 Γ τ × [ I 0 2 ( { 2 Γ g ¯ z [ p ( τ ) - p ( τ - τ ) ] } 1 / 2 ) - I 1 2 ( { 2 Γ g ¯ z [ p ( τ ) - p ( τ - τ ) ] } 1 / 2 ) ] } ,
p ( τ ) = 0 τ A ( τ ) 2 d τ .
I TR ( τ ) = ½ Γ g ¯ z A ( τ ) 2 ( I 0 2 { [ 2 Γ g ¯ z p ( τ ) ] 1 / 2 } - I 1 2 { [ 2 Γ g ¯ z p ( τ ) ] 1 / 2 } ) .
I TR ( τ ) = ½ Γ g ¯ z { I 0 2 [ ( 2 Γ τ g ¯ z ) 1 / 2 ] - I 1 2 [ ( 2 Γ τ g ¯ z ) 1 / 2 ] } .
I TR ( τ ) = ½ Γ g ¯ z I 0 ( Γ τ g ¯ z ) exp ( Γ τ g ¯ z ) .
I TR ( τ ) = ½ Γ g ¯ z C d s s - 1 f ( s ) exp ( s Γ τ g ¯ z ) × [ I 0 ( s Γ τ g ¯ z ) - I 1 ( s Γ τ g ¯ z ) ] ,
8 δ { ( δ + 1 ) exp [ Γ L τ ( δ - 1 ) ] + ( δ - 1 ) exp [ - Γ L τ ( δ + 1 ) ] } { ( δ + 1 ) 2 exp [ Γ L τ ( δ - 1 ) ] - ( δ - 1 ) 2 exp [ - Γ L τ ( δ + 1 ) ] } 2 .
I SS = 2 Γ ½ Γ g ¯ z A ( τ ) 2 0 τ d τ e - 2 Γ τ × [ I 0 2 ( { 2 Γ g ¯ z [ p ( τ ) - p ( τ - τ ) ] } 1 / 2 ) - I 1 2 ( { 2 Γ g ¯ z [ p ( τ ) - p ( τ - τ ) ] } 1 / 2 ) ] ,
I SS = 2 Γ 0 d τ e - 2 Γ τ I TR ( τ ) .
I SS = ½ Γ g ¯ z [ I 0 ( ½ g ¯ z ) - I 1 ( ½ g ¯ z ) ] exp ( ½ g ¯ z ) ,
I SS = ½ Γ g ¯ z / ( 1 - g ¯ z ) 1 / 2 ,
I SS AMP = I S 0 / ( 1 - g ¯ z ) .
I SS AMP = 0 I SS COH exp ( - g / g ¯ ) g ¯ d g .
I TR ( τ ) = α z 2 π A ( τ ) 2 0 π / 2 d θ I 1 { 2 cos θ [ α z p ( τ ) ] 1 / 2 } cos θ [ α z p ( τ ) ] 1 / 2 ,
( z / κ ) 1 / 2 I 1 [ 2 ( κ z ) 1 / 2 ] = 1 2 π i C d ζ ζ - 2 e ζ z e κ / ζ ,
I TR ( τ ) = α 2 π 1 2 π i 0 π / 2 d θ C d ζ e ζ z ζ α cos 2 θ × d d τ exp [ ζ - 1 α p ( τ ) cos 2 θ ] .
exp [ γ 0 τ A ( τ ) 2 d τ ] = 2 { ( 1 + r / q ) exp [ Γ L τ ( q - 1 ) ] + ( 1 - r / q ) exp [ - Γ L τ ( q + 1 ) ] } - 1 ,
exp ( γ 0 τ A ( τ ) 2 d τ ) = ( 1 - γ τ ) - 1 .
I TR ( τ ) = α 2 π 1 2 π i 0 π / 2 d θ C d s exp ( s z α τ cos 2 θ ) α τ cos 2 θ ( s - 1 ) 2 .
I TR ( τ ) = α 2 π 1 2 π i 0 π / 2 d θ C d s [ exp ( s z α τ cos 2 θ ) - 1 ] α τ cos 2 θ ( s - 1 ) 2 ,
I TR ( τ ) = α 2 π 1 2 π i 0 π / 2 d θ × C d s z s ( s - 1 ) 2 0 1 d x exp ( x s z α τ cos 2 θ ) .
I TR ( τ ) = α z 4 1 2 π i C d s s ( s - 1 ) 2 × exp ( ½ s z α τ ) [ I 0 ( ½ s z α τ ) - I 1 ( ½ s z α τ ) ] ,
I TR ( τ ) = ¼ α z I 0 ( ½ z α τ ) exp ( ½ z α τ ) .
I TR ( τ ) = α 2 π 1 2 π i 0 π / 2 d θ C d s exp ( s z α τ cos 2 θ ) α τ cos 2 θ f ( s ) s 2 ,
I TR ( τ ) = α z 2 π 0 π / 2 d θ I 1 [ 2 cos θ ( α z τ ) 1 / 2 ] cos θ ( α z τ ) 1 / 2 .

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