Abstract

A numerical study is presented of the steady-state and transient regimes in stimulated Raman scattering, including diffractive coupling of the fields and detuning of the Stokes field from resonance. In the steady-state regime, ring formation in the laser output intensity is observed as well as a ring in the Stokes output intensity when it is detuned from resonance. In the transient regime a solitonlike pulse is initiated by modulation of the phase of the input Stokes field. For Fresnel numbers between 5 and 50, we observe a simultaneous maximum of the on-axis laser and Stokes intensities after a π phase shift is introduced on the Stokes seed. At the same time the transverse profiles of the fields are narrowed and the laser intensity displays a satellite ring. It is found that the soliton remains relatively stable, although diffraction eventually leads to its decay.

© 1991 Optical Society of America

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References

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  1. F. Y. Chu and A. C. Scott, Phys. Rev. A 12, 2060 (1975); N. Tan-no, T. Shirahara, K. Yokoto, and H. Inaba, Phys. Rev. A 12, 159 (1975); T. M. Makhiladze, M. E. Sarychev, and L. A. Skelepin, Zh. Eksp. Teor. Fiz. 69, 499 (1975) [Sov. Phys. JETP 42, 255 (1976)]; D. J. Kaup, Physica D 6, 142 (1983); H. Steudel, Physica D 6, 155 (1983).
    [CrossRef]
  2. K. Druhl, R. G. Wenzel, and J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983); R. G. Wenzel, J. L. Carlsten, and K. Druhl, J. Statistic. Phys. 39, 621 (1985).
    [CrossRef]
  3. J. C. Englund and C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986); C. M. Bowden and J. C. Englund, Opt. Commun. 67, 71 (1988).
    [CrossRef] [PubMed]
  4. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 40, 6745 (1989).
    [CrossRef] [PubMed]
  5. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. Lett. 61, 66 (1988).
    [CrossRef] [PubMed]
  6. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 39, 6078 (1989).
    [CrossRef] [PubMed]
  7. M. Yousaf, K. J. Druhl, and S. A. Shakir, Physica D 30, 228 (1988).
    [CrossRef]
  8. D. C. MacPherson, J. L. Carlsten, and K. J. Druhl, J. Opt. Soc. Am. B 4, 1853 (1987).
    [CrossRef]
  9. J. Mostowski and B. Sobolewska, Phys. Rev. A 28, 2943 (1983); F. P. Mattar, H. M. Gibbs, S. L. McCall, and M. S. Feld, Phys. Rev. Lett. 46, 1123 (1981); P. D. Drummond and J. H. Eberly, Phys. Rev. A 25, 3446 (1982).
    [CrossRef]
  10. E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
    [CrossRef]
  11. J. W. Haus and M. Scalora, Phys Rev. A 42, 3149 (1990).
    [CrossRef] [PubMed]
  12. M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); M. G. Raymer and I. A. Walmsley, “Quantum coherence of stimulated Raman scattering,” Prog. Opt. 28, 183 (1990).
    [CrossRef]
  13. J. R. Ackerhalt and P. W. Milonni, Phys. Rev. A 33, 3185 (1986).
    [CrossRef] [PubMed]
  14. J. Mostowski and B. Sobolewska, Phys. Rev. A 34, 3109 (1986).
    [CrossRef] [PubMed]
  15. M. Strauss, J. Oreg, and A. Bar-Shalom, Phys. Rev. A 38, 4712 (1988).
    [CrossRef] [PubMed]
  16. J. V. Moloney, M. R. Belic, and H. M. Gibbs, Opt. Commun. 41, 379 (1982).
    [CrossRef]
  17. E. A. Sziklas and A. E. Siegman, Appl. Opt. 14, 1874 (1975).
    [CrossRef] [PubMed]
  18. M. Scalora and J. W. Haus, J. Opt. Soc. Am. B 6, 1714 (1989).
    [CrossRef]
  19. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).
  20. G. X. Jin, J. M. Yuan, L. M. Narducci, Y. S. Liu, and E. J. Seibert, Opt. Commun. 68, 379 (1988).
    [CrossRef]

1990 (1)

J. W. Haus and M. Scalora, Phys Rev. A 42, 3149 (1990).
[CrossRef] [PubMed]

1989 (3)

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 40, 6745 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 39, 6078 (1989).
[CrossRef] [PubMed]

M. Scalora and J. W. Haus, J. Opt. Soc. Am. B 6, 1714 (1989).
[CrossRef]

1988 (4)

M. Yousaf, K. J. Druhl, and S. A. Shakir, Physica D 30, 228 (1988).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

M. Strauss, J. Oreg, and A. Bar-Shalom, Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

G. X. Jin, J. M. Yuan, L. M. Narducci, Y. S. Liu, and E. J. Seibert, Opt. Commun. 68, 379 (1988).
[CrossRef]

1987 (1)

1986 (3)

J. C. Englund and C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986); C. M. Bowden and J. C. Englund, Opt. Commun. 67, 71 (1988).
[CrossRef] [PubMed]

J. R. Ackerhalt and P. W. Milonni, Phys. Rev. A 33, 3185 (1986).
[CrossRef] [PubMed]

J. Mostowski and B. Sobolewska, Phys. Rev. A 34, 3109 (1986).
[CrossRef] [PubMed]

1983 (3)

K. Druhl, R. G. Wenzel, and J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983); R. G. Wenzel, J. L. Carlsten, and K. Druhl, J. Statistic. Phys. 39, 621 (1985).
[CrossRef]

J. Mostowski and B. Sobolewska, Phys. Rev. A 28, 2943 (1983); F. P. Mattar, H. M. Gibbs, S. L. McCall, and M. S. Feld, Phys. Rev. Lett. 46, 1123 (1981); P. D. Drummond and J. H. Eberly, Phys. Rev. A 25, 3446 (1982).
[CrossRef]

E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
[CrossRef]

1982 (1)

J. V. Moloney, M. R. Belic, and H. M. Gibbs, Opt. Commun. 41, 379 (1982).
[CrossRef]

1981 (1)

M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); M. G. Raymer and I. A. Walmsley, “Quantum coherence of stimulated Raman scattering,” Prog. Opt. 28, 183 (1990).
[CrossRef]

1975 (2)

F. Y. Chu and A. C. Scott, Phys. Rev. A 12, 2060 (1975); N. Tan-no, T. Shirahara, K. Yokoto, and H. Inaba, Phys. Rev. A 12, 159 (1975); T. M. Makhiladze, M. E. Sarychev, and L. A. Skelepin, Zh. Eksp. Teor. Fiz. 69, 499 (1975) [Sov. Phys. JETP 42, 255 (1976)]; D. J. Kaup, Physica D 6, 142 (1983); H. Steudel, Physica D 6, 155 (1983).
[CrossRef]

E. A. Sziklas and A. E. Siegman, Appl. Opt. 14, 1874 (1975).
[CrossRef] [PubMed]

Ackerhalt, J. R.

J. R. Ackerhalt and P. W. Milonni, Phys. Rev. A 33, 3185 (1986).
[CrossRef] [PubMed]

Bar-Shalom, A.

M. Strauss, J. Oreg, and A. Bar-Shalom, Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

Belic, M. R.

J. V. Moloney, M. R. Belic, and H. M. Gibbs, Opt. Commun. 41, 379 (1982).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

Bowden, C. M.

J. C. Englund and C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986); C. M. Bowden and J. C. Englund, Opt. Commun. 67, 71 (1988).
[CrossRef] [PubMed]

Carlsten, J. L.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 40, 6745 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 39, 6078 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

D. C. MacPherson, J. L. Carlsten, and K. J. Druhl, J. Opt. Soc. Am. B 4, 1853 (1987).
[CrossRef]

K. Druhl, R. G. Wenzel, and J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983); R. G. Wenzel, J. L. Carlsten, and K. Druhl, J. Statistic. Phys. 39, 621 (1985).
[CrossRef]

Chu, F. Y.

F. Y. Chu and A. C. Scott, Phys. Rev. A 12, 2060 (1975); N. Tan-no, T. Shirahara, K. Yokoto, and H. Inaba, Phys. Rev. A 12, 159 (1975); T. M. Makhiladze, M. E. Sarychev, and L. A. Skelepin, Zh. Eksp. Teor. Fiz. 69, 499 (1975) [Sov. Phys. JETP 42, 255 (1976)]; D. J. Kaup, Physica D 6, 142 (1983); H. Steudel, Physica D 6, 155 (1983).
[CrossRef]

Claude, Y.

E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
[CrossRef]

Cormier, M.

E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
[CrossRef]

Druhl, K.

K. Druhl, R. G. Wenzel, and J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983); R. G. Wenzel, J. L. Carlsten, and K. Druhl, J. Statistic. Phys. 39, 621 (1985).
[CrossRef]

Druhl, K. J.

Englund, J. C.

J. C. Englund and C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986); C. M. Bowden and J. C. Englund, Opt. Commun. 67, 71 (1988).
[CrossRef] [PubMed]

Feld, M. S.

E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
[CrossRef]

Gibbs, H. M.

E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
[CrossRef]

J. V. Moloney, M. R. Belic, and H. M. Gibbs, Opt. Commun. 41, 379 (1982).
[CrossRef]

Haus, J. W.

Jin, G. X.

G. X. Jin, J. M. Yuan, L. M. Narducci, Y. S. Liu, and E. J. Seibert, Opt. Commun. 68, 379 (1988).
[CrossRef]

Liu, Y. S.

G. X. Jin, J. M. Yuan, L. M. Narducci, Y. S. Liu, and E. J. Seibert, Opt. Commun. 68, 379 (1988).
[CrossRef]

MacPherson, D. C.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 40, 6745 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 39, 6078 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

D. C. MacPherson, J. L. Carlsten, and K. J. Druhl, J. Opt. Soc. Am. B 4, 1853 (1987).
[CrossRef]

Mattar, F. P.

E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
[CrossRef]

McCall, S. L.

E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
[CrossRef]

Milonni, P. W.

J. R. Ackerhalt and P. W. Milonni, Phys. Rev. A 33, 3185 (1986).
[CrossRef] [PubMed]

Moloney, J. V.

J. V. Moloney, M. R. Belic, and H. M. Gibbs, Opt. Commun. 41, 379 (1982).
[CrossRef]

Mostowski, J.

J. Mostowski and B. Sobolewska, Phys. Rev. A 34, 3109 (1986).
[CrossRef] [PubMed]

J. Mostowski and B. Sobolewska, Phys. Rev. A 28, 2943 (1983); F. P. Mattar, H. M. Gibbs, S. L. McCall, and M. S. Feld, Phys. Rev. Lett. 46, 1123 (1981); P. D. Drummond and J. H. Eberly, Phys. Rev. A 25, 3446 (1982).
[CrossRef]

M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); M. G. Raymer and I. A. Walmsley, “Quantum coherence of stimulated Raman scattering,” Prog. Opt. 28, 183 (1990).
[CrossRef]

Narducci, L. M.

G. X. Jin, J. M. Yuan, L. M. Narducci, Y. S. Liu, and E. J. Seibert, Opt. Commun. 68, 379 (1988).
[CrossRef]

Oreg, J.

M. Strauss, J. Oreg, and A. Bar-Shalom, Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

Raymer, M. G.

M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); M. G. Raymer and I. A. Walmsley, “Quantum coherence of stimulated Raman scattering,” Prog. Opt. 28, 183 (1990).
[CrossRef]

Scalora, M.

Scott, A. C.

F. Y. Chu and A. C. Scott, Phys. Rev. A 12, 2060 (1975); N. Tan-no, T. Shirahara, K. Yokoto, and H. Inaba, Phys. Rev. A 12, 159 (1975); T. M. Makhiladze, M. E. Sarychev, and L. A. Skelepin, Zh. Eksp. Teor. Fiz. 69, 499 (1975) [Sov. Phys. JETP 42, 255 (1976)]; D. J. Kaup, Physica D 6, 142 (1983); H. Steudel, Physica D 6, 155 (1983).
[CrossRef]

Seibert, E. J.

G. X. Jin, J. M. Yuan, L. M. Narducci, Y. S. Liu, and E. J. Seibert, Opt. Commun. 68, 379 (1988).
[CrossRef]

Shakir, S. A.

M. Yousaf, K. J. Druhl, and S. A. Shakir, Physica D 30, 228 (1988).
[CrossRef]

Siegman, A. E.

Sobolewska, B.

J. Mostowski and B. Sobolewska, Phys. Rev. A 34, 3109 (1986).
[CrossRef] [PubMed]

J. Mostowski and B. Sobolewska, Phys. Rev. A 28, 2943 (1983); F. P. Mattar, H. M. Gibbs, S. L. McCall, and M. S. Feld, Phys. Rev. Lett. 46, 1123 (1981); P. D. Drummond and J. H. Eberly, Phys. Rev. A 25, 3446 (1982).
[CrossRef]

Strauss, M.

M. Strauss, J. Oreg, and A. Bar-Shalom, Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

Swanson, R. C.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 39, 6078 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 40, 6745 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

Sziklas, E. A.

Watson, E. A.

E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
[CrossRef]

Wenzel, R. G.

K. Druhl, R. G. Wenzel, and J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983); R. G. Wenzel, J. L. Carlsten, and K. Druhl, J. Statistic. Phys. 39, 621 (1985).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

Yousaf, M.

M. Yousaf, K. J. Druhl, and S. A. Shakir, Physica D 30, 228 (1988).
[CrossRef]

Yuan, J. M.

G. X. Jin, J. M. Yuan, L. M. Narducci, Y. S. Liu, and E. J. Seibert, Opt. Commun. 68, 379 (1988).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

J. V. Moloney, M. R. Belic, and H. M. Gibbs, Opt. Commun. 41, 379 (1982).
[CrossRef]

G. X. Jin, J. M. Yuan, L. M. Narducci, Y. S. Liu, and E. J. Seibert, Opt. Commun. 68, 379 (1988).
[CrossRef]

Phys Rev. A (1)

J. W. Haus and M. Scalora, Phys Rev. A 42, 3149 (1990).
[CrossRef] [PubMed]

Phys. Rev. A (9)

M. G. Raymer and J. Mostowski, Phys. Rev. A 24, 1980 (1981); M. G. Raymer and I. A. Walmsley, “Quantum coherence of stimulated Raman scattering,” Prog. Opt. 28, 183 (1990).
[CrossRef]

J. R. Ackerhalt and P. W. Milonni, Phys. Rev. A 33, 3185 (1986).
[CrossRef] [PubMed]

J. Mostowski and B. Sobolewska, Phys. Rev. A 34, 3109 (1986).
[CrossRef] [PubMed]

M. Strauss, J. Oreg, and A. Bar-Shalom, Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

J. Mostowski and B. Sobolewska, Phys. Rev. A 28, 2943 (1983); F. P. Mattar, H. M. Gibbs, S. L. McCall, and M. S. Feld, Phys. Rev. Lett. 46, 1123 (1981); P. D. Drummond and J. H. Eberly, Phys. Rev. A 25, 3446 (1982).
[CrossRef]

E. A. Watson, H. M. Gibbs, F. P. Mattar, M. Cormier, Y. Claude, S. L. McCall, and M. S. Feld, Phys. Rev. A 27, 1427 (1983); F. P. Mattar and C. M. Bowden, Phys. Rev. A 27, 345 (1983).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 39, 6078 (1989).
[CrossRef] [PubMed]

F. Y. Chu and A. C. Scott, Phys. Rev. A 12, 2060 (1975); N. Tan-no, T. Shirahara, K. Yokoto, and H. Inaba, Phys. Rev. A 12, 159 (1975); T. M. Makhiladze, M. E. Sarychev, and L. A. Skelepin, Zh. Eksp. Teor. Fiz. 69, 499 (1975) [Sov. Phys. JETP 42, 255 (1976)]; D. J. Kaup, Physica D 6, 142 (1983); H. Steudel, Physica D 6, 155 (1983).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. A 40, 6745 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

K. Druhl, R. G. Wenzel, and J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983); R. G. Wenzel, J. L. Carlsten, and K. Druhl, J. Statistic. Phys. 39, 621 (1985).
[CrossRef]

J. C. Englund and C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986); C. M. Bowden and J. C. Englund, Opt. Commun. 67, 71 (1988).
[CrossRef] [PubMed]

Physica D (1)

M. Yousaf, K. J. Druhl, and S. A. Shakir, Physica D 30, 228 (1988).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

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Figures (19)

Fig. 1
Fig. 1

Steady-state laser (solid curve) and Stokes (dashed curve) intensity versus longitudinal coordinate in plane-wave propagation. IL(0) = 100, IS(0) = 10−4, γ = 1.

Fig. 2
Fig. 2

Laser intensity transverse profile at steady state versus longitudinal coordinate. F = ∞, IL(0) = 100, IS(0) = 10−4, γ = 1.

Fig. 3
Fig. 3

Stokes intensity spatial dependence. See Fig. 2 for the parameter values.

Fig. 4
Fig. 4

Laser intensity transverse profile at steady state versus longitudinal coordinate, with F = 1. Other parameters are as in Fig. 2.

Fig. 5
Fig. 5

Steady-state transverse profile of the Stokes intensity versus longitudinal coordinate, with F = 1. Other parameters are as in Fig. 2.

Fig. 6
Fig. 6

Laser intensity versus space coordinates in short-medium propagation at steady state. F = 1, IL(0) = 100, IS(0) = 10−4, γ = 1.

Fig. 7
Fig. 7

Stokes intensity versus space coordinates in the steady-state regime. F = 2, γ = 1, Δ = −1.5γ.

Fig. 8
Fig. 8

On-axis laser intensity versus longitudinal coordinate and time. F = ∞, γ = 100, v = 40.

Fig. 9
Fig. 9

On-axis Stokes intensity versus longitudinal coordinate and time. F = ∞, γ = 100, v = 40.

Fig. 10
Fig. 10

On-axis laser intensity versus longitudinal coordinate and time. F =10, γ =100, v = 40.

Fig. 11
Fig. 11

On-axis Stokes intensity versus longitudinal coordinate and time. F = 10, γ = 100, v = 40.

Fig. 12
Fig. 12

Laser intensity versus transverse coordinate and time at the output (z = L = 1). F = 10, γ = 100, v = 40.

Fig. 13
Fig. 13

Stokes intensity versus transverse coordinate and time at the output (z = L = 1). F = 10, γ = 100, v = 40.

Fig. 14
Fig. 14

Laser (solid curve) and Stokes (dashed curve) integrated intensities for Figs. 12 and 13.

Fig. 15
Fig. 15

Laser intensity versus transverse coordinate and time at the output (z = L = 1). F = 2, γ = 100, v = 40.

Fig. 16
Fig. 16

Stokes intensity versus transverse coordinate and time at the output (z = L = 1). F = 2, γ = 100, v = 40.

Fig. 17
Fig. 17

Polarization versus transverse coordinate and time at the output (z = L = 1). F = 10, γ = 100, v = 40.

Fig. 18
Fig. 18

Same as Fig. 8 but with an induced phase shift of 0.968π at t = 0.01.

Fig. 19
Fig. 19

Laser field versus time at exit boundary that results from the use of different ramping rates for the initial Stokes boundary conditions. For all three peaks, T1 = 0.01. For the first peak the phase shift is instantaneous (α = ∞). T2 = 0.015 (α = 400) and T2 = 0.05 (α = 50) for the second and third peaks, respectively.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

z E L + 1 v t E L - i F 2 E L = - Q E S ,
z E S + 1 v t E S - i F 2 E S = Q * E L ,
t Q = - ( γ - i Δ ) Q + E L E S * ,
ξ E L - i F 2 E L = - Q E S ,
ξ E S - i F 2 E S = Q * E L ,
τ Q = - γ Q + E L E S * .
E L , S ( x , Δ ξ ) = exp ( i Δ ξ 2 F 2 ) × exp ( χ L , S d ξ ) exp ( i Δ ξ 2 F 2 ) E L , S ( x , 0 ) ,
E L , S ( x , Δ ξ ) = exp [ ( i Δ ξ / F ) 2 + χ L , S Δ ξ ] E L , S ( x , 0 ) .
E L , S ( x , Δ ξ ) = exp ( χ L , S Δ ξ ) E L , S ( x , 0 ) .
I L ( ξ ) = I 0 I L ( 0 ) exp ( - 2 I 0 ξ / γ ) I S ( 0 ) + I L ( 0 ) exp ( - 2 I 0 ξ / γ ) ,
I S ( ξ ) = I 0 I S ( 0 ) exp ( 2 I 0 ξ / γ ) I L ( 0 ) + I S ( 0 ) exp ( 2 I 0 ξ / γ ) ,
n S = - Δ γ 2 + Δ 2 E L 2 ,             n L = - Δ γ 2 + Δ 2 E S 2 .
E L ( x , y , τ ) = 10 exp [ - ( x 2 + y 2 ) ] ,
E S ( 0 , τ ) = { E 0 t < T 1 E 0 [ 1 - α ( t - T 1 ) ] T 1 t T 2 - E 0 t > T 2 ,
z E S + 1 v g t E S = K 2 Q * E L 0
t Q = - γ Q + K 1 E L 0 E S * ,
ξ E ˜ S = K 1 K 2 E L 0 2 L γ E ˜ S ,

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