Abstract

The phase behavior of solitons generated in the Raman amplification process has been interferometrically investigated. The phase jump by π responsible for the soliton formation was injected into the input pump pulse or the Stokes pulse. In both cases, the solitons with a different relative phase have been observed. The results of the numerical integration of the plane-wave Raman equations have shown that only in-phase or antiphase solitons are generated at zero frequency detuning from the exact Raman resonance when the phase jump is injected into the Stokes pulse or the pump pulse, respectively. Realizations with an arbitrary relative phase are possible for nonzero detunings. These detunings have the order of magnitude expected due to spectral fluctuations in the Stokes pulse and thus are one of the possible causes of the observed variations in the soliton phase.

© 2007 Optical Society of America

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  1. F. Y. F. Chu and A. C. Scott, "Inverse scattering transform for wave-wave scattering," Phys. Rev. A 12, 2060-2064 (1975).
    [CrossRef]
  2. H. Steudel, "Solitons in stimulated Raman scattering and resonant two-photon propagation," Physica D 6, 155-178 (1983).
    [CrossRef]
  3. K. Drühl, R. G. Wenzel, and J. L. Carlsten, "Observation of solitons in stimulated Raman scattering," Phys. Rev. Lett. 51, 1171-1174 (1983).
    [CrossRef]
  4. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Spontaneous solitons in stimulated Raman scattering," Phys. Rev. A 40, 6745-6747 (1989).
    [CrossRef] [PubMed]
  5. D. E. Gakhovich, A. S. Grabtchikov, and V. A. Orlovich, "Spontaneous solitons in short length geometry of stimulated Raman scattering," Opt. Commun. 102, 485-490 (1993).
    [CrossRef]
  6. S. Ya. Kilin, V. A. Orlovich, A. S. Grabtchikov, D. E. Gakhovich, A. V. Kachinsky, and I. I. Fedchenia, "Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuation: experimental manifestation in statistics of soliton-like random pulses in a depleted pump," Quantum Opt. 5, 223-239 (1993).
    [CrossRef]
  7. J. C. Englund and C. M. Bowden, "Spontaneous generation of Raman solitons from quantum noise," Phys. Rev. Lett. 57, 2661-2663 (1986).
    [CrossRef] [PubMed]
  8. M. Yousaf, K. J. Druhl, and S. A. Shakir, "Propagation of non-resonant temporal Raman solitons in the presence of coherence decay: a perturbation theoretical analysis," Physica D 30, 228-234 (1988).
    [CrossRef]
  9. S. Elyutin and J. N. Elgin, "Comments on a recent observation of solitons in stimulated Raman scattering," Opt. Commun. 60, 104-106 (1986).
    [CrossRef]
  10. C. Claude, F. Ginovart, and J. Leon, "Raman spikes of pump repletion are not solitons," Physica D 87, 348-355 (1995).
    [CrossRef]
  11. D. C. MacPherson, J. L. Carlsten, and Kai J. Drühl, "Generation of solitons in transient stimulated Raman scattering by optical phase shifts," J. Opt. Soc. Am. B 4, 1853-1859 (1987).
    [CrossRef]
  12. K. Midorikawa, H. Tashiro, Y. Akiyama, and M. Obara, "π-phase jump for soliton formation in stimulated Raman scattering," Phys. Rev. A 41, 562-565 (1990).
    [CrossRef] [PubMed]
  13. M. G. Raymer, Z. W. Li, and I. A. Walmsley, "Temporal quantum fluctuations in stimulated Raman scattering: coherent-modes description," Phys. Rev. Lett. 63, 1586-1589 (1989).
    [CrossRef] [PubMed]
  14. Y. Akiyama, K. Midorikawa, M. Obara, and H. Tashiro, "Measurement of a Stokes phase jump in spontaneously initiated stimulated Raman scattering," J. Opt. Soc. Am. B 8, 2459-2465 (1991).
    [CrossRef]
  15. R. C. Swanson, D. C. MacPherson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the decay of a Raman soliton," Phys. Rev. A 45, 450-457 (1992).
    [CrossRef] [PubMed]
  16. M. Scalora, S. Singh, and C. M. Bowden, "Anti-Stokes generation and soliton decay in stimulated Raman scattering," Phys. Rev. Lett. 70, 1248-1250 (1993).
    [CrossRef] [PubMed]
  17. J. R. Ackerhalt and P. W. Milonni, "Solitons and four-wave mixing," Phys. Rev. A 33, 3185-3198 (1986).
    [CrossRef] [PubMed]
  18. M. Scalora, "Dispersion and soliton propagation in stimulated Raman scattering," J. Opt. Soc. Am. B 11, 770-773 (1994).
    [CrossRef]
  19. J. W. Haus and M. Scalora, "Soliton decay and gain focusing in stimulated Raman scattering," Phys. Rev. A 42, 3149-3151 (1990).
    [CrossRef] [PubMed]
  20. M. Scalora and J. W. Haus, "Stimulated Raman scattering: diffractive coupling in transient and steady-state regimes," J. Opt. Soc. Am. B 8, 1003-1012 (1991).
    [CrossRef]
  21. C. M. Bowden and J. C. Englund, "Macroscopic manifestation of quantum noise," Opt. Commun. 67, 71-78 (1988).
    [CrossRef]
  22. J. C. Englund and C. M. Bowden, "Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman-soliton generation," Phys. Rev. A 46, 578-591 (1992).
    [CrossRef] [PubMed]
  23. A. S. Grabtchikov, D. E. Gakhovich, A. G. Shvedko, V. A. Orlovich, and K. J. Witte, "Observation of solitons with different phase behavior in stimulated Raman forward scattering," Phys. Rev. Lett. 81, 5808-5811 (1998).
    [CrossRef]
  24. F. Sanborn and C. R. Menyuk, "Transition from transient stationary behavior in stimulated Raman scattering," J. Opt. Soc. Am. B 13, 1921-1926 (1996).
    [CrossRef]
  25. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Stimulated Raman scattering in the visible with a multipass cell," IEEE J. Quantum Electron. 25, 1741-1746 (1989).
    [CrossRef]
  26. R. C. Swanson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the gain-narrowed Raman linewidth in H2," Phys. Rev. A 42, 6774-6783 (1990).
    [CrossRef] [PubMed]
  27. P. R. Battle, R. C. Swanson, and J. L. Carlsten, "Quantum limit on noise in a Raman amplifier," Phys. Rev. A 44, 1992-1930 (1991).
    [CrossRef]
  28. A. Penzkofer, A. Laubereau, and W. Kaiser, "High intensity Raman interactions," Prog. Quantum Electron. 6, 55-140 (1979).
    [CrossRef]

1998 (1)

A. S. Grabtchikov, D. E. Gakhovich, A. G. Shvedko, V. A. Orlovich, and K. J. Witte, "Observation of solitons with different phase behavior in stimulated Raman forward scattering," Phys. Rev. Lett. 81, 5808-5811 (1998).
[CrossRef]

1996 (1)

1995 (1)

C. Claude, F. Ginovart, and J. Leon, "Raman spikes of pump repletion are not solitons," Physica D 87, 348-355 (1995).
[CrossRef]

1994 (1)

1993 (3)

M. Scalora, S. Singh, and C. M. Bowden, "Anti-Stokes generation and soliton decay in stimulated Raman scattering," Phys. Rev. Lett. 70, 1248-1250 (1993).
[CrossRef] [PubMed]

D. E. Gakhovich, A. S. Grabtchikov, and V. A. Orlovich, "Spontaneous solitons in short length geometry of stimulated Raman scattering," Opt. Commun. 102, 485-490 (1993).
[CrossRef]

S. Ya. Kilin, V. A. Orlovich, A. S. Grabtchikov, D. E. Gakhovich, A. V. Kachinsky, and I. I. Fedchenia, "Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuation: experimental manifestation in statistics of soliton-like random pulses in a depleted pump," Quantum Opt. 5, 223-239 (1993).
[CrossRef]

1992 (2)

R. C. Swanson, D. C. MacPherson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the decay of a Raman soliton," Phys. Rev. A 45, 450-457 (1992).
[CrossRef] [PubMed]

J. C. Englund and C. M. Bowden, "Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman-soliton generation," Phys. Rev. A 46, 578-591 (1992).
[CrossRef] [PubMed]

1991 (3)

1990 (3)

K. Midorikawa, H. Tashiro, Y. Akiyama, and M. Obara, "π-phase jump for soliton formation in stimulated Raman scattering," Phys. Rev. A 41, 562-565 (1990).
[CrossRef] [PubMed]

J. W. Haus and M. Scalora, "Soliton decay and gain focusing in stimulated Raman scattering," Phys. Rev. A 42, 3149-3151 (1990).
[CrossRef] [PubMed]

R. C. Swanson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the gain-narrowed Raman linewidth in H2," Phys. Rev. A 42, 6774-6783 (1990).
[CrossRef] [PubMed]

1989 (3)

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Stimulated Raman scattering in the visible with a multipass cell," IEEE J. Quantum Electron. 25, 1741-1746 (1989).
[CrossRef]

M. G. Raymer, Z. W. Li, and I. A. Walmsley, "Temporal quantum fluctuations in stimulated Raman scattering: coherent-modes description," Phys. Rev. Lett. 63, 1586-1589 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Spontaneous solitons in stimulated Raman scattering," Phys. Rev. A 40, 6745-6747 (1989).
[CrossRef] [PubMed]

1988 (2)

M. Yousaf, K. J. Druhl, and S. A. Shakir, "Propagation of non-resonant temporal Raman solitons in the presence of coherence decay: a perturbation theoretical analysis," Physica D 30, 228-234 (1988).
[CrossRef]

C. M. Bowden and J. C. Englund, "Macroscopic manifestation of quantum noise," Opt. Commun. 67, 71-78 (1988).
[CrossRef]

1987 (1)

1986 (3)

J. R. Ackerhalt and P. W. Milonni, "Solitons and four-wave mixing," Phys. Rev. A 33, 3185-3198 (1986).
[CrossRef] [PubMed]

S. Elyutin and J. N. Elgin, "Comments on a recent observation of solitons in stimulated Raman scattering," Opt. Commun. 60, 104-106 (1986).
[CrossRef]

J. C. Englund and C. M. Bowden, "Spontaneous generation of Raman solitons from quantum noise," Phys. Rev. Lett. 57, 2661-2663 (1986).
[CrossRef] [PubMed]

1983 (2)

H. Steudel, "Solitons in stimulated Raman scattering and resonant two-photon propagation," Physica D 6, 155-178 (1983).
[CrossRef]

K. Drühl, R. G. Wenzel, and J. L. Carlsten, "Observation of solitons in stimulated Raman scattering," Phys. Rev. Lett. 51, 1171-1174 (1983).
[CrossRef]

1979 (1)

A. Penzkofer, A. Laubereau, and W. Kaiser, "High intensity Raman interactions," Prog. Quantum Electron. 6, 55-140 (1979).
[CrossRef]

1975 (1)

F. Y. F. Chu and A. C. Scott, "Inverse scattering transform for wave-wave scattering," Phys. Rev. A 12, 2060-2064 (1975).
[CrossRef]

Ackerhalt, J. R.

J. R. Ackerhalt and P. W. Milonni, "Solitons and four-wave mixing," Phys. Rev. A 33, 3185-3198 (1986).
[CrossRef] [PubMed]

Akiyama, Y.

Y. Akiyama, K. Midorikawa, M. Obara, and H. Tashiro, "Measurement of a Stokes phase jump in spontaneously initiated stimulated Raman scattering," J. Opt. Soc. Am. B 8, 2459-2465 (1991).
[CrossRef]

K. Midorikawa, H. Tashiro, Y. Akiyama, and M. Obara, "π-phase jump for soliton formation in stimulated Raman scattering," Phys. Rev. A 41, 562-565 (1990).
[CrossRef] [PubMed]

Battle, P. R.

R. C. Swanson, D. C. MacPherson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the decay of a Raman soliton," Phys. Rev. A 45, 450-457 (1992).
[CrossRef] [PubMed]

P. R. Battle, R. C. Swanson, and J. L. Carlsten, "Quantum limit on noise in a Raman amplifier," Phys. Rev. A 44, 1992-1930 (1991).
[CrossRef]

R. C. Swanson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the gain-narrowed Raman linewidth in H2," Phys. Rev. A 42, 6774-6783 (1990).
[CrossRef] [PubMed]

Bowden, C. M.

M. Scalora, S. Singh, and C. M. Bowden, "Anti-Stokes generation and soliton decay in stimulated Raman scattering," Phys. Rev. Lett. 70, 1248-1250 (1993).
[CrossRef] [PubMed]

J. C. Englund and C. M. Bowden, "Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman-soliton generation," Phys. Rev. A 46, 578-591 (1992).
[CrossRef] [PubMed]

C. M. Bowden and J. C. Englund, "Macroscopic manifestation of quantum noise," Opt. Commun. 67, 71-78 (1988).
[CrossRef]

J. C. Englund and C. M. Bowden, "Spontaneous generation of Raman solitons from quantum noise," Phys. Rev. Lett. 57, 2661-2663 (1986).
[CrossRef] [PubMed]

Carlsten, J. L.

R. C. Swanson, D. C. MacPherson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the decay of a Raman soliton," Phys. Rev. A 45, 450-457 (1992).
[CrossRef] [PubMed]

P. R. Battle, R. C. Swanson, and J. L. Carlsten, "Quantum limit on noise in a Raman amplifier," Phys. Rev. A 44, 1992-1930 (1991).
[CrossRef]

R. C. Swanson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the gain-narrowed Raman linewidth in H2," Phys. Rev. A 42, 6774-6783 (1990).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Stimulated Raman scattering in the visible with a multipass cell," IEEE J. Quantum Electron. 25, 1741-1746 (1989).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Spontaneous solitons in stimulated Raman scattering," Phys. Rev. A 40, 6745-6747 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, J. L. Carlsten, and Kai J. Drühl, "Generation of solitons in transient stimulated Raman scattering by optical phase shifts," J. Opt. Soc. Am. B 4, 1853-1859 (1987).
[CrossRef]

K. Drühl, R. G. Wenzel, and J. L. Carlsten, "Observation of solitons in stimulated Raman scattering," Phys. Rev. Lett. 51, 1171-1174 (1983).
[CrossRef]

Chu, F. Y. F.

F. Y. F. Chu and A. C. Scott, "Inverse scattering transform for wave-wave scattering," Phys. Rev. A 12, 2060-2064 (1975).
[CrossRef]

Claude, C.

C. Claude, F. Ginovart, and J. Leon, "Raman spikes of pump repletion are not solitons," Physica D 87, 348-355 (1995).
[CrossRef]

Druhl, K. J.

M. Yousaf, K. J. Druhl, and S. A. Shakir, "Propagation of non-resonant temporal Raman solitons in the presence of coherence decay: a perturbation theoretical analysis," Physica D 30, 228-234 (1988).
[CrossRef]

Drühl, K.

K. Drühl, R. G. Wenzel, and J. L. Carlsten, "Observation of solitons in stimulated Raman scattering," Phys. Rev. Lett. 51, 1171-1174 (1983).
[CrossRef]

Drühl, Kai J.

Elgin, J. N.

S. Elyutin and J. N. Elgin, "Comments on a recent observation of solitons in stimulated Raman scattering," Opt. Commun. 60, 104-106 (1986).
[CrossRef]

Elyutin, S.

S. Elyutin and J. N. Elgin, "Comments on a recent observation of solitons in stimulated Raman scattering," Opt. Commun. 60, 104-106 (1986).
[CrossRef]

Englund, J. C.

J. C. Englund and C. M. Bowden, "Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman-soliton generation," Phys. Rev. A 46, 578-591 (1992).
[CrossRef] [PubMed]

C. M. Bowden and J. C. Englund, "Macroscopic manifestation of quantum noise," Opt. Commun. 67, 71-78 (1988).
[CrossRef]

J. C. Englund and C. M. Bowden, "Spontaneous generation of Raman solitons from quantum noise," Phys. Rev. Lett. 57, 2661-2663 (1986).
[CrossRef] [PubMed]

Fedchenia, I. I.

S. Ya. Kilin, V. A. Orlovich, A. S. Grabtchikov, D. E. Gakhovich, A. V. Kachinsky, and I. I. Fedchenia, "Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuation: experimental manifestation in statistics of soliton-like random pulses in a depleted pump," Quantum Opt. 5, 223-239 (1993).
[CrossRef]

Gakhovich, D. E.

A. S. Grabtchikov, D. E. Gakhovich, A. G. Shvedko, V. A. Orlovich, and K. J. Witte, "Observation of solitons with different phase behavior in stimulated Raman forward scattering," Phys. Rev. Lett. 81, 5808-5811 (1998).
[CrossRef]

S. Ya. Kilin, V. A. Orlovich, A. S. Grabtchikov, D. E. Gakhovich, A. V. Kachinsky, and I. I. Fedchenia, "Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuation: experimental manifestation in statistics of soliton-like random pulses in a depleted pump," Quantum Opt. 5, 223-239 (1993).
[CrossRef]

D. E. Gakhovich, A. S. Grabtchikov, and V. A. Orlovich, "Spontaneous solitons in short length geometry of stimulated Raman scattering," Opt. Commun. 102, 485-490 (1993).
[CrossRef]

Ginovart, F.

C. Claude, F. Ginovart, and J. Leon, "Raman spikes of pump repletion are not solitons," Physica D 87, 348-355 (1995).
[CrossRef]

Grabtchikov, A. S.

A. S. Grabtchikov, D. E. Gakhovich, A. G. Shvedko, V. A. Orlovich, and K. J. Witte, "Observation of solitons with different phase behavior in stimulated Raman forward scattering," Phys. Rev. Lett. 81, 5808-5811 (1998).
[CrossRef]

D. E. Gakhovich, A. S. Grabtchikov, and V. A. Orlovich, "Spontaneous solitons in short length geometry of stimulated Raman scattering," Opt. Commun. 102, 485-490 (1993).
[CrossRef]

S. Ya. Kilin, V. A. Orlovich, A. S. Grabtchikov, D. E. Gakhovich, A. V. Kachinsky, and I. I. Fedchenia, "Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuation: experimental manifestation in statistics of soliton-like random pulses in a depleted pump," Quantum Opt. 5, 223-239 (1993).
[CrossRef]

Haus, J. W.

M. Scalora and J. W. Haus, "Stimulated Raman scattering: diffractive coupling in transient and steady-state regimes," J. Opt. Soc. Am. B 8, 1003-1012 (1991).
[CrossRef]

J. W. Haus and M. Scalora, "Soliton decay and gain focusing in stimulated Raman scattering," Phys. Rev. A 42, 3149-3151 (1990).
[CrossRef] [PubMed]

Kachinsky, A. V.

S. Ya. Kilin, V. A. Orlovich, A. S. Grabtchikov, D. E. Gakhovich, A. V. Kachinsky, and I. I. Fedchenia, "Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuation: experimental manifestation in statistics of soliton-like random pulses in a depleted pump," Quantum Opt. 5, 223-239 (1993).
[CrossRef]

Kaiser, W.

A. Penzkofer, A. Laubereau, and W. Kaiser, "High intensity Raman interactions," Prog. Quantum Electron. 6, 55-140 (1979).
[CrossRef]

Kilin, S. Ya.

S. Ya. Kilin, V. A. Orlovich, A. S. Grabtchikov, D. E. Gakhovich, A. V. Kachinsky, and I. I. Fedchenia, "Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuation: experimental manifestation in statistics of soliton-like random pulses in a depleted pump," Quantum Opt. 5, 223-239 (1993).
[CrossRef]

Laubereau, A.

A. Penzkofer, A. Laubereau, and W. Kaiser, "High intensity Raman interactions," Prog. Quantum Electron. 6, 55-140 (1979).
[CrossRef]

Leon, J.

C. Claude, F. Ginovart, and J. Leon, "Raman spikes of pump repletion are not solitons," Physica D 87, 348-355 (1995).
[CrossRef]

Li, Z. W.

M. G. Raymer, Z. W. Li, and I. A. Walmsley, "Temporal quantum fluctuations in stimulated Raman scattering: coherent-modes description," Phys. Rev. Lett. 63, 1586-1589 (1989).
[CrossRef] [PubMed]

MacPherson, D. C.

R. C. Swanson, D. C. MacPherson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the decay of a Raman soliton," Phys. Rev. A 45, 450-457 (1992).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Stimulated Raman scattering in the visible with a multipass cell," IEEE J. Quantum Electron. 25, 1741-1746 (1989).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Spontaneous solitons in stimulated Raman scattering," Phys. Rev. A 40, 6745-6747 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, J. L. Carlsten, and Kai J. Drühl, "Generation of solitons in transient stimulated Raman scattering by optical phase shifts," J. Opt. Soc. Am. B 4, 1853-1859 (1987).
[CrossRef]

Menyuk, C. R.

Midorikawa, K.

Y. Akiyama, K. Midorikawa, M. Obara, and H. Tashiro, "Measurement of a Stokes phase jump in spontaneously initiated stimulated Raman scattering," J. Opt. Soc. Am. B 8, 2459-2465 (1991).
[CrossRef]

K. Midorikawa, H. Tashiro, Y. Akiyama, and M. Obara, "π-phase jump for soliton formation in stimulated Raman scattering," Phys. Rev. A 41, 562-565 (1990).
[CrossRef] [PubMed]

Milonni, P. W.

J. R. Ackerhalt and P. W. Milonni, "Solitons and four-wave mixing," Phys. Rev. A 33, 3185-3198 (1986).
[CrossRef] [PubMed]

Obara, M.

Y. Akiyama, K. Midorikawa, M. Obara, and H. Tashiro, "Measurement of a Stokes phase jump in spontaneously initiated stimulated Raman scattering," J. Opt. Soc. Am. B 8, 2459-2465 (1991).
[CrossRef]

K. Midorikawa, H. Tashiro, Y. Akiyama, and M. Obara, "π-phase jump for soliton formation in stimulated Raman scattering," Phys. Rev. A 41, 562-565 (1990).
[CrossRef] [PubMed]

Orlovich, V. A.

A. S. Grabtchikov, D. E. Gakhovich, A. G. Shvedko, V. A. Orlovich, and K. J. Witte, "Observation of solitons with different phase behavior in stimulated Raman forward scattering," Phys. Rev. Lett. 81, 5808-5811 (1998).
[CrossRef]

S. Ya. Kilin, V. A. Orlovich, A. S. Grabtchikov, D. E. Gakhovich, A. V. Kachinsky, and I. I. Fedchenia, "Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuation: experimental manifestation in statistics of soliton-like random pulses in a depleted pump," Quantum Opt. 5, 223-239 (1993).
[CrossRef]

D. E. Gakhovich, A. S. Grabtchikov, and V. A. Orlovich, "Spontaneous solitons in short length geometry of stimulated Raman scattering," Opt. Commun. 102, 485-490 (1993).
[CrossRef]

Penzkofer, A.

A. Penzkofer, A. Laubereau, and W. Kaiser, "High intensity Raman interactions," Prog. Quantum Electron. 6, 55-140 (1979).
[CrossRef]

Raymer, M. G.

M. G. Raymer, Z. W. Li, and I. A. Walmsley, "Temporal quantum fluctuations in stimulated Raman scattering: coherent-modes description," Phys. Rev. Lett. 63, 1586-1589 (1989).
[CrossRef] [PubMed]

Sanborn, F.

Scalora, M.

M. Scalora, "Dispersion and soliton propagation in stimulated Raman scattering," J. Opt. Soc. Am. B 11, 770-773 (1994).
[CrossRef]

M. Scalora, S. Singh, and C. M. Bowden, "Anti-Stokes generation and soliton decay in stimulated Raman scattering," Phys. Rev. Lett. 70, 1248-1250 (1993).
[CrossRef] [PubMed]

M. Scalora and J. W. Haus, "Stimulated Raman scattering: diffractive coupling in transient and steady-state regimes," J. Opt. Soc. Am. B 8, 1003-1012 (1991).
[CrossRef]

J. W. Haus and M. Scalora, "Soliton decay and gain focusing in stimulated Raman scattering," Phys. Rev. A 42, 3149-3151 (1990).
[CrossRef] [PubMed]

Scott, A. C.

F. Y. F. Chu and A. C. Scott, "Inverse scattering transform for wave-wave scattering," Phys. Rev. A 12, 2060-2064 (1975).
[CrossRef]

Shakir, S. A.

M. Yousaf, K. J. Druhl, and S. A. Shakir, "Propagation of non-resonant temporal Raman solitons in the presence of coherence decay: a perturbation theoretical analysis," Physica D 30, 228-234 (1988).
[CrossRef]

Shvedko, A. G.

A. S. Grabtchikov, D. E. Gakhovich, A. G. Shvedko, V. A. Orlovich, and K. J. Witte, "Observation of solitons with different phase behavior in stimulated Raman forward scattering," Phys. Rev. Lett. 81, 5808-5811 (1998).
[CrossRef]

Singh, S.

M. Scalora, S. Singh, and C. M. Bowden, "Anti-Stokes generation and soliton decay in stimulated Raman scattering," Phys. Rev. Lett. 70, 1248-1250 (1993).
[CrossRef] [PubMed]

Steudel, H.

H. Steudel, "Solitons in stimulated Raman scattering and resonant two-photon propagation," Physica D 6, 155-178 (1983).
[CrossRef]

Swanson, R. C.

R. C. Swanson, D. C. MacPherson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the decay of a Raman soliton," Phys. Rev. A 45, 450-457 (1992).
[CrossRef] [PubMed]

P. R. Battle, R. C. Swanson, and J. L. Carlsten, "Quantum limit on noise in a Raman amplifier," Phys. Rev. A 44, 1992-1930 (1991).
[CrossRef]

R. C. Swanson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the gain-narrowed Raman linewidth in H2," Phys. Rev. A 42, 6774-6783 (1990).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Stimulated Raman scattering in the visible with a multipass cell," IEEE J. Quantum Electron. 25, 1741-1746 (1989).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Spontaneous solitons in stimulated Raman scattering," Phys. Rev. A 40, 6745-6747 (1989).
[CrossRef] [PubMed]

Tashiro, H.

Y. Akiyama, K. Midorikawa, M. Obara, and H. Tashiro, "Measurement of a Stokes phase jump in spontaneously initiated stimulated Raman scattering," J. Opt. Soc. Am. B 8, 2459-2465 (1991).
[CrossRef]

K. Midorikawa, H. Tashiro, Y. Akiyama, and M. Obara, "π-phase jump for soliton formation in stimulated Raman scattering," Phys. Rev. A 41, 562-565 (1990).
[CrossRef] [PubMed]

Walmsley, I. A.

M. G. Raymer, Z. W. Li, and I. A. Walmsley, "Temporal quantum fluctuations in stimulated Raman scattering: coherent-modes description," Phys. Rev. Lett. 63, 1586-1589 (1989).
[CrossRef] [PubMed]

Wenzel, R. G.

K. Drühl, R. G. Wenzel, and J. L. Carlsten, "Observation of solitons in stimulated Raman scattering," Phys. Rev. Lett. 51, 1171-1174 (1983).
[CrossRef]

Witte, K. J.

A. S. Grabtchikov, D. E. Gakhovich, A. G. Shvedko, V. A. Orlovich, and K. J. Witte, "Observation of solitons with different phase behavior in stimulated Raman forward scattering," Phys. Rev. Lett. 81, 5808-5811 (1998).
[CrossRef]

Yousaf, M.

M. Yousaf, K. J. Druhl, and S. A. Shakir, "Propagation of non-resonant temporal Raman solitons in the presence of coherence decay: a perturbation theoretical analysis," Physica D 30, 228-234 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Stimulated Raman scattering in the visible with a multipass cell," IEEE J. Quantum Electron. 25, 1741-1746 (1989).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Commun. (3)

S. Elyutin and J. N. Elgin, "Comments on a recent observation of solitons in stimulated Raman scattering," Opt. Commun. 60, 104-106 (1986).
[CrossRef]

D. E. Gakhovich, A. S. Grabtchikov, and V. A. Orlovich, "Spontaneous solitons in short length geometry of stimulated Raman scattering," Opt. Commun. 102, 485-490 (1993).
[CrossRef]

C. M. Bowden and J. C. Englund, "Macroscopic manifestation of quantum noise," Opt. Commun. 67, 71-78 (1988).
[CrossRef]

Phys. Rev. A (9)

J. C. Englund and C. M. Bowden, "Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman-soliton generation," Phys. Rev. A 46, 578-591 (1992).
[CrossRef] [PubMed]

R. C. Swanson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the gain-narrowed Raman linewidth in H2," Phys. Rev. A 42, 6774-6783 (1990).
[CrossRef] [PubMed]

P. R. Battle, R. C. Swanson, and J. L. Carlsten, "Quantum limit on noise in a Raman amplifier," Phys. Rev. A 44, 1992-1930 (1991).
[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, "Spontaneous solitons in stimulated Raman scattering," Phys. Rev. A 40, 6745-6747 (1989).
[CrossRef] [PubMed]

K. Midorikawa, H. Tashiro, Y. Akiyama, and M. Obara, "π-phase jump for soliton formation in stimulated Raman scattering," Phys. Rev. A 41, 562-565 (1990).
[CrossRef] [PubMed]

J. W. Haus and M. Scalora, "Soliton decay and gain focusing in stimulated Raman scattering," Phys. Rev. A 42, 3149-3151 (1990).
[CrossRef] [PubMed]

R. C. Swanson, D. C. MacPherson, P. R. Battle, and J. L. Carlsten, "Quantum statistics of the decay of a Raman soliton," Phys. Rev. A 45, 450-457 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

M. Scalora, S. Singh, and C. M. Bowden, "Anti-Stokes generation and soliton decay in stimulated Raman scattering," Phys. Rev. Lett. 70, 1248-1250 (1993).
[CrossRef] [PubMed]

M. G. Raymer, Z. W. Li, and I. A. Walmsley, "Temporal quantum fluctuations in stimulated Raman scattering: coherent-modes description," Phys. Rev. Lett. 63, 1586-1589 (1989).
[CrossRef] [PubMed]

K. Drühl, R. G. Wenzel, and J. L. Carlsten, "Observation of solitons in stimulated Raman scattering," Phys. Rev. Lett. 51, 1171-1174 (1983).
[CrossRef]

J. C. Englund and C. M. Bowden, "Spontaneous generation of Raman solitons from quantum noise," Phys. Rev. Lett. 57, 2661-2663 (1986).
[CrossRef] [PubMed]

A. S. Grabtchikov, D. E. Gakhovich, A. G. Shvedko, V. A. Orlovich, and K. J. Witte, "Observation of solitons with different phase behavior in stimulated Raman forward scattering," Phys. Rev. Lett. 81, 5808-5811 (1998).
[CrossRef]

Physica D (3)

M. Yousaf, K. J. Druhl, and S. A. Shakir, "Propagation of non-resonant temporal Raman solitons in the presence of coherence decay: a perturbation theoretical analysis," Physica D 30, 228-234 (1988).
[CrossRef]

H. Steudel, "Solitons in stimulated Raman scattering and resonant two-photon propagation," Physica D 6, 155-178 (1983).
[CrossRef]

C. Claude, F. Ginovart, and J. Leon, "Raman spikes of pump repletion are not solitons," Physica D 87, 348-355 (1995).
[CrossRef]

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A. Penzkofer, A. Laubereau, and W. Kaiser, "High intensity Raman interactions," Prog. Quantum Electron. 6, 55-140 (1979).
[CrossRef]

Quantum Opt. (1)

S. Ya. Kilin, V. A. Orlovich, A. S. Grabtchikov, D. E. Gakhovich, A. V. Kachinsky, and I. I. Fedchenia, "Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuation: experimental manifestation in statistics of soliton-like random pulses in a depleted pump," Quantum Opt. 5, 223-239 (1993).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Experimental setup: Nd:YAG, single-frequency Nd:YAG laser; T, telescope; M1, mirror (high reflection at 532 nm ); BS, beam splitter; A, attenuator (the half-wave plate and polarizer); OD, optical delay; M, electro-optical modulator; MC, multipass cell; M2, mirror (high transmission at 532 nm ); BC, beam combiner; W, optical wedge; F, glass filter; D, diaphragm; FD, photodetector.

Fig. 2
Fig. 2

Experimentally observed intensity profiles of the (a) laser pulse before (dashed curve) and after (solid curve) the modulator and (b) corresponding interference trace recorded when these pulses were superimposed in the Mach–Zehnder interferometer. The dotted line denotes the moment of time where the phase jump occurred.

Fig. 3
Fig. 3

Experimentally observed intensity profiles of the (a), (c), (e) input (dashed curve) and depleted (solid curve) pump pulses at the output from the Raman amplifier and (b), (d), (f) corresponding interference traces when the π phase jump was injected into the Stokes pulse.

Fig. 4
Fig. 4

Experimentally observed intensity profiles of the (a) input (dashed curve) and depleted (solid curve) pump pulses with injected π phase jump when no soliton was generated. (b) Corresponding interference trace.

Fig. 5
Fig. 5

Experimentally observed intensity profiles of the (a), (c), (e) input (dashed curve) and depleted (solid curve) pump pulses at the output from the Raman amplifier and (b), (d), (f) corresponding interference traces when the π phase jump was injected into the pump pulse.

Fig. 6
Fig. 6

(a) Histogram of the mean frequency distribution in the calculated Stokes pulses at the output from the Raman generator. (b) Examples of the numerically generated Stokes spectra with close to transform limited spectral widths (the standard deviation of 0.17 T 2 ) and the mean frequencies detuned from the resonant Stokes frequency by the values of 0.11 T 2 (solid curve) and 0.13 T 2 (dashed curve). Example of the broadband near resonant Stokes spectrum with a standard deviation of 0.53 T 2 [dotted curve, (b)].

Fig. 7
Fig. 7

Calculated intensity profiles of the (a), (d), (g) input (dashed curve) and depleted (solid curve) pump pulses, (b), (e), (h) the phase profiles, and (c), (f), (i) interference traces for different frequency detunings Δ w when the π phase jump was injected into the Stokes pulse: (a), (b), (c) Δ w = 0 ; (d), (e), (f) Δ w = 0.06 T 2 ; (g), (h), (i) Δ w = 0.14 T 2 .

Fig. 8
Fig. 8

Calculated intensity profiles of the (a), (d), (g) input (dashed curve) and depleted (solid curve) pump pulses, (b), (e), (h) the phase profiles, and (c), (f), (i) interference traces for different frequency detunings Δ w when the π phase jump was injected into the pump pulse: (a), (b), (c) Δ w = 0 ; (d), (e), (f) Δ w = 0.018 T 2 ; (g), (h), (i) Δ w = 0.048 T 2 .

Fig. 9
Fig. 9

Calculated intensity profiles of the (a) input (dashed curve) and depleted (solid curve) pump pulses and (b) corresponding interference trace for the resonant soliton propagation when the π phase jump was injected into the Stokes pulse.

Equations (14)

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S eff = l ( λ P + λ S ) 4 tan 1 ( l b ) ,
L eff = 1 ( T 2 R ) n 1 T 2 R l T
b = l ( 2 r l ) .
z A S = i k 2 Q * A P ,
z A P = i k 2 ( w P w S ) Q A S ,
τ Q = Q T 2 i k 1 A S * A P + F ,
F ( z , τ ) F ( z , τ ) = 0 ,
F * ( z , τ ) F ( z , τ ) = 2 T 2 N S eff δ ( z z ) δ ( τ τ ) ,
Q ( z , 0 ) Q ( z , 0 ) = 0 ,
Q * ( z , 0 ) Q ( z , 0 ) = 1 N S eff δ ( z z ) .
A S ( 0 , τ ) A S ( 0 , τ ) = 0 ,
A S * ( 0 , τ ) A S ( 0 , τ ) = 2 π w S c S eff δ ( τ τ ) ,
τ Q = ( 1 T 2 + i Δ w ) Q i k 1 A S * A P .
β ( τ ) = 1 1 + exp ( δ ( τ τ 0 ) ) 1 ,

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