Abstract

The π phase jump generated spontaneously in stimulated Raman scattering, which is the origin of Raman soliton formation, has been investigated. The probability of Raman soliton generation is measured as a function of the pressure of the Raman medium and the pump intensity. The relation between the soliton’s shape and the magnitude of the phase jump has been revealed by homodyne phase detection of the Stokes phase. These results are compared with numerical calculation, and qualitative agreement is obtained. The stochastic nature of Raman soliton generation is discussed in terms of the phase jump’s magnitude and evolution through the Raman medium.

© 1991 Optical Society of America

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  1. F. A. Hopf, “Phase-wave fluctuations in superfluorescence,” Phys. Rev. A 20, 2064–2073 (1979).
    [CrossRef]
  2. M. G. Raymer, K. Rza̦żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
    [CrossRef] [PubMed]
  3. I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
    [CrossRef]
  4. I. A. Walmsley and M. G. Reymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
    [CrossRef] [PubMed]
  5. M. G. Raymer, Z. W. Li, and I. A. Walmsley, “Temporal quantum fluctuations in stimulated Raman scattering: coherent-model description,” Phys. Rev. Lett. 63, 1586–1589 (1989).
    [CrossRef] [PubMed]
  6. K. Druhl, R. G. Wenzel, and J. L. Carlsten, “Observation of solitons in stimulated Raman scattering,” Phys. Rev. Lett. 51, 1171–1174 (1983).
    [CrossRef]
  7. C. M. Bowden and J. C. Englund, “Macroscopic manifestations of quantum noise,” Opt. Commun. 67, 71–78 (1988).
    [CrossRef]
  8. J. C. Englund and C. M. Bowden, “Spontaneous generation of Raman solitons from quantum noise,” Phys. Rev. Lett. 57, 2661–2663 (1986).
    [CrossRef] [PubMed]
  9. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the stimulated-Raman-scattering line-width,” Phys. Rev. Lett. 61, 66–69 (1988).
    [CrossRef] [PubMed]
  10. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuation and correlations in the stimulated Raman scattering spectrum,” Phys. Rev. A 39, 3487–3497 (1989).
    [CrossRef] [PubMed]
  11. 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]
  12. K. Midorikawa, H. Tashiro, Y. Aoki, K. Nagasaka, K. Toyoda, and S. Namba, “Room-temperature operation of a para-H2rotational Raman laser,” Appl. Phys. Lett. 47, 1033–1035 (1985).
    [CrossRef]
  13. D. C. MacPherson, J. L. Carlsten, and K. J. Druhl, “Generation of solitons in transient stimulated Raman scattering by optical phase shifts,” J. Opt. Soc. Am. B 4, 1853–1859 (1987).
    [CrossRef]
  14. A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
    [CrossRef]
  15. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Soliton initiation and decay in stimulated Raman scattering,” Phys. Rev. A 39, 6078–6081 (1989).
    [CrossRef] [PubMed]

1990 (1)

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]

1989 (3)

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuation and correlations in the stimulated Raman scattering spectrum,” Phys. Rev. A 39, 3487–3497 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Soliton initiation and decay in stimulated Raman scattering,” Phys. Rev. A 39, 6078–6081 (1989).
[CrossRef] [PubMed]

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

1988 (2)

C. M. Bowden and J. C. Englund, “Macroscopic manifestations of quantum noise,” Opt. Commun. 67, 71–78 (1988).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the stimulated-Raman-scattering line-width,” Phys. Rev. Lett. 61, 66–69 (1988).
[CrossRef] [PubMed]

1987 (1)

1986 (2)

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

I. A. Walmsley and M. G. Reymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
[CrossRef] [PubMed]

1985 (1)

K. Midorikawa, H. Tashiro, Y. Aoki, K. Nagasaka, K. Toyoda, and S. Namba, “Room-temperature operation of a para-H2rotational Raman laser,” Appl. Phys. Lett. 47, 1033–1035 (1985).
[CrossRef]

1983 (2)

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[CrossRef]

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

1982 (1)

1979 (2)

F. A. Hopf, “Phase-wave fluctuations in superfluorescence,” Phys. Rev. A 20, 2064–2073 (1979).
[CrossRef]

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

Akiyama, Y.

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]

Aoki, Y.

K. Midorikawa, H. Tashiro, Y. Aoki, K. Nagasaka, K. Toyoda, and S. Namba, “Room-temperature operation of a para-H2rotational Raman laser,” Appl. Phys. Lett. 47, 1033–1035 (1985).
[CrossRef]

Bowden, C. M.

C. M. Bowden and J. C. Englund, “Macroscopic manifestations 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.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuation and correlations in the stimulated Raman scattering spectrum,” Phys. Rev. A 39, 3487–3497 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Soliton initiation and decay in stimulated Raman scattering,” Phys. Rev. A 39, 6078–6081 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the stimulated-Raman-scattering line-width,” Phys. Rev. Lett. 61, 66–69 (1988).
[CrossRef] [PubMed]

D. C. MacPherson, J. L. Carlsten, and K. J. Druhl, “Generation of solitons in transient stimulated Raman scattering by optical phase shifts,” J. Opt. Soc. Am. B 4, 1853–1859 (1987).
[CrossRef]

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

Druhl, K.

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

Druhl, K. J.

Englund, J. C.

C. M. Bowden and J. C. Englund, “Macroscopic manifestations 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]

Hopf, F. A.

F. A. Hopf, “Phase-wave fluctuations in superfluorescence,” Phys. Rev. A 20, 2064–2073 (1979).
[CrossRef]

Kaiser, W.

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

Laubereau, A.

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

Li, Z. W.

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

MacPherson, D. C.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuation and correlations in the stimulated Raman scattering spectrum,” Phys. Rev. A 39, 3487–3497 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Soliton initiation and decay in stimulated Raman scattering,” Phys. Rev. A 39, 6078–6081 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the stimulated-Raman-scattering line-width,” Phys. Rev. Lett. 61, 66–69 (1988).
[CrossRef] [PubMed]

D. C. MacPherson, J. L. Carlsten, and K. J. Druhl, “Generation of solitons in transient stimulated Raman scattering by optical phase shifts,” J. Opt. Soc. Am. B 4, 1853–1859 (1987).
[CrossRef]

Midorikawa, K.

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]

K. Midorikawa, H. Tashiro, Y. Aoki, K. Nagasaka, K. Toyoda, and S. Namba, “Room-temperature operation of a para-H2rotational Raman laser,” Appl. Phys. Lett. 47, 1033–1035 (1985).
[CrossRef]

Mostowski, J.

Nagasaka, K.

K. Midorikawa, H. Tashiro, Y. Aoki, K. Nagasaka, K. Toyoda, and S. Namba, “Room-temperature operation of a para-H2rotational Raman laser,” Appl. Phys. Lett. 47, 1033–1035 (1985).
[CrossRef]

Namba, S.

K. Midorikawa, H. Tashiro, Y. Aoki, K. Nagasaka, K. Toyoda, and S. Namba, “Room-temperature operation of a para-H2rotational Raman laser,” Appl. Phys. Lett. 47, 1033–1035 (1985).
[CrossRef]

Obara, M.

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]

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-model description,” Phys. Rev. Lett. 63, 1586–1589 (1989).
[CrossRef] [PubMed]

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[CrossRef]

M. G. Raymer, K. Rza̦żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
[CrossRef] [PubMed]

Reymer, M. G.

I. A. Walmsley and M. G. Reymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
[CrossRef] [PubMed]

Rza?zewski, K.

Swanson, R. C.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuation and correlations in the stimulated Raman scattering spectrum,” Phys. Rev. A 39, 3487–3497 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Soliton initiation and decay in stimulated Raman scattering,” Phys. Rev. A 39, 6078–6081 (1989).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the stimulated-Raman-scattering line-width,” Phys. Rev. Lett. 61, 66–69 (1988).
[CrossRef] [PubMed]

Tashiro, H.

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]

K. Midorikawa, H. Tashiro, Y. Aoki, K. Nagasaka, K. Toyoda, and S. Namba, “Room-temperature operation of a para-H2rotational Raman laser,” Appl. Phys. Lett. 47, 1033–1035 (1985).
[CrossRef]

Toyoda, K.

K. Midorikawa, H. Tashiro, Y. Aoki, K. Nagasaka, K. Toyoda, and S. Namba, “Room-temperature operation of a para-H2rotational Raman laser,” Appl. Phys. Lett. 47, 1033–1035 (1985).
[CrossRef]

Walmsley, I. A.

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

I. A. Walmsley and M. G. Reymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
[CrossRef] [PubMed]

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[CrossRef]

Wenzel, R. G.

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

Appl. Phys. Lett. (1)

K. Midorikawa, H. Tashiro, Y. Aoki, K. Nagasaka, K. Toyoda, and S. Namba, “Room-temperature operation of a para-H2rotational Raman laser,” Appl. Phys. Lett. 47, 1033–1035 (1985).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

C. M. Bowden and J. C. Englund, “Macroscopic manifestations of quantum noise,” Opt. Commun. 67, 71–78 (1988).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (5)

I. A. Walmsley and M. G. Reymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
[CrossRef] [PubMed]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuation and correlations in the stimulated Raman scattering spectrum,” Phys. Rev. A 39, 3487–3497 (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]

F. A. Hopf, “Phase-wave fluctuations in superfluorescence,” Phys. Rev. A 20, 2064–2073 (1979).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Soliton initiation and decay in stimulated Raman scattering,” Phys. Rev. A 39, 6078–6081 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

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

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the stimulated-Raman-scattering line-width,” Phys. Rev. Lett. 61, 66–69 (1988).
[CrossRef] [PubMed]

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

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

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[CrossRef]

Prog. Quantum Electron. (1)

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

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup.

Fig. 2
Fig. 2

(a) Observed pulse shape of the incident (dashed curve) and depleted (solid line) pump pulses without an anomalous reversal of the pump depletion, (b)–(d) observed Raman solitons in depleted pump pulses. The pressures of the para-H2 are 1487, 1800, 1480, and 900 Torr in (a), (b), (c), and (d), respectively.

Fig. 3
Fig. 3

Probability of soliton generation as a function of (a) para-H2 pressure and (b) pump energy.

Fig. 4
Fig. 4

Stokes pulses and beat waveforms observed by homodyne detection. (a), (b) Stokes outputs emerging from the Raman cell. (c), (d) Observed beat waveforms of the Stokes pulses in (a) and (b), respectively. (a), (c) Waveforms without the phase jump in the Stokes waves; (b) and (d) are waveforms with the phase jump.

Fig. 5
Fig. 5

Observed pulse shapes of depleted pump pulses with solitons. The values of the phase jumps in their Stokes fields are estimated based on the numerical model.

Fig. 6
Fig. 6

Upper curves, calculated phases of the Stokes pulses; lower curves, calculated pump pulse shapes. (a), (b), (c), (d) Stokes waveforms after the 1st, 2nd, 27th, and 32nd passes, respectively, in a MPC. The Stokes π phase jump is added in (b); solitons are generated at the π phase jump in (c) and (d).

Fig. 7
Fig. 7

Calculated waveforms of the pump pulses and Stokes phases. The phase-jump angles of the incident Stokes pulses are 180, 175, 170, and 90 deg in (a), (b), (c), and (d), respectively.

Fig. 8
Fig. 8

Calculated waveforms with different initiation times of the Stokes phase jump. The positions of the Stokes phase jumps in the incident Stokes pulses are 74, 80, and 85 nsec in (a), (b), and (c), respectively. Anomalous pump reversal is generated at (a) 110, (b) 125, and (c) 145 nsec in the depleted pump pulses.

Fig. 9
Fig. 9

Probability of soliton generation as a function of (a) para-H2 pressure and (b) pump energy. The solid curves are the best fits based on the numerical model.

Equations (14)

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E s z = i π ω s c n s N ( α q ) E p Q * ,
E p z = i π ω p c n p N ( α q ) E s Q ,
Q t + Q T 2 = i 4 m ω q ( α q ) E p E s * ,
E p = 1 / 2 { E p exp [ i ( k p z - ω p t - ϕ p ) ] + c . c . } ,
E s = 1 / 2 { E s exp [ i ( k s z - ω s t - ϕ s ) ] + c . c . } ,
Q = 1 / 2 { Q exp [ i ( k q z - ω q t - ϕ q ) ] + c . c . } .
I p = c n p 8 π E p 2 ,             I s = c n s 8 π E s 2 ,
I s z = - K 1 ( I p I s ) 1 / 2 Q sin Φ ,
I p z = ω p ω s K 1 ( I p I s ) 1 / 2 Q sin Φ ,
Q t + Q T 2 = - K 2 ( I p I s ) 1 / 2 sin Φ ,
ϕ s z = K 1 2 ( I p / I s ) 1 / 2 Q cos Φ ,
ϕ p z = K 1 2 ω p ω s ( I p / I s ) 1 / 2 Q cos Φ ,
ϕ q t = K 2 ( I p I s ) 1 / 2 Q cos Φ ,
Φ = ϕ p - ϕ s - ϕ q , K 1 = 2 π c N [ 2 m ω q ω s ω p ( σ Ω ) ] 1 / 2 , K 2 = 2 π c ω s [ 2 n p n s ω p ω s ω q m ( σ Ω ) ] 1 / 2 , σ Ω = ω s 2 ω p 2 m ω q c 4 ( α q ) 2 ,

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