Abstract

I have discovered that in the coherent regime of ultrabroad-bandwidth Raman generation, a large number of long-lived soliton pulse trains are spontaneously generated. This novel solution of the dispersionless and highly transient regime, involving more than 40 distinct Raman lines of comparable amplitude, is found to be a strong attractor in the nonlinear dynamics, even when the system is initially far from this limit.

© 1995 Optical Society of America

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  1. Y. R. Shen, N. Bloembergen, Phys. Rev. 137, A1787 (1965).
    [CrossRef]
  2. C. S. Wang, Phys. Rev. 182, 482 (1969).
    [CrossRef]
  3. R. L. Carman, F. Shimuzu, C. S. Wang, N. Bloembergen, Phys. Rev. A 2, 60 (1970).
    [CrossRef]
  4. M. E. Mack, R. L. Carman, B. Reintjes, N. Bloembergen, Appl. Phys. Lett. 16, 209 (1970).
    [CrossRef]
  5. F. Y. F. Chu, A. C. Scott, Phys. Rev. A 12, 2060 (1975).
    [CrossRef]
  6. K. Drühl, R. G. Wenzel, J. L. Carlsten, Phys. Rev. Lett. 51, 1171 (1983).
    [CrossRef]
  7. R. G. Wenzel, J. L. Carsten, K. J. Drühl, J. Stat. Phys. 39, 621 (1985).
    [CrossRef]
  8. J. C. Englund, C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986).
    [CrossRef] [PubMed]
  9. J. C. Englund, C. M. Bowden, Phys. Rev. A 42, 2870 (1990).
    [CrossRef] [PubMed]
  10. D. C. MacPherson, R. C. Swanson, J. L. Carlsten, Phys. Rev. Lett. 61, 66 (1988).
    [CrossRef] [PubMed]
  11. D. C. MacPherson, R. C. Swanson, J. L. Carlsten, Phys. Rev. A 39, 6078 (1989).
    [CrossRef] [PubMed]
  12. C. R. Menyuk, Phys. Rev. Lett. 62, 2937 (1989).
    [CrossRef] [PubMed]
  13. L. L. Losev, A. P. Lutsenko, Kvantovaya Electron. (Moscow) 20, 1054 (1993).
  14. G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, M. J. Shaw, Opt. Lett. 19, 1400 (1994).
    [CrossRef] [PubMed]
  15. D. Eimerl, R. S. Hargrove, J. A. Paisner, Phys. Rev. Lett. 46, 651 (1981).
    [CrossRef]
  16. D. Eimerl, W. L. Kruer, E. M. Campbell, Comments Plasma Phys. 15, 85 (1992).
  17. D. Eimerl, D. Milam, J. Yu, Phys. Rev. Lett. 70, 2738 (1993).
    [CrossRef] [PubMed]
  18. A. P. Hickman, W. K. Bischel, Phys. Rev. A 37, 2516 (1988).
    [CrossRef] [PubMed]
  19. A. P. Hickman, J. A. Paisner, W. K. Bischel, Phys. Rev. A 33, 1788 (1986).
    [CrossRef] [PubMed]
  20. G. S. McDonald, G. H. C. New, “Coherence effects in ultrabroad bandwidth light generation,” submitted toPhys. Rev. A.
    [PubMed]
  21. J. N. Elgin, T. B. O’Hare, J. Phys. B 12, 159 (1979).
    [CrossRef]
  22. G. Hilfer, C. R. Menyuk, J. Opt. Soc. Am. B 7, 739 (1990).
    [CrossRef]
  23. M. Scalora, S. Singh, C. M. Bowden, Phys. Rev. Lett. 70, 1248 (1993).
    [CrossRef] [PubMed]
  24. S. J. Karttunen, R. R. E. Salomaa, Phys. Rev. Lett. 56, 604 (1986).
    [CrossRef] [PubMed]

1994 (1)

1993 (3)

L. L. Losev, A. P. Lutsenko, Kvantovaya Electron. (Moscow) 20, 1054 (1993).

D. Eimerl, D. Milam, J. Yu, Phys. Rev. Lett. 70, 2738 (1993).
[CrossRef] [PubMed]

M. Scalora, S. Singh, C. M. Bowden, Phys. Rev. Lett. 70, 1248 (1993).
[CrossRef] [PubMed]

1992 (1)

D. Eimerl, W. L. Kruer, E. M. Campbell, Comments Plasma Phys. 15, 85 (1992).

1990 (2)

J. C. Englund, C. M. Bowden, Phys. Rev. A 42, 2870 (1990).
[CrossRef] [PubMed]

G. Hilfer, C. R. Menyuk, J. Opt. Soc. Am. B 7, 739 (1990).
[CrossRef]

1989 (2)

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

C. R. Menyuk, Phys. Rev. Lett. 62, 2937 (1989).
[CrossRef] [PubMed]

1988 (2)

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

A. P. Hickman, W. K. Bischel, Phys. Rev. A 37, 2516 (1988).
[CrossRef] [PubMed]

1986 (3)

A. P. Hickman, J. A. Paisner, W. K. Bischel, Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

S. J. Karttunen, R. R. E. Salomaa, Phys. Rev. Lett. 56, 604 (1986).
[CrossRef] [PubMed]

J. C. Englund, C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986).
[CrossRef] [PubMed]

1985 (1)

R. G. Wenzel, J. L. Carsten, K. J. Drühl, J. Stat. Phys. 39, 621 (1985).
[CrossRef]

1983 (1)

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

1981 (1)

D. Eimerl, R. S. Hargrove, J. A. Paisner, Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

1979 (1)

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

1975 (1)

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

1970 (2)

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

M. E. Mack, R. L. Carman, B. Reintjes, N. Bloembergen, Appl. Phys. Lett. 16, 209 (1970).
[CrossRef]

1969 (1)

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

1965 (1)

Y. R. Shen, N. Bloembergen, Phys. Rev. 137, A1787 (1965).
[CrossRef]

Bischel, W. K.

A. P. Hickman, W. K. Bischel, Phys. Rev. A 37, 2516 (1988).
[CrossRef] [PubMed]

A. P. Hickman, J. A. Paisner, W. K. Bischel, Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

Bloembergen, N.

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

M. E. Mack, R. L. Carman, B. Reintjes, N. Bloembergen, Appl. Phys. Lett. 16, 209 (1970).
[CrossRef]

Y. R. Shen, N. Bloembergen, Phys. Rev. 137, A1787 (1965).
[CrossRef]

Bowden, C. M.

M. Scalora, S. Singh, C. M. Bowden, Phys. Rev. Lett. 70, 1248 (1993).
[CrossRef] [PubMed]

J. C. Englund, C. M. Bowden, Phys. Rev. A 42, 2870 (1990).
[CrossRef] [PubMed]

J. C. Englund, C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986).
[CrossRef] [PubMed]

Campbell, E. M.

D. Eimerl, W. L. Kruer, E. M. Campbell, Comments Plasma Phys. 15, 85 (1992).

Carlsten, J. L.

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

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

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

Carman, R. L.

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

M. E. Mack, R. L. Carman, B. Reintjes, N. Bloembergen, Appl. Phys. Lett. 16, 209 (1970).
[CrossRef]

Carsten, J. L.

R. G. Wenzel, J. L. Carsten, K. J. Drühl, J. Stat. Phys. 39, 621 (1985).
[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]

Drühl, K. J.

R. G. Wenzel, J. L. Carsten, K. J. Drühl, J. Stat. Phys. 39, 621 (1985).
[CrossRef]

Eimerl, D.

D. Eimerl, D. Milam, J. Yu, Phys. Rev. Lett. 70, 2738 (1993).
[CrossRef] [PubMed]

D. Eimerl, W. L. Kruer, E. M. Campbell, Comments Plasma Phys. 15, 85 (1992).

D. Eimerl, R. S. Hargrove, J. A. Paisner, Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

Elgin, J. N.

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

Englund, J. C.

J. C. Englund, C. M. Bowden, Phys. Rev. A 42, 2870 (1990).
[CrossRef] [PubMed]

J. C. Englund, C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986).
[CrossRef] [PubMed]

Hargrove, R. S.

D. Eimerl, R. S. Hargrove, J. A. Paisner, Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

Hickman, A. P.

A. P. Hickman, W. K. Bischel, Phys. Rev. A 37, 2516 (1988).
[CrossRef] [PubMed]

A. P. Hickman, J. A. Paisner, W. K. Bischel, Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

Hilfer, G.

Karttunen, S. J.

S. J. Karttunen, R. R. E. Salomaa, Phys. Rev. Lett. 56, 604 (1986).
[CrossRef] [PubMed]

Kruer, W. L.

D. Eimerl, W. L. Kruer, E. M. Campbell, Comments Plasma Phys. 15, 85 (1992).

Losev, L. L.

Lutsenko, A. P.

Mack, M. E.

M. E. Mack, R. L. Carman, B. Reintjes, N. Bloembergen, Appl. Phys. Lett. 16, 209 (1970).
[CrossRef]

MacPherson, D. C.

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

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

McDonald, G. S.

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, M. J. Shaw, Opt. Lett. 19, 1400 (1994).
[CrossRef] [PubMed]

G. S. McDonald, G. H. C. New, “Coherence effects in ultrabroad bandwidth light generation,” submitted toPhys. Rev. A.
[PubMed]

Menyuk, C. R.

Milam, D.

D. Eimerl, D. Milam, J. Yu, Phys. Rev. Lett. 70, 2738 (1993).
[CrossRef] [PubMed]

New, G. H. C.

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, M. J. Shaw, Opt. Lett. 19, 1400 (1994).
[CrossRef] [PubMed]

G. S. McDonald, G. H. C. New, “Coherence effects in ultrabroad bandwidth light generation,” submitted toPhys. Rev. A.
[PubMed]

O’Hare, T. B.

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

Paisner, J. A.

A. P. Hickman, J. A. Paisner, W. K. Bischel, Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

D. Eimerl, R. S. Hargrove, J. A. Paisner, Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

Reintjes, B.

M. E. Mack, R. L. Carman, B. Reintjes, N. Bloembergen, Appl. Phys. Lett. 16, 209 (1970).
[CrossRef]

Salomaa, R. R. E.

S. J. Karttunen, R. R. E. Salomaa, Phys. Rev. Lett. 56, 604 (1986).
[CrossRef] [PubMed]

Scalora, M.

M. Scalora, S. Singh, C. M. Bowden, Phys. Rev. Lett. 70, 1248 (1993).
[CrossRef] [PubMed]

Scott, A. C.

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

Shaw, M. J.

Shen, Y. R.

Y. R. Shen, N. Bloembergen, Phys. Rev. 137, A1787 (1965).
[CrossRef]

Shimuzu, F.

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

Singh, S.

M. Scalora, S. Singh, C. M. Bowden, Phys. Rev. Lett. 70, 1248 (1993).
[CrossRef] [PubMed]

Swanson, R. C.

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

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

Wang, C. S.

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

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

Wenzel, R. G.

R. G. Wenzel, J. L. Carsten, K. J. Drühl, J. Stat. Phys. 39, 621 (1985).
[CrossRef]

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

Yu, J.

D. Eimerl, D. Milam, J. Yu, Phys. Rev. Lett. 70, 2738 (1993).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

M. E. Mack, R. L. Carman, B. Reintjes, N. Bloembergen, Appl. Phys. Lett. 16, 209 (1970).
[CrossRef]

Comments Plasma Phys. (1)

D. Eimerl, W. L. Kruer, E. M. Campbell, Comments Plasma Phys. 15, 85 (1992).

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

J. Phys. B (1)

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

J. Stat. Phys. (1)

R. G. Wenzel, J. L. Carsten, K. J. Drühl, J. Stat. Phys. 39, 621 (1985).
[CrossRef]

Kvantovaya Electron (1)

L. L. Losev, A. P. Lutsenko, Kvantovaya Electron. (Moscow) 20, 1054 (1993).

Opt. Lett. (1)

Phys. Rev. (2)

Y. R. Shen, N. Bloembergen, Phys. Rev. 137, A1787 (1965).
[CrossRef]

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

Phys. Rev. A (6)

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

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

J. C. Englund, C. M. Bowden, Phys. Rev. A 42, 2870 (1990).
[CrossRef] [PubMed]

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

A. P. Hickman, W. K. Bischel, Phys. Rev. A 37, 2516 (1988).
[CrossRef] [PubMed]

A. P. Hickman, J. A. Paisner, W. K. Bischel, Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

D. Eimerl, D. Milam, J. Yu, Phys. Rev. Lett. 70, 2738 (1993).
[CrossRef] [PubMed]

C. R. Menyuk, Phys. Rev. Lett. 62, 2937 (1989).
[CrossRef] [PubMed]

D. Eimerl, R. S. Hargrove, J. A. Paisner, Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

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

J. C. Englund, C. M. Bowden, Phys. Rev. Lett. 57, 2661 (1986).
[CrossRef] [PubMed]

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

M. Scalora, S. Singh, C. M. Bowden, Phys. Rev. Lett. 70, 1248 (1993).
[CrossRef] [PubMed]

S. J. Karttunen, R. R. E. Salomaa, Phys. Rev. Lett. 56, 604 (1986).
[CrossRef] [PubMed]

Other (1)

G. S. McDonald, G. H. C. New, “Coherence effects in ultrabroad bandwidth light generation,” submitted toPhys. Rev. A.
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

Generated intensity profiles of (a) third anti-Stokes, (b) third Stokes, (c) eighth anti-Stokes, and (d) eighth Stokes waves (γ1 = 0, T2/tp = 4,Z = 250, and square input pulses). Each profile is plotted normalized to its peak value.

Fig. 2
Fig. 2

Collective characteristics of the Raman soliton pulse trains of Fig. 1: (a) source term for the polarization wave, (b) magnitude of the polarization (in units of 10−3), (c) sum of the wave intensities, (d) bandwidth generated (in units of the Stokes shift).

Fig. 3
Fig. 3

As in Fig. 1, except that T2/tp = 10 and Gaussian input pulses are used.

Fig. 4
Fig. 4

As in Fig. 2, except that T2/tp = 10, Gaussian input pulses are used, and |S|2 is in units of 10−1.

Equations (2)

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

A n Z = ω n 2 ω 0 [ P * A n + 1  exp ( i γ n + 1 Z ) P A n 1  exp ( i γ n Z ) ] ,
( T 2 t p ) P τ = P + S , S = j A j A j 1 *  exp ( i γ j Z ) .

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