Abstract

We experimentally observe a spontaneous temporal symmetry breaking instability in a coherently driven passive optical Kerr resonator. Using a time-symmetric configuration, we report output pulses with strongly asymmetric temporal and spectral intensity profiles, with up to 71% of the energy on the same side of the pump center frequency. The instability occurs above a certain pump power threshold but remarkably vanishes above a second threshold, in excellent agreement with theory. We also observe a generalized bistability in which an asymmetric output state coexists with a symmetric one in the same pumping conditions.

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    [CrossRef]
  2. P. W. Anderson, Science 177, 393 (1972).
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    [CrossRef]
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    [CrossRef]
  7. F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964).
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  8. P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964).
    [CrossRef]
  9. P. Kockaert and M. Haelterman, J. Opt. Soc. Am. B 16, 732 (1999).
    [CrossRef]
  10. T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. A 50, 5153 (1994).
    [CrossRef]
  11. C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, Phys. Rev. A 88, 033825 (2013).
    [CrossRef]
  12. T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, Phys. Rev. A 29, 1964 (1984).
    [CrossRef]
  13. C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 89, 083901 (2002).
    [CrossRef]
  14. P. G. Kevrekidis, Z. Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, Phys. Lett. A 340, 275 (2005).
    [CrossRef]
  15. M. Delqué, G. Fanjoux, H. Maillotte, P. Kockaert, T. Sylvestre, and M. Haelterman, Phys. Rev. A 83, 013807 (2011).
    [CrossRef]
  16. A. Shapere and F. Wilczek, Phys. Rev. Lett. 109, 160402 (2012).
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  17. G. Grynberg, M. Pinard, and P. Verkerk, Europhys. Lett. 9, 139 (1989).
    [CrossRef]
  18. E. G. Westhoff, V. Kneisel, Y. A. Logvin, T. Ackemann, and W. Lange, J. Opt. B 2, 386 (2000).
  19. L. Longchambon, N. Treps, T. Coudreau, J. Laurat, and C. Fabre, Opt. Lett. 30, 284 (2005).
    [CrossRef]
  20. M. Haelterman, G. Vitrant, and J. García-Mateos, in Nonlinear Guided Waves and their Applications, Vol. 6 of 1995 OSA Technical Digest Series (OSA, 1995), pp. 201–203.
  21. J. García-Mateos, F. C. Bienzobas, and M. Haelterman, Fiber Integr. Opt. 14, 337 (1995).
    [CrossRef]
  22. J. P. Torres, J. Boyce, and R. Y. Chiao, Phys. Rev. Lett. 83, 4293 (1999).
    [CrossRef]
  23. M. J. Schmidberger, D. Novoa, F. Biancalana, P. St.J. Russell, and N. Y. Joly, Opt. Express 22, 3045 (2014).
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  24. M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
    [CrossRef]
  25. L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
    [CrossRef]
  26. F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
    [CrossRef]
  27. S. Coen and M. Haelterman, Opt. Lett. 26, 39 (2001).
    [CrossRef]
  28. S. Coen, M. Haelterman, Ph. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, J. Opt. Soc. Am. B 15, 2283 (1998).
    [CrossRef]
  29. F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
    [CrossRef]
  30. S. Coen, M. Tlidi, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
    [CrossRef]

2014 (1)

2013 (2)

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, Phys. Rev. A 88, 033825 (2013).
[CrossRef]

2012 (1)

A. Shapere and F. Wilczek, Phys. Rev. Lett. 109, 160402 (2012).
[CrossRef]

2011 (1)

M. Delqué, G. Fanjoux, H. Maillotte, P. Kockaert, T. Sylvestre, and M. Haelterman, Phys. Rev. A 83, 013807 (2011).
[CrossRef]

2010 (1)

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

2005 (2)

P. G. Kevrekidis, Z. Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, Phys. Lett. A 340, 275 (2005).
[CrossRef]

L. Longchambon, N. Treps, T. Coudreau, J. Laurat, and C. Fabre, Opt. Lett. 30, 284 (2005).
[CrossRef]

2002 (1)

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef]

2001 (1)

2000 (1)

E. G. Westhoff, V. Kneisel, Y. A. Logvin, T. Ackemann, and W. Lange, J. Opt. B 2, 386 (2000).

1999 (3)

J. P. Torres, J. Boyce, and R. Y. Chiao, Phys. Rev. Lett. 83, 4293 (1999).
[CrossRef]

S. Coen, M. Tlidi, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

P. Kockaert and M. Haelterman, J. Opt. Soc. Am. B 16, 732 (1999).
[CrossRef]

1998 (1)

1995 (1)

J. García-Mateos, F. C. Bienzobas, and M. Haelterman, Fiber Integr. Opt. 14, 337 (1995).
[CrossRef]

1994 (1)

T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. A 50, 5153 (1994).
[CrossRef]

1992 (1)

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

1989 (1)

G. Grynberg, M. Pinard, and P. Verkerk, Europhys. Lett. 9, 139 (1989).
[CrossRef]

1987 (1)

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef]

1984 (1)

T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[CrossRef]

1972 (1)

P. W. Anderson, Science 177, 393 (1972).
[CrossRef]

1969 (1)

I. Prigogine, R. Lefever, A. Goldbeter, and M. Herschkowitz-Kaufman, Nature 223, 913 (1969).
[CrossRef]

1967 (1)

I. Prigogine and G. Nicolis, J. Chem. Phys. 46, 3542 (1967).
[CrossRef]

1964 (2)

F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964).
[CrossRef]

P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964).
[CrossRef]

1962 (1)

M. Baker and S. L. Glashow, Phys. Rev. 128, 2462 (1962).
[CrossRef]

Ackemann, T.

E. G. Westhoff, V. Kneisel, Y. A. Logvin, T. Ackemann, and W. Lange, J. Opt. B 2, 386 (2000).

Anderson, P. W.

P. W. Anderson, Science 177, 393 (1972).
[CrossRef]

Baker, M.

M. Baker and S. L. Glashow, Phys. Rev. 128, 2462 (1962).
[CrossRef]

Biancalana, F.

Bienzobas, F. C.

J. García-Mateos, F. C. Bienzobas, and M. Haelterman, Fiber Integr. Opt. 14, 337 (1995).
[CrossRef]

Boyce, J.

J. P. Torres, J. Boyce, and R. Y. Chiao, Phys. Rev. Lett. 83, 4293 (1999).
[CrossRef]

Brout, R.

F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964).
[CrossRef]

Cambournac, C.

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef]

Chen, Z.

P. G. Kevrekidis, Z. Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, Phys. Lett. A 340, 275 (2005).
[CrossRef]

Chiao, R. Y.

J. P. Torres, J. Boyce, and R. Y. Chiao, Phys. Rev. Lett. 83, 4293 (1999).
[CrossRef]

Coen, S.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

S. Coen and M. Haelterman, Opt. Lett. 26, 39 (2001).
[CrossRef]

S. Coen, M. Tlidi, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

S. Coen, M. Haelterman, Ph. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, J. Opt. Soc. Am. B 15, 2283 (1998).
[CrossRef]

Coudreau, T.

de Sterke, C. M.

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, Phys. Rev. A 88, 033825 (2013).
[CrossRef]

Delage, L.

Delqué, M.

M. Delqué, G. Fanjoux, H. Maillotte, P. Kockaert, T. Sylvestre, and M. Haelterman, Phys. Rev. A 83, 013807 (2011).
[CrossRef]

Emplit, Ph.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef]

S. Coen, M. Tlidi, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

S. Coen, M. Haelterman, Ph. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, J. Opt. Soc. Am. B 15, 2283 (1998).
[CrossRef]

Englert, F.

F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964).
[CrossRef]

Fabre, C.

Fanjoux, G.

M. Delqué, G. Fanjoux, H. Maillotte, P. Kockaert, T. Sylvestre, and M. Haelterman, Phys. Rev. A 83, 013807 (2011).
[CrossRef]

Frantzeskakis, D. J.

P. G. Kevrekidis, Z. Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, Phys. Lett. A 340, 275 (2005).
[CrossRef]

García-Mateos, J.

J. García-Mateos, F. C. Bienzobas, and M. Haelterman, Fiber Integr. Opt. 14, 337 (1995).
[CrossRef]

M. Haelterman, G. Vitrant, and J. García-Mateos, in Nonlinear Guided Waves and their Applications, Vol. 6 of 1995 OSA Technical Digest Series (OSA, 1995), pp. 201–203.

Glashow, S. L.

M. Baker and S. L. Glashow, Phys. Rev. 128, 2462 (1962).
[CrossRef]

Goldbeter, A.

I. Prigogine, R. Lefever, A. Goldbeter, and M. Herschkowitz-Kaufman, Nature 223, 913 (1969).
[CrossRef]

Gorza, S.-P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

Grynberg, G.

G. Grynberg, M. Pinard, and P. Verkerk, Europhys. Lett. 9, 139 (1989).
[CrossRef]

Haelterman, M.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

M. Delqué, G. Fanjoux, H. Maillotte, P. Kockaert, T. Sylvestre, and M. Haelterman, Phys. Rev. A 83, 013807 (2011).
[CrossRef]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef]

S. Coen and M. Haelterman, Opt. Lett. 26, 39 (2001).
[CrossRef]

P. Kockaert and M. Haelterman, J. Opt. Soc. Am. B 16, 732 (1999).
[CrossRef]

S. Coen, M. Tlidi, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

S. Coen, M. Haelterman, Ph. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, J. Opt. Soc. Am. B 15, 2283 (1998).
[CrossRef]

J. García-Mateos, F. C. Bienzobas, and M. Haelterman, Fiber Integr. Opt. 14, 337 (1995).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

M. Haelterman, G. Vitrant, and J. García-Mateos, in Nonlinear Guided Waves and their Applications, Vol. 6 of 1995 OSA Technical Digest Series (OSA, 1995), pp. 201–203.

Herschkowitz-Kaufman, M.

I. Prigogine, R. Lefever, A. Goldbeter, and M. Herschkowitz-Kaufman, Nature 223, 913 (1969).
[CrossRef]

Higgs, P. W.

P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964).
[CrossRef]

Jeyaratnam, J.

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, Phys. Rev. A 88, 033825 (2013).
[CrossRef]

Joly, N. Y.

Kabakova, I. V.

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, Phys. Rev. A 88, 033825 (2013).
[CrossRef]

Kevrekidis, P. G.

P. G. Kevrekidis, Z. Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, Phys. Lett. A 340, 275 (2005).
[CrossRef]

Kitano, M.

T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[CrossRef]

Kneisel, V.

E. G. Westhoff, V. Kneisel, Y. A. Logvin, T. Ackemann, and W. Lange, J. Opt. B 2, 386 (2000).

Kockaert, P.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

M. Delqué, G. Fanjoux, H. Maillotte, P. Kockaert, T. Sylvestre, and M. Haelterman, Phys. Rev. A 83, 013807 (2011).
[CrossRef]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef]

P. Kockaert and M. Haelterman, J. Opt. Soc. Am. B 16, 732 (1999).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Statistical Physics (Elsevier, 1980).

Lange, W.

E. G. Westhoff, V. Kneisel, Y. A. Logvin, T. Ackemann, and W. Lange, J. Opt. B 2, 386 (2000).

Laurat, J.

Lederer, F.

T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. A 50, 5153 (1994).
[CrossRef]

Lefever, R.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef]

I. Prigogine, R. Lefever, A. Goldbeter, and M. Herschkowitz-Kaufman, Nature 223, 913 (1969).
[CrossRef]

Leo, F.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Statistical Physics (Elsevier, 1980).

Logvin, Y. A.

E. G. Westhoff, V. Kneisel, Y. A. Logvin, T. Ackemann, and W. Lange, J. Opt. B 2, 386 (2000).

Longchambon, L.

Lugiato, L. A.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef]

Maillotte, H.

M. Delqué, G. Fanjoux, H. Maillotte, P. Kockaert, T. Sylvestre, and M. Haelterman, Phys. Rev. A 83, 013807 (2011).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef]

Malomed, B. A.

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, Phys. Rev. A 88, 033825 (2013).
[CrossRef]

P. G. Kevrekidis, Z. Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, Phys. Lett. A 340, 275 (2005).
[CrossRef]

Mussot, A.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

Nicolis, G.

I. Prigogine and G. Nicolis, J. Chem. Phys. 46, 3542 (1967).
[CrossRef]

Novoa, D.

Ogawa, T.

T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[CrossRef]

Okamoto, T.

T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[CrossRef]

Peschel, T.

T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. A 50, 5153 (1994).
[CrossRef]

Peschel, U.

T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. A 50, 5153 (1994).
[CrossRef]

Pinard, M.

G. Grynberg, M. Pinard, and P. Verkerk, Europhys. Lett. 9, 139 (1989).
[CrossRef]

Prigogine, I.

I. Prigogine, R. Lefever, A. Goldbeter, and M. Herschkowitz-Kaufman, Nature 223, 913 (1969).
[CrossRef]

I. Prigogine and G. Nicolis, J. Chem. Phys. 46, 3542 (1967).
[CrossRef]

Reynaud, F.

Russell, P. St.J.

Schmidberger, M. J.

Shapere, A.

A. Shapere and F. Wilczek, Phys. Rev. Lett. 109, 160402 (2012).
[CrossRef]

Simohamed, L. M.

Sylvestre, T.

M. Delqué, G. Fanjoux, H. Maillotte, P. Kockaert, T. Sylvestre, and M. Haelterman, Phys. Rev. A 83, 013807 (2011).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef]

Taki, M.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

Tlidi, M.

S. Coen, M. Tlidi, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

Torres, J. P.

J. P. Torres, J. Boyce, and R. Y. Chiao, Phys. Rev. Lett. 83, 4293 (1999).
[CrossRef]

Treps, N.

Trillo, S.

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Uddin, I.

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, Phys. Rev. A 88, 033825 (2013).
[CrossRef]

Vanderlinden, B.

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef]

Verkerk, P.

G. Grynberg, M. Pinard, and P. Verkerk, Europhys. Lett. 9, 139 (1989).
[CrossRef]

Vitrant, G.

M. Haelterman, G. Vitrant, and J. García-Mateos, in Nonlinear Guided Waves and their Applications, Vol. 6 of 1995 OSA Technical Digest Series (OSA, 1995), pp. 201–203.

Wabnitz, S.

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Weinstein, M. I.

P. G. Kevrekidis, Z. Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, Phys. Lett. A 340, 275 (2005).
[CrossRef]

Westhoff, E. G.

E. G. Westhoff, V. Kneisel, Y. A. Logvin, T. Ackemann, and W. Lange, J. Opt. B 2, 386 (2000).

Wilczek, F.

A. Shapere and F. Wilczek, Phys. Rev. Lett. 109, 160402 (2012).
[CrossRef]

Yabuzaki, T.

T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[CrossRef]

Europhys. Lett. (1)

G. Grynberg, M. Pinard, and P. Verkerk, Europhys. Lett. 9, 139 (1989).
[CrossRef]

Fiber Integr. Opt. (1)

J. García-Mateos, F. C. Bienzobas, and M. Haelterman, Fiber Integr. Opt. 14, 337 (1995).
[CrossRef]

J. Chem. Phys. (1)

I. Prigogine and G. Nicolis, J. Chem. Phys. 46, 3542 (1967).
[CrossRef]

J. Opt. B (1)

E. G. Westhoff, V. Kneisel, Y. A. Logvin, T. Ackemann, and W. Lange, J. Opt. B 2, 386 (2000).

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

Nat. Photonics (1)

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

Nature (1)

I. Prigogine, R. Lefever, A. Goldbeter, and M. Herschkowitz-Kaufman, Nature 223, 913 (1969).
[CrossRef]

Opt. Commun. (1)

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

P. G. Kevrekidis, Z. Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, Phys. Lett. A 340, 275 (2005).
[CrossRef]

Phys. Rev. (1)

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup: BPF, bandpass filter; EDFA, erbium-doped fiber amplifier; PC, polarization controller.

Fig. 2.
Fig. 2.

(a) SSB bifurcation diagram with symmetric (blue) and asymmetric (red) states (dotted parts are unstable), for Δ=0.92 and T0=2.3. (b) Asymmetric pulse temporal intensity profile obtained for X=6.4 (red) superimposed with the pump pulse (dashed green).

Fig. 3.
Fig. 3.

(a) Experimental output spectra (linear scale) for Δ=0.92 versus normalized pump power X. Right, spectrum obtained for X=6.4 (red) compared with the simulated one (black) and superimposed on the measured pump spectrum (dashed green). (b) Spectral asymmetry factor derived from (a) (red circles) and compared to numerical results without (light gray) and with (black) the β3 contribution. (c) Bifurcation diagram as in Fig. 2(a) (light gray curves) compared to that inclusive of the β3 contribution (color-coded with the asymmetry factor). Dotted parts correspond to unstable states.

Fig. 4.
Fig. 4.

As in Fig. 3 but for Δ=3.2. In (a) the top (bottom) panel was obtained for increasing (decreasing) values of X, respectively. The spectrum on the right corresponds to X=10. In (b)–(c), arrows indicate how the hysteresis is traveled through.

Fig. 5.
Fig. 5.

Experimental temporal intensity profiles of the two mirror-like stationary intracavity pulses (red and green) retrieved with FROG for (a) X=6.4, Δ=0.92 and (b) X=10, Δ=3.2. The dashed curves are the symmetric pulses observed at a low pump power level while the gray dotted curves are theoretical predictions.

Equations (1)

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E(z,τ)z=[1+i(|E|2Δ)+i2τ2]E+S(τ),

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