Abstract

We show numerically that bright and dark cavity solitons can be obtained in bidirectional class A ring lasers only if the phase invariance of the electromagnetic field is broken. The phase invariance symmetry is responsible for the existence of phase waves, which generate long-range interactions destroying the property of independence among otherwise localized structures. We improved the usual model describing such types of lasers, and we prove that it leads to genuine cavity solitons.

© 2008 Optical Society of America

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  1. http://www.funfacs.org.
  2. B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
    [CrossRef] [PubMed]
  3. U. Bortolozzo and S. Residori, Phys. Rev. Lett. 96, 037801 (2006).
    [CrossRef] [PubMed]
  4. V. B. Taranenko, I. Ganne, R. Kusselevitz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
  5. V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).
  6. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
    [CrossRef] [PubMed]
  7. Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, Phys. Rev. A 74, 023818 (2006).
    [CrossRef]
  8. X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
    [CrossRef]
  9. Y. Tanguy, T. Ackemann, and R. Jäger, Phys. Rev. A 74, 053824 (2006).
    [CrossRef]
  10. I. Perez-Arjona, J. V. Sanchez-Morcillo, and E. Roldan, Opt. Lett. 32, 3221 (2007).
    [CrossRef] [PubMed]
  11. The terms “dark” and “bright” solitons may lead to some misunderstandings. In , they refer to a local lack and overload of light, respectively, and are absolutely not related to the usual topological solitons observed in integrable dynamical systems. Also, contrary to the usual “cavity solitons” , the stability of the localized structures in does not result from a balance between bistability and modulational instability. This point is well described in D. Gomila, P. Colet, M. San Miguel, A. J. Scroggie, and G. L. Oppo, IEEE J. Quantum Electron. 39, 238 (2003).
    [CrossRef]
  12. H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, Phys. Rev. A 37, 470 (1988).
    [CrossRef] [PubMed]
  13. G. K. Harkness, W. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
    [CrossRef] [PubMed]
  14. W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
    [CrossRef] [PubMed]

2007 (1)

2006 (4)

U. Bortolozzo and S. Residori, Phys. Rev. Lett. 96, 037801 (2006).
[CrossRef] [PubMed]

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, Phys. Rev. A 74, 023818 (2006).
[CrossRef]

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

Y. Tanguy, T. Ackemann, and R. Jäger, Phys. Rev. A 74, 053824 (2006).
[CrossRef]

2003 (1)

The terms “dark” and “bright” solitons may lead to some misunderstandings. In , they refer to a local lack and overload of light, respectively, and are absolutely not related to the usual topological solitons observed in integrable dynamical systems. Also, contrary to the usual “cavity solitons” , the stability of the localized structures in does not result from a balance between bistability and modulational instability. This point is well described in D. Gomila, P. Colet, M. San Miguel, A. J. Scroggie, and G. L. Oppo, IEEE J. Quantum Electron. 39, 238 (2003).
[CrossRef]

2002 (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

2001 (2)

V. B. Taranenko, I. Ganne, R. Kusselevitz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).

V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).

2000 (1)

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

1996 (1)

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
[CrossRef] [PubMed]

1994 (1)

G. K. Harkness, W. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[CrossRef] [PubMed]

1988 (1)

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, Phys. Rev. A 37, 470 (1988).
[CrossRef] [PubMed]

Abraham, N. B.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, Phys. Rev. A 37, 470 (1988).
[CrossRef] [PubMed]

Ackemann, T.

Y. Tanguy, T. Ackemann, and R. Jäger, Phys. Rev. A 74, 053824 (2006).
[CrossRef]

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

Balle, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Barbay, S.

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, Phys. Rev. A 74, 023818 (2006).
[CrossRef]

Barland, S.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Bortolozzo, U.

U. Bortolozzo and S. Residori, Phys. Rev. Lett. 96, 037801 (2006).
[CrossRef] [PubMed]

Brambilla, M.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Caboche, E.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

Colet, P.

The terms “dark” and “bright” solitons may lead to some misunderstandings. In , they refer to a local lack and overload of light, respectively, and are absolutely not related to the usual topological solitons observed in integrable dynamical systems. Also, contrary to the usual “cavity solitons” , the stability of the localized structures in does not result from a balance between bistability and modulational instability. This point is well described in D. Gomila, P. Colet, M. San Miguel, A. J. Scroggie, and G. L. Oppo, IEEE J. Quantum Electron. 39, 238 (2003).
[CrossRef]

Feldmann, M.

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

Firth, W.

G. K. Harkness, W. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[CrossRef] [PubMed]

Firth, W. J.

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
[CrossRef] [PubMed]

Ganne, I.

V. B. Taranenko, I. Ganne, R. Kusselevitz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).

Geddes, J. B.

G. K. Harkness, W. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[CrossRef] [PubMed]

Giudici, M.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Gomila, D.

The terms “dark” and “bright” solitons may lead to some misunderstandings. In , they refer to a local lack and overload of light, respectively, and are absolutely not related to the usual topological solitons observed in integrable dynamical systems. Also, contrary to the usual “cavity solitons” , the stability of the localized structures in does not result from a balance between bistability and modulational instability. This point is well described in D. Gomila, P. Colet, M. San Miguel, A. J. Scroggie, and G. L. Oppo, IEEE J. Quantum Electron. 39, 238 (2003).
[CrossRef]

Hachair, X.

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, Phys. Rev. A 74, 023818 (2006).
[CrossRef]

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

Harkness, G. K.

G. K. Harkness, W. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[CrossRef] [PubMed]

Hoffer, L. M.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, Phys. Rev. A 37, 470 (1988).
[CrossRef] [PubMed]

Jager, R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Jäger, R.

Y. Tanguy, T. Ackemann, and R. Jäger, Phys. Rev. A 74, 053824 (2006).
[CrossRef]

Kheradmand, R.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

Knodl, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Kusselevitz, R.

V. B. Taranenko, I. Ganne, R. Kusselevitz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).

Kuszelewicz, R.

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, Phys. Rev. A 74, 023818 (2006).
[CrossRef]

Lange, W.

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

Leroy, L.

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, Phys. Rev. A 74, 023818 (2006).
[CrossRef]

Lippi, G. L.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, Phys. Rev. A 37, 470 (1988).
[CrossRef] [PubMed]

Lugiato, L. A.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Maggipinto, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Mandel, P.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, Phys. Rev. A 37, 470 (1988).
[CrossRef] [PubMed]

Mello, T.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, Phys. Rev. A 37, 470 (1988).
[CrossRef] [PubMed]

Menesguen, Y.

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, Phys. Rev. A 74, 023818 (2006).
[CrossRef]

Miller, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Moloney, J. V.

G. K. Harkness, W. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[CrossRef] [PubMed]

Oppo, G. L.

The terms “dark” and “bright” solitons may lead to some misunderstandings. In , they refer to a local lack and overload of light, respectively, and are absolutely not related to the usual topological solitons observed in integrable dynamical systems. Also, contrary to the usual “cavity solitons” , the stability of the localized structures in does not result from a balance between bistability and modulational instability. This point is well described in D. Gomila, P. Colet, M. San Miguel, A. J. Scroggie, and G. L. Oppo, IEEE J. Quantum Electron. 39, 238 (2003).
[CrossRef]

Pedaci, F.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

Perez-Arjona, I.

Prati, F.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

Protsenko, I.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

Residori, S.

U. Bortolozzo and S. Residori, Phys. Rev. Lett. 96, 037801 (2006).
[CrossRef] [PubMed]

Roldan, E.

Sagnes, I.

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, Phys. Rev. A 74, 023818 (2006).
[CrossRef]

San Miguel, M.

The terms “dark” and “bright” solitons may lead to some misunderstandings. In , they refer to a local lack and overload of light, respectively, and are absolutely not related to the usual topological solitons observed in integrable dynamical systems. Also, contrary to the usual “cavity solitons” , the stability of the localized structures in does not result from a balance between bistability and modulational instability. This point is well described in D. Gomila, P. Colet, M. San Miguel, A. J. Scroggie, and G. L. Oppo, IEEE J. Quantum Electron. 39, 238 (2003).
[CrossRef]

Sanchez-Morcillo, J. V.

Schäpers, B.

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

Scroggie, A. J.

The terms “dark” and “bright” solitons may lead to some misunderstandings. In , they refer to a local lack and overload of light, respectively, and are absolutely not related to the usual topological solitons observed in integrable dynamical systems. Also, contrary to the usual “cavity solitons” , the stability of the localized structures in does not result from a balance between bistability and modulational instability. This point is well described in D. Gomila, P. Colet, M. San Miguel, A. J. Scroggie, and G. L. Oppo, IEEE J. Quantum Electron. 39, 238 (2003).
[CrossRef]

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
[CrossRef] [PubMed]

Spinelli, L.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Tanguy, Y.

Y. Tanguy, T. Ackemann, and R. Jäger, Phys. Rev. A 74, 053824 (2006).
[CrossRef]

Taranenko, V. B.

V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).

V. B. Taranenko, I. Ganne, R. Kusselevitz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).

Tissoni, G.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Tredicce, J. R.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Weiss, C. O.

V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).

V. B. Taranenko, I. Ganne, R. Kusselevitz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).

Wright, E. M.

G. K. Harkness, W. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[CrossRef] [PubMed]

Zeghlache, H.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, Phys. Rev. A 37, 470 (1988).
[CrossRef] [PubMed]

Appl. Phys. B (2)

V. B. Taranenko, I. Ganne, R. Kusselevitz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).

V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).

IEEE J. Quantum Electron. (1)

The terms “dark” and “bright” solitons may lead to some misunderstandings. In , they refer to a local lack and overload of light, respectively, and are absolutely not related to the usual topological solitons observed in integrable dynamical systems. Also, contrary to the usual “cavity solitons” , the stability of the localized structures in does not result from a balance between bistability and modulational instability. This point is well described in D. Gomila, P. Colet, M. San Miguel, A. J. Scroggie, and G. L. Oppo, IEEE J. Quantum Electron. 39, 238 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, IEEE J. Sel. Top. Quantum Electron. 12, 339 (2006).
[CrossRef]

Nature (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (4)

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, Phys. Rev. A 37, 470 (1988).
[CrossRef] [PubMed]

G. K. Harkness, W. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[CrossRef] [PubMed]

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, Phys. Rev. A 74, 023818 (2006).
[CrossRef]

Y. Tanguy, T. Ackemann, and R. Jäger, Phys. Rev. A 74, 053824 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

U. Bortolozzo and S. Residori, Phys. Rev. Lett. 96, 037801 (2006).
[CrossRef] [PubMed]

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
[CrossRef] [PubMed]

Other (1)

http://www.funfacs.org.

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Figures (4)

Fig. 1
Fig. 1

Numerical simulation of Eqs. (1) with A = 1.35 and σ = 1.01 . The size of the box is 1000 . (a) and (b) correspond to the same spatiotemporal evolution, but (a) displays the evolution of the weak mode amplitude, while (b) shows the real part of strong mode.

Fig. 2
Fig. 2

Same regime of parameters as in Fig. 1. All the four plots are associated with the same single simulation and display the spatiotemporal evolution of the (a), (c) weak mode amplitude and of the (b), (d) strong mode real part.

Fig. 3
Fig. 3

Same regime of parameters as in Fig. 1, same size for the numerical box. The only difference stands in the boundary conditions and consists in a tiny modification of the pump profile. The dashed line in (c) is associated with the results shown in Figs. 1, 2, while the continuous line is the new pump profile used in the current figure. (a) and (b), respectively, display the weak mode amplitude and the strong mode real part.

Fig. 4
Fig. 4

Numerical simulation of Eq. (2) with A = 1.4 , σ = 1.01 , and l = m = 0.1 . The size of the box is 1000 ; the boundary conditions are the same as in Fig. 1. The figure displays the spatiotemporal evolution of the weak mode amplitude. Seven writing and four erasing processes can be identified.

Equations (4)

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E f t = ( A 1 E f 2 2 E b 2 ) E f + i 2 E f x 2 ,
E b t = ( A σ E b 2 2 E f 2 ) E b + i 2 E b x 2 ,
E f t = ( A 1 E f 2 2 E b 2 ) E f + i 2 E f x 2 + l ,
E b t = ( A σ E b 2 2 E f 2 ) E b + i 2 E b x 2 + m ,

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