Abstract

We study sudden changes in the chaotic output of an optically injected semiconductor laser. For what is believed to be the first time in this system, we identify bifurcations that cause abrupt changes between different chaotic outputs, or even sudden jumps between chaotic and periodic output. These sudden chaotic transitions involve attractors that exist for large regions in parameter space.

© 2001 Optical Society of America

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  1. C. R. Mirasso, P. Colet, and P. Garcia-Fernández, IEEE Photon. Technol. Lett. 8, 299 (1996).
    [CrossRef]
  2. F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, Phys. Rev. Lett. 49, 1217 (1982).
    [CrossRef]
  3. J. R. Tredicce, F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, J. Opt. Soc. Am. B 2, 173 (1985).
    [CrossRef]
  4. D. Dangoisse, P. Glorieux, and D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
    [CrossRef] [PubMed]
  5. H. G. Solari, E. Eschenazi, R. Gilmore, and J. Tredicce, Opt. Commun. 46, 64 (1983).
    [CrossRef]
  6. T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Al-sing, Phys. Rev. A 53, 4372 (1996).
    [CrossRef] [PubMed]
  7. S. Wieczorek, B. Krauskopf, and D. Lenstra, Opt. Commun. 172, 279 (1999).
    [CrossRef]
  8. V. Annovazzi-Lodi, S. Donati, and M. Manna, IEEE J. Quantum Electron. 30, 1537 (1994).
    [CrossRef]
  9. H. F. Chen and J. M. Liu, IEEE J. Quantum Electron. 36, 27 (2000).
    [CrossRef]
  10. G. B. Mindlin, X. J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990).
    [CrossRef] [PubMed]
  11. B. Krauskopf and D. Lenstra, AIP Conf. Proc. 548, 1 (2000).
    [CrossRef]
  12. E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, “AUTO 97,” http://indy.cs.concordia.ca/auto/main.html .
  13. A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, Not. Am. Math. Soc. 39, 303 (1992).
  14. B. Krauskopf and H. M. Osinga, J. Comp. Phys. 146, 404 (1998).
    [CrossRef]
  15. B. Krauskopf, S. Wieczorek, and D. Lenstra, Appl. Phys. Lett. 77, 1611 (2000).
    [CrossRef]
  16. C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
    [CrossRef]

2000 (3)

H. F. Chen and J. M. Liu, IEEE J. Quantum Electron. 36, 27 (2000).
[CrossRef]

B. Krauskopf and D. Lenstra, AIP Conf. Proc. 548, 1 (2000).
[CrossRef]

B. Krauskopf, S. Wieczorek, and D. Lenstra, Appl. Phys. Lett. 77, 1611 (2000).
[CrossRef]

1999 (1)

S. Wieczorek, B. Krauskopf, and D. Lenstra, Opt. Commun. 172, 279 (1999).
[CrossRef]

1998 (1)

B. Krauskopf and H. M. Osinga, J. Comp. Phys. 146, 404 (1998).
[CrossRef]

1996 (2)

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Al-sing, Phys. Rev. A 53, 4372 (1996).
[CrossRef] [PubMed]

C. R. Mirasso, P. Colet, and P. Garcia-Fernández, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

1994 (1)

V. Annovazzi-Lodi, S. Donati, and M. Manna, IEEE J. Quantum Electron. 30, 1537 (1994).
[CrossRef]

1992 (1)

A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, Not. Am. Math. Soc. 39, 303 (1992).

1990 (1)

G. B. Mindlin, X. J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990).
[CrossRef] [PubMed]

1986 (1)

D. Dangoisse, P. Glorieux, and D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

1985 (1)

1983 (1)

H. G. Solari, E. Eschenazi, R. Gilmore, and J. Tredicce, Opt. Commun. 46, 64 (1983).
[CrossRef]

1982 (2)

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, Phys. Rev. Lett. 49, 1217 (1982).
[CrossRef]

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

Al-sing, P. M.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Al-sing, Phys. Rev. A 53, 4372 (1996).
[CrossRef] [PubMed]

Annovazzi-Lodi, V.

V. Annovazzi-Lodi, S. Donati, and M. Manna, IEEE J. Quantum Electron. 30, 1537 (1994).
[CrossRef]

Arecchi, F. T.

J. R. Tredicce, F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, J. Opt. Soc. Am. B 2, 173 (1985).
[CrossRef]

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, Phys. Rev. Lett. 49, 1217 (1982).
[CrossRef]

Back, A.

A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, Not. Am. Math. Soc. 39, 303 (1992).

Champneys, A.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, “AUTO 97,” http://indy.cs.concordia.ca/auto/main.html .

Chen, H. F.

H. F. Chen and J. M. Liu, IEEE J. Quantum Electron. 36, 27 (2000).
[CrossRef]

Colet, P.

C. R. Mirasso, P. Colet, and P. Garcia-Fernández, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Dangoisse, D.

D. Dangoisse, P. Glorieux, and D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

Doedel, E.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, “AUTO 97,” http://indy.cs.concordia.ca/auto/main.html .

Donati, S.

V. Annovazzi-Lodi, S. Donati, and M. Manna, IEEE J. Quantum Electron. 30, 1537 (1994).
[CrossRef]

Erneux, T.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Al-sing, Phys. Rev. A 53, 4372 (1996).
[CrossRef] [PubMed]

Eschenazi, E.

H. G. Solari, E. Eschenazi, R. Gilmore, and J. Tredicce, Opt. Commun. 46, 64 (1983).
[CrossRef]

Fairgrieve, T.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, “AUTO 97,” http://indy.cs.concordia.ca/auto/main.html .

Garcia-Fernández, P.

C. R. Mirasso, P. Colet, and P. Garcia-Fernández, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Gavrielides, A.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Al-sing, Phys. Rev. A 53, 4372 (1996).
[CrossRef] [PubMed]

Gilmore, R.

G. B. Mindlin, X. J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990).
[CrossRef] [PubMed]

H. G. Solari, E. Eschenazi, R. Gilmore, and J. Tredicce, Opt. Commun. 46, 64 (1983).
[CrossRef]

Glorieux, P.

D. Dangoisse, P. Glorieux, and D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

Grebogi, C.

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

Guckenheimer, J.

A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, Not. Am. Math. Soc. 39, 303 (1992).

Hennequin, D.

D. Dangoisse, P. Glorieux, and D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

Hou, X. J.

G. B. Mindlin, X. J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990).
[CrossRef] [PubMed]

Kovanis, V.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Al-sing, Phys. Rev. A 53, 4372 (1996).
[CrossRef] [PubMed]

Krauskopf, B.

B. Krauskopf and D. Lenstra, AIP Conf. Proc. 548, 1 (2000).
[CrossRef]

B. Krauskopf, S. Wieczorek, and D. Lenstra, Appl. Phys. Lett. 77, 1611 (2000).
[CrossRef]

S. Wieczorek, B. Krauskopf, and D. Lenstra, Opt. Commun. 172, 279 (1999).
[CrossRef]

B. Krauskopf and H. M. Osinga, J. Comp. Phys. 146, 404 (1998).
[CrossRef]

Kuznetsov, Yu.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, “AUTO 97,” http://indy.cs.concordia.ca/auto/main.html .

Lenstra, D.

B. Krauskopf, S. Wieczorek, and D. Lenstra, Appl. Phys. Lett. 77, 1611 (2000).
[CrossRef]

B. Krauskopf and D. Lenstra, AIP Conf. Proc. 548, 1 (2000).
[CrossRef]

S. Wieczorek, B. Krauskopf, and D. Lenstra, Opt. Commun. 172, 279 (1999).
[CrossRef]

Lippi, G. L.

Liu, J. M.

H. F. Chen and J. M. Liu, IEEE J. Quantum Electron. 36, 27 (2000).
[CrossRef]

Manna, M.

V. Annovazzi-Lodi, S. Donati, and M. Manna, IEEE J. Quantum Electron. 30, 1537 (1994).
[CrossRef]

Meucci, R.

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, Phys. Rev. Lett. 49, 1217 (1982).
[CrossRef]

Mindlin, G. B.

G. B. Mindlin, X. J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990).
[CrossRef] [PubMed]

Mirasso, C. R.

C. R. Mirasso, P. Colet, and P. Garcia-Fernández, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Myers, M. R.

A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, Not. Am. Math. Soc. 39, 303 (1992).

Osinga, H. M.

B. Krauskopf and H. M. Osinga, J. Comp. Phys. 146, 404 (1998).
[CrossRef]

Ott, E.

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

Puccioni, G.

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, Phys. Rev. Lett. 49, 1217 (1982).
[CrossRef]

Puccioni, G. P.

Sandstede, B.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, “AUTO 97,” http://indy.cs.concordia.ca/auto/main.html .

Solari, H. G.

G. B. Mindlin, X. J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990).
[CrossRef] [PubMed]

H. G. Solari, E. Eschenazi, R. Gilmore, and J. Tredicce, Opt. Commun. 46, 64 (1983).
[CrossRef]

Tredicce, J.

H. G. Solari, E. Eschenazi, R. Gilmore, and J. Tredicce, Opt. Commun. 46, 64 (1983).
[CrossRef]

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, Phys. Rev. Lett. 49, 1217 (1982).
[CrossRef]

Tredicce, J. R.

Tufillaro, N. B.

G. B. Mindlin, X. J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990).
[CrossRef] [PubMed]

Wang, X.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, “AUTO 97,” http://indy.cs.concordia.ca/auto/main.html .

Wicklin, F. J.

A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, Not. Am. Math. Soc. 39, 303 (1992).

Wieczorek, S.

B. Krauskopf, S. Wieczorek, and D. Lenstra, Appl. Phys. Lett. 77, 1611 (2000).
[CrossRef]

S. Wieczorek, B. Krauskopf, and D. Lenstra, Opt. Commun. 172, 279 (1999).
[CrossRef]

Worfolk, P. A.

A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, Not. Am. Math. Soc. 39, 303 (1992).

Yorke, J. A.

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

AIP Conf. Proc. (1)

B. Krauskopf and D. Lenstra, AIP Conf. Proc. 548, 1 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

B. Krauskopf, S. Wieczorek, and D. Lenstra, Appl. Phys. Lett. 77, 1611 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

V. Annovazzi-Lodi, S. Donati, and M. Manna, IEEE J. Quantum Electron. 30, 1537 (1994).
[CrossRef]

H. F. Chen and J. M. Liu, IEEE J. Quantum Electron. 36, 27 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. R. Mirasso, P. Colet, and P. Garcia-Fernández, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

J. Comp. Phys. (1)

B. Krauskopf and H. M. Osinga, J. Comp. Phys. 146, 404 (1998).
[CrossRef]

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

Not. Am. Math. Soc. (1)

A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, Not. Am. Math. Soc. 39, 303 (1992).

Opt. Commun. (2)

H. G. Solari, E. Eschenazi, R. Gilmore, and J. Tredicce, Opt. Commun. 46, 64 (1983).
[CrossRef]

S. Wieczorek, B. Krauskopf, and D. Lenstra, Opt. Commun. 172, 279 (1999).
[CrossRef]

Phys. Rev. A (1)

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Al-sing, Phys. Rev. A 53, 4372 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

D. Dangoisse, P. Glorieux, and D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

G. B. Mindlin, X. J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990).
[CrossRef] [PubMed]

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, Phys. Rev. Lett. 49, 1217 (1982).
[CrossRef]

Other (1)

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, “AUTO 97,” http://indy.cs.concordia.ca/auto/main.html .

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Figures (5)

Fig. 1
Fig. 1

Bifurcation diagram in the K,ω plane.

Fig. 2
Fig. 2

Sudden growth of the chaotic attractor owing to an interior crisis when ω= increases from (a1)–(a4) 0.257 to (b1)–(b4) 0.2595 for K=0.19 (indicated in Fig.  1 by a vertical arrow).

Fig. 3
Fig. 3

Organization of the stable (gray) and unstable (black) manifolds in the Poincaré section n=0: (a) before, (b) at, and (c) after an interior crisis. Here K=0.19 is fixed (indicated in Fig.  1 by a vertical arrow), and (a) ω=0.255, (b) ω=0.257, (c) ω=0.2595.

Fig. 4
Fig. 4

Sudden destruction of a chaotic attractor owing to a boundary crisis when K decreases from (a1)–(a4) 0.84 to (b1)–(b4) 0.835 for fixed ω=1.1 (indicated in Fig.  1 by a horizontal arrow).

Fig. 5
Fig. 5

Organization of the stable (gray) and unstable (black) manifolds in the Poincaré section Ex=0: (a) before, (b) at, and (c) after a boundary crisis. Here ω=1.1 is fixed (indicated in Fig.  1 by a horizontal arrow) and (a) K=0.85, (b) K=0.839, (c) K=0.83.

Equations (1)

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E·=K+121+iαn-iωE,n·=-2Γ-1+2BnE2-1,

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