Abstract

We experimentally investigate an intermittent route to chaos in a photonic integrated circuit consisting of a semiconductor laser with time-delayed optical feedback from a short external cavity. The transition from a period-doubling dynamics to a fully-developed chaos reveals a stage intermittently exhibiting these two dynamics. We unveil the bifurcation mechanism underlying this route to chaos by using the Lang-Kobayashi model and demonstrate that the process is based on a phenomenon of attractor expansion initiated by a particular distribution of the local Lyapunov exponents. We emphasize on the crucial importance of the distribution of the steady-state solutions introduced by the time-delayed feedback on the existence of this intermittent dynamics.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  4. A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
    [Crossref] [PubMed]
  5. A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
    [Crossref] [PubMed]
  6. T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
    [Crossref]
  7. S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
    [Crossref] [PubMed]
  8. R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
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    [Crossref]
  11. O. Ushakov, S. Bauer, O. Brox, H.-J. Wünsche, and F. Henneberger, “Self-organization in semiconductor lasers with ultrashort optical feedback”, Phys. Rev. Lett. 92(4), 043902 (2004).
    [Crossref] [PubMed]
  12. A. Karsaklian Dal Bosco, K. Kanno, A. Uchida, M. Sciamanna, T. Harayama, and K. Yoshimura, “Cycles of self-pulsations in a photonic integrated circuit,” Phys. Rev. E 92(6), 062905 (2015).
    [Crossref]
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  14. A. Tabaka, K. Panajotov, I. Veretennicoff, and M. Sciamanna, “Bifurcation study of regular pulse packages in laser diodes subject to optical feedback,” Phys. Rev. E 70(3), 036211 (2004).
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  17. M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
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    [Crossref] [PubMed]
  21. C. Grebogi, E. Ott, F. Romeiras, and J. A. Yorke, “Critical exponents for crisis-induced intermittency,” Phys. Rev. A 36(11), 5365 (1987).
    [Crossref]
  22. M. Dubois, M. A. Rubio, and P. Berge, “Experimental evidence of intermittencies associated with a subharmonic bifurcation,” Phys. Rev. Lett. 51(16), 1446–1449 (1983).
    [Crossref]
  23. W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
    [Crossref] [PubMed]
  24. I. M. Kyprianidis, M. L. Petrani, J. A. Kalomiros, and A. N. Anagnostopoulos, “Crisis-induced intermittency in a third-order electrical circuit”, Phys. Rev. E 52(3), 2268 (1995).
    [Crossref]
  25. E. Covas and R. Tavakol, “Crisis-induced intermittency in truncated mean field dynamos,” arXiv preprint astroph/9708108 (1997).
  26. G. Tanaka, M. A. F. Sanjuan, and K. Aihara, “Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy”, Phys. Rev. E 71(1), 016219 (2005).
    [Crossref]
  27. J. Sacher, W. Elsäßer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224–2227 (1989).
    [Crossref] [PubMed]
  28. D. Y. Tang, J. Pujol, and C. O. Weiss, “Type-iii intermittency of a laser,” Phys. Rev. A 44(1), 35–38 (1991).
    [Crossref]
  29. D. Y. Tang, M. Y. Li, and C. O. Weiss, “Laser dynamics of type-i intermittency,” Phys. Rev. A 46(1), 676–678 (1992).
    [Crossref] [PubMed]
  30. T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
    [Crossref] [PubMed]
  31. I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers”, Phys. Rev. Lett. 76(2), 220 (1996).
    [Crossref] [PubMed]
  32. J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249 (1993).
    [Crossref] [PubMed]
  33. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [Crossref]
  34. A. Uchida, Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).
    [Crossref]
  35. K. Kanno and A. Uchida, “Finite-time lyapunov exponents in time-delayed nonlinear dynamical systems,” Phys. Rev. E 89(3), 032918 (2014).
    [Crossref]
  36. A. Prasad and R. Ramaswamy, “Characteristic distributions of finite-time lyapunov exponents,” Phys. Rev. E 60(3), 2761 (1999).
    [Crossref]
  37. C. Grebogi, E. Ott, and J. A. Yorke, “Critical exponent of chaotic transients in nonlinear dynamical systems,” Phys. Rev. Lett. 57(11), 1284 (1986).
    [Crossref] [PubMed]

2015 (3)

A. Karsaklian Dal Bosco, K. Kanno, A. Uchida, M. Sciamanna, T. Harayama, and K. Yoshimura, “Cycles of self-pulsations in a photonic integrated circuit,” Phys. Rev. E 92(6), 062905 (2015).
[Crossref]

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

J. P. Toomey, D. M. Kane, C. McMahon, A. Argyris, and D. Syvridis, “Integrated semiconductor laser with optical feedback: transition from short to long cavity regime,” Opt. Express 23(14), 18754–18762 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (2)

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421 (2013).
[Crossref]

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity”, Phys. Rev. E 87(6), 062913 (2013).
[Crossref]

2011 (2)

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[Crossref] [PubMed]

2010 (2)

2008 (1)

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

2005 (1)

G. Tanaka, M. A. F. Sanjuan, and K. Aihara, “Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy”, Phys. Rev. E 71(1), 016219 (2005).
[Crossref]

2004 (2)

A. Tabaka, K. Panajotov, I. Veretennicoff, and M. Sciamanna, “Bifurcation study of regular pulse packages in laser diodes subject to optical feedback,” Phys. Rev. E 70(3), 036211 (2004).
[Crossref]

O. Ushakov, S. Bauer, O. Brox, H.-J. Wünsche, and F. Henneberger, “Self-organization in semiconductor lasers with ultrashort optical feedback”, Phys. Rev. Lett. 92(4), 043902 (2004).
[Crossref] [PubMed]

2003 (1)

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

2002 (1)

T. Erneux, A. Gavrielides, and M. Sciamanna, “Stable microwave oscillations due to external-cavity-mode beating in laser diodes subject to optical feedback,” Phys. Rev. A 66(3), 033809 (2002).
[Crossref]

2001 (1)

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[Crossref] [PubMed]

1999 (1)

A. Prasad and R. Ramaswamy, “Characteristic distributions of finite-time lyapunov exponents,” Phys. Rev. E 60(3), 2761 (1999).
[Crossref]

1996 (1)

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers”, Phys. Rev. Lett. 76(2), 220 (1996).
[Crossref] [PubMed]

1995 (1)

I. M. Kyprianidis, M. L. Petrani, J. A. Kalomiros, and A. N. Anagnostopoulos, “Crisis-induced intermittency in a third-order electrical circuit”, Phys. Rev. E 52(3), 2268 (1995).
[Crossref]

1994 (1)

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
[Crossref] [PubMed]

1993 (1)

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249 (1993).
[Crossref] [PubMed]

1992 (1)

D. Y. Tang, M. Y. Li, and C. O. Weiss, “Laser dynamics of type-i intermittency,” Phys. Rev. A 46(1), 676–678 (1992).
[Crossref] [PubMed]

1991 (1)

D. Y. Tang, J. Pujol, and C. O. Weiss, “Type-iii intermittency of a laser,” Phys. Rev. A 44(1), 35–38 (1991).
[Crossref]

1989 (2)

J. Sacher, W. Elsäßer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224–2227 (1989).
[Crossref] [PubMed]

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

1987 (1)

C. Grebogi, E. Ott, F. Romeiras, and J. A. Yorke, “Critical exponents for crisis-induced intermittency,” Phys. Rev. A 36(11), 5365 (1987).
[Crossref]

1986 (1)

C. Grebogi, E. Ott, and J. A. Yorke, “Critical exponent of chaotic transients in nonlinear dynamical systems,” Phys. Rev. Lett. 57(11), 1284 (1986).
[Crossref] [PubMed]

1983 (1)

M. Dubois, M. A. Rubio, and P. Berge, “Experimental evidence of intermittencies associated with a subharmonic bifurcation,” Phys. Rev. Lett. 51(16), 1446–1449 (1983).
[Crossref]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Aihara, K.

G. Tanaka, M. A. F. Sanjuan, and K. Aihara, “Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy”, Phys. Rev. E 71(1), 016219 (2005).
[Crossref]

Akizawa, Y.

Anagnostopoulos, A. N.

I. M. Kyprianidis, M. L. Petrani, J. A. Kalomiros, and A. N. Anagnostopoulos, “Crisis-induced intermittency in a third-order electrical circuit”, Phys. Rev. E 52(3), 2268 (1995).
[Crossref]

Arai, K.

Argyris, A.

Bauer, S.

O. Ushakov, S. Bauer, O. Brox, H.-J. Wünsche, and F. Henneberger, “Self-organization in semiconductor lasers with ultrashort optical feedback”, Phys. Rev. Lett. 92(4), 043902 (2004).
[Crossref] [PubMed]

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

Berge, P.

M. Dubois, M. A. Rubio, and P. Berge, “Experimental evidence of intermittencies associated with a subharmonic bifurcation,” Phys. Rev. Lett. 51(16), 1446–1449 (1983).
[Crossref]

Bogris, A.

Brox, O.

O. Ushakov, S. Bauer, O. Brox, H.-J. Wünsche, and F. Henneberger, “Self-organization in semiconductor lasers with ultrashort optical feedback”, Phys. Rev. Lett. 92(4), 043902 (2004).
[Crossref] [PubMed]

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

Cawley, R.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

Chlouverakis, K. E.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

Coldren, L. A.

L. A. Coldren, Diode Lasers and Photonic Integrated Circuits (John Wiley and Sons, 2012).
[Crossref]

Covas, E.

E. Covas and R. Tavakol, “Crisis-induced intermittency in truncated mean field dynamos,” arXiv preprint astroph/9708108 (1997).

Davis, P.

Deligiannidis, S.

Ditto, W. L.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

Dubois, M.

M. Dubois, M. A. Rubio, and P. Berge, “Experimental evidence of intermittencies associated with a subharmonic bifurcation,” Phys. Rev. Lett. 51(16), 1446–1449 (1983).
[Crossref]

Elsäßer, W.

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[Crossref] [PubMed]

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers”, Phys. Rev. Lett. 76(2), 220 (1996).
[Crossref] [PubMed]

J. Sacher, W. Elsäßer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224–2227 (1989).
[Crossref] [PubMed]

Erneux, T.

T. Erneux, A. Gavrielides, and M. Sciamanna, “Stable microwave oscillations due to external-cavity-mode beating in laser diodes subject to optical feedback,” Phys. Rev. A 66(3), 033809 (2002).
[Crossref]

Fischer, I.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421 (2013).
[Crossref]

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[Crossref] [PubMed]

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers”, Phys. Rev. Lett. 76(2), 220 (1996).
[Crossref] [PubMed]

García-Ojalvo, J.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421 (2013).
[Crossref]

Gavrielides, A.

T. Erneux, A. Gavrielides, and M. Sciamanna, “Stable microwave oscillations due to external-cavity-mode beating in laser diodes subject to optical feedback,” Phys. Rev. A 66(3), 033809 (2002).
[Crossref]

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[Crossref] [PubMed]

Göbel, E.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers”, Phys. Rev. Lett. 76(2), 220 (1996).
[Crossref] [PubMed]

Göbel, E. O.

J. Sacher, W. Elsäßer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224–2227 (1989).
[Crossref] [PubMed]

Grebogi, C.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

C. Grebogi, E. Ott, F. Romeiras, and J. A. Yorke, “Critical exponents for crisis-induced intermittency,” Phys. Rev. A 36(11), 5365 (1987).
[Crossref]

C. Grebogi, E. Ott, and J. A. Yorke, “Critical exponent of chaotic transients in nonlinear dynamical systems,” Phys. Rev. Lett. 57(11), 1284 (1986).
[Crossref] [PubMed]

Grivas, E.

Hamacher, M.

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
[Crossref] [PubMed]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

Harayama, T.

A. Karsaklian Dal Bosco, K. Kanno, A. Uchida, M. Sciamanna, T. Harayama, and K. Yoshimura, “Cycles of self-pulsations in a photonic integrated circuit,” Phys. Rev. E 92(6), 062905 (2015).
[Crossref]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

Heil, T.

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[Crossref] [PubMed]

Henneberger, F.

O. Ushakov, S. Bauer, O. Brox, H.-J. Wünsche, and F. Henneberger, “Self-organization in semiconductor lasers with ultrashort optical feedback”, Phys. Rev. Lett. 92(4), 043902 (2004).
[Crossref] [PubMed]

Hsu, G.-H.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

Hunsperger, R.

R. Hunsperger, Integrated Optics: Theory and Technology (Springer, 1984).

Kalomiros, J. A.

I. M. Kyprianidis, M. L. Petrani, J. A. Kalomiros, and A. N. Anagnostopoulos, “Crisis-induced intermittency in a third-order electrical circuit”, Phys. Rev. E 52(3), 2268 (1995).
[Crossref]

Kane, D. M.

Kanno, K.

A. Karsaklian Dal Bosco, K. Kanno, A. Uchida, M. Sciamanna, T. Harayama, and K. Yoshimura, “Cycles of self-pulsations in a photonic integrated circuit,” Phys. Rev. E 92(6), 062905 (2015).
[Crossref]

K. Kanno and A. Uchida, “Finite-time lyapunov exponents in time-delayed nonlinear dynamical systems,” Phys. Rev. E 89(3), 032918 (2014).
[Crossref]

Karsaklian Dal Bosco, A.

A. Karsaklian Dal Bosco, K. Kanno, A. Uchida, M. Sciamanna, T. Harayama, and K. Yoshimura, “Cycles of self-pulsations in a photonic integrated circuit,” Phys. Rev. E 92(6), 062905 (2015).
[Crossref]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Kostelich, E.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

Kreissl, J.

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

Kyprianidis, I. M.

I. M. Kyprianidis, M. L. Petrani, J. A. Kalomiros, and A. N. Anagnostopoulos, “Crisis-induced intermittency in a third-order electrical circuit”, Phys. Rev. E 52(3), 2268 (1995).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Lenstra, D.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers”, Phys. Rev. Lett. 76(2), 220 (1996).
[Crossref] [PubMed]

Levine, A. M.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers”, Phys. Rev. Lett. 76(2), 220 (1996).
[Crossref] [PubMed]

Li, H.

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249 (1993).
[Crossref] [PubMed]

Li, M. Y.

D. Y. Tang, M. Y. Li, and C. O. Weiss, “Laser dynamics of type-i intermittency,” Phys. Rev. A 46(1), 676–678 (1992).
[Crossref] [PubMed]

Lu, D.

Masoller, C.

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity”, Phys. Rev. E 87(6), 062913 (2013).
[Crossref]

McInerney, J. G.

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249 (1993).
[Crossref] [PubMed]

McMahon, C.

Mirasso, C. R.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421 (2013).
[Crossref]

Ohtsubo, J.

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos, 3rd ed. (Springer Verlag, 2013).
[Crossref]

Ott, E.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

C. Grebogi, E. Ott, F. Romeiras, and J. A. Yorke, “Critical exponents for crisis-induced intermittency,” Phys. Rev. A 36(11), 5365 (1987).
[Crossref]

C. Grebogi, E. Ott, and J. A. Yorke, “Critical exponent of chaotic transients in nonlinear dynamical systems,” Phys. Rev. Lett. 57(11), 1284 (1986).
[Crossref] [PubMed]

Pan, B.

Panajotov, K.

A. Tabaka, K. Panajotov, I. Veretennicoff, and M. Sciamanna, “Bifurcation study of regular pulse packages in laser diodes subject to optical feedback,” Phys. Rev. E 70(3), 036211 (2004).
[Crossref]

Petrani, M. L.

I. M. Kyprianidis, M. L. Petrani, J. A. Kalomiros, and A. N. Anagnostopoulos, “Crisis-induced intermittency in a third-order electrical circuit”, Phys. Rev. E 52(3), 2268 (1995).
[Crossref]

Pikasis, E.

Prasad, A.

A. Prasad and R. Ramaswamy, “Characteristic distributions of finite-time lyapunov exponents,” Phys. Rev. E 60(3), 2761 (1999).
[Crossref]

Pujol, J.

D. Y. Tang, J. Pujol, and C. O. Weiss, “Type-iii intermittency of a laser,” Phys. Rev. A 44(1), 35–38 (1991).
[Crossref]

Radziunas, M.

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

Ramaswamy, R.

A. Prasad and R. Ramaswamy, “Characteristic distributions of finite-time lyapunov exponents,” Phys. Rev. E 60(3), 2761 (1999).
[Crossref]

Rauseo, S.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

Reinoso, J. A.

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity”, Phys. Rev. E 87(6), 062913 (2013).
[Crossref]

Romeiras, F.

C. Grebogi, E. Ott, F. Romeiras, and J. A. Yorke, “Critical exponents for crisis-induced intermittency,” Phys. Rev. A 36(11), 5365 (1987).
[Crossref]

Rubio, M. A.

M. Dubois, M. A. Rubio, and P. Berge, “Experimental evidence of intermittencies associated with a subharmonic bifurcation,” Phys. Rev. Lett. 51(16), 1446–1449 (1983).
[Crossref]

Sacher, J.

J. Sacher, W. Elsäßer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224–2227 (1989).
[Crossref] [PubMed]

Sanjuan, M. A. F.

G. Tanaka, M. A. F. Sanjuan, and K. Aihara, “Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy”, Phys. Rev. E 71(1), 016219 (2005).
[Crossref]

Sano, T.

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
[Crossref] [PubMed]

Sartorius, B.

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

Savage, H. T.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

Sciamanna, M.

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

A. Karsaklian Dal Bosco, K. Kanno, A. Uchida, M. Sciamanna, T. Harayama, and K. Yoshimura, “Cycles of self-pulsations in a photonic integrated circuit,” Phys. Rev. E 92(6), 062905 (2015).
[Crossref]

A. Tabaka, K. Panajotov, I. Veretennicoff, and M. Sciamanna, “Bifurcation study of regular pulse packages in laser diodes subject to optical feedback,” Phys. Rev. E 70(3), 036211 (2004).
[Crossref]

T. Erneux, A. Gavrielides, and M. Sciamanna, “Stable microwave oscillations due to external-cavity-mode beating in laser diodes subject to optical feedback,” Phys. Rev. A 66(3), 033809 (2002).
[Crossref]

Segnan, R.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

Shore, K. A.

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

Sieber, J.

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

Soriano, M. C.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421 (2013).
[Crossref]

Spano, M. L.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

Sunada, S.

Syvridis, D.

Tabaka, A.

A. Tabaka, K. Panajotov, I. Veretennicoff, and M. Sciamanna, “Bifurcation study of regular pulse packages in laser diodes subject to optical feedback,” Phys. Rev. E 70(3), 036211 (2004).
[Crossref]

Takahashi, R.

Tanaka, G.

G. Tanaka, M. A. F. Sanjuan, and K. Aihara, “Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy”, Phys. Rev. E 71(1), 016219 (2005).
[Crossref]

Tang, D. Y.

D. Y. Tang, M. Y. Li, and C. O. Weiss, “Laser dynamics of type-i intermittency,” Phys. Rev. A 46(1), 676–678 (1992).
[Crossref] [PubMed]

D. Y. Tang, J. Pujol, and C. O. Weiss, “Type-iii intermittency of a laser,” Phys. Rev. A 44(1), 35–38 (1991).
[Crossref]

Tavakol, R.

E. Covas and R. Tavakol, “Crisis-induced intermittency in truncated mean field dynamos,” arXiv preprint astroph/9708108 (1997).

Toomey, J. P.

Tsuzuki, K.

Uchida, A.

A. Karsaklian Dal Bosco, K. Kanno, A. Uchida, M. Sciamanna, T. Harayama, and K. Yoshimura, “Cycles of self-pulsations in a photonic integrated circuit,” Phys. Rev. E 92(6), 062905 (2015).
[Crossref]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

K. Kanno and A. Uchida, “Finite-time lyapunov exponents in time-delayed nonlinear dynamical systems,” Phys. Rev. E 89(3), 032918 (2014).
[Crossref]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

A. Uchida, Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).
[Crossref]

Ushakov, O.

O. Ushakov, S. Bauer, O. Brox, H.-J. Wünsche, and F. Henneberger, “Self-organization in semiconductor lasers with ultrashort optical feedback”, Phys. Rev. Lett. 92(4), 043902 (2004).
[Crossref] [PubMed]

van Tartwijk, G. H. M.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers”, Phys. Rev. Lett. 76(2), 220 (1996).
[Crossref] [PubMed]

Veretennicoff, I.

A. Tabaka, K. Panajotov, I. Veretennicoff, and M. Sciamanna, “Bifurcation study of regular pulse packages in laser diodes subject to optical feedback,” Phys. Rev. E 70(3), 036211 (2004).
[Crossref]

Wang, W.

Weiss, C. O.

D. Y. Tang, M. Y. Li, and C. O. Weiss, “Laser dynamics of type-i intermittency,” Phys. Rev. A 46(1), 676–678 (1992).
[Crossref] [PubMed]

D. Y. Tang, J. Pujol, and C. O. Weiss, “Type-iii intermittency of a laser,” Phys. Rev. A 44(1), 35–38 (1991).
[Crossref]

Wolfrum, M.

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

Wu, J.

Wu, Z.

Wünsche, H.-J.

O. Ushakov, S. Bauer, O. Brox, H.-J. Wünsche, and F. Henneberger, “Self-organization in semiconductor lasers with ultrashort optical feedback”, Phys. Rev. Lett. 92(4), 043902 (2004).
[Crossref] [PubMed]

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

Xia, G.

Ye, J.

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249 (1993).
[Crossref] [PubMed]

Yorke, J. A.

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

C. Grebogi, E. Ott, F. Romeiras, and J. A. Yorke, “Critical exponents for crisis-induced intermittency,” Phys. Rev. A 36(11), 5365 (1987).
[Crossref]

C. Grebogi, E. Ott, and J. A. Yorke, “Critical exponent of chaotic transients in nonlinear dynamical systems,” Phys. Rev. Lett. 57(11), 1284 (1986).
[Crossref] [PubMed]

Yoshimura, K.

A. Karsaklian Dal Bosco, K. Kanno, A. Uchida, M. Sciamanna, T. Harayama, and K. Yoshimura, “Cycles of self-pulsations in a photonic integrated circuit,” Phys. Rev. E 92(6), 062905 (2015).
[Crossref]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

Yu, L.

Zamora-Munt, J.

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity”, Phys. Rev. E 87(6), 062913 (2013).
[Crossref]

Zhao, L.

IEEE J. Quantum Electron. (2)

O. Brox, S. Bauer, M. Radziunas, M. Wolfrum, J. Sieber, J. Kreissl, B. Sartorius, and H.-J. Wünsche, “High-frequency pulsations in dfb lasers with amplified feedback,” IEEE J. Quantum Electron. 39(11), 1381–1387 (2003).
[Crossref]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

J. Lightwave Technol. (1)

Nat. Photonics (1)

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

Opt. Express (5)

Phys. Rev. A (7)

C. Grebogi, E. Ott, F. Romeiras, and J. A. Yorke, “Critical exponents for crisis-induced intermittency,” Phys. Rev. A 36(11), 5365 (1987).
[Crossref]

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249 (1993).
[Crossref] [PubMed]

D. Y. Tang, J. Pujol, and C. O. Weiss, “Type-iii intermittency of a laser,” Phys. Rev. A 44(1), 35–38 (1991).
[Crossref]

D. Y. Tang, M. Y. Li, and C. O. Weiss, “Laser dynamics of type-i intermittency,” Phys. Rev. A 46(1), 676–678 (1992).
[Crossref] [PubMed]

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

T. Erneux, A. Gavrielides, and M. Sciamanna, “Stable microwave oscillations due to external-cavity-mode beating in laser diodes subject to optical feedback,” Phys. Rev. A 66(3), 033809 (2002).
[Crossref]

Phys. Rev. E (7)

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity”, Phys. Rev. E 87(6), 062913 (2013).
[Crossref]

A. Tabaka, K. Panajotov, I. Veretennicoff, and M. Sciamanna, “Bifurcation study of regular pulse packages in laser diodes subject to optical feedback,” Phys. Rev. E 70(3), 036211 (2004).
[Crossref]

A. Karsaklian Dal Bosco, K. Kanno, A. Uchida, M. Sciamanna, T. Harayama, and K. Yoshimura, “Cycles of self-pulsations in a photonic integrated circuit,” Phys. Rev. E 92(6), 062905 (2015).
[Crossref]

I. M. Kyprianidis, M. L. Petrani, J. A. Kalomiros, and A. N. Anagnostopoulos, “Crisis-induced intermittency in a third-order electrical circuit”, Phys. Rev. E 52(3), 2268 (1995).
[Crossref]

G. Tanaka, M. A. F. Sanjuan, and K. Aihara, “Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy”, Phys. Rev. E 71(1), 016219 (2005).
[Crossref]

K. Kanno and A. Uchida, “Finite-time lyapunov exponents in time-delayed nonlinear dynamical systems,” Phys. Rev. E 89(3), 032918 (2014).
[Crossref]

A. Prasad and R. Ramaswamy, “Characteristic distributions of finite-time lyapunov exponents,” Phys. Rev. E 60(3), 2761 (1999).
[Crossref]

Phys. Rev. Lett. (8)

C. Grebogi, E. Ott, and J. A. Yorke, “Critical exponent of chaotic transients in nonlinear dynamical systems,” Phys. Rev. Lett. 57(11), 1284 (1986).
[Crossref] [PubMed]

J. Sacher, W. Elsäßer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224–2227 (1989).
[Crossref] [PubMed]

M. Dubois, M. A. Rubio, and P. Berge, “Experimental evidence of intermittencies associated with a subharmonic bifurcation,” Phys. Rev. Lett. 51(16), 1446–1449 (1983).
[Crossref]

W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and J. A. Yorke, “Experimental observation of crisis-induced intermittency and its critical exponent,” Phys. Rev. Lett. 63(9), 923 (1989).
[Crossref] [PubMed]

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers”, Phys. Rev. Lett. 76(2), 220 (1996).
[Crossref] [PubMed]

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[Crossref] [PubMed]

O. Ushakov, S. Bauer, O. Brox, H.-J. Wünsche, and F. Henneberger, “Self-organization in semiconductor lasers with ultrashort optical feedback”, Phys. Rev. Lett. 92(4), 043902 (2004).
[Crossref] [PubMed]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421 (2013).
[Crossref]

Other (5)

A. Uchida, Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).
[Crossref]

E. Covas and R. Tavakol, “Crisis-induced intermittency in truncated mean field dynamos,” arXiv preprint astroph/9708108 (1997).

R. Hunsperger, Integrated Optics: Theory and Technology (Springer, 1984).

L. A. Coldren, Diode Lasers and Photonic Integrated Circuits (John Wiley and Sons, 2012).
[Crossref]

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos, 3rd ed. (Springer Verlag, 2013).
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (504 KB)      Video for better understanding of Fig.5

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Figures (7)

Fig. 1
Fig. 1 Photonic integrated circuit. PD: photodiode, DFB laser: distributed feedback laser, SOA: semiconductor optical amplifier.
Fig. 2
Fig. 2 Experimental observation of intermittency as the feedback strength JSOA1 increases for a value of the injection current J equal to 3.0Jth. (a) Temporal waveforms and (b) RF spectra. (a-b.1) JSOA1=10.8 mA, (a-b.2) JSOA1=12.93 mA, (a-b.3) JSOA1=13.12 mA, (a-b.4) JSOA1=13.23 mA. (c) and (d) are zooms on the dashed boxes in traces (a.2) and (c), respectively.
Fig. 3
Fig. 3 (a) Experimental bifurcation diagram of the scenario in Fig. 2 (J/Jth=3.0). (b) Experimental two-dimensional bifurcation diagram showing evidence of intermittent dynamics in a wide range of parameters.
Fig. 4
Fig. 4 Numerical scenario showing intermittency as the feedback strength R increases. (a) Temporal waveforms, and (b) attractors. (a.1–b.1) R = 0.0963, (a.2-b.2) R = 0.0964, (a.3–b.3) R = 0.120. The temporal waveforms present the evolution of the laser intensity (black traces at the top) and the optical frequency shift (red traces at the bottom). In trace (a.2), the evolution of the optical frequency shift reveals that the succession of laminar regions (L) and bursts (B) in the time trace corresponds exactly to jumps between the two sub-attractors.
Fig. 5
Fig. 5 Distribution of the local Lyapunov exponents (LLE) in the phase space (a) without and (b) with intermittency (see Visualization 1 for a detailed evolution when the feedback strength increases). (c) Distribution of the LLE in the temporal evolution of the optical frequency shift.
Fig. 6
Fig. 6 (a) Distribution of the local Lyapunov exponents and (b) evolution of the values of the average and the standard deviation with the feedback strength R.
Fig. 7
Fig. 7 (a) Experimental and (b) numerical evolutions of the average laminar times in the intermittency transitions of Figs. 2 and 4. The critical values above which intermittency begins are JSOA1c = 10.9 mA and Rc = 0.0963. The squares are measured data, the straight lines are curve fittings.

Tables (1)

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Table 1 Parameter values in simulations

Equations (4)

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d E ( t ) d t = 1 2 [ G N ( N ( t ) N 0 ) 1 + ϵ E 2 ( t ) 1 τ p ] E ( t ) + κ E ( t τ e x t ) cos ( Θ ( t ) )
d Φ ( t ) d t = α 2 [ G N ( N ( t ) N 0 ) 1 + ϵ E 2 ( t ) 1 τ p ] κ E ( t τ e x t ) E ( t ) sin ( Θ ( t ) )
d N ( t ) d t = J N ( t ) τ s G N ( N ( t ) N 0 ) 1 + ϵ E 2 ( t ) E 2 ( t )
Θ ( t ) = ω τ e x t + Φ ( t ) Φ ( t τ e x t )

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