Abstract

We report rich nonlinear dynamics in integrated coupled lasers with ultra-short coupling delay. Mutually stable locking, period-1 oscillation, frequency locking, quasi-periodicity and chaos are observed experimentally. The dynamic behaviors are reproduced numerically by solving coupled delay differential equations that take the variation of both frequency detuning and coupling phase into account. Moreover, it is pointed out that the round-trip frequency is not involved in the above nonlinear dynamical behaviors. Instead, the relationship between the frequency detuning Δν and the relaxation oscillation frequency νr under mutual injection are found to be critical for the various observed dynamics in mutually coupled lasers with very short delay.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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  16. H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  24. F. G. Della Corte, G. Cocorullo, M. Iodice, I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77(11), 1614–1616 (2000).
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2013 (1)

2012 (1)

B. R. Cemlyn, D. Labukhin, I. D. Henning, M. J. Adams, “Dynamic Transitions in a Photonic Integrated Circuit,” J. Quantum Electron. 48(2), 261–268 (2012).
[CrossRef]

2011 (2)

K. Schires, A. Hurtado, I. D. Henning, M. J. Adams, “Comprehensive experimental analysis of nonlinear dynamics in an optically-injected semiconductor laser,” AIP Advances 1(3), 032131 (2011).
[CrossRef]

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

2010 (1)

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” J. Quantum Electron. 46(3), 421–428 (2010).
[CrossRef]

2009 (1)

2008 (1)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

2007 (2)

2006 (2)

H. Erzgraber, B. Krauskopf, D. Lenstra, “Compound Laser Modes of Mutually Delay-Coupled Lasers,” SIAM J. Appl. Dyn. Syst. 5(1), 30–65 (2006).
[CrossRef]

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 267(2), 464–468 (2006).
[CrossRef]

2005 (2)

H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
[CrossRef]

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

2004 (1)

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

2003 (1)

2001 (3)

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

T. Heil, I. Fischer, W. Elsässer, J. Mulet, C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

S. Tang, J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” J. Quantum Electron. 37(3), 329–336 (2001).
[CrossRef]

2000 (1)

F. G. Della Corte, G. Cocorullo, M. Iodice, I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77(11), 1614–1616 (2000).
[CrossRef]

1997 (1)

T. B. Simpson, J. M. Liu, K. F. Huang, K Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” J. Quantum Semiclass. Opt. 9(5), 765 (1997).

1993 (1)

J. Ye, H. Li, J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249–2252 (1993).
[CrossRef] [PubMed]

1990 (1)

J. Mork, J. Mark, B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65(16), 1999–2002 (1990).
[CrossRef]

Adams, M. J.

B. R. Cemlyn, D. Labukhin, I. D. Henning, M. J. Adams, “Dynamic Transitions in a Photonic Integrated Circuit,” J. Quantum Electron. 48(2), 261–268 (2012).
[CrossRef]

K. Schires, A. Hurtado, I. D. Henning, M. J. Adams, “Comprehensive experimental analysis of nonlinear dynamics in an optically-injected semiconductor laser,” AIP Advances 1(3), 032131 (2011).
[CrossRef]

M. P. Vaughan, I. Henning, M. J. Adams, L. J. Rivers, P. Cannard, I. F. Lealman, “Mutual optical injection in coupled DBR laser pairs,” Opt. Express 17(3), 2033–2041 (2009).
[CrossRef] [PubMed]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Arai, K.

Bauer, S.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

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

Brox, O.

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

Cannard, P.

Cemlyn, B. R.

B. R. Cemlyn, D. Labukhin, I. D. Henning, M. J. Adams, “Dynamic Transitions in a Photonic Integrated Circuit,” J. Quantum Electron. 48(2), 261–268 (2012).
[CrossRef]

Chan, S. C.

Cocorullo, G.

F. G. Della Corte, G. Cocorullo, M. Iodice, I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77(11), 1614–1616 (2000).
[CrossRef]

Davis, P.

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

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

De Vittorio, M.

Della Corte, F. G.

F. G. Della Corte, G. Cocorullo, M. Iodice, I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77(11), 1614–1616 (2000).
[CrossRef]

Elsaber, W.

E. Wille, M. Peil, I. Fischer, W. Elsaber, “Dynamical scenarios of mutually delay-coupled semiconductor lasers in the short coupling regime,” Proc. SPIE Semiconductor Lasers and Laser Dynamics5452, 41–50 (2004).
[CrossRef]

Elsaßer, W.

H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
[CrossRef]

Elsässer, W.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elsässer, J. Mulet, C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

Elsäßer, W.

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

Erzgraber, H.

H. Erzgraber, B. Krauskopf, D. Lenstra, “Compound Laser Modes of Mutually Delay-Coupled Lasers,” SIAM J. Appl. Dyn. Syst. 5(1), 30–65 (2006).
[CrossRef]

H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
[CrossRef]

Erzgräber, H.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Fischer, I.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
[CrossRef]

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

T. Heil, I. Fischer, W. Elsässer, J. Mulet, C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

E. Wille, M. Peil, I. Fischer, W. Elsaber, “Dynamical scenarios of mutually delay-coupled semiconductor lasers in the short coupling regime,” Proc. SPIE Semiconductor Lasers and Laser Dynamics5452, 41–50 (2004).
[CrossRef]

García-Ojalvo, J.

Gavrielides, A.

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

Goulding, D.

Gross, N.

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 267(2), 464–468 (2006).
[CrossRef]

Harayama, T.

Hegarty, S. P.

Heil, T.

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

T. Heil, I. Fischer, W. Elsässer, J. Mulet, C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

Henneberger, F.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

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

Henning, I.

Henning, I. D.

B. R. Cemlyn, D. Labukhin, I. D. Henning, M. J. Adams, “Dynamic Transitions in a Photonic Integrated Circuit,” J. Quantum Electron. 48(2), 261–268 (2012).
[CrossRef]

K. Schires, A. Hurtado, I. D. Henning, M. J. Adams, “Comprehensive experimental analysis of nonlinear dynamics in an optically-injected semiconductor laser,” AIP Advances 1(3), 032131 (2011).
[CrossRef]

Hirano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Huang, K. F.

T. B. Simpson, J. M. Liu, K. F. Huang, K Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” J. Quantum Semiclass. Opt. 9(5), 765 (1997).

Hurtado, A.

K. Schires, A. Hurtado, I. D. Henning, M. J. Adams, “Comprehensive experimental analysis of nonlinear dynamics in an optically-injected semiconductor laser,” AIP Advances 1(3), 032131 (2011).
[CrossRef]

Huyet, G.

Hwang, S. K.

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Iodice, M.

F. G. Della Corte, G. Cocorullo, M. Iodice, I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77(11), 1614–1616 (2000).
[CrossRef]

Kanter, I.

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 267(2), 464–468 (2006).
[CrossRef]

Karashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Kelleher, B.

Khaykovich, L.

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 267(2), 464–468 (2006).
[CrossRef]

Kinzel, W.

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 267(2), 464–468 (2006).
[CrossRef]

Korneyev, N.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Krauskopf, B.

H. Erzgraber, B. Krauskopf, D. Lenstra, “Compound Laser Modes of Mutually Delay-Coupled Lasers,” SIAM J. Appl. Dyn. Syst. 5(1), 30–65 (2006).
[CrossRef]

H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
[CrossRef]

Kreissl, J.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Labukhin, D.

B. R. Cemlyn, D. Labukhin, I. D. Henning, M. J. Adams, “Dynamic Transitions in a Photonic Integrated Circuit,” J. Quantum Electron. 48(2), 261–268 (2012).
[CrossRef]

Lealman, I. F.

Lenstra, D.

H. Erzgraber, B. Krauskopf, D. Lenstra, “Compound Laser Modes of Mutually Delay-Coupled Lasers,” SIAM J. Appl. Dyn. Syst. 5(1), 30–65 (2006).
[CrossRef]

H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
[CrossRef]

Li, H.

J. Ye, H. Li, J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249–2252 (1993).
[CrossRef] [PubMed]

Liu, D.

Liu, J. M.

S. C. Chan, S. K. Hwang, J. M. Liu, “Period-one oscillation for photonic microwave transmission using an optically injected semiconductor laser,” Opt. Express 15(22), 14921–14935 (2007).
[CrossRef] [PubMed]

S. Tang, J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” J. Quantum Electron. 37(3), 329–336 (2001).
[CrossRef]

T. B. Simpson, J. M. Liu, K. F. Huang, K Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” J. Quantum Semiclass. Opt. 9(5), 765 (1997).

Luo, Y.

Mark, J.

J. Mork, J. Mark, B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65(16), 1999–2002 (1990).
[CrossRef]

McInerney, J. G.

J. Ye, H. Li, J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249–2252 (1993).
[CrossRef] [PubMed]

Mirasso, C. R.

T. Heil, I. Fischer, W. Elsässer, J. Mulet, C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

Mork, J.

J. Mork, J. Mark, B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65(16), 1999–2002 (1990).
[CrossRef]

Mulet, J.

T. Heil, I. Fischer, W. Elsässer, J. Mulet, C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Passaseo, A.

Peil, M.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
[CrossRef]

E. Wille, M. Peil, I. Fischer, W. Elsaber, “Dynamical scenarios of mutually delay-coupled semiconductor lasers in the short coupling regime,” Proc. SPIE Semiconductor Lasers and Laser Dynamics5452, 41–50 (2004).
[CrossRef]

Rendina, I.

F. G. Della Corte, G. Cocorullo, M. Iodice, I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77(11), 1614–1616 (2000).
[CrossRef]

Rivers, L. J.

Rogister, F.

Rosenbluh, M.

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 267(2), 464–468 (2006).
[CrossRef]

Salhi, A.

Schires, K.

K. Schires, A. Hurtado, I. D. Henning, M. J. Adams, “Comprehensive experimental analysis of nonlinear dynamics in an optically-injected semiconductor laser,” AIP Advances 1(3), 032131 (2011).
[CrossRef]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Simpson, T. B.

T. B. Simpson, J. M. Liu, K. F. Huang, K Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” J. Quantum Semiclass. Opt. 9(5), 765 (1997).

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Sun, C. Z.

Sunada, S.

Tai, K

T. B. Simpson, J. M. Liu, K. F. Huang, K Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” J. Quantum Semiclass. Opt. 9(5), 765 (1997).

Tang, S.

S. Tang, J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” J. Quantum Electron. 37(3), 329–336 (2001).
[CrossRef]

Todaro, M. T.

Tromborg, B.

J. Mork, J. Mark, B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65(16), 1999–2002 (1990).
[CrossRef]

Tsuzuki, K.

Uchida, A.

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

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Ushakov, O.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

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

Vaughan, M. P.

Wille, E.

H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
[CrossRef]

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

E. Wille, M. Peil, I. Fischer, W. Elsaber, “Dynamical scenarios of mutually delay-coupled semiconductor lasers in the short coupling regime,” Proc. SPIE Semiconductor Lasers and Laser Dynamics5452, 41–50 (2004).
[CrossRef]

Wünsche, H. J.

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

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

Xiong, B.

Ye, J.

J. Ye, H. Li, J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249–2252 (1993).
[CrossRef] [PubMed]

Yoshi Mori, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Yoshimura, K.

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

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

. Quantum Semiclass. Opt. (1)

T. B. Simpson, J. M. Liu, K. F. Huang, K Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” J. Quantum Semiclass. Opt. 9(5), 765 (1997).

AIP Advances (1)

K. Schires, A. Hurtado, I. D. Henning, M. J. Adams, “Comprehensive experimental analysis of nonlinear dynamics in an optically-injected semiconductor laser,” AIP Advances 1(3), 032131 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

F. G. Della Corte, G. Cocorullo, M. Iodice, I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77(11), 1614–1616 (2000).
[CrossRef]

J. Quantum Electron. (3)

B. R. Cemlyn, D. Labukhin, I. D. Henning, M. J. Adams, “Dynamic Transitions in a Photonic Integrated Circuit,” J. Quantum Electron. 48(2), 261–268 (2012).
[CrossRef]

S. Tang, J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” J. Quantum Electron. 37(3), 329–336 (2001).
[CrossRef]

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” J. Quantum Electron. 46(3), 421–428 (2010).
[CrossRef]

Nat. Photonics (1)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshi Mori, K. Yoshimura, P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).

Opt. Commun. (2)

H. Erzgraber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsaßer, “Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios,” Opt. Commun. 255(4-6), 286–296 (2005).
[CrossRef]

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 267(2), 464–468 (2006).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (1)

J. Ye, H. Li, J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47(3), 2249–2252 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

J. Mork, J. Mark, B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65(16), 1999–2002 (1990).
[CrossRef]

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

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

T. Heil, I. Fischer, W. Elsässer, J. Mulet, C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

H. J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

SIAM J. Appl. Dyn. Syst. (1)

H. Erzgraber, B. Krauskopf, D. Lenstra, “Compound Laser Modes of Mutually Delay-Coupled Lasers,” SIAM J. Appl. Dyn. Syst. 5(1), 30–65 (2006).
[CrossRef]

Other (3)

E. Wille, M. Peil, I. Fischer, W. Elsaber, “Dynamical scenarios of mutually delay-coupled semiconductor lasers in the short coupling regime,” Proc. SPIE Semiconductor Lasers and Laser Dynamics5452, 41–50 (2004).
[CrossRef]

L. A. Coldren, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, 2012), Chap. 5.

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2006), Chap. 11.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup. (EDFA: Erbium doped fiber amplifier; PD: photodetector; ESA: electrical spectrum analyzer; OSA: optical spectrum analyzer; OSC: Oscilloscope. Dashed lines denote optical fibers and solid lines are electrical connections.)

Fig. 2
Fig. 2

Measured optical spectra and RF spectra of LD#1 and LD#2: (a) mutual locking and (b) FWM. The phase section is unbiased, and the currents on LD#1 and LD#2 are respectively (a) 40 mA, 41mA, and (b) 40 mA, 49 mA.

Fig. 3
Fig. 3

Measured optical spectra, RF spectra, and time series of optical output under (a) period-1, (b) quasi-periodicity, (c) chaos, and (d) and (e) frequency locking. The phase section is unbiased, and the currents on LD#1 and LD#2 are respectively (a) 40 mA, 42 mA, (b) 40 mA, 43 mA (c) 40 mA, 44 mA (d) 40 mA, 46 mA and (e) 40 mA, 48 mA.

Fig. 4
Fig. 4

Measured optical and RF spectra under the same condition as in Fig. 3(b) but with different coupling phases. The currents on LD#1, LD#2 and the phase section are 40 mA, 43 mA and 1 mA, respectively.

Fig. 5
Fig. 5

Bifurcation diagram of carrier densities in LD#1 and LD#2 with coupling phase as the bifurcation parameter. (A: mutual locking, B: quasi-periodic pulsing, C: frequency locking, D: chaotic state.)

Fig. 6
Fig. 6

Simulated optical spectra, RF spectra, optical intensity time series, and phase portraits of LD#1 and LD#2. (a) mutual locking, (b) and (c) frequency locking, (d) quasi-periodicity, and (e) chaos.

Equations (1)

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d E 1 d t = 1 2 ( 1 + i α ) g ( N 1 - N t h ) E 1 + κ τ i n E 2 ( t τ ) exp ( i ω 2 τ + i Δ ω t ) d N 1 d t = I 1 e V τ c 1 N 1 Γ g ( N 1 - N 0 ) | E 1 | 2 d E 2 d t = 1 2 ( 1 + i α ) g ( N 2 - N t h ) E 2 + κ τ i n E 1 ( t τ ) exp ( i ω 1 τ i Δ ω t ) d N 2 d t = I 2 e V τ c 1 N 2 Γ g ( N 2 - N 0 ) | E 2 | 2

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