Abstract

This Letter is the first to report experimental bifurcation diagrams of an external-cavity semiconductor laser (ECSL) in the low-to-moderate current injection regime and long-cavity case. Based on the bifurcation cascade behavior which was unveiled by Hohl and Gavrielides [Phys. Rev. Lett. 82, 1148–1151 (1999)], we present a detailed experimental investigation of the nonlinear dynamics of ECSLs and of the robustness of the cascade to changes in the current and cavity length. Also, we report for the first time a well resolved experimental Hopf bifurcation in an ECSL. Based on the Lang and Kobayashi model, we identify the dynamical regimes and the instabilities involved in the cascade, as well as the influence of the current and cavity length on the cascade.

© 2014 Optical Society of America

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  1. C. Masoller, N. B. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57, 1313–1322 (1998).
    [CrossRef]
  2. 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, 1999–2002 (1990).
    [CrossRef] [PubMed]
  3. G. H. M. van Tartwijk, G. P. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43–122 (1998).
    [CrossRef]
  4. J. Ohtsubo, Semiconductor Lasers-Stability, Instability and Chaos (Springer, Berlin, 2006).
  5. D. Brunner, X. Porte, M. C. Soriano, I. Fischer, “Real-time frequency dynamics and high-resolution spectra of a semiconductor laser with delayed feedback,” Sci. Rep. 2,732 (2012).
    [CrossRef] [PubMed]
  6. D. Rontani, M. Sciamanna, A. Locquet, D. S. Citrin, “Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks,” Phys. Rev. E 80, 066209 (2009).
    [CrossRef]
  7. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
    [CrossRef] [PubMed]
  8. W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. 33, 237–239 (2008).
    [CrossRef] [PubMed]
  9. F. Y. Lin, J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
    [CrossRef]
  10. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
    [CrossRef]
  11. M. C. Soriano, J. Garcia-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
    [CrossRef]
  12. Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
    [CrossRef] [PubMed]
  13. J. Mork, B. Tromborg, J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
    [CrossRef]
  14. J. Ye, H. Li, J. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47, 2249–2252 (1993).
    [CrossRef] [PubMed]
  15. T. Heil, I. Fischer, W. Elsasser, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
    [CrossRef]
  16. S. Wieczorek, W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282, 2367–2379 (2009).
    [CrossRef]
  17. K. Green, B. Krauskopf, F. Marten, D. Lenstra, “Bifurcation Analysis of a Spatially Extended Laser with Optical Feedback,” SIAM J. Appl. Dyn. Syst. 8, 222–252 (2009).
    [CrossRef]
  18. I. V. Ermakov, G. Van der Sande, J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability,” Commmun. Nonlinear Sci. and Numer. Simulat. 17, 4767–4779 (2012).
    [CrossRef]
  19. R. J. Reategui, A. V. Kir’yanov, A. N. Pisarchik, Y. O. Barmenkov, N. N. Il’ichev, “Experimental study and modeling of coexisting attractors and bifurcations in an erbium-doped fiber laser with diode-pump modulation,” Laser Phys. 14, 1277–1281 (2004).
  20. S. Valling, B. Krauskopf, T. Fordell, A. M. Lindberg, “Experimental bifurcation diagram of a solid state laser with optical injection,” Opt. Commun. 271, 532–542 (2007).
    [CrossRef]
  21. F. T. Arecchi, R. Meucci, G. Puccioni, J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser,” Phys. Rev. Lett. 49, 1217–1220 (1982).
    [CrossRef]
  22. A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
    [CrossRef]
  23. R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection-laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  24. A. Hohl, A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148–1151 (1999).
    [CrossRef]
  25. A. Ritter, H. Haug, “Theory of laser-diodes with weak optical feedback .2. limit- cycle behavior, quasi-periodicity, frequency locking, and route to chaos,” J. Opt. Soc. Am. B-Opt. Phys. 10, 145–154 (1993).
    [CrossRef]
  26. C. H. Henry, R. F. Kazarinov, “Instability of semiconductor-lasers due to optical feedback from distant reflectors,” IEEE J. Quantum Electron. 22, 294–301 (1986).
    [CrossRef]
  27. T. Heil, I. Fischer, W. Elaassser, J. Mulet, C. R. Mirasso, “Statistical properties of low-frequency fluctuations during single-mode operation in distributed-feedback lasers: experiments and modeling,” Opt. Lett. 24, 1275–1277 (1999).
    [CrossRef]
  28. F. R. Ruiz-Oliveras, A. N. Pisarchik, “Synchronization of semiconductor lasers with coexisting attractors,” Phys. Rev. E 79,016202 (2009).
    [CrossRef]

2013 (1)

M. C. Soriano, J. Garcia-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

2012 (3)

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
[CrossRef] [PubMed]

I. V. Ermakov, G. Van der Sande, J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability,” Commmun. Nonlinear Sci. and Numer. Simulat. 17, 4767–4779 (2012).
[CrossRef]

D. Brunner, X. Porte, M. C. Soriano, I. Fischer, “Real-time frequency dynamics and high-resolution spectra of a semiconductor laser with delayed feedback,” Sci. Rep. 2,732 (2012).
[CrossRef] [PubMed]

2009 (4)

D. Rontani, M. Sciamanna, A. Locquet, D. S. Citrin, “Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks,” Phys. Rev. E 80, 066209 (2009).
[CrossRef]

S. Wieczorek, W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282, 2367–2379 (2009).
[CrossRef]

K. Green, B. Krauskopf, F. Marten, D. Lenstra, “Bifurcation Analysis of a Spatially Extended Laser with Optical Feedback,” SIAM J. Appl. Dyn. Syst. 8, 222–252 (2009).
[CrossRef]

F. R. Ruiz-Oliveras, A. N. Pisarchik, “Synchronization of semiconductor lasers with coexisting attractors,” Phys. Rev. E 79,016202 (2009).
[CrossRef]

2008 (2)

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. 33, 237–239 (2008).
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

2007 (1)

S. Valling, B. Krauskopf, T. Fordell, A. M. Lindberg, “Experimental bifurcation diagram of a solid state laser with optical injection,” Opt. Commun. 271, 532–542 (2007).
[CrossRef]

2005 (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

2004 (2)

F. Y. Lin, J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[CrossRef]

R. J. Reategui, A. V. Kir’yanov, A. N. Pisarchik, Y. O. Barmenkov, N. N. Il’ichev, “Experimental study and modeling of coexisting attractors and bifurcations in an erbium-doped fiber laser with diode-pump modulation,” Laser Phys. 14, 1277–1281 (2004).

2000 (1)

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[CrossRef]

1999 (2)

1998 (3)

T. Heil, I. Fischer, W. Elsasser, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[CrossRef]

G. H. M. van Tartwijk, G. P. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43–122 (1998).
[CrossRef]

C. Masoller, N. B. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57, 1313–1322 (1998).
[CrossRef]

1993 (2)

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

A. Ritter, H. Haug, “Theory of laser-diodes with weak optical feedback .2. limit- cycle behavior, quasi-periodicity, frequency locking, and route to chaos,” J. Opt. Soc. Am. B-Opt. Phys. 10, 145–154 (1993).
[CrossRef]

1992 (1)

J. Mork, B. Tromborg, J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

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, 1999–2002 (1990).
[CrossRef] [PubMed]

1986 (1)

C. H. Henry, R. F. Kazarinov, “Instability of semiconductor-lasers due to optical feedback from distant reflectors,” IEEE J. Quantum Electron. 22, 294–301 (1986).
[CrossRef]

1982 (1)

F. T. Arecchi, R. Meucci, G. Puccioni, J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser,” Phys. Rev. Lett. 49, 1217–1220 (1982).
[CrossRef]

1980 (1)

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

Abraham, N. B.

C. Masoller, N. B. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57, 1313–1322 (1998).
[CrossRef]

Agrawal, G. P.

G. H. M. van Tartwijk, G. P. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43–122 (1998).
[CrossRef]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Andersen, O. K.

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[CrossRef]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

Arecchi, F. T.

F. T. Arecchi, R. Meucci, G. Puccioni, J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser,” Phys. Rev. Lett. 49, 1217–1220 (1982).
[CrossRef]

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

Barmenkov, Y. O.

R. J. Reategui, A. V. Kir’yanov, A. N. Pisarchik, Y. O. Barmenkov, N. N. Il’ichev, “Experimental study and modeling of coexisting attractors and bifurcations in an erbium-doped fiber laser with diode-pump modulation,” Laser Phys. 14, 1277–1281 (2004).

Brunner, D.

D. Brunner, X. Porte, M. C. Soriano, I. Fischer, “Real-time frequency dynamics and high-resolution spectra of a semiconductor laser with delayed feedback,” Sci. Rep. 2,732 (2012).
[CrossRef] [PubMed]

Chow, W. W.

S. Wieczorek, W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282, 2367–2379 (2009).
[CrossRef]

Citrin, D. S.

D. Rontani, M. Sciamanna, A. Locquet, D. S. Citrin, “Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks,” Phys. Rev. E 80, 066209 (2009).
[CrossRef]

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

Dambre, J.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
[CrossRef] [PubMed]

Danckaert, J.

I. V. Ermakov, G. Van der Sande, J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability,” Commmun. Nonlinear Sci. and Numer. Simulat. 17, 4767–4779 (2012).
[CrossRef]

Davis, P.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Duport, F.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
[CrossRef] [PubMed]

Elaassser, W.

Elsasser, W.

T. Heil, I. Fischer, W. Elsasser, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[CrossRef]

Ermakov, I. V.

I. V. Ermakov, G. Van der Sande, J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability,” Commmun. Nonlinear Sci. and Numer. Simulat. 17, 4767–4779 (2012).
[CrossRef]

Fischer, A. P. A.

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[CrossRef]

Fischer, I.

M. C. Soriano, J. Garcia-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

D. Brunner, X. Porte, M. C. Soriano, I. Fischer, “Real-time frequency dynamics and high-resolution spectra of a semiconductor laser with delayed feedback,” Sci. Rep. 2,732 (2012).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elaassser, J. Mulet, C. R. Mirasso, “Statistical properties of low-frequency fluctuations during single-mode operation in distributed-feedback lasers: experiments and modeling,” Opt. Lett. 24, 1275–1277 (1999).
[CrossRef]

T. Heil, I. Fischer, W. Elsasser, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[CrossRef]

Fordell, T.

S. Valling, B. Krauskopf, T. Fordell, A. M. Lindberg, “Experimental bifurcation diagram of a solid state laser with optical injection,” Opt. Commun. 271, 532–542 (2007).
[CrossRef]

Garcia-Ojalvo, J.

M. C. Soriano, J. Garcia-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

Gavrielides, A.

A. Hohl, A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148–1151 (1999).
[CrossRef]

Green, K.

K. Green, B. Krauskopf, F. Marten, D. Lenstra, “Bifurcation Analysis of a Spatially Extended Laser with Optical Feedback,” SIAM J. Appl. Dyn. Syst. 8, 222–252 (2009).
[CrossRef]

Haelterman, M.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
[CrossRef] [PubMed]

Haug, H.

A. Ritter, H. Haug, “Theory of laser-diodes with weak optical feedback .2. limit- cycle behavior, quasi-periodicity, frequency locking, and route to chaos,” J. Opt. Soc. Am. B-Opt. Phys. 10, 145–154 (1993).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, W. Elaassser, J. Mulet, C. R. Mirasso, “Statistical properties of low-frequency fluctuations during single-mode operation in distributed-feedback lasers: experiments and modeling,” Opt. Lett. 24, 1275–1277 (1999).
[CrossRef]

T. Heil, I. Fischer, W. Elsasser, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[CrossRef]

Henry, C. H.

C. H. Henry, R. F. Kazarinov, “Instability of semiconductor-lasers due to optical feedback from distant reflectors,” IEEE J. Quantum Electron. 22, 294–301 (1986).
[CrossRef]

Hirano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Hohl, A.

A. Hohl, A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148–1151 (1999).
[CrossRef]

Il’ichev, N. N.

R. J. Reategui, A. V. Kir’yanov, A. N. Pisarchik, Y. O. Barmenkov, N. N. Il’ichev, “Experimental study and modeling of coexisting attractors and bifurcations in an erbium-doped fiber laser with diode-pump modulation,” Laser Phys. 14, 1277–1281 (2004).

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Kazarinov, R. F.

C. H. Henry, R. F. Kazarinov, “Instability of semiconductor-lasers due to optical feedback from distant reflectors,” IEEE J. Quantum Electron. 22, 294–301 (1986).
[CrossRef]

Kir’yanov, A. V.

R. J. Reategui, A. V. Kir’yanov, A. N. Pisarchik, Y. O. Barmenkov, N. N. Il’ichev, “Experimental study and modeling of coexisting attractors and bifurcations in an erbium-doped fiber laser with diode-pump modulation,” Laser Phys. 14, 1277–1281 (2004).

Kobayashi, K.

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

Krauskopf, B.

K. Green, B. Krauskopf, F. Marten, D. Lenstra, “Bifurcation Analysis of a Spatially Extended Laser with Optical Feedback,” SIAM J. Appl. Dyn. Syst. 8, 222–252 (2009).
[CrossRef]

S. Valling, B. Krauskopf, T. Fordell, A. M. Lindberg, “Experimental bifurcation diagram of a solid state laser with optical injection,” Opt. Commun. 271, 532–542 (2007).
[CrossRef]

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Lang, R.

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

Larger, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

Lenstra, D.

K. Green, B. Krauskopf, F. Marten, D. Lenstra, “Bifurcation Analysis of a Spatially Extended Laser with Optical Feedback,” SIAM J. Appl. Dyn. Syst. 8, 222–252 (2009).
[CrossRef]

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[CrossRef]

Li, H.

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

Lin, F. Y.

F. Y. Lin, J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[CrossRef]

Lindberg, A. M.

S. Valling, B. Krauskopf, T. Fordell, A. M. Lindberg, “Experimental bifurcation diagram of a solid state laser with optical injection,” Opt. Commun. 271, 532–542 (2007).
[CrossRef]

Liu, J. M.

F. Y. Lin, J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[CrossRef]

Locquet, A.

D. Rontani, M. Sciamanna, A. Locquet, D. S. Citrin, “Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks,” Phys. Rev. E 80, 066209 (2009).
[CrossRef]

Luo, B.

Mark, J.

J. Mork, B. Tromborg, J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

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, 1999–2002 (1990).
[CrossRef] [PubMed]

Marten, F.

K. Green, B. Krauskopf, F. Marten, D. Lenstra, “Bifurcation Analysis of a Spatially Extended Laser with Optical Feedback,” SIAM J. Appl. Dyn. Syst. 8, 222–252 (2009).
[CrossRef]

Masoller, C.

C. Masoller, N. B. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57, 1313–1322 (1998).
[CrossRef]

Massar, S.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
[CrossRef] [PubMed]

McInerney, J.

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

Meucci, R.

F. T. Arecchi, R. Meucci, G. Puccioni, J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser,” Phys. Rev. Lett. 49, 1217–1220 (1982).
[CrossRef]

Mirasso, C. R.

M. C. Soriano, J. Garcia-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elaassser, J. Mulet, C. R. Mirasso, “Statistical properties of low-frequency fluctuations during single-mode operation in distributed-feedback lasers: experiments and modeling,” Opt. Lett. 24, 1275–1277 (1999).
[CrossRef]

Mork, J.

J. Mork, B. Tromborg, J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

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, 1999–2002 (1990).
[CrossRef] [PubMed]

Mulet, J.

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Ohtsubo, J.

J. Ohtsubo, Semiconductor Lasers-Stability, Instability and Chaos (Springer, Berlin, 2006).

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Pan, W.

Paquot, Y.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
[CrossRef] [PubMed]

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

Pisarchik, A. N.

F. R. Ruiz-Oliveras, A. N. Pisarchik, “Synchronization of semiconductor lasers with coexisting attractors,” Phys. Rev. E 79,016202 (2009).
[CrossRef]

R. J. Reategui, A. V. Kir’yanov, A. N. Pisarchik, Y. O. Barmenkov, N. N. Il’ichev, “Experimental study and modeling of coexisting attractors and bifurcations in an erbium-doped fiber laser with diode-pump modulation,” Laser Phys. 14, 1277–1281 (2004).

Porte, X.

D. Brunner, X. Porte, M. C. Soriano, I. Fischer, “Real-time frequency dynamics and high-resolution spectra of a semiconductor laser with delayed feedback,” Sci. Rep. 2,732 (2012).
[CrossRef] [PubMed]

Puccioni, G.

F. T. Arecchi, R. Meucci, G. Puccioni, J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser,” Phys. Rev. Lett. 49, 1217–1220 (1982).
[CrossRef]

Reategui, R. J.

R. J. Reategui, A. V. Kir’yanov, A. N. Pisarchik, Y. O. Barmenkov, N. N. Il’ichev, “Experimental study and modeling of coexisting attractors and bifurcations in an erbium-doped fiber laser with diode-pump modulation,” Laser Phys. 14, 1277–1281 (2004).

Ritter, A.

A. Ritter, H. Haug, “Theory of laser-diodes with weak optical feedback .2. limit- cycle behavior, quasi-periodicity, frequency locking, and route to chaos,” J. Opt. Soc. Am. B-Opt. Phys. 10, 145–154 (1993).
[CrossRef]

Rontani, D.

D. Rontani, M. Sciamanna, A. Locquet, D. S. Citrin, “Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks,” Phys. Rev. E 80, 066209 (2009).
[CrossRef]

Ruiz-Oliveras, F. R.

F. R. Ruiz-Oliveras, A. N. Pisarchik, “Synchronization of semiconductor lasers with coexisting attractors,” Phys. Rev. E 79,016202 (2009).
[CrossRef]

Schrauwen, B.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
[CrossRef] [PubMed]

Sciamanna, M.

D. Rontani, M. Sciamanna, A. Locquet, D. S. Citrin, “Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks,” Phys. Rev. E 80, 066209 (2009).
[CrossRef]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Shore, K. A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

Smerieri, A.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
[CrossRef] [PubMed]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Soriano, M. C.

M. C. Soriano, J. Garcia-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

D. Brunner, X. Porte, M. C. Soriano, I. Fischer, “Real-time frequency dynamics and high-resolution spectra of a semiconductor laser with delayed feedback,” Sci. Rep. 2,732 (2012).
[CrossRef] [PubMed]

Stolte, S.

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[CrossRef]

Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

Tredicce, J.

F. T. Arecchi, R. Meucci, G. Puccioni, J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser,” Phys. Rev. Lett. 49, 1217–1220 (1982).
[CrossRef]

Tromborg, B.

J. Mork, B. Tromborg, J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

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, 1999–2002 (1990).
[CrossRef] [PubMed]

Uchida, A.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Valling, S.

S. Valling, B. Krauskopf, T. Fordell, A. M. Lindberg, “Experimental bifurcation diagram of a solid state laser with optical injection,” Opt. Commun. 271, 532–542 (2007).
[CrossRef]

Van der Sande, G.

I. V. Ermakov, G. Van der Sande, J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability,” Commmun. Nonlinear Sci. and Numer. Simulat. 17, 4767–4779 (2012).
[CrossRef]

van Tartwijk, G. H. M.

G. H. M. van Tartwijk, G. P. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43–122 (1998).
[CrossRef]

Wang, M. Y.

Wieczorek, S.

S. Wieczorek, W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282, 2367–2379 (2009).
[CrossRef]

Ye, J.

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

Yoshimori, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Yoshimura, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Yousefi, M.

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[CrossRef]

Zhang, W. L.

Zhou, Z.

Zou, X. H.

Commmun. Nonlinear Sci. and Numer. Simulat. (1)

I. V. Ermakov, G. Van der Sande, J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability,” Commmun. Nonlinear Sci. and Numer. Simulat. 17, 4767–4779 (2012).
[CrossRef]

IEEE J. Quantum Electron. (4)

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[CrossRef]

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

C. H. Henry, R. F. Kazarinov, “Instability of semiconductor-lasers due to optical feedback from distant reflectors,” IEEE J. Quantum Electron. 22, 294–301 (1986).
[CrossRef]

J. Mork, B. Tromborg, J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

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

F. Y. Lin, J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[CrossRef]

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

A. Ritter, H. Haug, “Theory of laser-diodes with weak optical feedback .2. limit- cycle behavior, quasi-periodicity, frequency locking, and route to chaos,” J. Opt. Soc. Am. B-Opt. Phys. 10, 145–154 (1993).
[CrossRef]

Laser Phys. (1)

R. J. Reategui, A. V. Kir’yanov, A. N. Pisarchik, Y. O. Barmenkov, N. N. Il’ichev, “Experimental study and modeling of coexisting attractors and bifurcations in an erbium-doped fiber laser with diode-pump modulation,” Laser Phys. 14, 1277–1281 (2004).

Nat. Photon. (1)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).
[CrossRef] [PubMed]

Opt. Commun. (2)

S. Wieczorek, W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282, 2367–2379 (2009).
[CrossRef]

S. Valling, B. Krauskopf, T. Fordell, A. M. Lindberg, “Experimental bifurcation diagram of a solid state laser with optical injection,” Opt. Commun. 271, 532–542 (2007).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (3)

C. Masoller, N. B. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57, 1313–1322 (1998).
[CrossRef]

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

T. Heil, I. Fischer, W. Elsasser, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[CrossRef]

Phys. Rev. E (2)

D. Rontani, M. Sciamanna, A. Locquet, D. S. Citrin, “Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks,” Phys. Rev. E 80, 066209 (2009).
[CrossRef]

F. R. Ruiz-Oliveras, A. N. Pisarchik, “Synchronization of semiconductor lasers with coexisting attractors,” Phys. Rev. E 79,016202 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

A. Hohl, A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148–1151 (1999).
[CrossRef]

F. T. Arecchi, R. Meucci, G. Puccioni, J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser,” Phys. Rev. Lett. 49, 1217–1220 (1982).
[CrossRef]

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, 1999–2002 (1990).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

G. H. M. van Tartwijk, G. P. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43–122 (1998).
[CrossRef]

Rev. Mod. Phys. (1)

M. C. Soriano, J. Garcia-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

Sci. Rep. (2)

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic Reservoir Computing,” Sci. Rep. 2,287 (2012).
[CrossRef] [PubMed]

D. Brunner, X. Porte, M. C. Soriano, I. Fischer, “Real-time frequency dynamics and high-resolution spectra of a semiconductor laser with delayed feedback,” Sci. Rep. 2,732 (2012).
[CrossRef] [PubMed]

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

K. Green, B. Krauskopf, F. Marten, D. Lenstra, “Bifurcation Analysis of a Spatially Extended Laser with Optical Feedback,” SIAM J. Appl. Dyn. Syst. 8, 222–252 (2009).
[CrossRef]

Other (1)

J. Ohtsubo, Semiconductor Lasers-Stability, Instability and Chaos (Springer, Berlin, 2006).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup. PD: photodiode, BS: beam splitter, LP: linear polarizer, Q: quarter-wave plate, M: mirror, OI: optical isolator.

Fig. 2
Fig. 2

Experimental BD of I=11.24 mA and L=30 cm.

Fig. 3
Fig. 3

(a) Ellipse structure of fixed points in the phase-difference-vs.-N plane for κ = 0.009 and τ = 1 ns. (b) Numerical BD of p = 1.03 and L = 15 cm (τ = 1 ns).

Fig. 4
Fig. 4

Trajectory in phase space at τ = 1 ns. The circle indicates an ECM and the cross indicates an antimode (a) κ = 0.0014 (limit cycle), (b) 0.002 (quasi-period), (c) 0.0036, and (d) 0.00375.

Fig. 5
Fig. 5

Experimental optical spectrum with FP interferometer for (a) η = 0.0, (b) 0.10, (c) 0.13, (d) 0.16, (e) 0.18, (f) 0.2, (g) 0.24, (h) 0.26, (i) 0.3, (j) 0.33, (k) 0.35, (l) 0.4, (m) 0.42, and (n) 0.48. I = 11.24 mA and L = 30 cm. The arrows indicate the relaxation sidebands.

Fig. 6
Fig. 6

Experimental BDs for (a) I = 14.69 mA with L = 30 cm, I = 11.24 mA with L = (b) 15 cm and (c) 65 cm.

Fig. 7
Fig. 7

Numerical BD of p = 1.03, L = 65 cm and ωoτ = 0.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

d E d t = 1 + i α 2 ( 𝒢 1 τ p ) E ( t ) + κ τ in E ( t τ ) e i ω o τ ,
d N d t = p J th N ( t ) τ s 𝒢 | E | 2 .

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