Abstract

We analyze experimentally and theoretically the effects of delayed optical cross-feedback in semiconductor ring lasers. We show that under appropriate conditions, feeding of only one directional mode back into the counter-propagating mode leads to square-wave oscillations. In this regime, the laser switches regularly between the two counter-propagating modes with a period close to twice the roundtrip time in the external feedback loop. We find that these oscillations are robust and appear for a wide range of parameters as long as a small asymmetry in the linear coupling between both modes is present. We show that by increasing the feedback strength or the injection current, the square-wave oscillations gradually disappear. Due to noise, mode-hopping between stable lasing in one directional mode and square wave oscillations is observed in this transition region.

© 2012 OSA

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  1. T. Erneux and P. Glorieux, Laser Dynamics (Cambridge University Press, Cambridge, UK, 2010).
    [CrossRef]
  2. T. Erneux, Applied Delay Differential Equations (Springer, New York, 2009).
  3. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
    [CrossRef] [PubMed]
  4. L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
    [CrossRef] [PubMed]
  5. A. Gavrielides, T. Erneux, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 13, 2006–2008 (2006).
    [CrossRef]
  6. E. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclass. Opt. 6, L9–L12 (2004).
    [CrossRef]
  7. J. Mulet, M. Giudici, J. Javaloyes, and S. Balle, “Square-wave switching by crossed-polarization gain modulation in vertical-cavity semiconductor lasers,” Phys. Rev. A 76, 043801 (2007).
    [CrossRef]
  8. A. Gavrielides, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback,” Phys. Rev. E 81, 056209 (2010).
    [CrossRef]
  9. D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
    [CrossRef]
  10. C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment,” Phys. Rev. A 84, 023838 (2011).
    [CrossRef]
  11. M. Sciamanna, M. Virte, C. Masoller, and A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” to be published in Phys. Rev. E (2012).
    [CrossRef]
  12. T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
    [CrossRef]
  13. M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
    [CrossRef] [PubMed]
  14. V. R. Almeida, C. Barrios, R. Panepucci, M. Lipson, M. Foster, D. Ouzounov, and A. Gaeta, “All-optical switching on a silicon chip,” Opt. Lett. 29, 2867–2869 (2004).
    [CrossRef]
  15. L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
    [CrossRef]
  16. L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
    [CrossRef] [PubMed]
  17. L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
    [CrossRef]
  18. S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
    [CrossRef] [PubMed]
  19. M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, S. Donati, and P. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and mode,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
    [CrossRef]
  20. G. Van der Sande, L. Gelens, P. Tassin, A. Sciré, and J. Danckaert, “Two-dimensional phase-space analysis and bifurcation study of the dynamical behavior of a semiconductor ring laser,” J. Phys. B 41, 095402 (2008).
    [CrossRef]
  21. M. Sorel, P. Laybourn, A. Sciré, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
    [CrossRef]
  22. W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
    [CrossRef]
  23. L. Gelens, S. Beri, L. Mashall, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry,” Eur. Phys. J. D 58, 197–207 (2010).
    [CrossRef]
  24. M. S. Torre, A. Gavrielides, and C. Masoller, “Numerical characterization of transient polarization square-wave switching in two orthogonally coupled VCSELs,” Opt. Express 19, 20269–20278 (2011).
    [CrossRef] [PubMed]
  25. M. Yousefi, D. Lenstra, and G. Vemuri, “Carrier inversion noise has important influence on the dynamics of a semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 10, 955–960 (2004).
    [CrossRef]
  26. M. C. Soriano, T. Berkvens, G. Van der Sande, G. Verschaffelt, J. Danckaert, and I. Fischer, “Interplay of Current Noise and Delayed Optical Feedback on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. 47, 368–374 (2011).
    [CrossRef]

2011

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment,” Phys. Rev. A 84, 023838 (2011).
[CrossRef]

M. C. Soriano, T. Berkvens, G. Van der Sande, G. Verschaffelt, J. Danckaert, and I. Fischer, “Interplay of Current Noise and Delayed Optical Feedback on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. 47, 368–374 (2011).
[CrossRef]

M. S. Torre, A. Gavrielides, and C. Masoller, “Numerical characterization of transient polarization square-wave switching in two orthogonally coupled VCSELs,” Opt. Express 19, 20269–20278 (2011).
[CrossRef] [PubMed]

2010

A. Gavrielides, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback,” Phys. Rev. E 81, 056209 (2010).
[CrossRef]

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
[CrossRef]

L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
[CrossRef]

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

L. Gelens, S. Beri, L. Mashall, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry,” Eur. Phys. J. D 58, 197–207 (2010).
[CrossRef]

2009

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef] [PubMed]

2008

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

G. Van der Sande, L. Gelens, P. Tassin, A. Sciré, and J. Danckaert, “Two-dimensional phase-space analysis and bifurcation study of the dynamical behavior of a semiconductor ring laser,” J. Phys. B 41, 095402 (2008).
[CrossRef]

2007

J. Mulet, M. Giudici, J. Javaloyes, and S. Balle, “Square-wave switching by crossed-polarization gain modulation in vertical-cavity semiconductor lasers,” Phys. Rev. A 76, 043801 (2007).
[CrossRef]

2006

A. Gavrielides, T. Erneux, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 13, 2006–2008 (2006).
[CrossRef]

2005

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

2004

E. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclass. Opt. 6, L9–L12 (2004).
[CrossRef]

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

M. Yousefi, D. Lenstra, and G. Vemuri, “Carrier inversion noise has important influence on the dynamics of a semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 10, 955–960 (2004).
[CrossRef]

V. R. Almeida, C. Barrios, R. Panepucci, M. Lipson, M. Foster, D. Ouzounov, and A. Gaeta, “All-optical switching on a silicon chip,” Opt. Lett. 29, 2867–2869 (2004).
[CrossRef]

2003

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, S. Donati, and P. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and mode,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
[CrossRef]

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

2002

Aida, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Almeida, V. R.

Amonette, J.

A. Gavrielides, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback,” Phys. Rev. E 81, 056209 (2010).
[CrossRef]

A. Gavrielides, T. Erneux, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 13, 2006–2008 (2006).
[CrossRef]

Annovazzi-Lodi, V.

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

Appeltant, L.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

Argyris, A.

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

Balle, S.

J. Mulet, M. Giudici, J. Javaloyes, and S. Balle, “Square-wave switching by crossed-polarization gain modulation in vertical-cavity semiconductor lasers,” Phys. Rev. A 76, 043801 (2007).
[CrossRef]

M. Sorel, P. Laybourn, A. Sciré, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Barrios, C.

Beri, S.

L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
[CrossRef]

L. Gelens, S. Beri, L. Mashall, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry,” Eur. Phys. J. D 58, 197–207 (2010).
[CrossRef]

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Berkvens, T.

M. C. Soriano, T. Berkvens, G. Van der Sande, G. Verschaffelt, J. Danckaert, and I. Fischer, “Interplay of Current Noise and Delayed Optical Feedback on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. 47, 368–374 (2011).
[CrossRef]

Binsma, H.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Burner, G.

A. Gavrielides, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback,” Phys. Rev. E 81, 056209 (2010).
[CrossRef]

A. Gavrielides, T. Erneux, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 13, 2006–2008 (2006).
[CrossRef]

Colet, P.

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

Coomans, W.

L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
[CrossRef]

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

Dambre, J.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

Danckaert, J.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

M. C. Soriano, T. Berkvens, G. Van der Sande, G. Verschaffelt, J. Danckaert, and I. Fischer, “Interplay of Current Noise and Delayed Optical Feedback on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. 47, 368–374 (2011).
[CrossRef]

L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
[CrossRef]

L. Gelens, S. Beri, L. Mashall, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry,” Eur. Phys. J. D 58, 197–207 (2010).
[CrossRef]

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

G. Van der Sande, L. Gelens, P. Tassin, A. Sciré, and J. Danckaert, “Two-dimensional phase-space analysis and bifurcation study of the dynamical behavior of a semiconductor ring laser,” J. Phys. B 41, 095402 (2008).
[CrossRef]

Davis, J.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
[CrossRef]

Davis, P.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

de Vries, T.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

den Besten, J.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Donati, S.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, S. Donati, and P. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and mode,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
[CrossRef]

M. Sorel, P. Laybourn, A. Sciré, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Dorren, H.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Erneux, T.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
[CrossRef]

A. Gavrielides, T. Erneux, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 13, 2006–2008 (2006).
[CrossRef]

T. Erneux, Applied Delay Differential Equations (Springer, New York, 2009).

T. Erneux and P. Glorieux, Laser Dynamics (Cambridge University Press, Cambridge, UK, 2010).
[CrossRef]

Fischer, I.

M. C. Soriano, T. Berkvens, G. Van der Sande, G. Verschaffelt, J. Danckaert, and I. Fischer, “Interplay of Current Noise and Delayed Optical Feedback on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. 47, 368–374 (2011).
[CrossRef]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

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

Foster, M.

Gaeta, A.

García-Ojalvo, J.

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

Gavrielides, A.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment,” Phys. Rev. A 84, 023838 (2011).
[CrossRef]

M. S. Torre, A. Gavrielides, and C. Masoller, “Numerical characterization of transient polarization square-wave switching in two orthogonally coupled VCSELs,” Opt. Express 19, 20269–20278 (2011).
[CrossRef] [PubMed]

A. Gavrielides, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback,” Phys. Rev. E 81, 056209 (2010).
[CrossRef]

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
[CrossRef]

A. Gavrielides, T. Erneux, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 13, 2006–2008 (2006).
[CrossRef]

M. Sciamanna, M. Virte, C. Masoller, and A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” to be published in Phys. Rev. E (2012).
[CrossRef]

Gelens, L.

L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
[CrossRef]

L. Gelens, S. Beri, L. Mashall, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry,” Eur. Phys. J. D 58, 197–207 (2010).
[CrossRef]

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

G. Van der Sande, L. Gelens, P. Tassin, A. Sciré, and J. Danckaert, “Two-dimensional phase-space analysis and bifurcation study of the dynamical behavior of a semiconductor ring laser,” J. Phys. B 41, 095402 (2008).
[CrossRef]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Giudici, M.

J. Mulet, M. Giudici, J. Javaloyes, and S. Balle, “Square-wave switching by crossed-polarization gain modulation in vertical-cavity semiconductor lasers,” Phys. Rev. A 76, 043801 (2007).
[CrossRef]

Giuliani, G.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, S. Donati, and P. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and mode,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
[CrossRef]

M. Sorel, P. Laybourn, A. Sciré, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Glorieux, P.

T. Erneux and P. Glorieux, Laser Dynamics (Cambridge University Press, Cambridge, UK, 2010).
[CrossRef]

Heil, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Hill, M. T.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Javaloyes, J.

J. Mulet, M. Giudici, J. Javaloyes, and S. Balle, “Square-wave switching by crossed-polarization gain modulation in vertical-cavity semiconductor lasers,” Phys. Rev. A 76, 043801 (2007).
[CrossRef]

Khoe, G.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Larger, L.

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

Laybourn, P.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, S. Donati, and P. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and mode,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
[CrossRef]

M. Sorel, P. Laybourn, A. Sciré, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Lee, K.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
[CrossRef]

Leijtens, X.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Lenstra, D.

M. Yousefi, D. Lenstra, and G. Vemuri, “Carrier inversion noise has important influence on the dynamics of a semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 10, 955–960 (2004).
[CrossRef]

Lipson, M.

M, M. S.

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Mandel, P.

E. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclass. Opt. 6, L9–L12 (2004).
[CrossRef]

Mashal, L.

L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
[CrossRef]

Mashall, L.

L. Gelens, S. Beri, L. Mashall, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry,” Eur. Phys. J. D 58, 197–207 (2010).
[CrossRef]

Masoller, C.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment,” Phys. Rev. A 84, 023838 (2011).
[CrossRef]

M. S. Torre, A. Gavrielides, and C. Masoller, “Numerical characterization of transient polarization square-wave switching in two orthogonally coupled VCSELs,” Opt. Express 19, 20269–20278 (2011).
[CrossRef] [PubMed]

M. Sciamanna, M. Virte, C. Masoller, and A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” to be published in Phys. Rev. E (2012).
[CrossRef]

Massar, S.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

McKay, J.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
[CrossRef]

McLachlan, T.

A. Gavrielides, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback,” Phys. Rev. E 81, 056209 (2010).
[CrossRef]

A. Gavrielides, T. Erneux, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 13, 2006–2008 (2006).
[CrossRef]

Mestre, M.

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Mezosi, G.

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef] [PubMed]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Miglierina, R.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, S. Donati, and P. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and mode,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
[CrossRef]

M. Sorel, P. Laybourn, A. Sciré, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Miller, J.

A. Gavrielides, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback,” Phys. Rev. E 81, 056209 (2010).
[CrossRef]

A. Gavrielides, T. Erneux, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 13, 2006–2008 (2006).
[CrossRef]

Mirasso, C. R.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

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

Mooneyham, B.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
[CrossRef]

Mulet, J.

J. Mulet, M. Giudici, J. Javaloyes, and S. Balle, “Square-wave switching by crossed-polarization gain modulation in vertical-cavity semiconductor lasers,” Phys. Rev. A 76, 043801 (2007).
[CrossRef]

Oei, Y.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Ouzounov, D.

Panepucci, R.

Pesquera, L.

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

Schrauwen, B.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

Sciamanna, M.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment,” Phys. Rev. A 84, 023838 (2011).
[CrossRef]

M. Sciamanna, M. Virte, C. Masoller, and A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” to be published in Phys. Rev. E (2012).
[CrossRef]

Sciré, A.

G. Van der Sande, L. Gelens, P. Tassin, A. Sciré, and J. Danckaert, “Two-dimensional phase-space analysis and bifurcation study of the dynamical behavior of a semiconductor ring laser,” J. Phys. B 41, 095402 (2008).
[CrossRef]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, S. Donati, and P. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and mode,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
[CrossRef]

M. Sorel, P. Laybourn, A. Sciré, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Shore, K. A.

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

Smalbrugge, B.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Smit, M.

M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Sorel, M.

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef] [PubMed]

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, S. Donati, and P. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and mode,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
[CrossRef]

M. Sorel, P. Laybourn, A. Sciré, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Soriano, M. C.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

M. C. Soriano, T. Berkvens, G. Van der Sande, G. Verschaffelt, J. Danckaert, and I. Fischer, “Interplay of Current Noise and Delayed Optical Feedback on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. 47, 368–374 (2011).
[CrossRef]

Sukow, D.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment,” Phys. Rev. A 84, 023838 (2011).
[CrossRef]

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
[CrossRef]

A. Gavrielides, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback,” Phys. Rev. E 81, 056209 (2010).
[CrossRef]

A. Gavrielides, T. Erneux, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 13, 2006–2008 (2006).
[CrossRef]

Syvridis, D.

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

Tassin, P.

G. Van der Sande, L. Gelens, P. Tassin, A. Sciré, and J. Danckaert, “Two-dimensional phase-space analysis and bifurcation study of the dynamical behavior of a semiconductor ring laser,” J. Phys. B 41, 095402 (2008).
[CrossRef]

Torre, M. S.

Uchida, A.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Van der Sande, G.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

M. C. Soriano, T. Berkvens, G. Van der Sande, G. Verschaffelt, J. Danckaert, and I. Fischer, “Interplay of Current Noise and Delayed Optical Feedback on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. 47, 368–374 (2011).
[CrossRef]

L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
[CrossRef]

L. Gelens, S. Beri, L. Mashall, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry,” Eur. Phys. J. D 58, 197–207 (2010).
[CrossRef]

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

G. Van der Sande, L. Gelens, P. Tassin, A. Sciré, and J. Danckaert, “Two-dimensional phase-space analysis and bifurcation study of the dynamical behavior of a semiconductor ring laser,” J. Phys. B 41, 095402 (2008).
[CrossRef]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Vemuri, G.

M. Yousefi, D. Lenstra, and G. Vemuri, “Carrier inversion noise has important influence on the dynamics of a semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 10, 955–960 (2004).
[CrossRef]

Verschaffelt, G.

M. C. Soriano, T. Berkvens, G. Van der Sande, G. Verschaffelt, J. Danckaert, and I. Fischer, “Interplay of Current Noise and Delayed Optical Feedback on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. 47, 368–374 (2011).
[CrossRef]

L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
[CrossRef]

L. Gelens, S. Beri, L. Mashall, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry,” Eur. Phys. J. D 58, 197–207 (2010).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef] [PubMed]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. S. M, and J. Danckaert, “Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Viktorov, E.

E. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclass. Opt. 6, L9–L12 (2004).
[CrossRef]

Virte, M.

M. Sciamanna, M. Virte, C. Masoller, and A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” to be published in Phys. Rev. E (2012).
[CrossRef]

Yacomotti, A. M.

E. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclass. Opt. 6, L9–L12 (2004).
[CrossRef]

Yousefi, M.

M. Yousefi, D. Lenstra, and G. Vemuri, “Carrier inversion noise has important influence on the dynamics of a semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 10, 955–960 (2004).
[CrossRef]

Eur. Phys. J. D

L. Gelens, S. Beri, L. Mashall, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry,” Eur. Phys. J. D 58, 197–207 (2010).
[CrossRef]

IEEE J. Quantum Electron.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, S. Donati, and P. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and mode,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
[CrossRef]

M. C. Soriano, T. Berkvens, G. Van der Sande, G. Verschaffelt, J. Danckaert, and I. Fischer, “Interplay of Current Noise and Delayed Optical Feedback on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. 47, 368–374 (2011).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Yousefi, D. Lenstra, and G. Vemuri, “Carrier inversion noise has important influence on the dynamics of a semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 10, 955–960 (2004).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt.

E. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclass. Opt. 6, L9–L12 (2004).
[CrossRef]

J. Phys. B

G. Van der Sande, L. Gelens, P. Tassin, A. Sciré, and J. Danckaert, “Two-dimensional phase-space analysis and bifurcation study of the dynamical behavior of a semiconductor ring laser,” J. Phys. B 41, 095402 (2008).
[CrossRef]

Nat. Commun.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[CrossRef] [PubMed]

Nature

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
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M. T. Hill, H. Dorren, T. de Vries, X. Leijtens, J. den Besten, B. Smalbrugge, Y. Oei, H. Binsma, G. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. A

J. Mulet, M. Giudici, J. Javaloyes, and S. Balle, “Square-wave switching by crossed-polarization gain modulation in vertical-cavity semiconductor lasers,” Phys. Rev. A 76, 043801 (2007).
[CrossRef]

L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
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T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment,” Phys. Rev. A 84, 023838 (2011).
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W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

Phys. Rev. E

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
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A. Gavrielides, D. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, “Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback,” Phys. Rev. E 81, 056209 (2010).
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D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81, 025206 (2010).
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L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: Theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
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Other

M. Sciamanna, M. Virte, C. Masoller, and A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” to be published in Phys. Rev. E (2012).
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T. Erneux and P. Glorieux, Laser Dynamics (Cambridge University Press, Cambridge, UK, 2010).
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Figures (12)

Fig. 1
Fig. 1

A schematic view of the semiconductor ring laser and a sketch of the experimental setup. LF is the lensed fiber, SOA the semiconductor optical amplifier and C the circulator.

Fig. 2
Fig. 2

SRL’s optical output power in CW (green) and CCW (red) directions. Remark that the output power is fairly low, because no current is sent through the output waveguides.

Fig. 3
Fig. 3

Time traces of the CCW mode. Parameters are (a) Ir = 42mA, ISOA= 300mA and IWG = 10mA, (b) Ir =43mA, ISOA= 300mA and IWG = 10mA and (c) Ir = 44mA, ISOA= 300mA and IWG = 10mA. The temperature is stabilized at 23°C.

Fig. 4
Fig. 4

Time traces of the CCW mode. Parameters are Ir = 43 mA, IWG = 10mA, (a) ISOA = 0mA, (b) ISOA = 200mA, (c) ISOA = 400mA, and (d) ISOA = 500mA.

Fig. 5
Fig. 5

Mode resolved optical intensity of the CW mode (|Ecw|2, green) and the CCW mode (|Eccw|2, red) vs. injection current μ for a solitary SRL (η = 0) without noise (β= 0) obtained by numerical integration of Eqs. (1)(3). Full lines and dashed lines represent different stable attractors.

Fig. 6
Fig. 6

Intensity of the CCW mode obtained by numerical integration of Eqs. (1)(3) with μ =1.65, (a) η = 0.115ns−1, (b) η = 0.167ns−1, (c) η = 0.22ns−1, and (d) η = 0.273ns−1.

Fig. 7
Fig. 7

Intensity of the CCW mode obtained by numerical integration of Eqs. (1)(3) with η = 0.22ns−1, (a) μ =1.5 (b) μ =1.58, (c) μ =1.68, and (d) μ =1.7.

Fig. 8
Fig. 8

Time traces of the CCW mode. Parameters are (a) Ir = 42mA, ISOA= 300mA and IWG = 10mA, (b) Ir =43mA, ISOA= 300mA and IWG = 9mA and (c) Ir = 44mA, ISOA= 300mA and IWG = 14mA. Remark that the intensity levels in the subfigures are slightly different from each other because of the different waveguide currents.

Fig. 9
Fig. 9

Mode resolved intensity of the CCW mode (red) and CW mode (green) and total intensity (black) obtained by numerical integration of Eqs. (1)(3) with η = 0.19ns−1, μ =1.65 and β =0.

Fig. 10
Fig. 10

Orbit diagrams of mode resolved intensity of the CCW mode (red) and CW mode (green) vs. injection current μ obtained by numerical integration of Eqs. (1)(3) with η = 0.22ns−1, θ = 1.5 and β =0. In (a) and (c), μ is ramped up, while in (b) and (d), it is scanned downwards. SW: square waves. bi-Uni: bistable unidirectional regime.

Fig. 11
Fig. 11

Orbit diagrams of mode resolved intensity of the CCW mode (red) and CW mode (green) vs. feedback strength η obtained by numerical integration of Eqs. (1)(3) with μ = 1.65, θ = 1.5 and β =0.In (a) and (c), η is ramped up, while in (b) and (d), it is scanned downwards. SW: square waves.

Fig. 12
Fig. 12

Orbit diagrams of mode resolved intensity of the CCW mode (red) and CW mode (green) vs. feedback phase θ obtained by numerical integration of Eqs. (1)(3) with μ = 1.65, η = 0.22ns−1 and β =0.

Equations (5)

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E ˙ c c w = κ ( 1 + i α ) ( G c c w N 1 ) E c c w k ( 1 + δ k ) e i ϕ k E c w + F ˜ c c w ,
E ˙ c w = κ ( 1 + i α ) ( G c w N 1 ) E c w k ( 1 δ k ) e i ϕ k E c c w η e i θ E c c w ( t τ ) + F ˜ c w ,
N ˙ = γ ( μ N N G c w | E c w | 2 N G c c w | E c c w | 2 ) .
G c c w = 1 s | E c c w | 2 c | E c w | 2 ,
G c w = 1 s | E c w | 2 c | E c c w | 2 .

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