Abstract

The rate equations for a laser with a polarization rotated optical feedback are investigated both numerically and analytically. The frequency detuning between the polarization modes is now taken into account and we review all earlier studies in order to motivate the range of values of the fixed parameters. We find that two basic Hopf bifurcations leading to either stable sustained relaxation or square-wave oscillations appear in the detuning versus feedback rate diagram. We also identify two key parameters describing the differences between the total gains of the two polarization modes and discuss their effects on the periodic square-waves.

© 2014 Optical Society of America

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  1. K. Otsuka, J.-L. Chern, “High-speed picosecond pulse generation in semiconductor lasers with incoherent optical feedback,” Opt. Lett. 16, 1759–1761 (1991).
    [CrossRef] [PubMed]
  2. D.-L. Cheng, T.-C. Yen, J.-W. Chang, J.-K. Tsai, “Generation of high-speed single-wavelength optical pulses in semiconductor lasers with orthogonal-polarization optical feedback,” Opt. Commun. 222, 363–369 (2003).
    [CrossRef]
  3. W. H. Loh, Y. Ozeki, C. L. Tang, “High-frequency polarization self-modulation and chaotic phenomena in external cavity semiconductor lasers,” Appl. Phys. Lett. 56, 2613–2615 (1990).
    [CrossRef]
  4. A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 31, 2006–2008 (2006).
    [CrossRef] [PubMed]
  5. A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-waveforms in edge-emitting diode lasers subject to polarization rotated optical feedback,” in Physics and Simulation of Optoelectronic Devices XIV, M. Osinski, F. Henneberger, Y. Arakawa, eds., Proc. SPIE6115, 60–69 (2006).
  6. A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave oscillations in edge-emitting diode lasers with polarization rotated optical feedback,” in Semiconductor Laser and Laser Dynamics II, D. Lenstra, M. Pessa, I. H. White, eds., Proc. SPIE6184, 255–261 (2006).
  7. N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36, 4632–4634 (2011).
    [CrossRef] [PubMed]
  8. J. Mulet, M. Giudici, J. Javaloyes, S. Balle, “Square-wave switching by crossed-polarization gain modulation in vertical-cavity semiconductor lasers,” Phys. Rev. A 76,043801 (2007).
    [CrossRef]
  9. M. Marconi, J. Javaloyes, S. Barland, M. Giudici, S. Balle, “Robust square-wave polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87,013827 (2013).
    [CrossRef]
  10. D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: experiments and simulations,” Phys. Rev. A 86,033818 (2012).
    [CrossRef]
  11. S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547, (1993).
    [CrossRef]
  12. H. Li, A. Hohl, A. Gavrielides, H. Hou, K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357, (1998).
    [CrossRef]
  13. M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65,041801 (2002).
    [CrossRef]
  14. L. Mashal, G. Van der Sande, L. Gelens, J. Danckaert, G. Verschaffelt, “Square-wave oscillations in semiconductor ring lasers with delayed optical feedback,” Opt. Express 20, 22503–22516 (2012).
    [CrossRef] [PubMed]
  15. D. W. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81,025206 (2010).
    [CrossRef]
  16. C. Masoller, D. Sukow, A. Gavrielides, M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment,” Phys. Rev. A 84,023838 (2011).
    [CrossRef]
  17. M. Sciamanna, M. Virte, C. Masoller, A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” Phys. Rev. E 86,016218 (2011).
    [CrossRef]
  18. C. Masoller, M. Sciamanna, A. Gavrielides, “Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers,” Phil. Transac. Roy. Soc. A 371,20120471 (2013).
    [CrossRef]
  19. M. Peil, M. Jacquot, Y. Kouomou Chembo, L. Larger, T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic-oscillators,” Phys. Rev. E 79,026208 (2009).
    [CrossRef]
  20. L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
    [CrossRef]
  21. L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
    [CrossRef] [PubMed]
  22. S.A. Campbell, “Stability and bifurcation in the harmonic oscillator with multiple, delayed feedback loops,” Dynamics of Continuous, Discrete and Impulsive Systems 5, 225–235 (1999).
  23. F. M. Atay, “Oscillation control in delayed feedback systems,” in Dynamics, Bifurcations, and Control, F. Colonius, L. Grne, eds. (Lect. Notes in Control and Information Sciences 273, 2002), pp. 103–116.
    [CrossRef]
  24. Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaotic dynamics in semiconductor lasers subjected to polarization-rotated optical feedback,” Appl. Phys. Lett. 93,181105 (2008).
    [CrossRef]
  25. Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaos dynamics in semiconductor lasers with polarization-rotated optical feedback,” Opt. Rev. 17, 144–151 (2010).
    [CrossRef]
  26. T. Heil, A. Uchida, P. Davis, T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68,033811 (2003).
    [CrossRef]
  27. K. Hicke, M. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19,1501610 (2013).
    [CrossRef]
  28. G. Friart, “Routes to square-wave oscillations in a semiconductor laser subject to polarization rotated feedback”, MS Thesis in Physics, Université Libre de Bruxelles (2013).
  29. A. Gavrielides, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, 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]

2013

M. Marconi, J. Javaloyes, S. Barland, M. Giudici, S. Balle, “Robust square-wave polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87,013827 (2013).
[CrossRef]

C. Masoller, M. Sciamanna, A. Gavrielides, “Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers,” Phil. Transac. Roy. Soc. A 371,20120471 (2013).
[CrossRef]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
[CrossRef] [PubMed]

K. Hicke, M. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19,1501610 (2013).
[CrossRef]

2012

L. Mashal, G. Van der Sande, L. Gelens, J. Danckaert, G. Verschaffelt, “Square-wave oscillations in semiconductor ring lasers with delayed optical feedback,” Opt. Express 20, 22503–22516 (2012).
[CrossRef] [PubMed]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
[CrossRef]

D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: experiments and simulations,” Phys. Rev. A 86,033818 (2012).
[CrossRef]

2011

C. Masoller, D. Sukow, A. Gavrielides, 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, A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” Phys. Rev. E 86,016218 (2011).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36, 4632–4634 (2011).
[CrossRef] [PubMed]

2010

A. Gavrielides, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, 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]

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaos dynamics in semiconductor lasers with polarization-rotated optical feedback,” Opt. Rev. 17, 144–151 (2010).
[CrossRef]

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

2009

M. Peil, M. Jacquot, Y. Kouomou Chembo, L. Larger, T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic-oscillators,” Phys. Rev. E 79,026208 (2009).
[CrossRef]

2008

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaotic dynamics in semiconductor lasers subjected to polarization-rotated optical feedback,” Appl. Phys. Lett. 93,181105 (2008).
[CrossRef]

2007

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

2006

2003

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

D.-L. Cheng, T.-C. Yen, J.-W. Chang, J.-K. Tsai, “Generation of high-speed single-wavelength optical pulses in semiconductor lasers with orthogonal-polarization optical feedback,” Opt. Commun. 222, 363–369 (2003).
[CrossRef]

2002

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65,041801 (2002).
[CrossRef]

1999

S.A. Campbell, “Stability and bifurcation in the harmonic oscillator with multiple, delayed feedback loops,” Dynamics of Continuous, Discrete and Impulsive Systems 5, 225–235 (1999).

1998

H. Li, A. Hohl, A. Gavrielides, H. Hou, K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357, (1998).
[CrossRef]

1993

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547, (1993).
[CrossRef]

1991

1990

W. H. Loh, Y. Ozeki, C. L. Tang, “High-frequency polarization self-modulation and chaotic phenomena in external cavity semiconductor lasers,” Appl. Phys. Lett. 56, 2613–2615 (1990).
[CrossRef]

Aida, T.

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

Amonette, J.

A. Gavrielides, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, 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.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 31, 2006–2008 (2006).
[CrossRef] [PubMed]

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-waveforms in edge-emitting diode lasers subject to polarization rotated optical feedback,” in Physics and Simulation of Optoelectronic Devices XIV, M. Osinski, F. Henneberger, Y. Arakawa, eds., Proc. SPIE6115, 60–69 (2006).

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave oscillations in edge-emitting diode lasers with polarization rotated optical feedback,” in Semiconductor Laser and Laser Dynamics II, D. Lenstra, M. Pessa, I. H. White, eds., Proc. SPIE6184, 255–261 (2006).

Atay, F. M.

F. M. Atay, “Oscillation control in delayed feedback systems,” in Dynamics, Bifurcations, and Control, F. Colonius, L. Grne, eds. (Lect. Notes in Control and Information Sciences 273, 2002), pp. 103–116.
[CrossRef]

Balle, S.

M. Marconi, J. Javaloyes, S. Barland, M. Giudici, S. Balle, “Robust square-wave polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87,013827 (2013).
[CrossRef]

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

Barland, S.

M. Marconi, J. Javaloyes, S. Barland, M. Giudici, S. Balle, “Robust square-wave polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87,013827 (2013).
[CrossRef]

Blondel, M.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65,041801 (2002).
[CrossRef]

Brunner, D.

K. Hicke, M. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19,1501610 (2013).
[CrossRef]

Burner, G.

A. Gavrielides, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, 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.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 31, 2006–2008 (2006).
[CrossRef] [PubMed]

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-waveforms in edge-emitting diode lasers subject to polarization rotated optical feedback,” in Physics and Simulation of Optoelectronic Devices XIV, M. Osinski, F. Henneberger, Y. Arakawa, eds., Proc. SPIE6115, 60–69 (2006).

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave oscillations in edge-emitting diode lasers with polarization rotated optical feedback,” in Semiconductor Laser and Laser Dynamics II, D. Lenstra, M. Pessa, I. H. White, eds., Proc. SPIE6184, 255–261 (2006).

Campbell, S.A.

S.A. Campbell, “Stability and bifurcation in the harmonic oscillator with multiple, delayed feedback loops,” Dynamics of Continuous, Discrete and Impulsive Systems 5, 225–235 (1999).

Chang, J.-W.

D.-L. Cheng, T.-C. Yen, J.-W. Chang, J.-K. Tsai, “Generation of high-speed single-wavelength optical pulses in semiconductor lasers with orthogonal-polarization optical feedback,” Opt. Commun. 222, 363–369 (2003).
[CrossRef]

Chembo, Y.

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
[CrossRef] [PubMed]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
[CrossRef]

Cheng, D.-L.

D.-L. Cheng, T.-C. Yen, J.-W. Chang, J.-K. Tsai, “Generation of high-speed single-wavelength optical pulses in semiconductor lasers with orthogonal-polarization optical feedback,” Opt. Commun. 222, 363–369 (2003).
[CrossRef]

Chern, J.-L.

Choquette, K. D.

H. Li, A. Hohl, A. Gavrielides, H. Hou, K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357, (1998).
[CrossRef]

d’Huys, O.

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
[CrossRef] [PubMed]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
[CrossRef]

Dagenais, M.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547, (1993).
[CrossRef]

Danckaert, J.

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
[CrossRef] [PubMed]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
[CrossRef]

L. Mashal, G. Van der Sande, L. Gelens, J. Danckaert, G. Verschaffelt, “Square-wave oscillations in semiconductor ring lasers with delayed optical feedback,” Opt. Express 20, 22503–22516 (2012).
[CrossRef] [PubMed]

Davis, J.

D. W. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, 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, T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68,033811 (2003).
[CrossRef]

Deparis, O.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65,041801 (2002).
[CrossRef]

Erneux, T.

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
[CrossRef] [PubMed]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
[CrossRef]

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

M. Peil, M. Jacquot, Y. Kouomou Chembo, L. Larger, T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic-oscillators,” Phys. Rev. E 79,026208 (2009).
[CrossRef]

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 31, 2006–2008 (2006).
[CrossRef] [PubMed]

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65,041801 (2002).
[CrossRef]

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave oscillations in edge-emitting diode lasers with polarization rotated optical feedback,” in Semiconductor Laser and Laser Dynamics II, D. Lenstra, M. Pessa, I. H. White, eds., Proc. SPIE6184, 255–261 (2006).

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-waveforms in edge-emitting diode lasers subject to polarization rotated optical feedback,” in Physics and Simulation of Optoelectronic Devices XIV, M. Osinski, F. Henneberger, Y. Arakawa, eds., Proc. SPIE6115, 60–69 (2006).

Escalona-Moran, M.

K. Hicke, M. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19,1501610 (2013).
[CrossRef]

Fischer, I.

K. Hicke, M. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19,1501610 (2013).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36, 4632–4634 (2011).
[CrossRef] [PubMed]

Friart, G.

G. Friart, “Routes to square-wave oscillations in a semiconductor laser subject to polarization rotated feedback”, MS Thesis in Physics, Université Libre de Bruxelles (2013).

Gavrielides, A.

C. Masoller, M. Sciamanna, A. Gavrielides, “Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers,” Phil. Transac. Roy. Soc. A 371,20120471 (2013).
[CrossRef]

D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: experiments and simulations,” Phys. Rev. A 86,033818 (2012).
[CrossRef]

M. Sciamanna, M. Virte, C. Masoller, A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” Phys. Rev. E 86,016218 (2011).
[CrossRef]

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

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

A. Gavrielides, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, 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.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 31, 2006–2008 (2006).
[CrossRef] [PubMed]

H. Li, A. Hohl, A. Gavrielides, H. Hou, K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357, (1998).
[CrossRef]

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-waveforms in edge-emitting diode lasers subject to polarization rotated optical feedback,” in Physics and Simulation of Optoelectronic Devices XIV, M. Osinski, F. Henneberger, Y. Arakawa, eds., Proc. SPIE6115, 60–69 (2006).

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave oscillations in edge-emitting diode lasers with polarization rotated optical feedback,” in Semiconductor Laser and Laser Dynamics II, D. Lenstra, M. Pessa, I. H. White, eds., Proc. SPIE6184, 255–261 (2006).

Gelens, L.

Gilfillan, T.

D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: experiments and simulations,” Phys. Rev. A 86,033818 (2012).
[CrossRef]

Giudici, M.

M. Marconi, J. Javaloyes, S. Barland, M. Giudici, S. Balle, “Robust square-wave polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87,013827 (2013).
[CrossRef]

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

Heil, T.

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

Hicke, K.

K. Hicke, M. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19,1501610 (2013).
[CrossRef]

Hohl, A.

H. Li, A. Hohl, A. Gavrielides, H. Hou, K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357, (1998).
[CrossRef]

Hou, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357, (1998).
[CrossRef]

Jacquot, M.

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
[CrossRef] [PubMed]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
[CrossRef]

M. Peil, M. Jacquot, Y. Kouomou Chembo, L. Larger, T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic-oscillators,” Phys. Rev. E 79,026208 (2009).
[CrossRef]

Javaloyes, J.

M. Marconi, J. Javaloyes, S. Barland, M. Giudici, S. Balle, “Robust square-wave polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87,013827 (2013).
[CrossRef]

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

Jiang, S.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547, (1993).
[CrossRef]

Kojima, K.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547, (1993).
[CrossRef]

Kouomou Chembo, Y.

M. Peil, M. Jacquot, Y. Kouomou Chembo, L. Larger, T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic-oscillators,” Phys. Rev. E 79,026208 (2009).
[CrossRef]

Larger, L.

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
[CrossRef] [PubMed]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
[CrossRef]

M. Peil, M. Jacquot, Y. Kouomou Chembo, L. Larger, T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic-oscillators,” Phys. Rev. E 79,026208 (2009).
[CrossRef]

Lee, K.

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

Li, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357, (1998).
[CrossRef]

Loh, W. H.

W. H. Loh, Y. Ozeki, C. L. Tang, “High-frequency polarization self-modulation and chaotic phenomena in external cavity semiconductor lasers,” Appl. Phys. Lett. 56, 2613–2615 (1990).
[CrossRef]

Marconi, M.

M. Marconi, J. Javaloyes, S. Barland, M. Giudici, S. Balle, “Robust square-wave polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87,013827 (2013).
[CrossRef]

Mashal, L.

Masoller, C.

C. Masoller, M. Sciamanna, A. Gavrielides, “Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers,” Phil. Transac. Roy. Soc. A 371,20120471 (2013).
[CrossRef]

D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: experiments and simulations,” Phys. Rev. A 86,033818 (2012).
[CrossRef]

C. Masoller, D. Sukow, A. Gavrielides, 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, A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” Phys. Rev. E 86,016218 (2011).
[CrossRef]

McKay, J.

D. W. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, 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. W. Sukow, G. Burner, T. McLachlan, J. Miller, 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.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 31, 2006–2008 (2006).
[CrossRef] [PubMed]

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-waveforms in edge-emitting diode lasers subject to polarization rotated optical feedback,” in Physics and Simulation of Optoelectronic Devices XIV, M. Osinski, F. Henneberger, Y. Arakawa, eds., Proc. SPIE6115, 60–69 (2006).

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave oscillations in edge-emitting diode lasers with polarization rotated optical feedback,” in Semiconductor Laser and Laser Dynamics II, D. Lenstra, M. Pessa, I. H. White, eds., Proc. SPIE6184, 255–261 (2006).

Megret, P.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65,041801 (2002).
[CrossRef]

Miller, J.

A. Gavrielides, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, 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.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 31, 2006–2008 (2006).
[CrossRef] [PubMed]

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-waveforms in edge-emitting diode lasers subject to polarization rotated optical feedback,” in Physics and Simulation of Optoelectronic Devices XIV, M. Osinski, F. Henneberger, Y. Arakawa, eds., Proc. SPIE6115, 60–69 (2006).

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave oscillations in edge-emitting diode lasers with polarization rotated optical feedback,” in Semiconductor Laser and Laser Dynamics II, D. Lenstra, M. Pessa, I. H. White, eds., Proc. SPIE6184, 255–261 (2006).

Mirasso, C. R.

K. Hicke, M. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19,1501610 (2013).
[CrossRef]

Mooneyham, B.

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

Morgan, R. A.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547, (1993).
[CrossRef]

Mulet, J.

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

Ohtsubo, J.

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaos dynamics in semiconductor lasers with polarization-rotated optical feedback,” Opt. Rev. 17, 144–151 (2010).
[CrossRef]

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaotic dynamics in semiconductor lasers subjected to polarization-rotated optical feedback,” Appl. Phys. Lett. 93,181105 (2008).
[CrossRef]

Oliver, N.

Otsuka, K.

Ozeki, Y.

W. H. Loh, Y. Ozeki, C. L. Tang, “High-frequency polarization self-modulation and chaotic phenomena in external cavity semiconductor lasers,” Appl. Phys. Lett. 56, 2613–2615 (1990).
[CrossRef]

Pan, Z.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547, (1993).
[CrossRef]

Peil, M.

M. Peil, M. Jacquot, Y. Kouomou Chembo, L. Larger, T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic-oscillators,” Phys. Rev. E 79,026208 (2009).
[CrossRef]

Pope, B.

D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: experiments and simulations,” Phys. Rev. A 86,033818 (2012).
[CrossRef]

Rogister, F.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65,041801 (2002).
[CrossRef]

Sciamanna, M.

C. Masoller, M. Sciamanna, A. Gavrielides, “Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers,” Phil. Transac. Roy. Soc. A 371,20120471 (2013).
[CrossRef]

C. Masoller, D. Sukow, A. Gavrielides, 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, A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” Phys. Rev. E 86,016218 (2011).
[CrossRef]

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65,041801 (2002).
[CrossRef]

Shogenji, R.

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaos dynamics in semiconductor lasers with polarization-rotated optical feedback,” Opt. Rev. 17, 144–151 (2010).
[CrossRef]

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaotic dynamics in semiconductor lasers subjected to polarization-rotated optical feedback,” Appl. Phys. Lett. 93,181105 (2008).
[CrossRef]

Soriano, M. C.

K. Hicke, M. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19,1501610 (2013).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36, 4632–4634 (2011).
[CrossRef] [PubMed]

Sukow, D.

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

Sukow, D. W.

D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: experiments and simulations,” Phys. Rev. A 86,033818 (2012).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36, 4632–4634 (2011).
[CrossRef] [PubMed]

A. Gavrielides, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, 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. W. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, 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. W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave oscillations in edge-emitting diode lasers with polarization rotated optical feedback,” in Semiconductor Laser and Laser Dynamics II, D. Lenstra, M. Pessa, I. H. White, eds., Proc. SPIE6184, 255–261 (2006).

Sukow, D.W.

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Opt. Lett. 31, 2006–2008 (2006).
[CrossRef] [PubMed]

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-waveforms in edge-emitting diode lasers subject to polarization rotated optical feedback,” in Physics and Simulation of Optoelectronic Devices XIV, M. Osinski, F. Henneberger, Y. Arakawa, eds., Proc. SPIE6115, 60–69 (2006).

Takeuchi, Y.

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaos dynamics in semiconductor lasers with polarization-rotated optical feedback,” Opt. Rev. 17, 144–151 (2010).
[CrossRef]

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaotic dynamics in semiconductor lasers subjected to polarization-rotated optical feedback,” Appl. Phys. Lett. 93,181105 (2008).
[CrossRef]

Tang, C. L.

W. H. Loh, Y. Ozeki, C. L. Tang, “High-frequency polarization self-modulation and chaotic phenomena in external cavity semiconductor lasers,” Appl. Phys. Lett. 56, 2613–2615 (1990).
[CrossRef]

Torre, M. S.

D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: experiments and simulations,” Phys. Rev. A 86,033818 (2012).
[CrossRef]

Tsai, J.-K.

D.-L. Cheng, T.-C. Yen, J.-W. Chang, J.-K. Tsai, “Generation of high-speed single-wavelength optical pulses in semiconductor lasers with orthogonal-polarization optical feedback,” Opt. Commun. 222, 363–369 (2003).
[CrossRef]

Uchida, A.

T. Heil, A. Uchida, P. Davis, 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.

Verschaffelt, G.

Virte, M.

M. Sciamanna, M. Virte, C. Masoller, A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” Phys. Rev. E 86,016218 (2011).
[CrossRef]

Weicker, L.

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
[CrossRef] [PubMed]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
[CrossRef]

Yen, T.-C.

D.-L. Cheng, T.-C. Yen, J.-W. Chang, J.-K. Tsai, “Generation of high-speed single-wavelength optical pulses in semiconductor lasers with orthogonal-polarization optical feedback,” Opt. Commun. 222, 363–369 (2003).
[CrossRef]

Appl. Phys. Lett.

W. H. Loh, Y. Ozeki, C. L. Tang, “High-frequency polarization self-modulation and chaotic phenomena in external cavity semiconductor lasers,” Appl. Phys. Lett. 56, 2613–2615 (1990).
[CrossRef]

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547, (1993).
[CrossRef]

H. Li, A. Hohl, A. Gavrielides, H. Hou, K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357, (1998).
[CrossRef]

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaotic dynamics in semiconductor lasers subjected to polarization-rotated optical feedback,” Appl. Phys. Lett. 93,181105 (2008).
[CrossRef]

Dynamics of Continuous, Discrete and Impulsive Systems

S.A. Campbell, “Stability and bifurcation in the harmonic oscillator with multiple, delayed feedback loops,” Dynamics of Continuous, Discrete and Impulsive Systems 5, 225–235 (1999).

IEEE J. Sel. Top. Quantum Electron.

K. Hicke, M. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19,1501610 (2013).
[CrossRef]

Opt. Commun.

D.-L. Cheng, T.-C. Yen, J.-W. Chang, J.-K. Tsai, “Generation of high-speed single-wavelength optical pulses in semiconductor lasers with orthogonal-polarization optical feedback,” Opt. Commun. 222, 363–369 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Rev.

Y. Takeuchi, R. Shogenji, J. Ohtsubo, “Chaos dynamics in semiconductor lasers with polarization-rotated optical feedback,” Opt. Rev. 17, 144–151 (2010).
[CrossRef]

Phil. Trans. R. Soc. A

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Slow-fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A 371,20120459 (2013).
[CrossRef] [PubMed]

Phil. Transac. Roy. Soc. A

C. Masoller, M. Sciamanna, A. Gavrielides, “Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers,” Phil. Transac. Roy. Soc. A 371,20120471 (2013).
[CrossRef]

Phys. Rev. A

C. Masoller, D. Sukow, A. Gavrielides, 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, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65,041801 (2002).
[CrossRef]

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

M. Marconi, J. Javaloyes, S. Barland, M. Giudici, S. Balle, “Robust square-wave polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87,013827 (2013).
[CrossRef]

D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: experiments and simulations,” Phys. Rev. A 86,033818 (2012).
[CrossRef]

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

Phys. Rev. E

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

M. Sciamanna, M. Virte, C. Masoller, A. Gavrielides, “Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers,” Phys. Rev. E 86,016218 (2011).
[CrossRef]

M. Peil, M. Jacquot, Y. Kouomou Chembo, L. Larger, T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic-oscillators,” Phys. Rev. E 79,026208 (2009).
[CrossRef]

L. Weicker, T. Erneux, O. d’Huys, J. Danckaert, M. Jacquot, Y. Chembo, L. Larger, “Strongly asymmetric square-waves of time delayed systems,” Phys. Rev. E 86,055201 (2012).
[CrossRef]

Other

F. M. Atay, “Oscillation control in delayed feedback systems,” in Dynamics, Bifurcations, and Control, F. Colonius, L. Grne, eds. (Lect. Notes in Control and Information Sciences 273, 2002), pp. 103–116.
[CrossRef]

A. Gavrielides, T. Erneux, D.W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-waveforms in edge-emitting diode lasers subject to polarization rotated optical feedback,” in Physics and Simulation of Optoelectronic Devices XIV, M. Osinski, F. Henneberger, Y. Arakawa, eds., Proc. SPIE6115, 60–69 (2006).

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, J. Amonette, “Square-wave oscillations in edge-emitting diode lasers with polarization rotated optical feedback,” in Semiconductor Laser and Laser Dynamics II, D. Lenstra, M. Pessa, I. H. White, eds., Proc. SPIE6184, 255–261 (2006).

G. Friart, “Routes to square-wave oscillations in a semiconductor laser subject to polarization rotated feedback”, MS Thesis in Physics, Université Libre de Bruxelles (2013).

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Figures (5)

Fig. 1
Fig. 1

Stability diagram for the zero solution of Eq. (1). The Hopf bifurcation lines H1 and H2 are defined by (2) and (3), respectively. There are no other bifurcations for the chosen ranges of a and τ.

Fig. 2
Fig. 2

Stability diagram in terms of the frequency detuning Ω versus feedback rate η. The values of the fixed parameters are k = 0.8 (implying β = 0.125), α = 2, P = 0.5, T = 150, and θ = 103. Figure left: The line HRO corresponds to the first Hopf bifurcation of the steady state that leads to fast relaxation oscillations. The line HSW marks the transition to the square-wave oscillations. It is given by (25). Triangles mark parameter values chosen for the numerical simulations. Figure right: blow-up of the region where the two Hopf bifurcation lines are close. They intersect at two codimension 2 bifurcation points characterized by two pairs of distinct imaginary eigenvalues.

Fig. 3
Fig. 3

At Ω = −0.2, the first Hopf bifurcation leads to relaxation oscillations. (c) η = 0.078, small amplitude oscillations near the Hopf bifurcation point; (d) η = 0.105, fast relaxation oscillations slightly before the bifurcation of the Period 2 square-wave oscillations; (e) η = 0.12, square-wave oscillations slightly above its bifurcation point.

Fig. 4
Fig. 4

At Ω = −0.15, the first Hopf bifurcation corresponds to a bifurcation to Period 2 square-waves. (a) η = 0.125 small amplitude oscillations very close to the bifurcation point (b) η = 0.13 fully developed square-waves. The values of the other parameters are the same as in Fig. (2).

Fig. 5
Fig. 5

Asymmetric square-waves. The values of the parameters are P = 0.5, α = 2, T = 150, θ = 2000, k = 0.9, Ω = 0, and η = 0.4.

Tables (4)

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Table 1 Dimensionless parameters.

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Table 2 Values of the parameters

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Table 3 Values of the parameters. Questions marks indicate unclear or non documented values.

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Table 4 Values of the parameters.

Equations (61)

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x + x = a ( x ( t τ ) x ) .
H 1 : a = 1 2 ( π 2 τ 2 1 ) and ω 1 = π τ 1 ,
H 2 : τ = 2 π and ω 2 = 1 .
f R O 1 2 π 2 P T and f D 1 2 τ ,
d E T E d t = 1 2 ( 1 + i α ) ( G 1 ( n n 0 ) γ 1 ) E T E ,
d E T M d t = 1 2 ( 1 + i α ) ( G 2 ( n n 0 ) γ 2 ) E T M + γ E T E ( t τ ) exp ( i Δ t i C ) ,
d n d t = J γ s n ( n n 0 ) ( G 1 | E T E | 2 + G 2 | E T M | 2 ) .
d Y 1 d s = ( 1 + i α ) N Y 1 ,
d Y 2 d s = ( 1 + i α ) k ( N β ) Y 2 + η k Y 1 ( s θ ) exp ( i Ω s i C ) ,
T d N d s = P N ( 1 + 2 N ) [ | Y 1 | 2 + | Y 2 | 2 ] .
k G 2 G 1 and β 1 2 ( γ 2 G 1 γ 1 G 2 1 ) .
β = 1 2 k ( 1 k )
d E 1 d s = ( 1 + i α ) N E 1 ,
d E 2 d s = i Ω E 2 + ( 1 + i α ) k ( N β ) E 2 + η k E 1 ( s θ ) ,
T d N d s = P N ( 1 + 2 N ) [ | E 1 | 2 + | E 2 | 2 ] .
d A 1 d s = N A 1 ,
d A 2 d s = k ( N β ) A 2 + η k A 1 ( s θ ) cos ( Φ ) ,
d Φ d s = Ω + α [ N ( s θ ) k ( N β ) ] η k A 1 ( s θ ) A 2 sin ( Φ ) ,
T d N d s = P N ( 1 + 2 N ) ( A 1 2 + A 2 2 ) .
A 1 2 = [ ( k β ) 2 + ( Ω + α k β ) 2 ] P ( k β ) 2 + ( Ω + α k β ) 2 + η 2 k ,
A 2 2 = η 2 k P ( k β ) 2 + ( Ω + α k β ) 2 + η 2 k
tan ( Φ ) = Ω + α k β k β .
P + A 2 2 ( exp ( λ θ ) 1 ) = 0
A 2 2 = P / 2 and ω = π / θ .
η 2 k = ( k β ) 2 + ( Ω + α k β ) 2 .
N A 1 = 0 .
( 1 ) : N = A 1 ( s θ ) = 0 , A 2 = 0 , A 1 = P ,
( 2 ) : A 1 = N ( s θ ) = 0 , A 1 ( s θ ) = P .
A 2 = P N 1 + 2 N ,
tan ( Φ ) = Ω α k ( N β ) k ( N β ) ,
η 2 k P = { k 2 ( N β ) 2 + [ Ω α k ( N β ) ] 2 } P N 1 + 2 N .
d a 1 d s = N a 1
d E T E d t = 1 2 ( 1 + i α ) ( G 1 ( n n 0 ) γ p ) E T E ,
d E T M d t = 1 2 ( 1 + i α ) ( G 2 ( n n 0 ) γ p ) E T M + γ E T E ( t τ ) exp ( i C ) ,
d n d t = J γ s n ( n n 0 ) ( G 1 | E T E | 2 + G 2 | E T M | 2 )
s = γ p t , N = 1 2 [ G 1 γ p 1 ( n n 0 ) 1 ] , Y 1 = γ s 1 G 1 2 E T E , Y 2 = γ s 1 G 2 2 E T M
d Y 1 d s = ( 1 + i α ) N Y 1 ,
d Y 2 d s = ( 1 + i α ) k ( N β ) Y 2 + η k Y 1 ( s θ ) exp ( i C ) ,
T d N d s = P N ( 1 + 2 N ) ( | Y 1 | 2 + | Y 2 | 2 )
T = γ p γ s , θ = γ p τ , k = G 2 G 1 , β = 1 2 ( G 1 G 2 1 ) ,
P = G 1 γ p 1 γ s 1 2 ( J J t h ) , J t h = ( n 0 + 1 G 1 γ p 1 ) 1 γ s 1 .
d E T E d t = 1 2 ( 1 i α ) G 1 ( n n t h T E ) E T E ,
d E T M d t = 1 2 ( 1 i α ) G 2 ( n n t h T M ) E T M + γ E T E ( t τ ) exp [ i ( Δ t + C ) ] ,
d n d t = J n τ s ( n n 0 ) ( G 1 | E 1 | 2 + G 2 | E 2 | 2 )
G 1 ( n n 0 ) = τ p h 1 + G 1 ( n n t h T E ) , G 2 ( n n 0 ) = τ p h 1 + G 2 ( n n t h T M ) .
n t h T M = n t h T E + τ p h 1 ( G 2 1 G 1 1 ) .
N = G 1 τ p h 2 ( n n t h T E ) , Y 1 = G 1 τ s 2 E T E , Y 2 = G 2 τ s 2 E T M , s = t / τ p h
n n 2 = n n 1 + n 1 n 2 = 2 N G 1 τ p h 2 τ p h G 1 1 2 ( G 1 G 2 1 ) = 2 N G 1 τ p h 2 τ p h G 1 β
d Y 1 d s = ( 1 i α ) N Y 1
d Y 2 d s = ( 1 i α ) k ( N β ) Y 2 + η k Y 1 ( s θ ) exp [ i ( Ω s + C ) ]
T d N d s = P N ( 1 + 2 N ) ( | Y 1 | 2 + | Y 2 | 2 )
k = G 2 / G 1 , η = γ τ p h , T = τ s τ p h 1 , J t h = n t τ s , P = G 1 τ p h τ s 2 ( J J t h ) , θ = τ τ p h 1 , Ω = Δ τ p h .
d E | | d t = 1 2 ( 1 + i α ) ( g | | ( N N T ) γ | | ) E | | ,
d E d t = 1 2 ( 1 + i α ) ( g ( N N T ) γ ) E + κ E | | ( t τ e c ) ,
d N d t = I e γ e N ( N N T ) ( g | | | E | | | 2 + g | E | 2 ) .
s = γ | | t , n = 1 2 [ g | | γ | | 1 ( N N T ) 1 ] , Y 1 = γ e 1 g | | 2 E | | , Y 2 = γ e 1 g 2 E ,
d Y 1 d s = ( 1 + i α ) N Y 1 ,
d Y 2 d s = ( 1 + i α ) k ( N β ) Y 2 + η k Y 1 ( s θ ) ,
T d N d s = P N ( 1 + 2 N ) ( | Y 1 | 2 + | Y 2 | 2 )
T = γ | | / γ e , k = g / g | | , β = ( 1 k ) / ( 2 k ) , η = κ / γ | | ,
P = 1 2 g | | γ | | 1 γ e 1 ( I e I t h e ) , and I t h e = γ e ( N + + 1 g | | γ | | 1 ) .

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