Abstract

We report experimentally a bistability between two limit cycles (i.e. time-periodic dynamics) in a free-running vertical-cavity surface-emitting laser. The two limit cycles originate from a bifurcation on two elliptically polarized states which exhibit a small frequency difference and whose main axes are symmetrical with respect to the linear polarization eigenaxes at threshold. We demonstrate theoretically that this peculiar behavior can be explained in the framework of the spin-flip model model by taking into account a small misalignment between the phase and amplitude anisotropies.

© 2014 Optical Society of America

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  1. K. D. Choquette, D. A. Richie, R. E. Leibenguth, “Temperature dependence of gain-guided vertical cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
    [CrossRef]
  2. K. D. Choquette, R. P. Schneider, K. L. Lear, R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
    [CrossRef]
  3. M. van Exter, M. Willemsen, J. Woerdman, “Polarization fluctuations in vertical-cavity semiconductor lasers,” Phys. Rev. A 58, 4191–4205 (1998).
    [CrossRef]
  4. T. Ackemann, M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
    [CrossRef]
  5. M. Sondermann, T. Ackemann, S. Balle, J. Mulet, K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004).
    [CrossRef]
  6. L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
    [CrossRef]
  7. L. Olejniczak, K. Panajotov, H. Thienpont, M. Sciamanna, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers.” Opt. Express 19, 2476–2484 (2011).
    [CrossRef] [PubMed]
  8. M. Virte, K. Panajotov, H. Thienpont, M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
    [CrossRef]
  9. K. Panajotov, F. Prati, Polarization dynamics of vcsels, in VCSELs (Springer, 2013), 181–231.
  10. K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
    [CrossRef]
  11. M. San Miguel, Q. Feng, J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
    [CrossRef] [PubMed]
  12. J. Martin-Regalado, F. Prati, M. San Miguel, N. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quant. Electron. 33, 765–783 (1997).
    [CrossRef]
  13. M. Virte, K. Panajotov, M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87, 013834 (2013).
    [CrossRef]
  14. F. Prati, P. Caccia, M. Bache, F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
    [CrossRef]
  15. M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers.” Phys. Rev. A 54, 1647–1660 (1996).
    [CrossRef] [PubMed]
  16. M. Travagnin, “Linear anisotropies and polarization properties of vertical-cavity surface-emitting semiconductor lasers,” Phys. Rev. A 56, 4094–4105 (1997).
    [CrossRef]
  17. F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
    [CrossRef]
  18. T. Erneux, J. Danckaert, K. Panajotov, I. Veretennicoff, “Two-variable reduction of the San MiguelFeng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
    [CrossRef]

2013 (1)

M. Virte, K. Panajotov, M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87, 013834 (2013).
[CrossRef]

2012 (1)

M. Virte, K. Panajotov, H. Thienpont, M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

2011 (1)

2009 (1)

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
[CrossRef]

2006 (1)

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

2004 (2)

F. Prati, P. Caccia, M. Bache, F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

M. Sondermann, T. Ackemann, S. Balle, J. Mulet, K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004).
[CrossRef]

2001 (1)

T. Ackemann, M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
[CrossRef]

1999 (1)

T. Erneux, J. Danckaert, K. Panajotov, I. Veretennicoff, “Two-variable reduction of the San MiguelFeng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[CrossRef]

1998 (2)

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

M. van Exter, M. Willemsen, J. Woerdman, “Polarization fluctuations in vertical-cavity semiconductor lasers,” Phys. Rev. A 58, 4191–4205 (1998).
[CrossRef]

1997 (2)

J. Martin-Regalado, F. Prati, M. San Miguel, N. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quant. Electron. 33, 765–783 (1997).
[CrossRef]

M. Travagnin, “Linear anisotropies and polarization properties of vertical-cavity surface-emitting semiconductor lasers,” Phys. Rev. A 56, 4094–4105 (1997).
[CrossRef]

1996 (1)

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers.” Phys. Rev. A 54, 1647–1660 (1996).
[CrossRef] [PubMed]

1995 (2)

M. San Miguel, Q. Feng, J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
[CrossRef] [PubMed]

K. D. Choquette, R. P. Schneider, K. L. Lear, R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[CrossRef]

1994 (1)

K. D. Choquette, D. A. Richie, R. E. Leibenguth, “Temperature dependence of gain-guided vertical cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[CrossRef]

Abraham, N.

J. Martin-Regalado, F. Prati, M. San Miguel, N. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quant. Electron. 33, 765–783 (1997).
[CrossRef]

Ackemann, T.

M. Sondermann, T. Ackemann, S. Balle, J. Mulet, K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004).
[CrossRef]

T. Ackemann, M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
[CrossRef]

Bache, M.

F. Prati, P. Caccia, M. Bache, F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

Balle, S.

M. Sondermann, T. Ackemann, S. Balle, J. Mulet, K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004).
[CrossRef]

Bimberg, D.

L. Olejniczak, K. Panajotov, H. Thienpont, M. Sciamanna, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers.” Opt. Express 19, 2476–2484 (2011).
[CrossRef] [PubMed]

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Caccia, P.

F. Prati, P. Caccia, M. Bache, F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

Castelli, F.

F. Prati, P. Caccia, M. Bache, F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

Choquette, K. D.

K. D. Choquette, R. P. Schneider, K. L. Lear, R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[CrossRef]

K. D. Choquette, D. A. Richie, R. E. Leibenguth, “Temperature dependence of gain-guided vertical cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[CrossRef]

Danckaert, J.

T. Erneux, J. Danckaert, K. Panajotov, I. Veretennicoff, “Two-variable reduction of the San MiguelFeng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[CrossRef]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Erneux, T.

T. Erneux, J. Danckaert, K. Panajotov, I. Veretennicoff, “Two-variable reduction of the San MiguelFeng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[CrossRef]

Feng, Q.

M. San Miguel, Q. Feng, J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
[CrossRef] [PubMed]

Fiol, G.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Hopfer, F.

L. Olejniczak, K. Panajotov, H. Thienpont, M. Sciamanna, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers.” Opt. Express 19, 2476–2484 (2011).
[CrossRef] [PubMed]

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Jansen van Doorn, A. K.

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers.” Phys. Rev. A 54, 1647–1660 (1996).
[CrossRef] [PubMed]

Kovsh, a. R.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Krestnikov, I. L.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Kuntz, M.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Lear, K. L.

K. D. Choquette, R. P. Schneider, K. L. Lear, R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[CrossRef]

Ledentsov, N. N.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Leibenguth, R. E.

K. D. Choquette, R. P. Schneider, K. L. Lear, R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[CrossRef]

K. D. Choquette, D. A. Richie, R. E. Leibenguth, “Temperature dependence of gain-guided vertical cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[CrossRef]

Livshits, D. L.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Martin-Regalado, J.

J. Martin-Regalado, F. Prati, M. San Miguel, N. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quant. Electron. 33, 765–783 (1997).
[CrossRef]

Mikhrin, S. S.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Moloney, J.

M. San Miguel, Q. Feng, J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
[CrossRef] [PubMed]

Mulet, J.

M. Sondermann, T. Ackemann, S. Balle, J. Mulet, K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004).
[CrossRef]

Mutig, A.

L. Olejniczak, K. Panajotov, H. Thienpont, M. Sciamanna, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers.” Opt. Express 19, 2476–2484 (2011).
[CrossRef] [PubMed]

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Olejniczak, L.

L. Olejniczak, K. Panajotov, H. Thienpont, M. Sciamanna, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers.” Opt. Express 19, 2476–2484 (2011).
[CrossRef] [PubMed]

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
[CrossRef]

Panajotov, K.

M. Virte, K. Panajotov, M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87, 013834 (2013).
[CrossRef]

M. Virte, K. Panajotov, H. Thienpont, M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

L. Olejniczak, K. Panajotov, H. Thienpont, M. Sciamanna, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers.” Opt. Express 19, 2476–2484 (2011).
[CrossRef] [PubMed]

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
[CrossRef]

M. Sondermann, T. Ackemann, S. Balle, J. Mulet, K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004).
[CrossRef]

T. Erneux, J. Danckaert, K. Panajotov, I. Veretennicoff, “Two-variable reduction of the San MiguelFeng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[CrossRef]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

K. Panajotov, F. Prati, Polarization dynamics of vcsels, in VCSELs (Springer, 2013), 181–231.

Peeters, M.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Prati, F.

F. Prati, P. Caccia, M. Bache, F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, N. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quant. Electron. 33, 765–783 (1997).
[CrossRef]

K. Panajotov, F. Prati, Polarization dynamics of vcsels, in VCSELs (Springer, 2013), 181–231.

Richie, D. A.

K. D. Choquette, D. A. Richie, R. E. Leibenguth, “Temperature dependence of gain-guided vertical cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[CrossRef]

Ryvkin, B.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

San Miguel, M.

J. Martin-Regalado, F. Prati, M. San Miguel, N. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quant. Electron. 33, 765–783 (1997).
[CrossRef]

M. San Miguel, Q. Feng, J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
[CrossRef] [PubMed]

Schneider, R. P.

K. D. Choquette, R. P. Schneider, K. L. Lear, R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[CrossRef]

Sciamanna, M.

M. Virte, K. Panajotov, M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87, 013834 (2013).
[CrossRef]

M. Virte, K. Panajotov, H. Thienpont, M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

L. Olejniczak, K. Panajotov, H. Thienpont, M. Sciamanna, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers.” Opt. Express 19, 2476–2484 (2011).
[CrossRef] [PubMed]

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
[CrossRef]

Shchukin, V. a.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Sondermann, M.

M. Sondermann, T. Ackemann, S. Balle, J. Mulet, K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004).
[CrossRef]

T. Ackemann, M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
[CrossRef]

Thienpont, H.

M. Virte, K. Panajotov, H. Thienpont, M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

L. Olejniczak, K. Panajotov, H. Thienpont, M. Sciamanna, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers.” Opt. Express 19, 2476–2484 (2011).
[CrossRef] [PubMed]

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
[CrossRef]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Travagnin, M.

M. Travagnin, “Linear anisotropies and polarization properties of vertical-cavity surface-emitting semiconductor lasers,” Phys. Rev. A 56, 4094–4105 (1997).
[CrossRef]

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers.” Phys. Rev. A 54, 1647–1660 (1996).
[CrossRef] [PubMed]

van Exter, M.

M. van Exter, M. Willemsen, J. Woerdman, “Polarization fluctuations in vertical-cavity semiconductor lasers,” Phys. Rev. A 58, 4191–4205 (1998).
[CrossRef]

van Exter, M. P.

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers.” Phys. Rev. A 54, 1647–1660 (1996).
[CrossRef] [PubMed]

Veretennicoff, I.

T. Erneux, J. Danckaert, K. Panajotov, I. Veretennicoff, “Two-variable reduction of the San MiguelFeng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[CrossRef]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Virte, M.

M. Virte, K. Panajotov, M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87, 013834 (2013).
[CrossRef]

M. Virte, K. Panajotov, H. Thienpont, M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

Werner, P.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Willemsen, M.

M. van Exter, M. Willemsen, J. Woerdman, “Polarization fluctuations in vertical-cavity semiconductor lasers,” Phys. Rev. A 58, 4191–4205 (1998).
[CrossRef]

Woerdman, J.

M. van Exter, M. Willemsen, J. Woerdman, “Polarization fluctuations in vertical-cavity semiconductor lasers,” Phys. Rev. A 58, 4191–4205 (1998).
[CrossRef]

Woerdman, J. P.

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers.” Phys. Rev. A 54, 1647–1660 (1996).
[CrossRef] [PubMed]

Zakharov, N. D.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. a. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, a. R. Kovsh, N. D. Zakharov, P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106 (2006).
[CrossRef]

K. D. Choquette, D. A. Richie, R. E. Leibenguth, “Temperature dependence of gain-guided vertical cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[CrossRef]

T. Ackemann, M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
[CrossRef]

IEEE J. Quant. Electron. (1)

J. Martin-Regalado, F. Prati, M. San Miguel, N. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quant. Electron. 33, 765–783 (1997).
[CrossRef]

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

K. D. Choquette, R. P. Schneider, K. L. Lear, R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, D. Bimberg, “Polarization switching in quantum-dot vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 21, 1008–1010 (2009).
[CrossRef]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Nat. Photonics (1)

M. Virte, K. Panajotov, H. Thienpont, M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

Opt. Commun. (1)

M. Sondermann, T. Ackemann, S. Balle, J. Mulet, K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (7)

M. van Exter, M. Willemsen, J. Woerdman, “Polarization fluctuations in vertical-cavity semiconductor lasers,” Phys. Rev. A 58, 4191–4205 (1998).
[CrossRef]

T. Erneux, J. Danckaert, K. Panajotov, I. Veretennicoff, “Two-variable reduction of the San MiguelFeng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[CrossRef]

M. San Miguel, Q. Feng, J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
[CrossRef] [PubMed]

M. Virte, K. Panajotov, M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87, 013834 (2013).
[CrossRef]

F. Prati, P. Caccia, M. Bache, F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers.” Phys. Rev. A 54, 1647–1660 (1996).
[CrossRef] [PubMed]

M. Travagnin, “Linear anisotropies and polarization properties of vertical-cavity surface-emitting semiconductor lasers,” Phys. Rev. A 56, 4094–4105 (1997).
[CrossRef]

Other (1)

K. Panajotov, F. Prati, Polarization dynamics of vcsels, in VCSELs (Springer, 2013), 181–231.

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Figures (3)

Fig. 1
Fig. 1

Experimental observations of the limit cycle bistability. (a) Polarization resolved LI curve at +45° and −45°, with respect to the LP at threshold, in red and black respectively, for increasing (solid) and decreasing (dashed) injection current. (b) Time-series recorded at a current of 1.85 mA when increasing (blue) and decreasing (red) current. (c)–(d) Plot of the time-series extrema versus increasing (top, c) and decreasing current (bottom, d). (e)–(f) FFT of the time-series versus increasing (top, e) and decreasing current (bottom, f). Time series considered for panels b to f are recorded at 0° with DC removed.

Fig. 2
Fig. 2

Evolution of the emission without asymmetry, i.e. with aligned phase and amplitude anisotropies. (a)–(d) Polarization of the emitted light given by the trajectory of the system in the (Re(EX), Re(EY)) phase plane in the 4 cases identified in (f). (e) Polarization resolved LI curve for −45°, 0°, +45° and 90° with respect to the polarization at threshold in black, green, red and blue respectively. (f) Extrema of the polarization resolved output power time-series at +45° and −45° in red and black respectively.

Fig. 3
Fig. 3

Impact of the asymmetry on the VCSEL dynamics. (a)–(d) Polarization resolved LI curves for −45°, 0°, +45° and 90° with respect to the polarization at threshold in black, green, red and blue respectively. (b)–(e) Extrema of the polarization resolved output power time-series at +45° and −45° in red and black respectively. Inset in (e) shows a zoom of the transition between the two limit cycles. (c)–(f) Normalized radio-frequency spectrum of the polarization resolved time-series at +45°. Those results are given for increasing (top) and decreasing (bottom) normalized injection current. The blue dashed vertical lines show the limits of the bistability region.

Equations (6)

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d E ± d t = κ ( 1 + i α ) ( N ± n 1 ) E ± ( i γ p + ( cos ( 2 θ ) isin ( 2 θ ) ) γ a ) E
d N d t = μ N ( N + n ) | E + | 2 ( N n ) | E | 2
d n d t = γ s n ( N + n ) | E + | 2 + ( N n ) | E | 2
d R + d t = κ ( N + n 1 ) R + γ a ¯ R cos ( ϕ ) γ p + ¯ R sin ( ϕ )
d R d t = κ ( N n 1 ) R γ a ¯ R + cos ( ϕ ) + γ p ¯ R + sin ( ϕ )
d ϕ d t = 2 κ α n + γ a ¯ sin ( ϕ ) ( R R + + R + R ) + ( γ p ¯ R + R γ p + ¯ R R + ) cos ( ϕ )

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