Abstract

We analyze theoretically nonlinear dynamics of an optically injected two-mode quantum dot laser lasing simultaneously from the ground and excited states. We show that although the external optical signal is injected into the ground-state mode alone, it can lead to the generation of regular picosecond pulses and pulse packages in the intensity of the excited-state mode. Generation of regular streams of picosecond pulses is attributed to an intrinsic gain switching mechanism where the relaxation time is modulated by the oscillations in the occupation of the ground and excited energy states.

© 2010 Optical Society of America

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  1. R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
    [CrossRef]
  2. T. B. Simpson, J. M. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron. 32, 1456–1468 (1996).
    [CrossRef]
  3. T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 7, 709–711 (1995).
    [CrossRef]
  4. S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
    [CrossRef]
  5. M. Sciamanna and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
    [CrossRef]
  6. M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
    [CrossRef]
  7. I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
    [CrossRef]
  8. S. Osborne, A. Amann, K. Buckley, G. Ryan, S. P. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
    [CrossRef]
  9. A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state lasing in quantum-dot lasers,” Appl. Phys. Lett. 82, 1818–1820 (2003).
    [CrossRef]
  10. E. A. Viktorov, P. Mandel, I. O’Driscoll, O. Carroll, G. Huyet, J. Houlihan, and Y. Tanguy, “Low-frequency fluctuations in two-state quantum dot lasers,” Opt. Lett. 31, 2302–2304 (2006).
    [CrossRef] [PubMed]
  11. M. A. Cataluna, D. I. Nikitichev, S. Mikroulis, H. Simos, C. Simos, Ch. Mesaritakis, D. Syvridis, I. Krestnikov, D. Livshits, and E. U. Rafailov, “Dual-wavelength mode-locked quantum-dot laser, via ground and excited state transitions: experimental and theoretical investigation,” Opt. Express 18, 12832–12838 (2010).
    [CrossRef] [PubMed]
  12. D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
    [CrossRef] [PubMed]
  13. L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807 (2010).
    [CrossRef]
  14. D. R. Matthews, H. D. Summers, P. M. Smowton, and M. Hopkinson, “Experimental investigation of the effect of wetting-layer states on the gain–current characteristic of quantum-dot lasers,” Appl. Phys. Lett. 81, 4904–4906 (2002).
    [CrossRef]
  15. K. Gündoğdu, K. C. Hall, T. F. Boggess, D. G. Deppe, and O. B. Shchekin, “Ultrafast electron capture into p-modulation-doped quantum dots,” Appl. Phys. Lett. 85, 4570–4572 (2004).
    [CrossRef]
  16. S. Osborne, K. Buckley, A. Amann, and S. O’Brien, “All-optical memory based on the injection locking bistability of a two-color laser diode,” Opt. Express 17, 6293–6300 (2009).
    [CrossRef] [PubMed]
  17. E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, Auto-07p, http://indy.cs.concordia.ca/auto/.
  18. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering (Perseus Books, 1994).

2010 (2)

2009 (3)

2007 (2)

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

2006 (2)

E. A. Viktorov, P. Mandel, I. O’Driscoll, O. Carroll, G. Huyet, J. Houlihan, and Y. Tanguy, “Low-frequency fluctuations in two-state quantum dot lasers,” Opt. Lett. 31, 2302–2304 (2006).
[CrossRef] [PubMed]

M. Sciamanna and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

2005 (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

2004 (1)

K. Gündoğdu, K. C. Hall, T. F. Boggess, D. G. Deppe, and O. B. Shchekin, “Ultrafast electron capture into p-modulation-doped quantum dots,” Appl. Phys. Lett. 85, 4570–4572 (2004).
[CrossRef]

2003 (1)

A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state lasing in quantum-dot lasers,” Appl. Phys. Lett. 82, 1818–1820 (2003).
[CrossRef]

2002 (1)

D. R. Matthews, H. D. Summers, P. M. Smowton, and M. Hopkinson, “Experimental investigation of the effect of wetting-layer states on the gain–current characteristic of quantum-dot lasers,” Appl. Phys. Lett. 81, 4904–4906 (2002).
[CrossRef]

1996 (1)

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron. 32, 1456–1468 (1996).
[CrossRef]

1995 (1)

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 7, 709–711 (1995).
[CrossRef]

1982 (1)

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
[CrossRef]

Amann, A.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. P. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

S. Osborne, K. Buckley, A. Amann, and S. O’Brien, “All-optical memory based on the injection locking bistability of a two-color laser diode,” Opt. Express 17, 6293–6300 (2009).
[CrossRef] [PubMed]

Boggess, T. F.

K. Gündoğdu, K. C. Hall, T. F. Boggess, D. G. Deppe, and O. B. Shchekin, “Ultrafast electron capture into p-modulation-doped quantum dots,” Appl. Phys. Lett. 85, 4570–4572 (2004).
[CrossRef]

Buckley, K.

S. Osborne, K. Buckley, A. Amann, and S. O’Brien, “All-optical memory based on the injection locking bistability of a two-color laser diode,” Opt. Express 17, 6293–6300 (2009).
[CrossRef] [PubMed]

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. P. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

Carroll, O.

Cataluna, M. A.

Champneys, A.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, Auto-07p, http://indy.cs.concordia.ca/auto/.

Chen, J. X.

A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state lasing in quantum-dot lasers,” Appl. Phys. Lett. 82, 1818–1820 (2003).
[CrossRef]

Deppe, D. G.

K. Gündoğdu, K. C. Hall, T. F. Boggess, D. G. Deppe, and O. B. Shchekin, “Ultrafast electron capture into p-modulation-doped quantum dots,” Appl. Phys. Lett. 85, 4570–4572 (2004).
[CrossRef]

Doedel, E.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, Auto-07p, http://indy.cs.concordia.ca/auto/.

Fairgrieve, T.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, Auto-07p, http://indy.cs.concordia.ca/auto/.

Fiore, A.

A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state lasing in quantum-dot lasers,” Appl. Phys. Lett. 82, 1818–1820 (2003).
[CrossRef]

Gatare, I.

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

Gauthier-Lafaye, O.

A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state lasing in quantum-dot lasers,” Appl. Phys. Lett. 82, 1818–1820 (2003).
[CrossRef]

Gavrielides, A.

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron. 32, 1456–1468 (1996).
[CrossRef]

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 7, 709–711 (1995).
[CrossRef]

Goulding, D.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

Greene, G.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

Gündogdu, K.

K. Gündoğdu, K. C. Hall, T. F. Boggess, D. G. Deppe, and O. B. Shchekin, “Ultrafast electron capture into p-modulation-doped quantum dots,” Appl. Phys. Lett. 85, 4570–4572 (2004).
[CrossRef]

Hall, K. C.

K. Gündoğdu, K. C. Hall, T. F. Boggess, D. G. Deppe, and O. B. Shchekin, “Ultrafast electron capture into p-modulation-doped quantum dots,” Appl. Phys. Lett. 85, 4570–4572 (2004).
[CrossRef]

Hartnett, M.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

Hegarty, S. P.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. P. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

Hopkinson, M.

D. R. Matthews, H. D. Summers, P. M. Smowton, and M. Hopkinson, “Experimental investigation of the effect of wetting-layer states on the gain–current characteristic of quantum-dot lasers,” Appl. Phys. Lett. 81, 4904–4906 (2002).
[CrossRef]

Houlihan, J.

Huye, G.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

Huyet, G.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. P. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

E. A. Viktorov, P. Mandel, I. O’Driscoll, O. Carroll, G. Huyet, J. Houlihan, and Y. Tanguy, “Low-frequency fluctuations in two-state quantum dot lasers,” Opt. Lett. 31, 2302–2304 (2006).
[CrossRef] [PubMed]

Krauskopf, B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

Krestnikov, I.

Kuznetsov, Yu.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, Auto-07p, http://indy.cs.concordia.ca/auto/.

Lang, R.

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
[CrossRef]

Lenstra, D.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

Liu, J. M.

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron. 32, 1456–1468 (1996).
[CrossRef]

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 7, 709–711 (1995).
[CrossRef]

Livshits, D.

Mandel, P.

Markus, A.

A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state lasing in quantum-dot lasers,” Appl. Phys. Lett. 82, 1818–1820 (2003).
[CrossRef]

Matthews, D. R.

D. R. Matthews, H. D. Summers, P. M. Smowton, and M. Hopkinson, “Experimental investigation of the effect of wetting-layer states on the gain–current characteristic of quantum-dot lasers,” Appl. Phys. Lett. 81, 4904–4906 (2002).
[CrossRef]

McInerney, J. G.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

Mesaritakis, Ch.

Mielnik, S.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

Mikroulis, S.

Nikitichev, D. I.

Nizette, M.

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

O’Brien, S.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. P. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

S. Osborne, K. Buckley, A. Amann, and S. O’Brien, “All-optical memory based on the injection locking bistability of a two-color laser diode,” Opt. Express 17, 6293–6300 (2009).
[CrossRef] [PubMed]

O’Driscoll, I.

Olejniczak, L.

L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807 (2010).
[CrossRef]

Osborne, S.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. P. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

S. Osborne, K. Buckley, A. Amann, and S. O’Brien, “All-optical memory based on the injection locking bistability of a two-color laser diode,” Opt. Express 17, 6293–6300 (2009).
[CrossRef] [PubMed]

Panajotov, K.

L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807 (2010).
[CrossRef]

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

M. Sciamanna and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

Paranthoen, C.

A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state lasing in quantum-dot lasers,” Appl. Phys. Lett. 82, 1818–1820 (2003).
[CrossRef]

Platz, C.

A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state lasing in quantum-dot lasers,” Appl. Phys. Lett. 82, 1818–1820 (2003).
[CrossRef]

Rachinskii, D.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

Rafailov, E. U.

Rasskazov, O.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Mielnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huye, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
[CrossRef] [PubMed]

Ryan, G.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. P. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

Sandstede, B.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, Auto-07p, http://indy.cs.concordia.ca/auto/.

Sciamanna, M.

L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807 (2010).
[CrossRef]

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

M. Sciamanna and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

Shchekin, O. B.

K. Gündoğdu, K. C. Hall, T. F. Boggess, D. G. Deppe, and O. B. Shchekin, “Ultrafast electron capture into p-modulation-doped quantum dots,” Appl. Phys. Lett. 85, 4570–4572 (2004).
[CrossRef]

Simos, C.

Simos, H.

Simpson, T. B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron. 32, 1456–1468 (1996).
[CrossRef]

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 7, 709–711 (1995).
[CrossRef]

Smowton, P. M.

D. R. Matthews, H. D. Summers, P. M. Smowton, and M. Hopkinson, “Experimental investigation of the effect of wetting-layer states on the gain–current characteristic of quantum-dot lasers,” Appl. Phys. Lett. 81, 4904–4906 (2002).
[CrossRef]

Strogatz, S. H.

S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering (Perseus Books, 1994).

Summers, H. D.

D. R. Matthews, H. D. Summers, P. M. Smowton, and M. Hopkinson, “Experimental investigation of the effect of wetting-layer states on the gain–current characteristic of quantum-dot lasers,” Appl. Phys. Lett. 81, 4904–4906 (2002).
[CrossRef]

Syvridis, D.

Tanguy, Y.

Thienpont, H.

L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807 (2010).
[CrossRef]

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

Viktorov, E. A.

Wang, X.

E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, and X. Wang, Auto-07p, http://indy.cs.concordia.ca/auto/.

Wieczorek, S.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

Appl. Phys. Lett. (3)

D. R. Matthews, H. D. Summers, P. M. Smowton, and M. Hopkinson, “Experimental investigation of the effect of wetting-layer states on the gain–current characteristic of quantum-dot lasers,” Appl. Phys. Lett. 81, 4904–4906 (2002).
[CrossRef]

K. Gündoğdu, K. C. Hall, T. F. Boggess, D. G. Deppe, and O. B. Shchekin, “Ultrafast electron capture into p-modulation-doped quantum dots,” Appl. Phys. Lett. 85, 4570–4572 (2004).
[CrossRef]

A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state lasing in quantum-dot lasers,” Appl. Phys. Lett. 82, 1818–1820 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

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Figures (10)

Fig. 1
Fig. 1

Intensities of the GS (black) and ES (gray) modes versus current for different values of the relaxation rate to the empty GS.

Fig. 2
Fig. 2

(a) Extrema map for J = 17 . Representation of respective shades of gray: light gray L 1 —locked GS mode and suppressed ES one (lack of extrema); light gray L 2 —locked GS mode but unsuppressed ES one (lack of extrema); dark gray U 2 —time-periodic pulsations (two extrema); white U 3 —oscillations characterized by three extrema; gray U > 3 —complex dynamics characterized by more than thee extrema, possibly chaotic. (b) Two-parameter bifurcation diagram calculated by AUTO [17]. Solid gray curve H denotes Hopf bifurcation, dotted gray curve S denotes saddle-node bifurcation, and solid black curve T denotes transcritical bifurcation. BT and ST are codimensional two points at which the saddle-node–Hopf bifurcation curves and saddle-node and transcritical bifurcation curves, respectively, are tangent.

Fig. 3
Fig. 3

One-parameter bifurcation diagram for J = 17 , S m = 1.5 × 10 4   J / m 3 when sweeping the detuning either (a) from negative to positive or (b) from positive to negative values. Black corresponds to the GS mode, whereas gray corresponds to the ES mode.

Fig. 4
Fig. 4

Temporal evolution of (a) GS (left axis) and ES (right axis) mode intensities, and (b) occupation of the GS: solid black curve f GS (right axis), ES: solid gray curve f ES (left axis), and WL: dotted black curve f WL (left axis). Horizontal black and gray lines represent threshold occupation of the GS and ES, respectively. (c) Modulation of the relaxation (black) and capture (gray) times resulting from changes in the occupation of the respective energy levels (left axis) and the difference between the capture 0.25 C 0 f WL ( 1 f ES ) and relaxation R 0 f ES ( 1 f GS ) processes (dotted gray curve, right axis); S m = 6 × 10 4   J / m 3 , Δ = 9   GHz .

Fig. 5
Fig. 5

Repetition rate (black) and the full width at half-maximum (gray) of pulses generated from the ES.

Fig. 6
Fig. 6

One-parameter bifurcation diagram for (a) S m = 6.0 × 10 4   J / m 3 and (b) S m = 1.5 × 10 4   J / m 3 showing the behavior of the GS (black) and ES (gray) modes in close proximity to the two-mode Hopf bifurcation.

Fig. 7
Fig. 7

One-parameter bifurcation diagram for J = 17 , S m = 1.5 × 10 4   J / m 3 for the GS (black) and ES (gray) modes, when sweeping the detuning either (a) from small to large or (b) from large to small negative values. Arrows 1–4 correspond to time traces in Fig. 8, graphs 1–4.

Fig. 8
Fig. 8

Temporal evolution of the GS (black) and ES (gray) mode intensities for S m = 1.5 × 10 4   J / m 3 and 1: Δ = 4.5   GHz , 2: Δ = 9.0   GHz , 3: Δ = 15.0   GHz , 4: Δ = 50.0   GHz .

Fig. 9
Fig. 9

(a) Extrema map for J = 20 . (b) Two-parameter bifurcation diagram calculated with AUTO [17]. The labeling and color coding are the same as in Fig. 2.

Fig. 10
Fig. 10

Temporal evolution of the GS (black) and ES (gray) mode intensities for (a) S m = 10 4   J / m 3 , Δ = 6   GHz and (b) S m = 4 × 10 4   J / m 3 , Δ = 6   GHz . J = 20 .

Equations (22)

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d E ES d t = 1 2 v g g ES ( 2 f ES 1 γ s v g g ES ) ( 1 + i α ) E ES ,
d E GS d t = 1 2 v g g GS ( 2 f GS 1 γ s v g g GS ) ( 1 + i α ) E GS + i Δ E GS + γ s S m ω ,
d f WL d t = J Q D q γ n f WL f WL ( 1 f ES ) τ c 0 ,
d f ES d t = γ n f ES + f WL ( 1 f ES ) 4 τ c 0 f ES ( 1 f GS ) τ o 0 v g σ ( 2 f ES 1 ) | E ES | 2 ,
d f GS d t = γ n f GS + 2 f ES ( 1 f GS ) τ o 0 v g σ ( 2 f GS 1 ) | E GS | 2 .
I GS , ES = | E GS , ES | 2
d I ES d t = 2 a ES ( 2 f ES 1 γ ES ) I ES ,
d F GS d t = a GS ( 2 f GS 1 γ GS ) ( 1 + i α ) F GS + i Δ F GS + B S m ,
d f WL d t = J f WL C 0 f WL ( 1 f ES ) ,
d f ES d t = f ES + 0.25 C 0 f WL ( 1 f ES ) R 0 f ES ( 1 f GS ) ( 2 f ES 1 ) I E S ,
d f GS d t = f GS + 2 R 0 f ES ( 1 f GS ) ( 2 f GS 1 ) | F GS | 2 .
f GS = γ GS + 1 2 .
f WL = J 1 + C 0 ( 1 f ES ) .
a f ES 2 + b f ES + c = 0 ,
a = C 0 [ 1 + R 0 ( 1 γ GS + 1 2 ) ] ,
b = [ 4 ( R 0 ( 1 γ GS + 1 2 ) + 1 ) ( 1 + C 0 ) + C 0 J ] ,
c = C 0 J .
| F GS | 2 = 2 R 0 f ES ( 1 f GS ) f GS γ GS .
f GS = γ GS + 1 2 ,
f ES = γ ES + 1 2 .
f WL = J 1 + C 0 ( 1 γ ES + 1 2 ) .
| F ES | 2 = 0.25 C 0 f WL ( 1 f ES ) f ES R 0 f ES ( 1 f GS ) γ GS .

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