Abstract

We investigate the impact of short optical feedback on a two-state quantum dot laser. A region in the feedback parameter space is identified, where the laser emission periodically alternates between oscillation bursts from the quantum dot ground and excited state, i.e. two-color anti-phase oscillation bursts. We compare these results to the low-frequency fluctuations and regular pulse packages of single-color semiconductor lasers and show via an in-depth bifurcation analysis, that the two-color oscillation bursts originate from a torus-bifurcation of a two-state periodic orbit. A cascade of further period-doubling bifurcations produces chaotic dynamics of the burst envelope. Our findings showcase the rich dynamics and complexity, which can be generated via the interaction of electronic and photonic time scales in quantum dot lasers with optical feedback.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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  53. J. Sacher, D. Baums, P. Panknin, W. Elsäßer, and E. O. Göbel, “Intensity instabilites of semiconductor lasers under current modulation external light injection, and delayed feedback,” Phys. Rev. A 45(3), 1893–1905 (1992).
    [Crossref]
  54. T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling route to chaos in a semiconductor laser subject to optical injection,” Appl. Phys. Lett. 64(26), 3539–3541 (1994).
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2019 (2)

M. Dillane, B. Tykalewicz, D. Goulding, B. Garbin, S. Barland, and B. Kelleher, “Square wave excitability in quantum dot lasers under optical injection,” Opt. Lett. 44(2), 347–350 (2019).
[Crossref]

M. Dillane, I. Dubinkin, N. Fedorov, T. Erneux, D. Goulding, B. Kelleher, and E. A. Viktorov, “Excitable interplay between lasing quantum dot states,” Phys. Rev. E 100(1), 012202 (2019).
[Crossref]

2018 (3)

2017 (5)

S. Meinecke, B. Lingnau, A. Röhm, and K. Lüdge, “Stability in optically injected two-state quantum-dot lasers,” Ann. Phys. (Berl.) 529(12), 1600279 (2017).
[Crossref]

B. Kelleher, B. Tykalewicz, D. Goulding, N. Fedorov, I. Dubinkin, T. Erneux, and E. A. Viktorov, “Two-color bursting oscillations,” Sci. Rep. 7(1), 8414 (2017).
[Crossref]

B. Kelleher, M. J. Wishon, A. Locquet, D. Goulding, B. Tykalewicz, G. Huyet, and E. A. Viktorov, “Delay induced high order locking effects in semiconductor lasers,” Chaos 27(11), 114325 (2017).
[Crossref]

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J. 9(2), 1–12 (2017).
[Crossref]

R. Pawlus, S. Breuer, and M. Virte, “Relative intensity noise reduction in a dual-state quantum-dot laser by optical feedback,” Opt. Lett. 42(21), 4259–4262 (2017).
[Crossref]

2016 (4)

C. Mesaritakis, A. Kapsalis, A. Bogris, and D. Syvridis, “Artificial neuron based on integrated semiconductor quantum dot mode-locked lasers,” Sci. Rep. 6(1), 39317 (2016).
[Crossref]

M. Virte, R. Pawlus, W. Elsäßer, K. Panajotov, M. Sciamanna, and S. Breuer, “Range-dependent effects of optical feedback on multimode two-color quantum dot lasers,” Proc. SPIE 9892, 98920W (2016).
[Crossref]

B. Tykalewicz, D. Goulding, S. P. Hegarty, G. Huyet, I. Dubinkin, N. Fedorov, T. Erneux, E. A. Viktorov, and B. Kelleher, “Optically induced hysteresis in a two-state quantum dot laser,” Opt. Lett. 41(5), 1034–1037 (2016).
[Crossref]

E. A. Viktorov, I. Dubinkin, N. Fedorov, T. Erneux, B. Tykalewicz, S. P. Hegarty, G. Huyet, D. Goulding, and B. Kelleher, “Injection-induced, tunable all-optical gating in a two-state quantum dot laser,” Opt. Lett. 41(15), 3555–3558 (2016).
[Crossref]

2015 (3)

A. Röhm, B. Lingnau, and K. Lüdge, “Understanding ground-state quenching in quantum-dot lasers,” IEEE J. Quantum Electron. 51(1), 1–11 (2015).
[Crossref]

A. Röhm, B. Lingnau, and K. Lüdge, “Ground-state modulation-enhancement by two-state lasing in quantum-dot laser devices,” Appl. Phys. Lett. 106(19), 191102 (2015).
[Crossref]

B. Lingnau and K. Lüdge, “Analytic characterization of the dynamic regimes of quantum-dot lasers,” Photonics 2(2), 402–413 (2015).
[Crossref]

2014 (5)

2013 (3)

B. Lingnau, W. W. Chow, E. Schöll, and K. Lüdge, “Feedback and injection locking instabilities in quantum-dot lasers: a microscopically based bifurcation analysis,” New J. Phys. 15(9), 093031 (2013).
[Crossref]

W. W. Chow and F. Jahnke, “On the physics of semiconductor quantum dots for applications in lasers and quantum optics,” Prog. Quantum Electron. 37(3), 109–184 (2013).
[Crossref]

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421–470 (2013).
[Crossref]

2012 (4)

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Schöll, and K. Lüdge, “Optically injected quantum dot lasers - impact of nonlinear carrier lifetimes on frequency locking dynamics,” New J. Phys. 14(5), 053018 (2012).
[Crossref]

C. Bonatto, B. Kelleher, G. Huyet, and S. P. Hegarty, “Transition from unidirectional to delayed bidirectional coupling in optically coupled semiconductor lasers,” Phys. Rev. E 85(2), 026205 (2012).
[Crossref]

B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α-factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E 86(6), 065201 (2012).
[Crossref]

B. Globisch, C. Otto, E. Schöll, and K. Lüdge, “Influence of carrier lifetimes on the dynamical behavior of quantum-dot lasers subject to optical feedback,” Phys. Rev. E 86(4), 046201 (2012).
[Crossref]

2011 (1)

N. Majer, S. Dommers-Völkel, J. Gomis-Bresco, U. Woggon, K. Lüdge, and E. Schöll, “Impact of carrier-carrier scattering and carrier heating on pulse train dynamics of quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 99(13), 131102 (2011).
[Crossref]

2010 (1)

C. Otto, K. Lüdge, and E. Schöll, “Modeling quantum dot lasers with optical feedback: sensitivity of bifurcation scenarios,” Phys. Status Solidi B 247, 829–845 (2010).
[Crossref]

2009 (3)

K. Lüdge and E. Schöll, “Quantum-dot lasers – desynchronized nonlinear dynamics of electrons and holes,” IEEE J. Quantum Electron. 45(11), 1396–1403 (2009).
[Crossref]

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(2), 023834 (2009).
[Crossref]

A. B. Wang, Y. C. Wang, and J. F. Wang, “Route to broadband chaos in a chaotic laser diode subject to optical injection,” Opt. Lett. 34(8), 1144 (2009).
[Crossref]

2007 (2)

V. Rottschäfer and B. Krauskopf, “The ECM-backbone of the Lang-Kobayashi equations: A geometric picture,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 17(05), 1575–1588 (2007).
[Crossref]

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98(15), 153903 (2007).
[Crossref]

2005 (2)

M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “spectra of 1.3-μm self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening of optical gain under current injectionmodeling room-temperature lasing,” J. Appl. Phys. 97(4), 043523 (2005).
[Crossref]

E. A. Viktorov, P. Mandel, J. Houlihan, G. Huyet, and Y. Tanguy, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett. 87(5), 053113 (2005).
[Crossref]

2004 (1)

T. R. Nielsen, P. Gartner, and F. Jahnke, “Many-body theory of carrier capture and relaxation in semiconductor quantum-dot lasers,” Phys. Rev. B 69(23), 235314 (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(12), 1818–1820 (2003).
[Crossref]

2002 (1)

B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, and T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66(4), 046216 (2002).
[Crossref]

2001 (1)

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[Crossref]

2000 (2)

T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, “Bifurcation to mixed external cavity mode solutions for semiconductor lasers subject to optical feedback,” Opt. Commun. 183(5-6), 467–477 (2000).
[Crossref]

E. A. Viktorov and P. Mandel, “Low frequency fluctuations in a multimode semiconductor laser with optical feedback,” Phys. Rev. Lett. 85(15), 3157–3160 (2000).
[Crossref]

1997 (1)

M. Grundmann and D. Bimberg, “Theory of random population for quantum dots,” Phys. Rev. B 55(15), 9740–9745 (1997).
[Crossref]

1996 (1)

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. O. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76(2), 220–223 (1996).
[Crossref]

1994 (2)

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719–2726 (1994).
[Crossref]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling route to chaos in a semiconductor laser subject to optical injection,” Appl. Phys. Lett. 64(26), 3539–3541 (1994).
[Crossref]

1993 (1)

A. A. Tager and B. B. Elenkrig, “Stability regimes and high-frequency modulation of laser diodes with short external cavity,” IEEE J. Quantum Electron. 29(12), 2886–2890 (1993).
[Crossref]

1992 (2)

J. Mørk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback-Theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[Crossref]

J. Sacher, D. Baums, P. Panknin, W. Elsäßer, and E. O. Göbel, “Intensity instabilites of semiconductor lasers under current modulation external light injection, and delayed feedback,” Phys. Rev. A 45(3), 1893–1905 (1992).
[Crossref]

1983 (1)

C. Grebogi, E. Ott, and J. A. Yorke, “Crises, sudden changes in chaotic attractors, and transient chaos,” Phys. D 7(1-3), 181–200 (1983).
[Crossref]

Ackemann, T.

J. Robertson, T. Ackemann, L. F. Lester, and A. Hurtado, “Externally-triggered activation and inhibition of optical pulsating regimes in quantum-dot mode-locked lasers,” Sci. Rep. 8(1), 12515 (2018).
[Crossref]

Akiyama, T.

M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “spectra of 1.3-μm self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening of optical gain under current injectionmodeling room-temperature lasing,” J. Appl. Phys. 97(4), 043523 (2005).
[Crossref]

Akizawa, Y.

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J. 9(2), 1–12 (2017).
[Crossref]

Alsing, P. M.

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M. Dillane, I. Dubinkin, N. Fedorov, T. Erneux, D. Goulding, B. Kelleher, and E. A. Viktorov, “Excitable interplay between lasing quantum dot states,” Phys. Rev. E 100(1), 012202 (2019).
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B. Kelleher, B. Tykalewicz, D. Goulding, N. Fedorov, I. Dubinkin, T. Erneux, and E. A. Viktorov, “Two-color bursting oscillations,” Sci. Rep. 7(1), 8414 (2017).
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B. Tykalewicz, D. Goulding, S. P. Hegarty, G. Huyet, I. Dubinkin, N. Fedorov, T. Erneux, E. A. Viktorov, and B. Kelleher, “Optically induced hysteresis in a two-state quantum dot laser,” Opt. Lett. 41(5), 1034–1037 (2016).
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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(12), 1818–1820 (2003).
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I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsäßer, E. O. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76(2), 220–223 (1996).
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T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
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T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, “Bifurcation to mixed external cavity mode solutions for semiconductor lasers subject to optical feedback,” Opt. Commun. 183(5-6), 467–477 (2000).
[Crossref]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling route to chaos in a semiconductor laser subject to optical injection,” Appl. Phys. Lett. 64(26), 3539–3541 (1994).
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N. Majer, S. Dommers-Völkel, J. Gomis-Bresco, U. Woggon, K. Lüdge, and E. Schöll, “Impact of carrier-carrier scattering and carrier heating on pulse train dynamics of quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 99(13), 131102 (2011).
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M. Dillane, I. Dubinkin, N. Fedorov, T. Erneux, D. Goulding, B. Kelleher, and E. A. Viktorov, “Excitable interplay between lasing quantum dot states,” Phys. Rev. E 100(1), 012202 (2019).
[Crossref]

M. Dillane, B. Tykalewicz, D. Goulding, B. Garbin, S. Barland, and B. Kelleher, “Square wave excitability in quantum dot lasers under optical injection,” Opt. Lett. 44(2), 347–350 (2019).
[Crossref]

B. Kelleher, M. J. Wishon, A. Locquet, D. Goulding, B. Tykalewicz, G. Huyet, and E. A. Viktorov, “Delay induced high order locking effects in semiconductor lasers,” Chaos 27(11), 114325 (2017).
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B. Kelleher, B. Tykalewicz, D. Goulding, N. Fedorov, I. Dubinkin, T. Erneux, and E. A. Viktorov, “Two-color bursting oscillations,” Sci. Rep. 7(1), 8414 (2017).
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E. A. Viktorov, I. Dubinkin, N. Fedorov, T. Erneux, B. Tykalewicz, S. P. Hegarty, G. Huyet, D. Goulding, and B. Kelleher, “Injection-induced, tunable all-optical gating in a two-state quantum dot laser,” Opt. Lett. 41(15), 3555–3558 (2016).
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B. Tykalewicz, D. Goulding, S. P. Hegarty, G. Huyet, D. M. Byrne, R. Phelan, and B. Kelleher, “All-optical switching with a dual-state, single-section quantum dot laser via optical injection,” Opt. Lett. 39(15), 4607–4610 (2014).
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A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J. 9(2), 1–12 (2017).
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M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “spectra of 1.3-μm self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening of optical gain under current injectionmodeling room-temperature lasing,” J. Appl. Phys. 97(4), 043523 (2005).
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B. Tykalewicz, D. Goulding, S. P. Hegarty, G. Huyet, I. Dubinkin, N. Fedorov, T. Erneux, E. A. Viktorov, and B. Kelleher, “Optically induced hysteresis in a two-state quantum dot laser,” Opt. Lett. 41(5), 1034–1037 (2016).
[Crossref]

E. A. Viktorov, I. Dubinkin, N. Fedorov, T. Erneux, B. Tykalewicz, S. P. Hegarty, G. Huyet, D. Goulding, and B. Kelleher, “Injection-induced, tunable all-optical gating in a two-state quantum dot laser,” Opt. Lett. 41(15), 3555–3558 (2016).
[Crossref]

B. Tykalewicz, D. Goulding, S. P. Hegarty, G. Huyet, D. M. Byrne, R. Phelan, and B. Kelleher, “All-optical switching with a dual-state, single-section quantum dot laser via optical injection,” Opt. Lett. 39(15), 4607–4610 (2014).
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[Crossref]

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(2), 023834 (2009).
[Crossref]

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98(15), 153903 (2007).
[Crossref]

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T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[Crossref]

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B. Kelleher, M. J. Wishon, A. Locquet, D. Goulding, B. Tykalewicz, G. Huyet, and E. A. Viktorov, “Delay induced high order locking effects in semiconductor lasers,” Chaos 27(11), 114325 (2017).
[Crossref]

B. Tykalewicz, D. Goulding, S. P. Hegarty, G. Huyet, I. Dubinkin, N. Fedorov, T. Erneux, E. A. Viktorov, and B. Kelleher, “Optically induced hysteresis in a two-state quantum dot laser,” Opt. Lett. 41(5), 1034–1037 (2016).
[Crossref]

E. A. Viktorov, I. Dubinkin, N. Fedorov, T. Erneux, B. Tykalewicz, S. P. Hegarty, G. Huyet, D. Goulding, and B. Kelleher, “Injection-induced, tunable all-optical gating in a two-state quantum dot laser,” Opt. Lett. 41(15), 3555–3558 (2016).
[Crossref]

B. Tykalewicz, D. Goulding, S. P. Hegarty, G. Huyet, D. M. Byrne, R. Phelan, and B. Kelleher, “All-optical switching with a dual-state, single-section quantum dot laser via optical injection,” Opt. Lett. 39(15), 4607–4610 (2014).
[Crossref]

C. Bonatto, B. Kelleher, G. Huyet, and S. P. Hegarty, “Transition from unidirectional to delayed bidirectional coupling in optically coupled semiconductor lasers,” Phys. Rev. E 85(2), 026205 (2012).
[Crossref]

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(2), 023834 (2009).
[Crossref]

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98(15), 153903 (2007).
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A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J. 9(2), 1–12 (2017).
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M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “spectra of 1.3-μm self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening of optical gain under current injectionmodeling room-temperature lasing,” J. Appl. Phys. 97(4), 043523 (2005).
[Crossref]

Jahnke, F.

W. W. Chow and F. Jahnke, “On the physics of semiconductor quantum dots for applications in lasers and quantum optics,” Prog. Quantum Electron. 37(3), 109–184 (2013).
[Crossref]

T. R. Nielsen, P. Gartner, and F. Jahnke, “Many-body theory of carrier capture and relaxation in semiconductor quantum-dot lasers,” Phys. Rev. B 69(23), 235314 (2004).
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C. Mesaritakis, A. Kapsalis, A. Bogris, and D. Syvridis, “Artificial neuron based on integrated semiconductor quantum dot mode-locked lasers,” Sci. Rep. 6(1), 39317 (2016).
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A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J. 9(2), 1–12 (2017).
[Crossref]

Kelleher, B.

M. Dillane, I. Dubinkin, N. Fedorov, T. Erneux, D. Goulding, B. Kelleher, and E. A. Viktorov, “Excitable interplay between lasing quantum dot states,” Phys. Rev. E 100(1), 012202 (2019).
[Crossref]

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J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Schöll, and K. Lüdge, “Optically injected quantum dot lasers - impact of nonlinear carrier lifetimes on frequency locking dynamics,” New J. Phys. 14(5), 053018 (2012).
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C. Otto, K. Lüdge, and E. Schöll, “Modeling quantum dot lasers with optical feedback: sensitivity of bifurcation scenarios,” Phys. Status Solidi B 247, 829–845 (2010).
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M. Virte, S. Breuer, M. Sciamanna, and K. Panajotov, “Switching between ground and excited states by optical feedback in a quantum dot laser diode,” Appl. Phys. Lett. 105(12), 121109 (2014).
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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(12), 1818–1820 (2003).
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Pausch, J.

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Schöll, and K. Lüdge, “Optically injected quantum dot lasers - impact of nonlinear carrier lifetimes on frequency locking dynamics,” New J. Phys. 14(5), 053018 (2012).
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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(12), 1818–1820 (2003).
[Crossref]

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D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98(15), 153903 (2007).
[Crossref]

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D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98(15), 153903 (2007).
[Crossref]

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J. Robertson, T. Ackemann, L. F. Lester, and A. Hurtado, “Externally-triggered activation and inhibition of optical pulsating regimes in quantum-dot mode-locked lasers,” Sci. Rep. 8(1), 12515 (2018).
[Crossref]

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T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, “Bifurcation to mixed external cavity mode solutions for semiconductor lasers subject to optical feedback,” Opt. Commun. 183(5-6), 467–477 (2000).
[Crossref]

Röhm, A.

S. Meinecke, B. Lingnau, A. Röhm, and K. Lüdge, “Stability in optically injected two-state quantum-dot lasers,” Ann. Phys. (Berl.) 529(12), 1600279 (2017).
[Crossref]

A. Röhm, B. Lingnau, and K. Lüdge, “Understanding ground-state quenching in quantum-dot lasers,” IEEE J. Quantum Electron. 51(1), 1–11 (2015).
[Crossref]

A. Röhm, B. Lingnau, and K. Lüdge, “Ground-state modulation-enhancement by two-state lasing in quantum-dot laser devices,” Appl. Phys. Lett. 106(19), 191102 (2015).
[Crossref]

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B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, and T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66(4), 046216 (2002).
[Crossref]

J. Sieber, K. Engelborghs, T. Luzyanina, G. Samaey, and D. Roose, DDE-BIFTOOL Manual - Bifurcation analysis of delay differential equations (2014).

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V. Rottschäfer and B. Krauskopf, “The ECM-backbone of the Lang-Kobayashi equations: A geometric picture,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 17(05), 1575–1588 (2007).
[Crossref]

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(2), 023834 (2009).
[Crossref]

Sacher, J.

J. Sacher, D. Baums, P. Panknin, W. Elsäßer, and E. O. Göbel, “Intensity instabilites of semiconductor lasers under current modulation external light injection, and delayed feedback,” Phys. Rev. A 45(3), 1893–1905 (1992).
[Crossref]

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J. Sieber, K. Engelborghs, T. Luzyanina, G. Samaey, and D. Roose, DDE-BIFTOOL Manual - Bifurcation analysis of delay differential equations (2014).

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[Crossref]

Schöll, E.

C. Otto, B. Lingnau, E. Schöll, and K. Lüdge, “Manipulating coherence resonance in a quantum dot semiconductor laser via electrical pumping,” Opt. Express 22(11), 13288 (2014).
[Crossref]

B. Lingnau, W. W. Chow, E. Schöll, and K. Lüdge, “Feedback and injection locking instabilities in quantum-dot lasers: a microscopically based bifurcation analysis,” New J. Phys. 15(9), 093031 (2013).
[Crossref]

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Schöll, and K. Lüdge, “Optically injected quantum dot lasers - impact of nonlinear carrier lifetimes on frequency locking dynamics,” New J. Phys. 14(5), 053018 (2012).
[Crossref]

B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α-factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E 86(6), 065201 (2012).
[Crossref]

B. Globisch, C. Otto, E. Schöll, and K. Lüdge, “Influence of carrier lifetimes on the dynamical behavior of quantum-dot lasers subject to optical feedback,” Phys. Rev. E 86(4), 046201 (2012).
[Crossref]

N. Majer, S. Dommers-Völkel, J. Gomis-Bresco, U. Woggon, K. Lüdge, and E. Schöll, “Impact of carrier-carrier scattering and carrier heating on pulse train dynamics of quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 99(13), 131102 (2011).
[Crossref]

C. Otto, K. Lüdge, and E. Schöll, “Modeling quantum dot lasers with optical feedback: sensitivity of bifurcation scenarios,” Phys. Status Solidi B 247, 829–845 (2010).
[Crossref]

K. Lüdge and E. Schöll, “Quantum-dot lasers – desynchronized nonlinear dynamics of electrons and holes,” IEEE J. Quantum Electron. 45(11), 1396–1403 (2009).
[Crossref]

Sciamanna, M.

M. Virte, R. Pawlus, W. Elsäßer, K. Panajotov, M. Sciamanna, and S. Breuer, “Range-dependent effects of optical feedback on multimode two-color quantum dot lasers,” Proc. SPIE 9892, 98920W (2016).
[Crossref]

M. Virte, S. Breuer, M. Sciamanna, and K. Panajotov, “Switching between ground and excited states by optical feedback in a quantum dot laser diode,” Appl. Phys. Lett. 105(12), 121109 (2014).
[Crossref]

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J. Sieber, K. Engelborghs, T. Luzyanina, G. Samaey, and D. Roose, DDE-BIFTOOL Manual - Bifurcation analysis of delay differential equations (2014).

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T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling route to chaos in a semiconductor laser subject to optical injection,” Appl. Phys. Lett. 64(26), 3539–3541 (1994).
[Crossref]

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M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421–470 (2013).
[Crossref]

Sugawara, M.

M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “spectra of 1.3-μm self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening of optical gain under current injectionmodeling room-temperature lasing,” J. Appl. Phys. 97(4), 043523 (2005).
[Crossref]

Syvridis, D.

C. Mesaritakis, A. Kapsalis, A. Bogris, and D. Syvridis, “Artificial neuron based on integrated semiconductor quantum dot mode-locked lasers,” Sci. Rep. 6(1), 39317 (2016).
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E. A. Viktorov, P. Mandel, J. Houlihan, G. Huyet, and Y. Tanguy, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett. 87(5), 053113 (2005).
[Crossref]

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J. Mørk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback-Theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[Crossref]

Tykalewicz, B.

Tylaite, E.

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Schöll, and K. Lüdge, “Optically injected quantum dot lasers - impact of nonlinear carrier lifetimes on frequency locking dynamics,” New J. Phys. 14(5), 053018 (2012).
[Crossref]

Uchida, A.

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J. 9(2), 1–12 (2017).
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R. Pawlus, S. Breuer, and M. Virte, “Relative intensity noise reduction in a dual-state quantum-dot laser by optical feedback,” Opt. Lett. 42(21), 4259–4262 (2017).
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Opt. Express (4)

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M. Dillane, B. Tykalewicz, D. Goulding, B. Garbin, S. Barland, and B. Kelleher, “Square wave excitability in quantum dot lasers under optical injection,” Opt. Lett. 44(2), 347–350 (2019).
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[Crossref]

E. A. Viktorov, I. Dubinkin, N. Fedorov, T. Erneux, B. Tykalewicz, S. P. Hegarty, G. Huyet, D. Goulding, and B. Kelleher, “Injection-induced, tunable all-optical gating in a two-state quantum dot laser,” Opt. Lett. 41(15), 3555–3558 (2016).
[Crossref]

R. Pawlus, S. Breuer, and M. Virte, “Relative intensity noise reduction in a dual-state quantum-dot laser by optical feedback,” Opt. Lett. 42(21), 4259–4262 (2017).
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L. C. Lin, C. Y. Chen, H. Huang, D. Arsenijević, D. Bimberg, F. Grillot, and F. Y. Lin, “Comparison of optical feedback dynamics of InAs/GaAs quantum-dot lasers emitting solely on ground or excited states,” Opt. Lett. 43(2), 210–213 (2018).
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A. B. Wang, Y. C. Wang, and J. F. Wang, “Route to broadband chaos in a chaotic laser diode subject to optical injection,” Opt. Lett. 34(8), 1144 (2009).
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Photonics (1)

B. Lingnau and K. Lüdge, “Analytic characterization of the dynamic regimes of quantum-dot lasers,” Photonics 2(2), 402–413 (2015).
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Phys. D (1)

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[Crossref]

Phys. Rev. A (3)

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[Crossref]

E. A. Viktorov and P. Mandel, “Low frequency fluctuations in a multimode semiconductor laser with optical feedback,” Phys. Rev. Lett. 85(15), 3157–3160 (2000).
[Crossref]

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: The short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
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Proc. SPIE (1)

M. Virte, R. Pawlus, W. Elsäßer, K. Panajotov, M. Sciamanna, and S. Breuer, “Range-dependent effects of optical feedback on multimode two-color quantum dot lasers,” Proc. SPIE 9892, 98920W (2016).
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Sci. Rep. (3)

B. Kelleher, B. Tykalewicz, D. Goulding, N. Fedorov, I. Dubinkin, T. Erneux, and E. A. Viktorov, “Two-color bursting oscillations,” Sci. Rep. 7(1), 8414 (2017).
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D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures (John Wiley & Sons Ltd., 1999).

T. Erneux and P. Glorieux, Laser Dynamics (Cambridge University Press, 2010).

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Figures (7)

Fig. 1.
Fig. 1. (a) Sketch of the setup. A frequency selective mirror only couples back light at the frequency of the GS emission. (b) Sketch of the band structure across one quantum dot (QD). Charge carrier variables are denoted in green and their coupling via scattering processes is indicated by dark green arrows. Recombination of GS and ES charge carriers is represented by red and blue arrows respectively.
Fig. 2.
Fig. 2. (a) Input-output characteristics of the solitary two-state laser with the pump current normalized to the threshold current. The GS emission (orange) exhibits a rollover after the onset of ES emission (purple) and full quenching at higher pump currents. Operating point at $J = 1.4J_\textrm {GS}^\textrm {th}$ with $P_0 = 20.17\,\textrm {mW}$. (b) Feedback induced dynamics in the feedback strength, feedback phase plane at $\tau = 150\textrm {ps}$. The steady output-power at the GS frequency is color coded in orange. Blue and green colors indicate period one and higher order oscillations. Hatches denote two-state lasing. Enclosed by a two-state lasing region, the emission completely switches from the GS to the ES. The purple line represents the parameter range shown in the bifurcation scan Fig. 3. (c) Time series of the GS (orange) and ES (purple) emission power exemplifying the complex oscillations in the green region in (b) at $C=0.849,K=0.127$.
Fig. 3.
Fig. 3. Bifurcation diagram along the feedback strength $K$ at $C=0.849$ (indicated by the purple line in Fig. 2). (a) and (b): local maxima of the GS and ES emission, respectively. (c): GS relative frequency shift. Solid and dashed lines indicate steady-state and periodic-orbit solutions obtained by path continuation. Thick and thin lines represent stable and unstable solutions. Orange and blue lines represent the first and second GS ECM. Green and purple lines represent the GS and ES emission of the two-state lasing solution. Local maxima of the two-state oscillation bursts solutions are obtained by direct integration and are shown in pale green and purple colors. We show Andronov-Hopf (H, squares), transcritical (TC, diamonds), torus (T, circles) and saddle-node (SN, stars) bifurcations, which connect solutions and/or cause a transition from stable to unstable. The vertical dashed lines labeled [a]-[e] indicate the parameters shown in Fig. 5.
Fig. 4.
Fig. 4. Optical spectrum (a) and low frequency power spectrum (b) for increasing feedback strengths where the color encodes the spectral power. $\delta \nu$ denotes the relative frequency with respect to the solitary lasing frequency. Vertical dashed lines labeled [a]-[e] indicate the feedback strengths shown in Fig. 5. Vertical dotted blue lines indicate the labeled bifurcations.
Fig. 5.
Fig. 5. Time traces and phase-space projections within the oscillation bursts regime for $K \in \{0.1210, 0.1220, 0.1250, 0.1295, 0.1305\}$. Left column (a1)-(e1): time traces of the GS (orange and green) and ES power (purple); prange and green lines correspond to the same trajectory, which is either close to the first GS ECM or to the ghost of the two-state ECM. Middle column (a2)-(e2): trajectory in a phase-space projection onto the GS inversion and instantaneous frequency shift $\langle \delta \nu \rangle _{\tau }$. Open orange circles represent the unstable first GS ECM, green circles the two-state ECM, green diamonds the transcritical bifurcation of the two-state ECM, blue stars the saddle-node bifurcation of the second GS ECM and the blue circle the stable second GS ECM as introduced in Fig. 3. Right column (a3)-(e3): trajectory projected onto the GS power, ES power, GS inversion space. Orange lines represent the Poincaré map created by the intersection of the trajectories with surfaces of constant ES powers (gray surfaces).
Fig. 6.
Fig. 6. Zoom of the bifurcation diagram in Fig. 3(a) and Fig. 4(b) showing local maxima of the GS power (a) and power spectra of the GS emission (b). A period-doubling cascade leads to chaotic motion of the oscillation bursts slow envelope. Vertical gray dashed lines indicate the feedback parameters used in Figs. 5(d)–5(e) and Fig. 7 respectively.
Fig. 7.
Fig. 7. Low frequency chaos produced by the dynamics of the bursting oscillations envelope at $K=0.12985$. Time series of the GS and ES power at two different time scales (a), power spectrum of the GS at two different frequency scales (b), phase-space projection onto the GS inversion and instantaneous frequency shift $\langle \delta \nu \rangle _{\tau }$ (c) and Poincaré map of the GS power $P^\textrm {GS}$ and inversion $\rho _\textrm {inv}$ produced by the intersection with the surface of constant ES power (d).

Tables (2)

Tables Icon

Table 1. Parameters used for numerical calculations unless noted otherwise.

Tables Icon

Table 2. Fit parameters for charge-carrier scattering processes, extracted from microscopic calculations for a GS confinement energy of 64(35) meV and a GS-ES separation of 50(20) meV for electrons (holes), and T=300 K.

Equations (14)

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

d dt ρ b, a m = W m ρ e,a m ρ h,a m + S b,a m,cap + S b,a m,rel g m ( ρ e,a m + ρ h,a m 1 ) ν m Z QD f a | E m | 2 η m 2
d dt ρ b,i m = W m ρ e,i m ρ h,i m + S b,i m,cap + S b,i m,rel
d dt w b = + J R loss w w e w h m { G S , E S } 2 ν m N QD ( f a S b,a m , c a p + f i S b,i m , c a p )
S b,x m,cap = S b,in m, cap ( 1 ρ b,x m ) S b,out m,cap ρ b,x m
S b,x m,rel = ± 1 ν m [ S b,in rel ( 1 ρ b,x GS ) ρ b,x ES S b,out rel ( 1 ρ b,x ES ) ρ b,x GS ]
d dt E GS = [ g GS ( ρ e,a GS + ρ h,a GS 1 ) i δ ω GS κ GS ] E GS + K κ GS e i C E GS ( t τ )
d dt E ES = [ g ES ( ρ e,a ES + ρ h,a ES 1 ) κ ES ] E ES
δ ω GS = δ ω ES [ f a ( ρ e,a ES + ρ h,a ES ) + f i ( ρ e,i ES + ρ h,i ES ) ] + δ ω QW e w e + δ ω QW h w h
P out m = 2 κ m ϵ b V mode | E m | 2
S b,in m,cap ( w b ) = A m,b w b 2 B m,b + w b
S b,in rel ( w b ) = C b w b D b + w b
S b,out m,cap = S b,in m,cap exp ( E F,b eq ε m,b k B T ) ,
S b,out rel = S b,in rel exp ( ε ES,b ε GS,b k B T ) ,
E F,b eq = E b,0 QW + k B T ln [ exp ( w b D b 2D k B T ) 1 ] ,

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