Abstract

Excitability and coherence resonance are studied in a semiconductor quantum dot laser under short optical self-feedback. For low pump levels, these are observed close to a homoclinic bifurcation, which is in correspondence with earlier observations in quantum well lasers. However, for high pump levels, we find excitability close to a boundary crisis of a chaotic attractor. We demonstrate that in contrast to the homoclinic bifurcation the crisis and thus the excitable regime is highly sensitive to the pump current. The excitability threshold increases with the pump current, which permits to adjust the sensitivity of the excitable unit to noise as well as to shift the optimal noise strength, at which maximum coherence is observed. The shift adds up to more than one order of magnitude, which strongly facilitates experimental realizations.

© 2014 Optical Society of America

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2014 (1)

A. Vüllings, E. Schöll, B. Lindner, “Spectra of delay-coupled heterogeneous noisy nonlinear oscillators,” Eur. Phys. J. B 87, 31 (2014).
[CrossRef]

2013 (6)

A. Zakharova, A. Feoktistov, T. Vadivasova, E. Schöll, “Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation,” Eur. Phys. J. Spec. Top. 222, 2481–2495 (2013).
[CrossRef]

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

S. Wilkinson, B. Lingnau, J. Korn, E. Schöll, K. Lüdge, “Influence of noise on the signal properties of quantum-dot semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 19, 1900106 (2013).
[CrossRef]

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

B. Romeira, J. Javaloyes, C. N. Ironside, J. M. L. Figueiredo, S. Balle, O. Piro, “Excitability and optical pulse generation in semiconductor lasers driven by resonant tunneling diode photo-detectors,” Opt. Express 21, 20931–20940 (2013).
[CrossRef] [PubMed]

D. Ziemann, R. Aust, B. Lingnau, E. Schöll, K. Lüdge, “Optical injection enables coherence resonance in quantum-dot lasers,” Europhys. Lett. 103, 14002 (2013).
[CrossRef]

2012 (7)

B. Kelleher, S. P. Hegarty, G. Huyet, “Modified relaxation oscillation parameters in optically injected semiconductor lasers,” J. Opt. Soc. Am. B 29, 2249–2254 (2012).
[CrossRef]

S. Perrone, R. Vilaseca, C. Masoller, “Stochastic logic gate that exploits noise and polarization bistability in an optically injected vcsel,” Opt. Express 20, 22692–22699 (2012).
[CrossRef] [PubMed]

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

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

C. Otto, B. Globisch, K. Lüdge, E. Schöll, T. Erneux, “Complex dynamics of semiconductor quantum dot lasers subject to delayed optical feedback,” Int. J. Bif. Chaos 22, 1250246 (2012).
[CrossRef]

B. Lingnau, K. Lüdge, W. W. Chow, E. Schöll, “Influencing modulation properties of quantum-dot semiconductor lasers by electron lifetime engineering,” Appl. Phys. Lett. 101, 131107 (2012).
[CrossRef]

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

2011 (5)

M. Virte, A. Karsaklian Dal Bosco, D. Wolfersberger, M. Sciamanna, “Chaos crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback,” Phys. Rev. A 84, 043836 (2011).
[CrossRef]

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

K. Lüdge, E. Schöll, E. A. Viktorov, T. Erneux, “Analytic approach to modulation properties of quantum dot lasers,” J. Appl. Phys. 109, 103112 (2011).
[CrossRef]

B. Kelleher, C. Bonatto, G. Huyet, S. P. Hegarty, “Excitability in optically injected semiconductor lasers: Contrasting quantum-well- and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
[CrossRef]

F. Pedaci, Z. Huang, P. van Hese, S. Barland, L. Deuker, “Excitable particles in an optical torque wrench,” Nat. Phys. 7, 259–264 (2011).
[CrossRef]

2010 (6)

L. Olejniczak, K. Panajotov, H. Thienpont, 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]

C. Otto, K. Lüdge, E. Schöll, “Modeling quantum dot lasers with optical feedback: sensitivity of bifurcation scenarios,” Phys. Stat. Sol. (B) 247, 829–845 (2010).

A. Zakharova, T. Vadivasova, V. Anishchenko, A. Koseska, J. Kurths, “Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator,” Phys. Rev. E 81, 011106 (2010).
[CrossRef]

S. A. Brandstetter, M. A. Dahlem, E. Schöll, “Interplay of time-delayed feedback control and temporally correlated noise in excitable systems,” Phil. Trans. R. Soc. A 368, 391 (2010).
[CrossRef]

S. Sergeyev, K. O’Mahoney, S. Popov, A. T. Friberg, “Coherence and anticoherence resonance in high-concentration erbium-doped fiber laser,” Opt. Lett. 35, 3736 (2010).
[CrossRef] [PubMed]

K. Lüdge, E. Schöll, “Nonlinear dynamics of doped semiconductor quantum dot lasers,” Eur. Phys. J. D 58, 167–174 (2010).
[CrossRef]

2009 (5)

K. Green, “Stability near threshold in a semiconductor laser subject to optical feedback: A bifurcation analysis of the Lang-Kobayashi equations,” Phys. Rev. E 79, 036210 (2009).
[CrossRef]

F. T. Arecchi, R. Meucci, “Stochastic and coherence resonance in lasers: homoclinic chaos and polarization bistability,” Eur. Phys. J. B 67, 93–100 (2009).
[CrossRef]

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

B. Kelleher, D. Goulding, S. P. Hegarty, G. Huyet, D. Y. Cong, A. Martinez, A. Lemaitre, A. Ramdane, M. Fischer, F. Gerschütz, J. Koeth, “Excitable phase slips in an injection-locked single-mode quantum-dot laser,” Opt. Lett. 34, 440–442 (2009).
[CrossRef] [PubMed]

V. Flunkert, O. D’Huys, J. Danckaert, I. Fischer, E. Schöll, “Bubbling in delay-coupled lasers,” Phys. Rev. E 79, 065201 (R) (2009).
[CrossRef]

2008 (2)

V. Z. Tronciu, “Excitability and coherence resonance of a DFB laser with passive dispersive reflector,” Moldavian Journal of the Physical Sciences 7, 516 (2008).

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
[CrossRef] [PubMed]

2007 (6)

M. Radziunas, A. Glitzky, U. Bandelow, M. Wolfrum, U. Troppenz, J. Kreissl, W. Rehbein, “Improving the Modulation Bandwidth in Semiconductor Lasers by Passive Feedback,” IEEE J. Sel. Top. Quantum Electron. 13, 136–142 (2007).
[CrossRef]

V. Rottschäfer, B. Krauskopf, “The ECM-backbone of the Lang-Kobayashi equations: A geometric picture,” Int. J. Bif. Chaos 17, 1575–1588 (2007).
[CrossRef]

O. Ushakov, N. Korneyev, M. Radziunas, H. J. Wünsche, F. Henneberger, “Excitability of chaotic transients in a semiconductor laser,” Europhys. Lett. 79, 30004 (2007).
[CrossRef]

M. Gioannini, I. Montrosset, “Numerical analysis of the frequency chirp in quantum-dot semiconductor lasers,” IEEE J. Quantum Electron. 43, 941–949 (2007).
[CrossRef]

T. Erneux, E. A. Viktorov, P. Mandel, “Time scales and relaxation dynamics in quantum-dot lasers,” Phys. Rev. A 76, 023819 (2007).
[CrossRef]

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

2006 (1)

J. Hizanidis, A. G. Balanov, A. Amann, E. Schöll, “Noise-induced front motion: signature of a global bifurcation,” Phys. Rev. Lett. 96, 244104 (2006).
[CrossRef] [PubMed]

2005 (2)

O. V. Ushakov, H. J. Wünsche, F. Henneberger, I. A. Khovanov, L. Schimansky-Geier, M. A. Zaks, “Coherence resonance near a Hopf bifurcation,” Phys. Rev. Lett. 95, 123903 (2005).
[CrossRef] [PubMed]

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

2004 (7)

S. Wieczorek, D. Lenstra, “Spontaneously excited pulses in an optically driven semiconductor laser,” Phys. Rev. E 69, 016218 (2004).
[CrossRef]

N. B. Janson, A. G. Balanov, E. Schöll, “Delayed feedback as a means of control of noise-induced motion,” Phys. Rev. Lett. 93, 010601 (2004).
[CrossRef] [PubMed]

A. G. Balanov, N. B. Janson, E. Schöll, “Control of noise-induced oscillations by delayed feedback,” Physica D 199, 1–12 (2004).
[CrossRef]

R. Wetzler, A. Wacker, E. Schöll, “Non-local Auger effect in quantum dot devices,” Semicond. Sci. Technol. 19, S43 (2004).
[CrossRef]

T. R. Nielsen, P. Gartner, F. Jahnke, “Many-body theory of carrier capture and relaxation in semiconductor quantum-dot lasers,” Phys. Rev. B 69, 235314 (2004).
[CrossRef]

G. Huyet, D. O’Brien, S. P. Hegarty, J. G. McInerney, A. V. Uskov, D. Bimberg, C. Ribbat, V. M. Ustinov, A. E. Zhukov, S. S. Mikhrin, A. R. Kovsh, J. K. White, K. Hinzer, A. J. SpringThorpe, “Quantum dot semiconductor lasers with optical feedback,” phys. stat. sol. (b) 201, 345–352 (2004).
[CrossRef]

N. B. Janson, A. G. Balanov, E. Schöll, “Delayed feedback as a means of control of noise-induced motion,” Phys. Rev. Lett. 93, 010601 (2004).
[CrossRef] [PubMed]

2003 (2)

T. Heil, I. Fischer, W. Elsäßer, B. Krauskopf, K. Green, A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
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B. Krauskopf, K. Schneider, J. Sieber, S. Wieczorek, M. Wolfrum, “Excitability and self-pulsations near homoclinic bifurcations in semiconductor laser systems,” Opt. Commun. 215, 367 (2003).
[CrossRef]

2002 (2)

S. Wieczorek, B. Krauskopf, D. Lenstra, “Multipulse excitability in a semiconductor laser with optical injection,” Phys. Rev. Lett. 88, 063901 (2002).
[CrossRef] [PubMed]

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

2001 (2)

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

H. J. Wünsche, O. Brox, M. Radziunas, F. Henneberger, “Excitability of a semiconductor laser by a two-mode homoclinic bifurcation,” Phys. Rev. Lett. 88, 023901 (2001).
[CrossRef]

2000 (1)

G. Giacomelli, M. Giudici, S. Balle, J. R. Tredicce, “Experimental evidence of coherence resonance in an optical system,” Phys. Rev. Lett. 84, 3298 (2000).
[CrossRef] [PubMed]

1999 (2)

J. L. A. Dubbeldam, B. Krauskopf, D. Lenstra, “Excitability and coherence resonance in lasers with saturable absorber,” Phys. Rev. E 60, 6580 (1999).
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J. L. A. Dubbeldam, B. Krauskopf, “Self-pulsations of lasers with saturable absorber: dynamics and bifurcations,” Opt. Commun. 159, 325–338 (1999).
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1998 (1)

L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
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1997 (3)

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 (1997).
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1993 (1)

G. Hu, T. Ditzinger, C. Z. Ning, H. Haken, “Stochastic resonance without external periodic force,” Phys. Rev. Lett. 71, 807 (1993).
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1983 (1)

C. Grebogi, E. Ott, J. A. Yorke, “Crises, sudden changes in chaotic attractors, and transient chaos,” Physica D 7, 181–200 (1983).
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1980 (1)

R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
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1970 (1)

A. N. Zaikin, A. M. Zhabotinsky, “Concentration wave propagation in two-dimensional liquid-phase self-oscillating system,” Nature 225, 535–537 (1970). 10.1038/225535b0.
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1948 (1)

A. L. Hodgkin, “The local electric changes associated with repetitive action in a medullated axon,” J. Physiol. 107, 165 (1948).
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J. Hizanidis, A. G. Balanov, A. Amann, E. Schöll, “Noise-induced front motion: signature of a global bifurcation,” Phys. Rev. Lett. 96, 244104 (2006).
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A. Zakharova, T. Vadivasova, V. Anishchenko, A. Koseska, J. Kurths, “Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator,” Phys. Rev. E 81, 011106 (2010).
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F. T. Arecchi, R. Meucci, “Stochastic and coherence resonance in lasers: homoclinic chaos and polarization bistability,” Eur. Phys. J. B 67, 93–100 (2009).
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A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
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D. Ziemann, R. Aust, B. Lingnau, E. Schöll, K. Lüdge, “Optical injection enables coherence resonance in quantum-dot lasers,” Europhys. Lett. 103, 14002 (2013).
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Balanov, A. G.

J. Hizanidis, A. G. Balanov, A. Amann, E. Schöll, “Noise-induced front motion: signature of a global bifurcation,” Phys. Rev. Lett. 96, 244104 (2006).
[CrossRef] [PubMed]

N. B. Janson, A. G. Balanov, E. Schöll, “Delayed feedback as a means of control of noise-induced motion,” Phys. Rev. Lett. 93, 010601 (2004).
[CrossRef] [PubMed]

A. G. Balanov, N. B. Janson, E. Schöll, “Control of noise-induced oscillations by delayed feedback,” Physica D 199, 1–12 (2004).
[CrossRef]

N. B. Janson, A. G. Balanov, E. Schöll, “Delayed feedback as a means of control of noise-induced motion,” Phys. Rev. Lett. 93, 010601 (2004).
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Balle, S.

Bandelow, U.

M. Radziunas, A. Glitzky, U. Bandelow, M. Wolfrum, U. Troppenz, J. Kreissl, W. Rehbein, “Improving the Modulation Bandwidth in Semiconductor Lasers by Passive Feedback,” IEEE J. Sel. Top. Quantum Electron. 13, 136–142 (2007).
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F. Pedaci, Z. Huang, P. van Hese, S. Barland, L. Deuker, “Excitable particles in an optical torque wrench,” Nat. Phys. 7, 259–264 (2011).
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G. Huyet, D. O’Brien, S. P. Hegarty, J. G. McInerney, A. V. Uskov, D. Bimberg, C. Ribbat, V. M. Ustinov, A. E. Zhukov, S. S. Mikhrin, A. R. Kovsh, J. K. White, K. Hinzer, A. J. SpringThorpe, “Quantum dot semiconductor lasers with optical feedback,” phys. stat. sol. (b) 201, 345–352 (2004).
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D. Bimberg, M. Grundmann, N. N. Ledentsov, Quantum Dot Heterostructures (John Wiley & Sons Ltd., New York, 1999).

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A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
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B. Kelleher, C. Bonatto, G. Huyet, S. P. Hegarty, “Excitability in optically injected semiconductor lasers: Contrasting quantum-well- and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
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S. A. Brandstetter, M. A. Dahlem, E. Schöll, “Interplay of time-delayed feedback control and temporally correlated noise in excitable systems,” Phil. Trans. R. Soc. A 368, 391 (2010).
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Brox, O.

H. J. Wünsche, O. Brox, M. Radziunas, F. Henneberger, “Excitability of a semiconductor laser by a two-mode homoclinic bifurcation,” Phys. Rev. Lett. 88, 023901 (2001).
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A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
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B. Lingnau, W. W. Chow, E. Schöll, K. Lüdge, “Feedback and injection locking instabilities in quantum-dot lasers: a microscopically based bifurcation analysis,” New J. Phys. 15, 093031 (2013).
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B. Lingnau, K. Lüdge, W. W. Chow, E. Schöll, “Failure of the α-factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E 86, 065201(R) (2012).
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B. Lingnau, K. Lüdge, W. W. Chow, E. Schöll, “Influencing modulation properties of quantum-dot semiconductor lasers by electron lifetime engineering,” Appl. Phys. Lett. 101, 131107 (2012).
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W. W. Chow, S. W. Koch, Semiconductor-Laser Fundamentals (Springer, Berlin, 1999).
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V. Flunkert, O. D’Huys, J. Danckaert, I. Fischer, E. Schöll, “Bubbling in delay-coupled lasers,” Phys. Rev. E 79, 065201 (R) (2009).
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Dahlem, M. A.

S. A. Brandstetter, M. A. Dahlem, E. Schöll, “Interplay of time-delayed feedback control and temporally correlated noise in excitable systems,” Phil. Trans. R. Soc. A 368, 391 (2010).
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V. Flunkert, O. D’Huys, J. Danckaert, I. Fischer, E. Schöll, “Bubbling in delay-coupled lasers,” Phys. Rev. E 79, 065201 (R) (2009).
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Deuker, L.

F. Pedaci, Z. Huang, P. van Hese, S. Barland, L. Deuker, “Excitable particles in an optical torque wrench,” Nat. Phys. 7, 259–264 (2011).
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G. Hu, T. Ditzinger, C. Z. Ning, H. Haken, “Stochastic resonance without external periodic force,” Phys. Rev. Lett. 71, 807 (1993).
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N. Majer, S. Dommers-Völkel, J. Gomis-Bresco, U. Woggon, K. Lüdge, E. Schöll, “Impact of carrier-carrier scattering and carrier heating on pulse train dynamics of quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 99, 131102 (2011).
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Dubbeldam, J. L. A.

J. L. A. Dubbeldam, B. Krauskopf, D. Lenstra, “Excitability and coherence resonance in lasers with saturable absorber,” Phys. Rev. E 60, 6580 (1999).
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J. L. A. Dubbeldam, B. Krauskopf, “Self-pulsations of lasers with saturable absorber: dynamics and bifurcations,” Opt. Commun. 159, 325–338 (1999).
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T. Heil, I. Fischer, W. Elsäßer, B. Krauskopf, K. Green, A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

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

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

C. Otto, B. Globisch, K. Lüdge, E. Schöll, T. Erneux, “Complex dynamics of semiconductor quantum dot lasers subject to delayed optical feedback,” Int. J. Bif. Chaos 22, 1250246 (2012).
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T. Erneux, E. A. Viktorov, P. Mandel, “Time scales and relaxation dynamics in quantum-dot lasers,” Phys. Rev. A 76, 023819 (2007).
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B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66, 046216 (2002).
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T. Erneux, P. Glorieux, Laser Dynamics (Cambridge University Press, UK, 2010).
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C. Otto, K. Lüdge, E. A. Viktorov, T. Erneux, “Quantum dot laser tolerance to optical feedback,” in “Nonlinear Laser Dynamics - From Quantum Dots to Cryptography,”, K. Lüdge, ed. (WILEY-VCH, Weinheim, 2012), Chap. 6, pp. 141–162.

Feoktistov, A.

A. Zakharova, A. Feoktistov, T. Vadivasova, E. Schöll, “Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation,” Eur. Phys. J. Spec. Top. 222, 2481–2495 (2013).
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Figueiredo, J. M. L.

Fischer, I.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
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V. Flunkert, O. D’Huys, J. Danckaert, I. Fischer, E. Schöll, “Bubbling in delay-coupled lasers,” Phys. Rev. E 79, 065201 (R) (2009).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, B. Krauskopf, K. Green, A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

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

Fischer, M.

Flunkert, V.

V. Flunkert, O. D’Huys, J. Danckaert, I. Fischer, E. Schöll, “Bubbling in delay-coupled lasers,” Phys. Rev. E 79, 065201 (R) (2009).
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Friberg, A. T.

Gammaitoni, L.

L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
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García-Ojalvo, J.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
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C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, Berlin, 2002).

Gartner, P.

T. R. Nielsen, P. Gartner, F. Jahnke, “Many-body theory of carrier capture and relaxation in semiconductor quantum-dot lasers,” Phys. Rev. B 69, 235314 (2004).
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Gavrielides, A.

T. Heil, I. Fischer, W. Elsäßer, B. Krauskopf, K. Green, A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

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

Gerschütz, F.

Giacomelli, G.

G. Giacomelli, M. Giudici, S. Balle, J. R. Tredicce, “Experimental evidence of coherence resonance in an optical system,” Phys. Rev. Lett. 84, 3298 (2000).
[CrossRef] [PubMed]

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 (1997).
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Gioannini, M.

M. Gioannini, I. Montrosset, “Numerical analysis of the frequency chirp in quantum-dot semiconductor lasers,” IEEE J. Quantum Electron. 43, 941–949 (2007).
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Giudici, M.

G. Giacomelli, M. Giudici, S. Balle, J. R. Tredicce, “Experimental evidence of coherence resonance in an optical system,” Phys. Rev. Lett. 84, 3298 (2000).
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M. Giudici, C. Green, G. Giacomelli, U. Nespolo, J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 (1997).
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Glitzky, A.

M. Radziunas, A. Glitzky, U. Bandelow, M. Wolfrum, U. Troppenz, J. Kreissl, W. Rehbein, “Improving the Modulation Bandwidth in Semiconductor Lasers by Passive Feedback,” IEEE J. Sel. Top. Quantum Electron. 13, 136–142 (2007).
[CrossRef]

Globisch, B.

C. Otto, B. Globisch, K. Lüdge, E. Schöll, T. Erneux, “Complex dynamics of semiconductor quantum dot lasers subject to delayed optical feedback,” Int. J. Bif. Chaos 22, 1250246 (2012).
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B. Globisch, C. Otto, E. Schöll, K. Lüdge, “Influence of carrier lifetimes on the dynamical behavior of quantum-dot lasers subject to optical feedback,” Phys. Rev. E 86, 046201 (2012).
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T. Erneux, P. Glorieux, Laser Dynamics (Cambridge University Press, UK, 2010).
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N. Majer, S. Dommers-Völkel, J. Gomis-Bresco, U. Woggon, K. Lüdge, E. Schöll, “Impact of carrier-carrier scattering and carrier heating on pulse train dynamics of quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett. 99, 131102 (2011).
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B. Kelleher, D. Goulding, S. P. Hegarty, G. Huyet, D. Y. Cong, A. Martinez, A. Lemaitre, A. Ramdane, M. Fischer, F. Gerschütz, J. Koeth, “Excitable phase slips in an injection-locked single-mode quantum-dot laser,” Opt. Lett. 34, 440–442 (2009).
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D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, G. Huyet, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. 98, 153903 (2007).
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C. Grebogi, E. Ott, J. A. Yorke, “Crises, sudden changes in chaotic attractors, and transient chaos,” Physica D 7, 181–200 (1983).
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M. Giudici, C. Green, G. Giacomelli, U. Nespolo, J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 (1997).
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K. Green, “Stability near threshold in a semiconductor laser subject to optical feedback: A bifurcation analysis of the Lang-Kobayashi equations,” Phys. Rev. E 79, 036210 (2009).
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T. Heil, I. Fischer, W. Elsäßer, B. Krauskopf, K. Green, A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
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Greene, G.

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

Grundmann, M.

D. Bimberg, M. Grundmann, N. N. Ledentsov, Quantum Dot Heterostructures (John Wiley & Sons Ltd., New York, 1999).

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

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G. Hu, T. Ditzinger, C. Z. Ning, H. Haken, “Stochastic resonance without external periodic force,” Phys. Rev. Lett. 71, 807 (1993).
[CrossRef]

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A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
[CrossRef] [PubMed]

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L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

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

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B. Kelleher, S. P. Hegarty, G. Huyet, “Modified relaxation oscillation parameters in optically injected semiconductor lasers,” J. Opt. Soc. Am. B 29, 2249–2254 (2012).
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B. Kelleher, C. Bonatto, G. Huyet, S. P. Hegarty, “Excitability in optically injected semiconductor lasers: Contrasting quantum-well- and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
[CrossRef]

B. Kelleher, D. Goulding, S. P. Hegarty, G. Huyet, D. Y. Cong, A. Martinez, A. Lemaitre, A. Ramdane, M. Fischer, F. Gerschütz, J. Koeth, “Excitable phase slips in an injection-locked single-mode quantum-dot laser,” Opt. Lett. 34, 440–442 (2009).
[CrossRef] [PubMed]

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

G. Huyet, D. O’Brien, S. P. Hegarty, J. G. McInerney, A. V. Uskov, D. Bimberg, C. Ribbat, V. M. Ustinov, A. E. Zhukov, S. S. Mikhrin, A. R. Kovsh, J. K. White, K. Hinzer, A. J. SpringThorpe, “Quantum dot semiconductor lasers with optical feedback,” phys. stat. sol. (b) 201, 345–352 (2004).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, W. Elsäßer, B. Krauskopf, K. Green, A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

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

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O. Ushakov, N. Korneyev, M. Radziunas, H. J. Wünsche, F. Henneberger, “Excitability of chaotic transients in a semiconductor laser,” Europhys. Lett. 79, 30004 (2007).
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H. J. Wünsche, O. Brox, M. Radziunas, F. Henneberger, “Excitability of a semiconductor laser by a two-mode homoclinic bifurcation,” Phys. Rev. Lett. 88, 023901 (2001).
[CrossRef]

Hinzer, K.

G. Huyet, D. O’Brien, S. P. Hegarty, J. G. McInerney, A. V. Uskov, D. Bimberg, C. Ribbat, V. M. Ustinov, A. E. Zhukov, S. S. Mikhrin, A. R. Kovsh, J. K. White, K. Hinzer, A. J. SpringThorpe, “Quantum dot semiconductor lasers with optical feedback,” phys. stat. sol. (b) 201, 345–352 (2004).
[CrossRef]

Hizanidis, J.

J. Hizanidis, A. G. Balanov, A. Amann, E. Schöll, “Noise-induced front motion: signature of a global bifurcation,” Phys. Rev. Lett. 96, 244104 (2006).
[CrossRef] [PubMed]

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A. L. Hodgkin, “The local electric changes associated with repetitive action in a medullated axon,” J. Physiol. 107, 165 (1948).
[PubMed]

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G. Hu, T. Ditzinger, C. Z. Ning, H. Haken, “Stochastic resonance without external periodic force,” Phys. Rev. Lett. 71, 807 (1993).
[CrossRef]

Huang, Z.

F. Pedaci, Z. Huang, P. van Hese, S. Barland, L. Deuker, “Excitable particles in an optical torque wrench,” Nat. Phys. 7, 259–264 (2011).
[CrossRef]

Huyet, G.

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[CrossRef]

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Figures (5)

Figure 1
Figure 1

(a): Sketch of the laser under delayed optical feedback. (b): Sketch of band structure.

Figure 2
Figure 2

Deterministic dynamics: (a): Bifurcation diagram of local maxima of photon number Nph vs. feedback strength K for pump current J = 2Jth (brown dots), where Jth ist the threshold current. Thick blue and green lines denote the steady state photon numbers N ph s of the stable parts of the first and the second ECM, respectively, and the black dashed line denotes N ph s of the unstable antimode. Insets show time traces of Nph for fixed K. (b): Frequency deviations δωs of the ECMs vs. K. Solid and dashed lines denote stable and unstable solutions, respectively. Hopf and limit points are denoted by red dots and open black circles, respectively. Blue, red, and black (gray) arrows indicate the feedback strengths of the Hopf points (KH), the homoclinic bifurcation (Khom), and the boundary crisis (Kcris), respectively. (c): Same as (a) but for higher J = 3Jth (black dots) and J = 4Jth (gray dots). Parameters as in Table 1.

Figure 3
Figure 3

Subthreshold (green lines) and super-threshold (blue lines) excitations of deterministic system in the bistable regime. (a) and (b): Close to a homoclinic bifurcation for K = 0.229 and J = 2Jth. (c) and (d): Close to a boundary crisis of chaotic attractor for K = 0.23 and J = 3Jth. Blue and green triangles in the closeups mark the starting points of the perturbed trajectories for super- and subthreshold perturbations, respectively. Black lines denote the steady state photon number of the unstable anti-mode of the 2nd ECM-pair. (a) and (c): Time series of the perturbed trajectories. (b) and (d): Projections of the trajectories onto the (Nph, We)-plane. Green dots indicate the position of the stable 2nd ECM-mode. Parameters as in Table 1.

Figure 4
Figure 4

Stochastic dynamics: (a)(c): Time series for J = 2Jth and K = 0.2292 for different β indicated by gray dashed lines in (d). βopt denotes the noise strength at the maximum of the coherence time. Central panel (d): Normalized standard deviation of inter-spike interval RT (blue dots) for J = 2Jth and coherence time tcor (normalized to its maximum value t cor max) versus noise strength β for J = 2Jth (red triangles), J = 3Jth (black stars), and J = 4Jth (gray hexagons). In physical units the maximal coherence times are τ ph t cor max ( J = 2 J th ) = 2.50 ns, τ ph t cor max ( J = 3 J th ) = 2.39 ns, and τ ph t cor max ( J = 4 J th ) = 1.93 ns. The feedback strength is K = 0.22921 for J = 2Jth, K = 0.23325 for J = 3Jth, and K = 0.24515 for J = 4Jth, respectively. (e)(g): Time series for J = 3Jth and K = 0.233325 for different β indicated by gray dashed lines in (d). Parameters as in Table 1.

Figure 5
Figure 5

Dependence of (a): the feedback strength Kcris, at which the boundary crisis, occurs (red triangles), (b): the photon number of the threshold Δ N ph thr (normalized to the photon number without feedback N ph 0) (green hexagones), and (c): the optimal noise strength βopt (blue circles) on pump current J (normalized to its threshold value Jth). The dashed lines are best fits. Parameters as in Table 1.

Tables (2)

Tables Icon

Table 1 Parameter values used in the numerical simulations.

Tables Icon

Table 2 Physical parameters used in the simulation of the QD laser model unless stated otherwise.

Equations (31)

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( t ) = 1 + i α 2 [ g ( ρ e + ρ h 1 ) 1 ] ( t ) + k e i C ( t τ ) + β r sp ρ e ρ h ξ ( t ) ,
ρ e = γ [ F e r w ( ρ e + ρ h 1 ) | | 2 ρ e ρ h ] ,
ρ h = γ [ F h r w ( ρ e + ρ h 1 ) | | 2 ρ e ρ h ] ,
W e = γ [ J F e c W e W h ] ,
W h = γ [ J F h c W e W h ] .
ξ ( t ) = ξ a ( t ) + i ξ b ( t ) , ξ i ( t ) = 0 , ξ a ( t ) ξ b ( t ˜ ) = δ a , b δ ( t t ˜ ) , for ξ i ( t ) , i { a , b } .
W h = ρ e + W e ρ h .
( , ρ e / h , W e / h ) = ( N ph s e i δ ω s t , ρ e / h s , W e / h s ) ,
ρ inv s = k cos ( δ ω s τ + C ) ,
δ ω s = α ρ inv s k sin ( δ ω s τ + C ) ,
0 = γ [ F e s r w ( ρ e s + ρ h s 1 ) N ph s ρ e s ρ h s ] ,
0 = γ [ F h s r w ( ρ e s + ρ h s 1 ) N ph s ρ e s ρ h s ] ,
0 = J F e s c W e s W h s ,
0 = J F h s c W e s W h s ,
ρ inv 1 2 [ g ( ρ e + ρ h 1 ) 1 ]
δ ω s = k eff sin ( δ ω s τ + C + arctan ( α ) ) ,
ρ e s = 1 2 [ 1 + g 2 k cos ( δ ω s + C ) g + W h s W e s ] ,
ρ h s = 1 2 [ 1 + g 2 k cos ( δ ω s + C ) g + W e s W h s ] .
N ph s = g r w ( 1 2 k cos ( δ ω s + C ) ) [ J ρ e s ρ h s c W e s W h s ] = g r w ( 1 2 k cos ( δ ω s + C ) ) [ J J th ] ,
t cor 0 + | Ψ y ( s ) | d s ,
R T T ISI 2 T ISI 2 T ISI ,
ρ n ( t ) ρ inv 2 ( t ) ρ inv , n , with ρ inv , n t n , b t n , e ρ inv 2 ( t ˜ ) d t ˜ ,
t n t n , b t n , e ρ n ( t ˜ ) t ˜ d t ˜ .
d d t = 1 + i α 2 [ 2 W ¯ Z a QD ( ρ e + ρ h 1 ) τ p h 1 ] + K τ in e i C ( t t ec ) + β Z a QD W ρ e ρ h ξ ,
d ρ e d t = S e in ( 1 ρ e ) S e out ρ e W ¯ ( ρ e + ρ h 1 ) N ph W ρ e ρ h ,
d ρ h d t = S h in ( 1 ρ h ) S h out ρ h W ¯ ( ρ e + ρ h 1 ) N ph W ρ e ρ h ,
d w e d t = j e 0 2 N QD [ S e in ( 1 ρ e ) S e out ρ e ] B S w e w h ,
d w h d t = j e 0 2 N QD [ S h in ( 1 ρ h ) S h out ρ h ] B S w e w h .
ξ ( t ) = ξ a ( t ) + i ξ b ( t ) , ξ i ( t ) = 0 , ξ a ( t ) ξ b ( t ˜ ) = δ a , b δ ( t t ˜ ) , for ξ i ( t ) , i { a , b } .
S e / h out ( w e , w h ) = S e / h in ( w e , w h ) e Δ E e / h k bo 𝒯 [ w e / h e D e / h k bo 𝒯 1 ] 1 .
g 2 a L W ¯ A N a QD τ ph , k = K τ ph τ in , τ = τ ec τ ph , r sp W Z a QD τ ph , γ τ ph W , r w W ¯ W , J j 2 N QD e 0 W , c B S 2 N QD W , and s e / h in / out 1 W S e / h in / out .

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