×

Bifurcation analysis of the Yamada model for a pulsing semiconductor laser with saturable absorber and delayed optical feedback. (English) Zbl 1366.34113

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
78A60 Lasers, masers, optical bistability, nonlinear optics
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] N. B. Abraham, L. A. Lugiato, and L. M. Narducci, Overview of instabilities in laser systems, J. Opt. Soc. Amer. B, 2 (1985), pp. 7–14.
[2] G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, Van Nostrand Reinhold, New York, 1993.
[3] S. Barbay, personnal communication, 2016.
[4] S. Barbay, R. Kuszelewicz, and A. M. Yacomotti, Excitability in a semiconductor laser with saturable absorber, Optics Lett., 36 (2011), pp. 4476–4478.
[5] E. J. Doedel, B. Krauskopf, and H. M. Osinga, Global invariant manifolds in the transition to preturbulence in the Lorenz system, Indag. Math., 22 (2011), pp. 111–240. · Zbl 1246.37037
[6] J. L. A. Dubbeldam and B. Krauskopf, Self-pulsations of lasers with saturable absorber: Dynamics and bifurcations, Optics Commun., 159 (1999), pp. 325–338.
[7] J. L. A. Dubbeldam, B. Krauskopf, and D. Lenstra, Excitability and coherence resonance in lasers with saturable absorber, Phys. Rev. E, 60 (1999), pp. 6580–6588.
[8] T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, Control of cavity solitons and dynamical states in a monolithic vertical cavity laser with saturable absorber, Eur. Phys. J. D, 59 (2010), pp. 91–96.
[9] K. Engelborghs, T. Luzyanina, and D. Roose, Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL, ACM Trans. Math. Software, 28 (2002), pp. 1–21. · Zbl 1070.65556
[10] K. Engelborghs, T. Luzyanina, and G. Samaey, DDE-BIFTOOL v. 2.00: A Matlab Package for Bifurcation Analysis of Delay Differential Equations, Tech. report, Department of Computer Science, KU Leuven, Leuven, Belgium, 2001.
[11] T. Erneux, Q-switching bifurcation in a laser with a saturable absorber, J. Opt. Soc. Amer. B, 5 (1988), pp. 1063–109.
[12] M. Georgiou and T. Erneux, Pulsating laser oscillations depend on extremely-small-amplitude noise, Phys. Rev. A, 45 (1992).
[13] M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, Andronov bifurcation and excitability in semiconductor lasers with optical feedback, Phys. Rev. E, 55 (1997).
[14] K. Green and B. Krauskopf, Global bifurcations and bistability at the locking boundaries of a semiconductor laser with phase-conjugate feedback, Phys. Rev. E, 66 (2002).
[15] E. M. Izhikevich, Which model to use for cortical spiking neurons?, IEEE Trans. Neural Networks, 15 (2004), pp. 1063–1070.
[16] E. M. Izhikevich, Dynamical Systems in Neuroscience, MIT Press, Cambridge, MA, 2007.
[17] L. Jaurigue, A. Pimenov, D. Rachinskii, E. Schöll, K. Lüdge, and A. G. Vladimirov, Timing jitter of passively-mode-locked semiconductor lasers subject to optical feedback: A semi-analytic approach, Phys. Rev. A, 92 (2015), 053807.
[18] L. Jaurigue, E. Schöll, and K. Lüdge, Passively mode-locked lasers subject to optical feedback: The role of amplitude-phase coupling, in proceedings of Numerical Simulation of Optoelectronic Devices, IEEE, 2014.
[19] C. K. R. T. Jones, Geometric singular perturbation theory, in Dynamical Systems, Lecture Notes in Math. 1609, Springer, New York, 1995, pp. 44–118. · Zbl 0840.58040
[20] D. M. Kane and K. A. Shore, eds., Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, Wiley, New York, 2005.
[21] A. Keane, B. Krauskopf, and C. Postlethwaite, Delayed feedback versus seasonal forcing: Resonance phenomena in an el nino southern oscillation model, SIAM J. Appl. Dyn. Syst., 14 (2015), pp. 1229–1257. · Zbl 1320.37038
[22] J. Kennedy, How indecomposable continua arise in dynamical systemsa, Ann. New York Acad. Sci., 704 (1993), pp. 180–201. · Zbl 0829.54023
[23] B. Krauskopf, G. R. Gray, and D. Lenstra, Semiconductor laser with phase-conjugate feedback: Dynamics and bifurcations, Phys. Rev. E, 58 (1998).
[24] B. Krauskopf and D. Lenstra, eds., Fundamental Issues of Nonlinear Laser Dynamics, American Institute of Physics, College Park, MD, 2000.
[25] B. Krauskopf, H. M. Osinga, E. J. Doedel, M. E. Henderson, J. Guckenheimer, A. Vladimirsky, M. Dellnitz, and O. Junge, A survey of methods for computing (un) stable manifolds of vector fields, Int. J. Bifur. Chaos, 15 (2005), pp. 763–791. · Zbl 1086.34002
[26] B. Krauskopf, H. M. Osinga, and J. Galan-Vioque, eds., Numerical Continuation Methods for Dynamical Systems, Springer, New York, 2007. · Zbl 1117.65005
[27] B. Krauskopf, K. Schneider, J. Sieber, S. Wieczorek, and M. Wolfrum, Excitability and self-pulsations near homoclinic bifurcations in semiconductor laser systems, Optics Commun., 215 (2003), pp. 367–379.
[28] B. Krauskopf, S. Terrien, N. G. R. Broderick, and S. Barbay, Quasiperiodic dynamics in a micropillar laser with saturable absorber and delayed optical feedback, in Proceedings of the Australian Conference on Optical Fibre Technology, Optical Society of America, 2016.
[29] B. Krauskopf and J. J. Walker, Bifurcation Study of a Semiconductor Laser with Saturable Absorber and Delayed Optical Feedback, Wiley, New York, 2012, pp. 161–181.
[30] Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Appl. Math. Sci. 112, Springer, New York, 2013.
[31] R. Lang and K. Kobayashi, External optical feedback effects on semiconductor injection laser properties, IEEE J. Quantum Electronics, 16 (1980), pp. 347–355.
[32] F. Lelievre, Etude de micropilier laser neuromimétique soumis à une rétroinjection avec délai (investigation of a neuromimetic micropillar laser with delayed feedback), Master’s thesis, Laboratoire de Photonique et Nanostructure, CNRS, Marcoussis, France, 2015.
[33] K. Lüdge, ed., Nonlinear Laser Dynamics: From Quantum Dots to Cryptography, Wiley, New York, 2012.
[34] M. Marconi, J. Javaloyes, S. Balle, and M. Giudici, How lasing localized structures evolve out of passive mode locking, Phys. Rev. Lett., 112 (2014), 223901.
[35] J. Mork, B. Tromborg, and J. Mark, Chaos in semiconductor lasers with optical feedback: Theory and experiment, IEEE J. Quantum Electronics, 28 (1992), pp. 93–108.
[36] T. W. Mossberg, Time-domain frequency-selective optical data storage, Optics Lett., 7 (1982), pp. 77–79.
[37] J. Ohtsubo and P. Davis, Chaotic optical communication, in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, D. M. Kane and K. A. Shore, eds., Wiley, New York, 2005.
[38] C. Otto, K. Lüdge, A. G. Vladimirov, M. Wolfrum, and E. Schöll, Delay-induced dynamics and jitter reduction of passively mode-locked semiconductor lasers subject to optical feedback, New J. Phys., 14 (2012).
[39] D. Pieroux and T. Erneux, Bridges of periodic solutions and tori in semiconductor lasers subject to delay, Phys. Rev. Lett., 87 (2001).
[40] D. Pieroux, T. Erneux, and K. Otsuka, Minimal model of a class-b laser with delayed feedback: Cascading branching of periodic solutions and period-doubling bifurcation, Phys. Rev. A, 50 (1994).
[41] K. Pyragas, Continuous control of chaos by self-controlling feedback, Phys. Lett. A, 170 (1992), pp. 421–428.
[42] E. U. Rafailov, M. A. Cataluna, and W. Sibbett, Mode-locked quantum-dot lasers, Nat. Photon., 1 (2007), pp. 395–401, .
[43] B. Romeira, R. Avó, J. M. L. Figueiredo, S. Barland, and J. Javaloyes, Regenerative memory in time-delayed neuromorphic photonic resonators, Sci. Rep., 6 (2016).
[44] D. Roose and R. Szalai, Continuation and bifurcation analysis of delay differential equations, in Numerical Continuation Methods for Dynamical Systems, Springer, New York, 2007, pp. 359–399. · Zbl 1132.34001
[45] F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, Relative refractory period in an excitable semiconductor laser, Phys. Rev. Lett., 112 (2014).
[46] F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, Temporal summation in a neuromimetic micropillar laser, Optics Lett., 40 (2015), pp. 5690–5693.
[47] L. F. Shampine and S. Thompson, Solving DDEs in MATLAB, Appl. Numer. Math., 37 (2001), pp. 441–458. · Zbl 0983.65079
[48] K. A. Shore, Non-linear dynamics and chaos in semiconductor laser devices, Solid-State electronics, 30 (1987), pp. 59–65.
[49] J. Sieber, K. Engelborghs, T. Luzyanina, G. Samaey, and D. Roose, DDE-BIFTOOL v. 3.1 Manual—Bifurcation Analysis of Delay Differential Equations, Tech. report, , 2015.
[50] J. M. S. Solorio, D. W. Sukow, D. R. Hicks, and A. Gavrielides, Bifurcations in a semiconductor laser subject to delayed incoherent feedback, Optics Commun., 214 (2002), pp. 327–334.
[51] J. R. Tredicce, Excitability in laser systems: The experimental side, AIP Conf. Proc., 548 (2000), pp. 238–259.
[52] G. H. M. van Tartwijk and M. San Miguel, Optical feedback on self-pulsating semiconductor lasers, IEEE J. Quantum Electronics, 32 (1996), pp. 1191–1202.
[53] A. G. Vladimirov and D. Turaev, Model for passive mode locking in semiconductor lasers, Phys. Rev. A, 72 (2005).
[54] A. G. Vladimirov, D. Turaev, and G. Kozyreff, Delay differential equations for mode-locked semiconductor lasers, Optics Lett., 29 (2004), pp. 1221–1223.
[55] C. E. Webb and J. D. C. Jones, Handbook of Laser Technology and Applications: Laser Design and Laser Systems, CRC Press, Boca Raton, FL, 2004.
[56] S. Wieczorek, B. Krauskopf, and D. Lenstra, A unifying view of bifurcations in a semiconductor laser subject to optical injection, Optics Commun., 172 (1999), pp. 279–295.
[57] H. G. Winful, Y. C. Chen, and J. M. Liu, Frequency locking, quasiperiodicity, and chaos in modulated self-pulsing semiconductor lasers, Appl. Phys. Lett., 48 (1986), pp. 616–618.
[58] M. Yamada, A theoretical analysis of self-sustained pulsation phenomena in narrow-stripe semiconductor lasers, IEEE J. Quantum Electronics, 29 (1993), pp. 1330–1336.
[59] S. Yanchuk and P. Perlikowski, Delay and periodicity, Phys. Rev. E, 79 (2009), 046221.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.