Quantum-Dot Laser Dynamics

  • Benjamin LingnauEmail author
Part of the Springer Theses book series (Springer Theses)


The stability of semiconductor laser operation plays a crucial role in almost every possible application of these devices (Erneux, Glorieux, Laser dynamics, Cambridge University Press, UK, 2010) [1], (Lüdge, Nonlinear laser dynamics—from quantum dots to cryptography, Wiley, Weinheim, 2012) [2], (Chow, Jahnke, Prog Quantum Electron 37:109–184, 2013) [3], (Otto, Dynamics of quantum dot lasers—effects of optical feedback and external optical injection, Springer, Heidelberg, 2014) [4]. In most fields of operation, one would require a stable steady-state output with constant intensity that follows any change in external operating parameters instantaneously, thus enabling, e.g., arbitrarily fast switching of the laser output. In reality such requirements can naturally never be met.


  1. 1.
    T. Erneux, P. Glorieux, Laser Dynamics (Cambridge University Press, UK, 2010)CrossRefGoogle Scholar
  2. 2.
    K. Lüdge, Nonlinear Laser Dynamics—From Quantum Dots to Cryptography (Wiley, Weinheim, 2012)zbMATHGoogle Scholar
  3. 3.
    W.W. Chow, F. Jahnke, On the physics of semiconductor quantum dots for applications in lasers and quantum optics. Prog. Quantum Electron. 37, 109–184 (2013)ADSCrossRefGoogle Scholar
  4. 4.
    C. Otto, Dynamics of Quantum Dot Lasers—Effects of Optical Feedback and External Optical Injection, Springer Theses (Springer, Heidelberg, 2014)CrossRefGoogle Scholar
  5. 5.
    K. Lüdge, E. Schöll, Quantum-dot lasers—desynchronized nonlinear dynamics of electrons and holes. IEEE J. Quantum Electron. 45, 1396–1403 (2009)CrossRefGoogle Scholar
  6. 6.
    N. Majer, K. Lüdge, E. Schöll, Cascading enables ultrafast gain recovery dynamics of quantum dot semiconductor optical amplifiers. Phys. Rev. B 82, 235301 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    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)ADSCrossRefGoogle Scholar
  8. 8.
    B. Lingnau, W.W. Chow, K. Lüdge, Amplitude-phase coupling and chirp in quantum-dot lasers: influence of charge carrier scattering dynamics. Opt. Express 22, 4867–4879 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    F.T. Arecchi, G.L. Lippi, G.P. Puccioni, J.R. Tredicce, Deterministic chaos in laser with injected signal. Opt. Commun. 51, 308–315 (1984)ADSCrossRefGoogle Scholar
  10. 10.
    J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, Berlin, 2005)zbMATHGoogle Scholar
  11. 11.
    H. Zeghlache, P. Mandel, N.B. Abraham, C.O. Weiss, Phase and amplitude dynamics in the laser Lorenz model. Phys. Rev. A 38, 3128–3131 (1988)ADSCrossRefGoogle Scholar
  12. 12.
    C.O. Weiss, N.B. Abraham, U. Hübner, Homoclinic and heteroclinic chaos in a single-mode laser. Phys. Rev. Lett. 61, 1587–1590 (1988)ADSCrossRefGoogle Scholar
  13. 13.
    C.Z. Ning, H. Haken, Detuned lasers and the complex Lorenz equations: Subcritical and supercritical hopf bifurcations. Phys. Rev. A 41, 3826–3837 (1990)ADSCrossRefGoogle Scholar
  14. 14.
    L.A. Coldren, S.W. Corzine, M. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd edn., Wiley series in microwave and optical enginieering (Wiley, 2012)Google Scholar
  15. 15.
    E. Schöll, H.G. Schuster (eds.), Handbook of Chaos Control (Wiley, Weinheim, 2008). Second completely revised and enlarged editionzbMATHGoogle Scholar
  16. 16.
    J. Mørk, B. Tromborg, J. Mark, Chaos in semiconductor lasers with optical feedback-theory and experiment. IEEE J. Quantum Electron. 28, 93–108 (1992)ADSCrossRefGoogle Scholar
  17. 17.
    A.M. Levine, G.H.M. van Tartwijk, D. Lenstra, T. Erneux, Diode lasers with optical feedback: stability of the maximum gain mode. Phys. Rev. A 52, R3436–R3439 (1995)ADSCrossRefGoogle Scholar
  18. 18.
    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)Google Scholar
  19. 19.
    S.L. Chuang, Physics of Optoelectronic Devices (Wiley, New York, 1995)Google Scholar
  20. 20.
    K. Lüdge, E. Schöll, Nonlinear dynamics of doped semiconductor quantum dot lasers. Eur. Phys. J. D 58, 167–174 (2010)CrossRefGoogle Scholar
  21. 21.
    R. Heitz, H. Born, F. Guffarth, O. Stier, A. Schliwa, A. Hoffmann, D. Bimberg, Existence of a phonon bottleneck for excitons in quantum dots. Phys. Rev. B 64, 241305(R) (2001)ADSCrossRefGoogle Scholar
  22. 22.
    M. Kuntz, N.N. Ledentsov, D. Bimberg, A.R. Kovsh, V.M. Ustinov, A.E. Zhukov, Y.M. Shernyakov, Spectrotemporal response of 1.3 \(\upmu \)m quantum-dot lasers. Appl. Phys. Lett. 81, 3846–3848 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    M. Ishida, M. Sugawara, T. Yamamoto, N. Hatori, H. Ebe, Y. Nakata, Y. Arakawa, Theoretical study on high-speed modulation of Fabry-Pérot and distributed-feedback quantum-dot lasers: K-factor-limited bandwidth and 10 Gbit/s eye diagrams. J. Appl. Phys. 101, 013108 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    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)ADSCrossRefGoogle Scholar
  25. 25.
    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)ADSCrossRefGoogle Scholar
  26. 26.
    T.R. Nielsen, P. Gartner, M. Lorke, J. Seebeck, F. Jahnke, Coulomb scattering in nitride-based self-assembled quantum dot systems. Phys. Rev. B 72, 235311 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    A. Wilms, D. Breddermann, P. Mathe, Theory of direct capture from two- and three-dimensional reservoirs to quantum dot states. Phys. Stat. Sol. (c) 9, 1278 (2012)CrossRefGoogle Scholar
  28. 28.
    P. Borri, W. Langbein, J.M. Hvam, F. Heinrichsdorff, M.H. Mao, D. Bimberg, Ultrafast gain dynamics in InAs–InGaAs quantum-dot amplifiers. IEEE Photon. Technol. Lett. 12, 594–596 (2000)ADSCrossRefGoogle Scholar
  29. 29.
    S. Dommers, V.V. Temnov, U. Woggon, J. Gomis, J. Martinez-Pastor, M. Lämmlin, D. Bimberg, Complete ground state gain recovery after ultrashort double pulses in quantum dot based semiconductor optical amplifier. Appl. Phys. Lett. 90, 033508 (2007)ADSCrossRefGoogle Scholar
  30. 30.
    T. Piwonski, I. O’Driscoll, J. Houlihan, G. Huyet, R.J. Manning, A.V. Uskov, Carrier capture dynamics of InAs/GaAs quantum dots. Appl. Phys. Lett. 90, 122108 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    J. Gomis-Bresco, S. Dommers, V.V. Temnov, U. Woggon, M. Lämmlin, D. Bimberg, E. Malić, M. Richter, E. Schöll, A. Knorr, Impact of Coulomb scattering on the ultrafast gain recovery in InGaAs quantum dots. Phys. Rev. Lett. 101, 256803 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    Y. Kaptan, H. Schmeckebier, B. Herzog, D. Arsenijević, M. Kolarczik, V. Mikhelashvili, N. Owschimikow, G. Eisenstein, D. Bimberg, U. Woggon, Gain dynamics of quantum dot devices for dual-state operation. Appl. Phys. Lett. 104, 062604 (2014)CrossRefGoogle Scholar
  33. 33.
    K. Lüdge, E. Schöll, E.A. Viktorov, T. Erneux, Analytic approach to modulation properties of quantum dot lasers. J. Appl. Phys. 109, 103112 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    T. Erneux, E.A. Viktorov, P. Mandel, Time scales and relaxation dynamics in quantum-dot lasers. Phys. Rev. A 76, 023819 (2007)ADSCrossRefGoogle Scholar
  35. 35.
    B. Lingnau, K. Lüdge, Analytic characterization of the dynamic regimes of quantum-dot lasers. Photonics 2, 402–413 (2015)CrossRefGoogle Scholar
  36. 36.
    W.W. Chow, S.W. Koch, Semiconductor-Laser Fundamentals (Springer, Berlin, 1999)zbMATHCrossRefGoogle Scholar
  37. 37.
    A. Fiore, A. Markus, Differential gain and gain compression in quantum-dot lasers. IEEE J. Quantum Electron. 43, 287–294 (2007)Google Scholar
  38. 38.
    D. Bimberg, Quantum dot based nanophotonics and nanoelectronics. Electron. Lett. 44, 168 (2008)CrossRefGoogle Scholar
  39. 39.
    W.W. Chow, M. Lorke, F. Jahnke, Will quantum dots replace quantum wells as the active medium of choice in future semiconductor lasers? IEEE J. Sel. Top. Quantum Electron. 17, 1349–1355 (2011)CrossRefGoogle Scholar
  40. 40.
    D. Bimberg, N.N. Ledentsov, M. Grundmann, F. Heinrichsdorff, Edge und surface emitting quantum dot lasers. IEDM Tech. Dig. pp. 381–384 (1997)Google Scholar
  41. 41.
    M. Ishida, N. Hatori, T. Akiyama, K. Otsubo, Y. Nakata, H. Ebe, M. Sugawara, Y. Arakawa, Photon lifetime dependence of modulation efficiency and \(K\) factor im \(1.3\,\upmu \)m self-assembled \(InAs/GaAs\) quantum-dot lasers: Impact of capture time and maximum modal gain on modulation bandwidth. Appl. Phys. Lett. 85, 4145 (2004)ADSCrossRefGoogle Scholar
  42. 42.
    M. Sugawara, N. Hatori, M. Ishida, H. Ebe, Y. Arakawa, T. Akiyama, K. Otsubo, T. Yamamoto, Y. Nakata, Recent progress in self-assembled quantum-dot optical devices for optical telecommunication: temperature-insensitive 10 Gbs directly modulated lasers and 40 Gbs signal-regenerative amplifiers. J. Phys. D 38, 2126–2134 (2005)ADSCrossRefGoogle Scholar
  43. 43.
    M. Gioannini, M. Rossetti, Time-domain traveling wave model of quantum dot DFB lasers. IEEE J. Sel. Top. Quantum Electron. 17, 1318–1326 (2011)CrossRefGoogle Scholar
  44. 44.
    C. Wang, F. Grillot, J. Even, Impacts of wetting layer and excited state on the modulation response of quantum-dot lasers. IEEE J. Quantum Electron. 48, 1144–1150 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    L.V. Asryan, R.A. Suris, Upper limit for the modulation bandwidth of a quantum dot laser. Appl. Phys. Lett. 96, 221112 (2010)ADSCrossRefGoogle Scholar
  46. 46.
    C. Tong, D. Xu, S.F. Yoon, Carrier relaxation and modulation response of 1.3-\(\upmu \)m InAs-GaAs quantum dot lasers. J. Lightwave Technol. 27, 5442 (2009)ADSCrossRefGoogle Scholar
  47. 47.
    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)ADSCrossRefGoogle Scholar
  48. 48.
    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)Google Scholar
  49. 49.
    F. Grillot, N. Dubey, Influence of the linewidth enhancement factor on the modulation response of a nanostructure-based semiconductor laser operating under external optical feedback. Proc. SPIE 7933, 79330E (2011)ADSCrossRefGoogle Scholar
  50. 50.
    C.H. Henry, Theory of the linewidth of semiconductor lasers. IEEE J. Quantum Electron. 18, 259–264 (1982)ADSCrossRefGoogle Scholar
  51. 51.
    P.M. Smowton, E.J. Pearce, H.C. Schneider, W.W. Chow, M. Hopkinson, Filamentation and linewidth enhancement factor in InGaAs quantum dot lasers. Appl. Phys. Lett. 81, 3251–3253 (2002)ADSCrossRefGoogle Scholar
  52. 52.
    C. Ribbat, R.L. Sellin, I. Kaiander, F. Hopfer, N.N. Ledentsov, D. Bimberg, A.R. Kovsh, V.M. Ustinov, A.E. Zhukov, M.V. Maximov, Complete suppression of filamentation and superior beam quality in quantum-dot lasers. Appl. Phys. Lett. 82, 952–954 (2003)ADSCrossRefGoogle Scholar
  53. 53.
    S. Wieczorek, B. Krauskopf, T. Simpson, D. Lenstra, The dynamical complexity of optically injected semiconductor lasers. Phys. Rep. 416, 1–128 (2005)ADSCrossRefGoogle Scholar
  54. 54.
    B. Lingnau, K. Lüdge, W.W. Chow, E. Schöll, Failure of the \(\alpha \)-factor in describing dynamical instabilities and chaos in quantum-dot lasers. Phys. Rev. E 86, 065201(R) (2012)ADSCrossRefGoogle Scholar
  55. 55.
    I. Reidler, Y. Aviad, M. Rosenbluh, I. Kanter, Ultrahigh-speed random number generation based on a chaotic semiconductor laser. Phys. Rev. Lett. 103, 024102 (2009)ADSCrossRefGoogle Scholar
  56. 56.
    N. Oliver, M.C. Soriano, D.W. Sukow, I. Fischer, Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation. Opt. Lett. 36, 4632–4634 (2011)ADSCrossRefGoogle Scholar
  57. 57.
    T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, Theory of fast nondeterministic physical random-bit generation with chaotic lasers. Phys. Rev. E 85, 046215 (2012)ADSCrossRefGoogle Scholar
  58. 58.
    R.M. Nguimdo, G. Verschaffelt, J. Danckaert, X.J.M. Leijtens, J. Bolk, G. Van der Sande, Fast random bits generation based on a single chaotic semiconductor ring laser. Opt. Express 20, 28603–28613 (2012)ADSCrossRefGoogle Scholar
  59. 59.
    V.Z. Tronciu, C.R. Mirasso, P. Colet, Chaos-based communications using semiconductor lasers subject to feedback from an integrated double cavity. J. Phys. B: At. Mol. Opt. Phys. 41, 155401 (2008)ADSCrossRefGoogle Scholar
  60. 60.
    A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization (Wiley, 2012)Google Scholar
  61. 61.
    L. Larger, J.M. Dudley, Nonlinear dynamics: optoelectronic chaos. Nature 465, 41–42 (2010)ADSCrossRefGoogle Scholar
  62. 62.
    F. Böhm, A. Zakharova, E. Schöll, K. Lüdge, Amplitude-phase coupling drives chimera states in globally coupled laser networks. Phys. Rev. E 91, 040901 (R) (2015)MathSciNetCrossRefGoogle Scholar
  63. 63.
    N. Wiener, Generalized harmonic analysis. Acta Math. 55, 117–258 (1930)MathSciNetzbMATHCrossRefGoogle Scholar
  64. 64.
    P. Gartner, J. Seebeck, F. Jahnke, Relaxation properties of the quantum kinetics of carrier-LO-phonon interaction in quantum wells and quantum dots. Phys. Rev. B 73, 115307 (2006)ADSCrossRefGoogle Scholar
  65. 65.
    A.L. Schawlow, C.H. Townes, Infrared and optical masers. Phys. Rev. 112, 1940 (1958)ADSCrossRefGoogle Scholar
  66. 66.
    M.W. Fleming, A. Mooradian, Fundamental line broadening of single-mode GaAlAs diode lasers. Appl. Phys. Lett. 38, 511–513 (1981)ADSCrossRefGoogle Scholar
  67. 67.
    M. Lax, Classical noise. V. Noise in self-sustained oscillators. Phys. Rev. 160, 290 (1967)ADSCrossRefGoogle Scholar
  68. 68.
    Z. Toffano, A. Destrez, C. Birocheau, L. Hassine, New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold. Electron. Lett. 28, 9–11 (1992)CrossRefGoogle Scholar
  69. 69.
    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)ADSCrossRefGoogle Scholar
  70. 70.
    F. Grillot, B. Dagens, J.G. Provost, H. Su, L.F. Lester, Gain compression and above-threshold linewidth enhancement factor in 1.3\(\upmu \)m InAs/GaAs quantum-dot lasers. IEEE J. Quantum Electron. 44, 946–951 (2008)ADSCrossRefGoogle Scholar
  71. 71.
    K.C. Kim, I.K. Han, J.I. Lee, T.G. Kim, Gain-dependent linewidth enhancement factor in the quantum dot structures. Nanotechnology 21, 134010 (2010)ADSCrossRefGoogle Scholar
  72. 72.
    B. Kelleher, D. Goulding, G. Huyet, E.A. Viktorov, T. Erneux, S.P. Hegarty, Dimensional signature on noise-induced excitable statistics in an optically injected semiconductor laser. Phys. Rev. E 84, 026208 (2011)ADSCrossRefGoogle Scholar
  73. 73.
    M. Asada, Y. Miyamoto, Y. Suematsu, Gain and the threshold of three-dimensional quantum-box lasers. IEEE J. Quantum Electron. 22, 1915–1921 (1986)ADSCrossRefGoogle Scholar
  74. 74.
    D. Bimberg, N. Kirstaedter, N.N. Ledentsov, Z.I. Alferov, P.S. Kop’ev, V. Ustinov, InGaAs-GaAs quantum-dot lasers. IEEE J. Sel. Top. Quantum Electron. 3, 196–205 (1997)CrossRefGoogle Scholar
  75. 75.
    T.C. Newell, D.J. Bossert, A. Stintz, B. Fuchs, K.J. Malloy, L.F. Lester, Gain and linewidth enhancement factor in InAs quantum-dot laser diodes. IEEE Photonics Technol. Lett. 11, 1527–1529 (1999)ADSCrossRefGoogle Scholar
  76. 76.
    P.K. Kondratko, S.L. Chuang, G. Walter, T. Chung, N. Holonyak, Observations of near-zero linewidth enhancement factor in a quantum-well coupled quantum-dot laser. Appl. Phys. Lett. 83, 4818 (2004)ADSCrossRefGoogle Scholar
  77. 77.
    R.R. Alexander, D. Childs, H. Agarwal, K.M. Groom, H.Y. Liu, M. Hopkinson, R.A. Hogg, Zero and controllable linewidth enhancement factor in p-doped 1.3 \(\upmu \)m quantum dot lasers. Jpn. J. Appl. Phys. 46, 2421 (2007)ADSCrossRefGoogle Scholar
  78. 78.
    B. Dagens, A. Markus, J. Chen, J.G. Provost, D. Make, O. Le Gouezigou, J. Landreau, A. Fiore, B. Thedrez, Giant linewidth enhancement factor and purely frequency modulated emission from quantum dot laser. Electron. Lett. 41, 323–324 (2005)CrossRefGoogle Scholar
  79. 79.
    D.Y. Cong, A. Martinez, K. Merghem, G. Moreau, A. Lemaitre, J.G. Provost, O. Le Gouezigou, M. Fischer, I. Krestnikov, A.R. Kovsh, A. Ramdane, Optimisation of \(\alpha \)-factor for quantum dot InAs/GaAs fabry-perot lasers emitting at \(1.3 \upmu \)m. Electron. Lett. 43, 222–224 (2007)CrossRefGoogle Scholar
  80. 80.
    H. Su, L.F. Lester, Dynamic properties of quantum dot distributed feedback lasers: high speed, linewidth and chirp. J. Phys. D: Appl. Phys. 38, 2112–2118 (2005)ADSCrossRefGoogle Scholar
  81. 81.
    Z.J. Jiao, Z.G. Lu, J.R. Liu, P.J. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, X.P. Zhang, Linewidth enhancement factor of InAs/InP quantum dot lasers around \(1.5\upmu \)m. Opt. Commun. 285, 4372–4375 (2012)ADSCrossRefGoogle Scholar
  82. 82.
    S. Melnik, G. Huyet, A.V. Uskov, The linewidth enhancement factor \(\alpha \) of quantum dot semiconductor lasers. Opt. Express 14, 2950–2955 (2006)ADSCrossRefGoogle Scholar
  83. 83.
    M. Gioannini, I. Montrosset, Numerical analysis of the frequency chirp in quantum-dot semiconductor lasers. IEEE J. Quantum Electron. 43, 941–949 (2007)ADSCrossRefGoogle Scholar
  84. 84.
    B. Lingnau, K. Lüdge, W.W. Chow, E. Schöll, Many-body effects and self-contained phase dynamics in an optically injected quantum-dot laser, in Semiconductor Lasers and Laser Dynamics, vol. 8432, Proceedings of SPIE 53, ed. by V. Brussels, K. Panajotov, M. Sciamanna, A.A. Valle, R. Michalzik (2012), p. 84321J–1Google Scholar
  85. 85.
    G.P. Agrawal, C.M. Bowden, Concept of linewidth enhancement factor in semiconductor lasers: its usefulness and limitations. IEEE Photonics Technol. Lett. 5, 640–642 (1993)ADSCrossRefGoogle Scholar
  86. 86.
    R. Adler, A study of locking phenomena in oscillators. Proc. IEEE 61, 1380–1385 (1973)CrossRefGoogle Scholar
  87. 87.
    L.E. Erickson, A. Szabo, Spectral narrowing of dye laser output by injection of monochromatic radiation into the laser cavity. Appl. Phys. Lett. 18, 433 (1971)ADSCrossRefGoogle Scholar
  88. 88.
    Y. Liu, H.K. Liu, Y. Braiman, Injection locking of individual broad-area lasers in an integrated high-power diode array. Appl. Phys. Lett. 81, 978 (2002)ADSCrossRefGoogle Scholar
  89. 89.
    X. Jin, S.L. Chuang, Bandwidth enhancement of Fabry-Perot quantum-well lasers by injection-locking. Solid-State Electron. 50, 1141–1149 (2006)ADSCrossRefGoogle Scholar
  90. 90.
    N.B. Terry, N.A. Naderi, M. Pochet, A.J. Moscho, L.F. Lester, V. Kovanis, Bandwidth enhancement of injection-locked 1.3 \(\upmu \)m quantum-dot DFB laser. Electron. Lett. 44, 904–905 (2008)CrossRefGoogle Scholar
  91. 91.
    E.K. Lau, L.J. Wong, M.C. Wu, Enhanced modulation characteristics of optical injection-locked lasers: a tutorial. IEEE J. Sel. Top. Quantum Electron. 15, 618 (2009)CrossRefGoogle Scholar
  92. 92.
    E.K. Lau, X. Zhao, H.-K. Sung, D. Parekh, C.J. Chang-Hasnain, M.C. Wu, Strong optical injection-locked semiconductor lasers demonstrating >100-Ghz resonance frequencies and 80-Ghz intrinsic bandwidths. Opt. Express 16, 6609 (2008)ADSCrossRefGoogle Scholar
  93. 93.
    N.A. Naderi, M. Pochet, F. Grillot, N.B. Terry, V. Kovanis, L.F. Lester, Modeling the injection-locked behavior of a quantum dash semiconductor laser. IEEE J. Sel. Top. Quantum Electron. 15, 563 (2009)CrossRefGoogle Scholar
  94. 94.
    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)ADSCrossRefGoogle Scholar
  95. 95.
    J.R. Tredicce, F.T. Arecchi, G.L. Lippi, G.P. Puccioni, Instabilities in lasers with an injected signal. J. Opt. Soc. Am. B 2, 173–183 (1985)ADSCrossRefGoogle Scholar
  96. 96.
    T.B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, P.M. Alsing, Period-doubling route to chaos in a semiconductor laser subject to optical injection. Appl. Phys. Lett. 64, 3539–3541 (1994)ADSCrossRefGoogle Scholar
  97. 97.
    A. Gavrielides, V. Kovanis, P.M. Varangis, T. Erneux, G. Lythe, Coexisting periodic attractors in injection-locked diode lasers. Quantum Semiclass. Opt. 9, 785 (1997)ADSCrossRefGoogle Scholar
  98. 98.
    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)ADSCrossRefGoogle Scholar
  99. 99.
    S. Osborne, K. Buckley, A. Amann, S. O’Brien, All-optical memory based on the injection locking bistability of a two-color laser diode. Opt. Express 17, 6293–6300 (2009)ADSCrossRefGoogle Scholar
  100. 100.
    S. Osborne, P. Heinricht, N. Brandonisio, A. Amann, S. O’Brien, Wavelength switching dynamics of two-colour semiconductor lasers with optical injection and feedback. Semicond. Sci. Technol. 27, 094001 (2012)ADSCrossRefGoogle Scholar
  101. 101.
    A. Hurtado, I.D. Henning, M.J. Adams, L.F. Lester, Generation of tunable millimeter-wave and THz signals with an optically injected quantum dot distributed feedback laser. IEEE Photonics J. 5, 5900107 (2013)CrossRefGoogle Scholar
  102. 102.
    V.I. Arnold, Small denominators i, mappings of the circumference onto itself. Am. Math. Soc. Transl. 46, 213–284 (1965)zbMATHCrossRefGoogle Scholar
  103. 103.
    A. Murakami, K.A. Shore, Analogy between optically-driven injection-locked laser diodes and driven damped linear oscillators. Phys. Rev. A 73, 043804–043804–9 (2005)ADSCrossRefGoogle Scholar
  104. 104.
    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)ADSCrossRefGoogle Scholar
  105. 105.
    D. Ziemann, R. Aust, B. Lingnau, E. Schöll, K. Lüdge, Optical injection enables coherence resonance in quantum-dot lasers. Europhys. Lett. 103, 14002–p1–14002–p6 (2013)CrossRefGoogle Scholar
  106. 106.
    E.C. Mos, J.J.L. Hoppenbrouwers, M.T. Hill, M.W. Blum, J.J.H.B. Schleipen, H. de Waardt, Optical neuron by use of a laser diode with injection seeding and external optical feedback. IEEE Trans. Neural Netw. 11, 988–996 (2000)CrossRefGoogle Scholar
  107. 107.
    B. Krauskopf, W.A. van der Graaf, D. Lenstra, Bifurcations of relaxation oscillations in an optically injected diode laser. J. Opt. Soc. Am. B 9, 797 (1997)MathSciNetGoogle Scholar
  108. 108.
    M.G. Zimmermann, M.A. Natiello, H.G. Solari, Shilnikov-saddle-node interaction near a codimension 2 bifurcation: laser with injected signal. Phys. D 109, 293–314 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  109. 109.
    M. Nizette, T. Erneux, A. Gavrielides, V. Kovanis, Averaged equations for injection locked semiconductor lasers. Phys. D 161, 220 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  110. 110.
    J. Thévenin, M. Romanelli, M. Vallet, M. Brunel, T. Erneux, Resonance assisted synchronization of coupled oscillators: frequency locking without phase locking. Phys. Rev. Lett. 107, 104101 (2011)ADSCrossRefGoogle Scholar
  111. 111.
    B. Kelleher, D. Goulding, B. Baselga Pascual, S.P. Hegarty, G. Huyet, Bounded phase phenomena in the optically injected laser. Phys. Rev. E 85, 046212 (2012)ADSCrossRefGoogle Scholar
  112. 112.
    M. Romanelli, L. Wang, M. Brunel, M. Vallet, Measuring the universal synchronization properties of driven oscillators across a hopf instability. Opt. Express 22, 7364 (2014)ADSCrossRefGoogle Scholar
  113. 113.
    D. Bimberg, Semiconductor Nanostructures (Springer, Berlin, 2008)CrossRefGoogle Scholar
  114. 114.
    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)ADSCrossRefGoogle Scholar
  115. 115.
    B. Krauskopf, H.M. Osinga, J. Galán-Vioque, Numerical Continuation Methods for Dynamical Systems: Path Following and Boundary Value Problems (Springer, New York, 2007)zbMATHCrossRefGoogle Scholar
  116. 116.
    K. Lüdge, R. Aust, G. Fiol, M. Stubenrauch, D. Arsenijević, D. Bimberg, E. Schöll, Large signal response of semiconductor quantum-dot lasers. IEEE J. Quantum Electron. 46, 1755–1762 (2010)ADSCrossRefGoogle Scholar
  117. 117.
    M. Gioannini, Ground-state quenching in two-state lasing quantum dot lasers. J. Appl. Phys. 111, 043108 (2012)ADSCrossRefGoogle Scholar
  118. 118.
    E.J. Doedel, H.B. Keller, J.P. Kervenez, Numerical analysis and control of bifurcation problems. (I) Bifurcation in finite dimensions. Int. J. Bifurc. Chaos 1, 493–520 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  119. 119.
    E.J. Doedel, B.E. Oldeman, Auto-07P: Continuation and Bifurcation Software for Ordinary Differential Equations (Concordia University, Montreal, 2009)Google Scholar
  120. 120.
    P. Besnard, B. Meziane, G.M. Stephan, Feedback phenomena in a semiconductor laser induced by distant reflectors. IEEE J. Quantum Electron. 29, 1271–1284 (1993)ADSCrossRefGoogle Scholar
  121. 121.
    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)ADSCrossRefGoogle Scholar
  122. 122.
    D.M. Kane, K.A. Shore (eds.), Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (Wiley, Weinheim, 2005)Google Scholar
  123. 123.
    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)ADSCrossRefGoogle Scholar
  124. 124.
    B. Kim, N. Li, A. Locquet, D.S. Citrin, Experimental bifurcation-cascade diagram of an external-cavity semiconductor laser. Opt. Express 22, 2348 (2014)ADSCrossRefGoogle Scholar
  125. 125.
    Y. Cho, M. Umeda, Chaos in laser oscillations with delayed feedback; numerical analysis and observation using semiconductor laser. J. Opt. Soc. Am. B 1, 497–498 (1984)ADSGoogle Scholar
  126. 126.
    C.H. Henry, R.F. Kazarinov, Instability of semiconductor lasers due to optical feedback from distant reflectors. IEEE J. Quantum Electron. 22, 294–301 (1986)ADSCrossRefGoogle Scholar
  127. 127.
    N. Schunk, K. Petermann, Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback. IEEE J. Quantum Electron. 24, 1242–1247 (1988)ADSCrossRefGoogle Scholar
  128. 128.
    G.H.M. van Tartwijk, G.P. Agrawal, Laser instabilities: a modern perspective. Prog. Quantum Electron. 22, 43–122 (1998)ADSCrossRefGoogle Scholar
  129. 129.
    J. Ohtsubo, Feedback induced instability and chaos in semiconductor lasers and their applications. Opt. Rev. 6, 1–15 (1999)CrossRefGoogle Scholar
  130. 130.
    A. Ahlborn, U. Parlitz, Laser stabilization with multiple-delay feedback control. Opt. Lett. 31, 465–467 (2006)ADSCrossRefGoogle Scholar
  131. 131.
    S. Schikora, P. Hövel, H.J. Wünsche, E. Schöll, F. Henneberger, All-optical noninvasive control of unstable steady states in a semiconductor laser. Phys. Rev. Lett. 97, 213902 (2006)ADSCrossRefGoogle Scholar
  132. 132.
    T. Dahms, P. Hövel, E. Schöll, Stabilizing continuous-wave output in semiconductor lasers by time-delayed feedback. Phys. Rev. E 78, 056213 (2008)ADSCrossRefGoogle Scholar
  133. 133.
    E. Schöll, P. Hövel, V. Flunkert, M.A. Dahlem, Time-delayed feedback control: from simple models to lasers and neural systems, in Complex Time-Delay Systems: Theory and Applications, ed. by F.M. Atay (Springer, Berlin, 2010), pp. 85–150Google Scholar
  134. 134.
    B. Dahmani, L. Hollberg, R. Drullinger, Frequency stabilization of semiconductor lasers by resonant optical feedback. Opt. Lett. 12, 876 (1987)ADSCrossRefGoogle Scholar
  135. 135.
    P. Spano, S. Piazzolla, M. Tamburrini, Theory of noise in semiconductor-lasers in the presence of optical feedback. IEEE J. Quantum Electron. 20, 350–357 (1984)ADSCrossRefGoogle Scholar
  136. 136.
    V. Flunkert, E. Schöll, Suppressing noise-induced intensity pulsations in semiconductor lasers by means of time-delayed feedback. Phys. Rev. E 76, 066202 (2007)ADSCrossRefGoogle Scholar
  137. 137.
    K. Merghem, R. Rosales, S. Azouigui, A. Akrout, A. Martinez, F. Lelarge, G.H. Duan, G. Aubin, A. Ramdane, Low noise performance of passively mode locked quantum-dash-based lasers under external optical feedback. Appl. Phys. Lett. 95, 131111 (2009)ADSCrossRefGoogle Scholar
  138. 138.
    C.Y. Lin, F. Grillot, N.A. Naderi, Y. Li, L.F. Lester, rf linewidth reduction in a quantum dot passively mode-locked laser subject to external optical feedback. Appl. Phys. Lett. 96, 051118 (2010)ADSCrossRefGoogle Scholar
  139. 139.
    J.P. Goedgebuer, L. Larger, H. Porte, Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode. Phys. Rev. Lett. 80, 2249–2252 (1998)ADSCrossRefGoogle Scholar
  140. 140.
    H.D.I. Abarbanel, M.B. Kennel, L. Illing, S. Tang, H.F. Chen, J.M. Liu, Synchronization and communication using semiconductor lasers with optoelectronic feedback. IEEE J. Quantum Electron. 37, 1301–1311 (2001)ADSCrossRefGoogle Scholar
  141. 141.
    G. Fiol, M. Kleinert, D. Arsenijević, D. Bimberg, \(1.3 \mu m\) range 40 GHz quantum-dot mode-locked laser under external continuous wave light injection or optical feedback. Semicond. Sci. Technol. 26, 014006 (2011)ADSCrossRefGoogle Scholar
  142. 142.
    C. Otto, K. Lüdge, A.G. Vladimirov, M. Wolfrum, E. Schöll, Delay induced dynamics and jitter reduction of passively mode-locked semiconductor laser subject to optical feedback. New J. Phys. 14, 113033 (2012)ADSCrossRefGoogle Scholar
  143. 143.
    D. Arsenijević, M. Kleinert, D. Bimberg, Phase noise and jitter reduction by optical feedback on passively mode-locked quantum-dot lasers. Appl. Phys. Lett. 103, 231101 (2013)ADSCrossRefGoogle Scholar
  144. 144.
    C. Otto, L.C. Jaurigue, E. Schöll, K. Lüdge, Optimization of timing jitter reduction by optical feedback for a passively mode-locked laser. IEEE Photonics J. 6, 1501814 (2014)CrossRefGoogle Scholar
  145. 145.
    M.T. Hill, E.E. Frietman, H. de Waardt, G.-D. Khoe, H.J.S. Dorren, All fiber-optic neural network using coupled SOA based ring lasers. IEEE Trans. Neural Netw. 13, 1504–1513 (2002)CrossRefGoogle Scholar
  146. 146.
    Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, Optoelectronic reservoir computing. Sci. Rep. 2, 287 (2012)ADSCrossRefGoogle Scholar
  147. 147.
    F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, All-optical reservoir computing. Opt. Express 20, 22783–22795 (2012)ADSCrossRefGoogle Scholar
  148. 148.
    R.M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics. Opt. Express 22, 8672–8686 (2014)ADSCrossRefGoogle Scholar
  149. 149.
    N.N. Rozanov, Kinetics of a solid-state laser with an additional moving mirror. Sov. J. Quantum Electron. 4, 1191 (1975)ADSCrossRefGoogle Scholar
  150. 150.
    R. Lang, K. Kobayashi, External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron. 16, 347–355 (1980)ADSCrossRefGoogle Scholar
  151. 151.
    T. Erneux, Applied Delay Differential Equations (Springer, New York, 2009)zbMATHGoogle Scholar
  152. 152.
    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)ADSMathSciNetCrossRefGoogle Scholar
  153. 153.
    H. Erzgräber, D. Lenstra, B. Krauskopf, A.P.A. Fischer, G. Vemuri, Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory. Phys. Rev. E 76, 026212 (2007)ADSCrossRefGoogle Scholar
  154. 154.
    D. O’Brien, S.P. Hegarty, G. Huyet, A.V. Uskov, Sensitivity of quantum-dot semiconductor lasers to optical feedback. Opt. Lett. 29, 1072 (2004)ADSCrossRefGoogle Scholar
  155. 155.
    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)ADSzbMATHCrossRefGoogle Scholar
  156. 156.
    C. Otto, B. Globisch, K. Lüdge, E. Schöll, T. Erneux, Complex dynamics of semiconductor quantum dot lasers subject to delayed optical feedback. Int. J. Bifurc. Chaos 22, 1250246 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  157. 157.
    R. Lang, M.O. Scully, W.E. Lamb Jr, Why is the laser line so narrow? a theory of single-quasimode laser operation. Phys. Rev. A 7, 1788–1797 (1973)ADSCrossRefGoogle Scholar
  158. 158.
    S.A. Shakir, W.W. Chow, Semiclassical theory of coupled lasers. Phys. Rev. A 32, 983–991 (1985)ADSCrossRefGoogle Scholar
  159. 159.
    M.H. Rose, M. Lindberg, W.W. Chow, S.W. Koch, M. Sargent, Composite-cavity-mode approach to single-mode semiconductor-laser feedback instabilities. Phys. Rev. A 46, 603–611 (1992)ADSCrossRefGoogle Scholar
  160. 160.
    S. Tarucha, T. Honda, T. Saku, Reduction of quantized conductance at low temperatures observed in 2 to 10 \(\upmu \)m-long quantum wires. Solid State Commun. 94, 413 (1995)ADSCrossRefGoogle Scholar
  161. 161.
    D. Lenstra, Statistical-theory of the multistable external-feedback laser. Opt. Commun. 81, 209–214 (1991)ADSCrossRefGoogle Scholar
  162. 162.
    V. Flunkert, O. D’Huys, J. Danckaert, I. Fischer, E. Schöll, Bubbling in delay-coupled lasers. Phys. Rev. E 79, 065201 (R) (2009)ADSCrossRefGoogle Scholar
  163. 163.
    A. Hohl, A. Gavrielides, Bifurcation cascade in a semiconductor laser subject to optical feedback. Phys. Rev. Lett. 82, 1148–1151 (1999)ADSCrossRefGoogle Scholar
  164. 164.
    D. Pieroux, T. Erneux, B. Haegeman, K. Engelborghs, D. Roose, Bridges of periodic solutions and tori in semiconductor lasers subject to delay. Phys. Rev. Lett. 87, 193901 (2001)ADSCrossRefGoogle Scholar
  165. 165.
    C. Harder, K. Vahala, A. Yariv, Measurement of the linewidth enhancement factor alpha of semiconductor lasers. Appl. Phys. Lett. 42, 328–330 (1983)ADSCrossRefGoogle Scholar
  166. 166.
    S. Gerhard, C. Schilling, F. Gerschütz, M. Fischer, J. Koeth, I. Krestnikov, A.R. Kovsh, M. Kamp, S. Höfling, A. Forchel, Frequency-dependent linewidth enhancement factor of quantum-dot lasers. IEEE Photonics Technol. Lett. 20, 1736–1738 (2008)ADSCrossRefGoogle Scholar
  167. 167.
    A. Martinez, K. Merghem, L. Ferlazzo, C. Dupuis, A. Ramdane, J.G. Provost, B. Dagens, O. Le Gouezigou, O. Gauthier-Lafaye, Static and dynamic measurements of the \(\alpha \)-factor of five-quantum-dot-layer single-mode lasers emitting at 1.3\(\upmu \)m on GaAs. Appl. Phys. Lett. 86, 211115 (2005)ADSCrossRefGoogle Scholar
  168. 168.
    T. Fordell, A.M. Lindberg, Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser. IEEE J. Quantum Electron. 43, 6–15 (2007)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

Personalised recommendations