Predictability of extreme intensity pulses in optically injected semiconductor lasers

Abstract The predictability of extreme intensity pulses emitted by an optically injected semiconductor laser is studied numerically, by using a well-known rate equation model. We show that symbolic ordinal time-series analysis allows to identify the patterns of intensity oscillations that are likely to occur before an extreme pulse. The method also gives information about patterns which are unlikely to occur before an extreme pulse. The specific patterns identified capture the topology of the underlying chaotic attractor and depend on the model parameters. The methodology proposed here can be useful for analyzing data recorded from other complex systems that generate extreme fluctuations in their output signals.

[1]  Mohammad-Reza Alam Predictability horizon of oceanic rogue waves , 2014, 1407.0152.

[2]  K. Lehnertz,et al.  Route to extreme events in excitable systems. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  C. Field Managing the risks of extreme events and disasters to advance climate change adaption , 2012 .

[4]  Massimiliano Zanin,et al.  Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review , 2012, Entropy.

[5]  S. Sugavanam,et al.  The laminar–turbulent transition in a fibre laser , 2013, Nature Photonics.

[6]  T. Geisel,et al.  Random focusing of tsunami waves , 2015, Nature Physics.

[7]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[8]  T. Stocker,et al.  Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation. A Special Report of Working Groups I and II of IPCC Intergovernmental Panel on Climate Change , 2012 .

[9]  H. Kantz,et al.  Extreme Events in Nature and Society , 2006 .

[10]  Daan Lenstra,et al.  The dynamical complexity of optically injected semiconductor lasers , 2005 .

[11]  Umberto Bortolozzo,et al.  Rogue waves and their generating mechanisms in different physical contexts , 2013 .

[12]  F T Arecchi,et al.  Mixed-mode oscillations via canard explosions in light-emitting diodes with optoelectronic feedback. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  R. Pachauri Managing the Risks of Extreme Events and Disasters , 2012 .

[14]  Jörn Davidsen,et al.  Earthquake interevent time distribution for induced micro-, nano-, and picoseismicity. , 2013, Physical review letters.

[15]  PAUL EMBRECHTS,et al.  Modelling of extremal events in insurance and finance , 1994, Math. Methods Oper. Res..

[16]  A. Deluca,et al.  Data-driven prediction of thresholded time series of rainfall and self-organized criticality models. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Didier Sornette,et al.  Predictability and suppression of extreme events in a chaotic system. , 2013, Physical review letters.

[18]  Cristina Masoller,et al.  Deterministic optical rogue waves. , 2011, Physical review letters.

[19]  Vassilios Kovanis,et al.  Labyrinth bifurcations in optically injected diode lasers , 2010 .

[20]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[21]  T. Geisel,et al.  Statistics of Extreme Waves in Random Media , 2013, 1311.4578.

[22]  O A Rosso,et al.  Distinguishing noise from chaos. , 2007, Physical review letters.

[23]  C. Masoller,et al.  Controlling the likelihood of rogue waves in an optically injected semiconductor laser via direct current modulation , 2014 .

[24]  Cristina Masoller,et al.  Rogue waves in optically injected lasers: Origin, predictability, and suppression , 2013 .

[25]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[26]  Didier Sornette,et al.  Predictability of catastrophic events: Material rupture, earthquakes, turbulence, financial crashes, and human birth , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Klaus Lehnertz,et al.  Extreme events in excitable systems and mechanisms of their generation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[29]  S. K. Turitsyn,et al.  Unveiling Temporal Correlations Characteristic of a Phase Transition in the Output Intensity of a Fiber Laser. , 2016, Physical review letters.

[30]  H. Kantz,et al.  Recurrence time analysis, long-term correlations, and extreme events. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Ricardo Sevilla-Escoboza,et al.  Rogue waves in a multistable system. , 2011, Physical review letters.

[32]  B. Jalali,et al.  Optical rogue waves , 2007, Nature.

[33]  J. Tredicce,et al.  Extreme events in chaotic lasers with modulated parameter. , 2014, Optics express.

[34]  Rudi Podgornik S. Albeverio, V. Jentsch, H. Kantz (eds.): Extreme events in nature and society. (The Frontiers Collection) , 2007 .

[35]  G. Steinmeyer,et al.  Predictability of rogue events. , 2015, Physical review letters.