Measuring algorithmic complexity in chaotic lasers

Abstract: Thanks to the simplicity and robustness of its calculation methods, algorithmic (or Kolmogorov) complexity appears as a useful tool to reveal chaotic dynamics when experimental time series are too short and noisy to apply Takens' reconstruction theorem. We measure the complexity in chaotic regimes, with and without extreme events (sometimes called optical rogue waves), of three different all-solid-state lasers: Kerr lens mode locking femtosecond Ti: Sapphire ("fast" saturable absorber), Nd:YVO4 + Cr:YAG ("slow" saturable absorber) and Nd:YVO4 with modulated losses. We discuss how complexity characterizes the dynamics in an understandable way in all cases, and how it provides a correction factor to the horizon of predictability given by Lyapunov exponents. This approach may be especially convenient to implement schemes of chaos control in real time.