Measuring algorithmic complexity in chaotic lasers

TL;DR

This paper demonstrates how algorithmic complexity can effectively characterize chaotic laser dynamics, including extreme events, and serve as a practical tool for chaos control and predictability assessment.

Contribution

It introduces the use of Kolmogorov complexity to analyze chaotic laser signals, providing a simple, robust method applicable to noisy, short data sequences, and offers insights into chaos control.

Findings

Complexity characterizes chaotic laser regimes effectively.

Provides a correction to Lyapunov-based predictability horizons.

Applicable to different laser types and regimes, including rogue waves.

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.