Forecasting Events in the Complex Dynamics of a Semiconductor Laser with Optical Feedback

Abstract

Complex systems performing spiking dynamics are widespread in Nature. They cover from earthquakes, to neurons, variable stars, social networks, or stock markets. Understanding and characterizing their dynamics is relevant in order to detect transitions, or to predict unwanted extreme events. Here we study, under an ordinal patterns analysis, the output intensity of a semiconductor laser with feedback in a regime where it develops a complex spiking behavior. We unveil that, in the transitions towards and from the spiking regime, the complex dynamics presents two competing behaviors that can be distinguished with a thresholding method. Then we use time and intensity correlations to forecast different types of events, and transitions in the dynamics of the system.

Correlations Preceding High-Intensity Events in the Chaotic Dynamics of a Raman Fiber Laser

“…Comparing these patterns probabilities with those of [ 23 ] where a similar analysis was performed, we find that the most probable OPs do not coincide; each system has different preferences.…”

“…This method has been used to characterize complex dynamics based on the patterns’ probabilities [ 25 , 26 , 27 , 28 ], to distinguish between stochasticity and determinism [ 29 ], or to identify transitions in the dynamics of complex networks [ 30 ]. In a recent paper [ 23 ], the method was used to classify events into two types and to forecast when the system decides to change from one type of event to the other one.…”

“…They analyzed intensity correlations and found that some preferred patterns took place before the system triggered one extreme event. In [ 23 ], the authors analyzed the experimental times series of a low-power diode laser submitted to optical feedback in the low-frequency fluctuations regime, close to the lasing threshold of the laser (below 1 mW). They analyzed the temporal correlations of the events and also found some preferred patterns happening before a change from low- to high-intensity events and from high- to the low-intensity events.…”

Forecasting Events in the Chaotic Dynamics of a Fiber Laser

“…This method has been used to characterize complex dynamics based on the patterns probabilities [9,12,18,19], to distinguish between stochasticity and determinism [20], or to identify transitions in the dynamics of complex networks [21]. In a recent paper [22] the method was used to classify events into two types, and to forecast when the system decides to change from one type of events to the other one.…”

Exploiting the Nonlinear Dynamics of Optically Injected Semiconductor Lasers for Optical Sensing

“…In addition, in contrast to what can be achieved in other fields, optics laser systems allow to record long datasets containing large numbers of extreme events. Such optical "big data" has also been used for testing data analysis tools for extreme event prediction [9][10][11].…”