Characterizing temporal correlations in the output of a semiconductor laser with optical feedback

We perform an experimental study of the dynamics of a semiconductor laser with optical feedback. We use two event-based methods to characterize the time series of the emitted intensity, one based on events that are defined by threshold-crossings (we refer to this method as spikes analysis), and the other one on events that are defined by intensity minima that are below a threshold (we refer to this method as peak analysis). By applying ordinal analysis to sequences of time intervals between consecutive events, we identify temporal correlations in the timing of the events that vary with the method used to define the events, as well as with the experimental control parameters, the laser pump current and feedback strength. The events defined by spike analysis are usually slower than those defined by peak analysis (their frequencies depend on the experimental conditions and are typically $\approx 10$ MHz and $\approx 1$ GHz respectively). We show that the two methods used to define events in the intensity time series provide a complementary characterization of the dynamics. We also find, with the two methods and in broad parameter regions, that the ordinal probabilities are organized in clusters formed by pairs of probabilities with similar values. We propose three diagnostic tools to analyze the clustering of the ordinal probabilities.