Quantifying the synchronization of the spikes emitted by coupled lasers

Synchronization phenomena is ubiquitous in nature, and in spite of having been studied for decades, it still attracts a lot of attention as is still challenging to detect and quantify, directly from the analysis of noisy signals. Semiconductor lasers are ideal for performing experiments because they are stochastic, nonlinear, and inexpensive and display different synchronization regimes that can be controlled by tuning the lasers' parameters. Here, we analyze experiments done with two mutually optically coupled lasers. Due to the delay in the coupling (due to the finite time the light takes to travel between the lasers), the lasers synchronize with a lag: the intensity time traces show well-defined spikes, and a spike in the intensity of one laser may occur shortly before (or shortly after) a spike in the intensity of the other laser. Measures that quantify the degree of synchronization of the lasers from the analysis of the intensity signals do not fully quantify the synchronicity of the spikes because they also take into account the synchronization of fast irregular fluctuations that occur between spikes. By analyzing only the coincidence of the spike times, we show that event synchronization measures quantify spike synchronization remarkably well. We show that these measures allow us to quantify the degree of synchronization and, also, to identify the leading laser and the lagging one.