Mapping the dynamic complexity and synchronization in unidirectionally coupled external-cavity semiconductor lasers using permutation entropy

We present a systematic approach to identify the relation between the complexity of chaotic signals generated by an external-cavity semiconductor laser (ECSL) and the synchronization quality in unidirectionally coupled ECSLs. The complexity and synchronization quality are characterized by the permutation entropy and the cross-correlation coefficient, respectively. The numerical simulations show that the dynamic complexity is related to the synchronization performance, i.e., higher complexity results in lower correlation. More specifically, by focusing on numerical simulations of unidirectionally coupled ECSLs, we further present the two-dimensional maps of complexity and synchronization regions over a wide parameter space investigated, and then associate the variation of synchronization quality with the changes of the complexity degree.