We numerically study the synchronization of two unidirectionally coupled single-mode semiconductor lasers in a master-slave configuration. The master laser is an external-cavity laser that operates in a chaotic regime while for the slave laser we consider two configurations. In the first one, the slave laser is also an external-cavity laser, subjected to, its own optical feedback and the optical injection from the master laser. In the second one, the slave laser is subject only to the optical injection from the master laser. Depending on the operating conditions the synchronization between the two lasers, whenever it exists, can be either isochronous or anticipated. We perform a detailed study of the parameter regions in which these synchronization regimes occur and how small variations of parameter yield one or the other type of synchronization or an unsynchronized regime.

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