Dynamics of a semiconductor laser array with delayed global coupling - art. no. 016613

We study the dynamics of an array of single mode semiconductor lasers globa lly but weakly coupled by a common external feedback mirror and by-nearest neighbor interactions. We seek to determine the conditions under which all lasers of the array are in phase, whether in a steady, periodic, quasiperio dic, or chaotic regime, in order to maximize the output far field intensity . We show that the delay may be a useful control parameter to achieve in-ph ase synchronization. For the in-phase steady state, there is a competition between a delay-induced Hopf bifurcation leading to an in-phase periodic re gime and a delay-independent Hopf bifurcation leading to an antiphased peri odic regime. Both regimes are described analytically and secondary Hopf bif urcations to quasiperiodic solutions are found. Close to the stable steady state, the array is described by a set of Kuramoto equations for the phases of the fields. Above the first Hopf bifurcation, these equations are gener alized by the addition of second and third order time derivatives of the ph ases.