Periodic and quasiperiodic regimes in self-coupled lasers

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Abstract
We explore the bifurcation diagrams of self-coupled unidirectional single-mode ring lasers. We focus our attention on nearly identical lasers with an intermediate coupling and in the limit where the atomic polarizations can be adiabatically eliminated. We determine analytically the domains of a stable steady state, bounded by Hopf bifurcations. We study the stability of the emerging branch of periodic solutions and in one case determine the presence of a secondary Hopf bifurcation leading to quasiperiodic solutions. These results are complemented by a set of numerically determined bifurcation diagrams that display the behavior of the solutions far from the bifurcation points.