Global investigation of the influence of the phase of subharmonic excitation of a driven system

Adding a small subharmonic perturbation to the driving signal of a modulated laser allows one to control its dynamics. The influence of the phase of such a perturbation has been investigated both experimentally and by numerical simulations on a model of a fiber laser subjected to pump modulation. Depending on the operating conditions, the laser destabilizes through a period-doubling cascade or via quasiperiodicity. Suitably phased subharmonic perturbations can stabilize periodic orbits, shift the whole bifurcation diagram, and induce new crises. Experimental observations are in excellent agreement with the predictions from a simple model of the fiber laser.