Feedback control of mode-locked lasers with a tendency to Q-switch

Control of lasers has a long history and, during the last decade, numerous works have been performed with the aim of testing various schemes of control of unstable states (periodic or stationary). Recently, there has been a renew of interest in techniques allowing control of steady states. As a main reason, a set of lasers with commercial applications (lasers mode-locked with semiconductor saturable absorbers) have a strong tendency to undergo an instability that brings the system into an unwanted Q-switch regime. In fact it is often difficult to avoid this instability because its origin (saturable losses) is unfortunately the ingredient needed for obtaining the desired physical effect (mode-locking of ultrashort pulses). Here, we present two aspects of this problem. First we show numerically that a simple technique used for stabilizing steady states in continuous-wave lasers can be used for stabilizing the desired state (regular mode-locking) in mode-locked lasers. This technique allows an easier optimization of lasers properties (pulse duration, etc.) by allowing to work in unusual regions of parameter values. These results are in agreement with the experimental demonstration of Schibli et al. Then, we show that stabilization of the desired state is not a sufficient condition for successful control. Indeed, if the desired state coexists with another unwanted state, the state eventually reached will depend on the full history of the system, and the stabilized state can be still out of reach. We show that this problem is all the more important when limitations are imposed on the allowed pump power. From the bifurcation analysis of the system, we deduce a protocol that permit to bring the system to the stabilized state.