CONTROLLING EXTENDED SYSTEMS WITH SPATIALLY FILTERED, TIME-DELAYED FEEDBACK

We investigate a control technique for spatially extended systems comb ining spatial filtering with a previously studied form of time-delay f eedback. The scheme is naturally suited to real-time control of optica l systems. We apply the control scheme to a model of a transversely ex tended semiconductor laser in which a desirable, coherent traveling-wa ve state exists, but is a member of a nowhere stable family. Our schem e stabilizes this state and directs the system towards it from realist ic, distant, and noisy initial conditions. As confirmed by numerical s imulation, a linear stability analysis about the controlled state accu rately predicts when the scheme is successful and illustrates some key features of the control including the individual merit of, and interp lay between, the spatial and temporal degrees of freedom in the contro l.