Control and forcing of spontaneous optical patterns

Erik Benkler

Institute of Applied Physics, Darmstadt University of Technology,
Hochschulstraße 4A, 64289 Darmstadt, Germany

Abstract: Driven, spatially extended nonlinear systems play an important role in optics. Many of them exhibit unwanted spatial or spatio-temporal instabilities, e.g. beam filamentation. On the other hand, a well directed selection of system-inherent patterns would be desirable both from a basic point of view and for possible applications in information processing. We investigated methods to manipulate the output state of an optical pattern forming system. A single feedback system with a liquid crystal light valve as optical nonlinearity has been used. Pattern formation in this system is already quite well understood.

There are two ways to modify the output state of a pattern forming system: Control or forcing. In the control method, the actual output state of the system is analysed. The difference between the actual state and the target pattern of the control constitutes the control signal. This control signal in turn is fed back to the system. In turn, the output state is moved towards the desired state. Since the system is spatially extended, the actual state, the target state, and the control signal are spatially extended, too. The used control method is the 2D spatial analogon of a classical feedback control in dynamic systems without spatial degrees of freedom. In contrast to purely temporal systems, the two-dimensionality of the system leads to a much larger manifold from which the solutions are to be stabilized, e.g. there can be patterns with the same periodicity, but different symmetries or orientations.

A very compact generation of the control signal is possible in Fourier space and allows, after transformation to real space, a manipulation of the entire transversal plane. Optics provides all means to implement such a highly parallel control scheme experimentally. We verified that the control signal approaches zero when the target state is reached. For this reason, the solutions of the system are not altered, but only their stability. By stabilization of 'hidden' unstable solutions we were able to access their bifurcation diagrams for a comparison with theory. By means of this purely spatial control we even removed spatio-temporal disorder up to a certain degree.

Another approach to influence the output state of a pattern forming system is to force it to a certain state. For this, we added a patterned light field with a certain strength to the input field, regardless of the actual output state. We found that if the periodicity of the forcing signal coincides with unstable wavenumbers of the free running system, it locks to the forcing pattern. Otherwise a competition between patterns of different periodicities induces complex spatio-temporal disorder.