Stabilization, Selection, and Tracking of Unstable Patterns by Fourier Space Techniques

A new method for the stabilization and manipulation of unstable states of a pattern forming system is presented. The technique is applied to an optical system where unstable homogeneous solutions, rolls, squares, hexagons, and honeycombs are all stabilized and tracked. The control consists of a small spatial modulation to the input pump field, which is derived from the Fourier transform of the output electric field. Once stabilization is achieved, the control vanishes. The method can be used as a numerical tool for pattern forming systems to determine the existence and stability of solutions.