Transverse pattern formation and its control in photorefractive optics

A wealth of periodic transverse patterns is observed in nonlinear optical, photorefractive single-feedback systems. It is the extension of a photorefractive medium in the direction of propagation of the laser beam that allows for the formation of stable hexagons, squares, rhombuses and dodecagons above the first bifurcation of the system. In this article we review the formation of these periodic patterns and present linear and nonlinear stability analyses that predict the type of pattern to appear. Amplitude equations for the interactions of unstable sidebands are introduced. We compare numerical and experimental results on two-dimensional transverse pattern formation. We present control methods for the invasive and non-invasive manipulation of different pattern states using a Fourier filtering technique.