Patterns, fronts and structures in a Liquid-Crystal-Light-Valve with optical feedback

Abstract The basic mechanisms of optical pattern formation are reviewed, with particular reference to a system based on a Liquid-Crystal-Light-Valve with optical feedback. The system is described in different configurations, corresponding to the experiments that have led to the most fascinating observations, such as the optical crystals and quasi-crystals, the geometrical frustration leading to domain coexistence and competition, the super-lattices characterized by couplings of different wave vectors at different lengths and orientations. The purely diffractive and purely interferential cases are discussed separately, in such a way to outline the main features of the two types of optical feedback and to give a better understanding of the complex behaviors observed when both are simultaneously present. The role of nonlocality in the optical feedback loop, such as rotation or drift, is put into evidence, showing how this parameter drives the symmetry selection in the pattern-forming process. The linear stability analysis for pattern formation is given with the most relevant analytical results, whereas the nonlinear behavior of pattern dynamics are described and discussed with reference to the experimental findings. In particular, one-dimensional experiments are reported, which allow a direct comparison with models for the secondary instabilities of patterns. For the diffractive case, it is shown that optical wave patterns undergo a destabilization process that is a dissipative generalization of the classical three-wave interaction in nonlinear optics. For the interferential case, an analysis of the transition to spatio-temporal chaos is reported. Finally, a more fundamental approach to the liquid crystal physics is presented, showing how the Freedericksz transition becomes a first-order one in the presence of a light-driven feedback. In the corresponding experimental regime, instead of patterns there are fronts connecting different metastable states. When the bistability coexists with pattern formation, due to the diffractive feedback, stable localized structures can be excited in the system, either in the form of isolated or bound states. Highly ordered clusters of localized structures may also be obtained by choosing a close recurrence for the feedback rotation angle. Recent results on the dynamics of localized structures are reported, showing a complex radial and azimuthal motion along concentric rings, as selected by the diffractive feedback.