Two-beam energy exchange in a hybrid photorefractive-flexoelectric liquid-crystal cell

We develop a semiquantitative theory to describe the experimentally observed energy gain when two light beams intersect in hybrid organic-inorganic photorefractives. These systems consist of a nematic liquid-crystal (LC) layer placed between two photorefractive windows. A periodic space-charge field is induced by the interfering light beams in the photorefractive windows. The field penetrates into the LC, interacting with the nematic director and giving rise to a diffraction grating. LC flexoelectricity is the principal physical mechanism driving the grating structure. Each light beam diffracts from the induced grating, leading to an apparent energy gain and loss within each beam. The LC optics is described in the Bragg regime. In the theory the exponential gain coefficient is a product of a beam interference term, a flexoelectricity term and a space-charge term. The theory has been compared with results of an experimental study on hybrid cells filled with the LC mixture TL 205. Experimentally the energy gain is maximal at much lower grating wave numbers than is predicted by naive theory. However, if the director reorientation is cubic rather than linear in the space-charge field term, then good agreement between theory and experiment can be achieved using only a single fitting parameter. We provide a semiquantitative argument to justify this nonlinearity in terms of electric-field-induced local phase separation between different components of the liquid crystal.