Pattern formation steered by front dynamics in liquid crystals

Abstract

This thesis is devoted to the experimental characterization of nonlinear waves connecting two steady states in liquid crystals cells out of equilibrium. This characterization was achieved by the study of two experimental setups: Liquid crystal light valve with optical feedback and photoisomerization process in dye-doped liquid crystal cells. In the first chapter, we present the theoretical and experimental framework required to understand the present thesis. In the second chapter, it is presented the study of pattern formation induced by photoisomerization process of liquid crystal cell with dopants. Experimentally, for planar cells, photoisomerization process induces a nematic isotropic phase transition. For twisted cells, the light beam induces the emergence of stripe patterns. Theoretically, the phase transition and the emergence of stripe patterns are described by an adequate proposed model. In the third chapter, we investigate the front propagation between an unstable state and a stable one in a forced spatial medium. Unexpectedly, the average speed of fronts decreases when the strength of the forcing increases. Theoretically, an amplitude equation allows the characterization of the front speed as a function of the forcing parameters. Likewise, from the amplitude equation, we derive an equation for the front position, which corresponds to a prototype model of a ratchet dynamic. In the fourth chapter, we study the front propagation into a stable state in the context of pattern forming systems. Experimentally, based on on a dye-doped liquid crystal cell, it is observed the gradual emergence of concentric rings that propagate from the center. Concentric rings are an unstable state and the nematic phase is a stable one. Therefore, we observe the propagation of an unstable state into a stable one. Theoretically, we reveal the necessary features to observe the propagation of an unstable state into a stable one. To observe these intriguing phenomena, the system under study needs a half stable equilibrium and a stable state with higher energy. In the fifth chapter, it is investigated the non-variational effects in the modification of the front propagation speed. The liquid crystal light valve with optical feedback allows us to modify the free diffraction length, which in turn, controls the intensity of non-variational effects. Experimentally, we observe that the speed changes from a plateau to a growing regime, while varying the free diffraction length. Indeed, the behavior exhibited by the front speed corresponds to a pulled-pushed transition. Theoretically, an adequate amplitude equation is derived, which allows us to reveal a pulled-pushed transition. To our knowledge, this is the first time this transition is experimentally reported and studied. In chapter six, we present and analyze experimental difficulties and some related perspectives. Finally, in chapter seven, we summarize the conclusions of the thesis.