Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films

Abstract

An s-polarized laser beam that impinges at small incidence angle on a homeotropically aligned nematic liquid crystal produces very interesting nonlinear phenomena. In this paper, we show that, due to the symmetry of the system, a cascade of successive homoclinic gluing bifurcations is responsible for the transition towards a stochastic regime in the experiment. We compare the experimental results with a model describing a sequence of gluing bifurcations.

A Phenomenological Approach to Normal Form Modeling: A Case Study in Laser Induced Nematodynamics

“…More than the choice of pedagogical point of view, it seems to us that the example that we treat (the laser induced nematodynamics experiment studied in [11], [30], and [8]) is enough of a challenge to allow us to claim the value of the approach on the basis of the success on this case.…”

“…A similar experimental setting was theoretically investigated in [15], that followed former experimental studies of such system (see for instance [7,10,32] and references therein). Then the results in [30] were revisited in [8] in view of Demeter & Kramer [1999]. Gluing bifurcations (which were first systematically studied in [14], following the work in [3] and [41]) were recognized by Demeter and Kramer in the simplest non-trivial version of their Galerkin type truncation model, resulting from the coupling of the nematodynamics with the Maxwell equations [15].…”

“…As we shall demonstrate on the basis of the experimental signals, this is not the proper symmetry to model the experiment (at least if one restricts oneself to the three main degrees of freedom). The signal tells us that it is the central symmetry that holds true in the experimental setting used in [8,11,30]. We thus propose to model the experiments in [8,11,30] using a new approach, the approach being in fact the main content of the paper.…”

“…The signal tells us that it is the central symmetry that holds true in the experimental setting used in [8,11,30]. We thus propose to model the experiments in [8,11,30] using a new approach, the approach being in fact the main content of the paper. These experiences are collectively called hereafter the laser induced nematodynamics experiment: we understand that other experimental settings could be implemented, but only the one used in these three papers will be considered here.…”

“…The time series observed in the work reported in [11], [30], and [8] for each value of the control parameter most often correspond to a quantity Θ(t), which is the azimuthal angle of the major axis of the ellipse that represents the polarization state of the light trasmitted by the sample. The definition of Θ in terms of two of the Stokes parameters is mostly irrelevant for the rest of the discussion, but we have recalled it in Fig.…”