Numerical study of optically induced director oscillations in nematic liquid crystals: Transition to chaos via homoclinic gluings and the role of backflow

We investigate the director oscillations of a homeotropically aligned nematic liquid crystal that are generated by cw laser radiation incident at a slightly oblique angle. The full nematodynamic equations are solved numerically, and it is shown that the inclusion of backflow leads to a qualitative change of the theoretical bifurcation scenario at moderate to high intensities. Very good correspondence is achieved with recent observations. The route to chaos via a sequence of homoclinic gluing bifurcations, whose existence was suggested by simple models, but doubted by recent calculations and experiments, is shown to exist in a parameter region unexplored by experiments.

Figure 1

Geometry of the setup: an ordinary wave incident on a cell of homeotropic nematic at a slightly oblique angle.

Figure 2

Bifurcation diagram as a function of the dimensionless intensity $\rho$ and angle of incidence $\alpha$. The lines are explained in the text. ${\rho }_{TB}=3.12,{\alpha }_{TB}=10.21°$.

Figure 3

Limit cycles at $\alpha =5°$ and various intensities: (a) $\rho =2.1$ (dashed lines) and $\rho =2.426$ (solid lines), (b) $\rho =3.0$, (c) $\rho =3.8$ (both solid and dashed lines), and (d) $\rho =4.4$.

Figure 4

Limit cycles for a $50\mu \mathrm{m}$ thick sample at $\rho =2.9$ and various angles of incidence: (a) $\alpha =10.45°$ (dashed line) and $\alpha =10.408°$ (solid line), (b) $\alpha =10.35°$ (solid line) and $\alpha =10.31°$, (dashed line), (c) $\alpha =10.3°$, and (d) $\alpha =10.25°$.