- Optically induced orientational transitions in nematic liquid crystals (2004)
- I have presented in this thesis a theoretical study of some dynamical phenomena and orientational transitions induced by intense light in homeotropically oriented nematic layers. A large number of experiments has been performed in such systems and various interesting dynamical regimes have been identified. However, systematical theories capable of describing the observed phenomena have been derived for some cases only. In other cases oversimplified models exist with limited applicability. In Chapter 2 I considered the case of a circularly polarized plane light wave incident perpendicularly on the layer. I have constructed a theory that is capable of describing the observed regimes of director motion and the transitions between them in detail. The first instability is the Freedericksz transition from the homeotropic state to a small-amplitude reoriented state with uniform director precession around the layer normal. With increasing light intensity, this state destabilizes via a supercritical Hopf bifurcation and a new frequency in the time Fourier spectra of the dynamical variables appears. This regime is quasiperiodic and corresponds to a precession and nutation of the director. As the intensity increases further, this state disappears at a certain critical value where the period of nutation becomes infinite. There a strongly hysteretic transition to a state with large reorientation occurs via a homoclinic bifurcation. The homoclinic orbit involved is of the simplest type where a limit cycle collides with a saddle point having one unstable direction. The new state corresponds to a uniform precession of the director, however, with very large period and with large reorientation. I have also investigated the influence of an additional static electric field on the dynamical scenario described above. In Chapter 3 the treatment is generalized to the case of elliptically polarized light. The complete bifurcation diagram with the light intensity and the ellipticity as control parameters has been calculated in the region where rotating states exist. I have shown that for a fairly narrow region of ellipticities close to circular polarization the first periodic rotating state loses its stability in a supercritical Hopf bifurcation. I have found that with increasing light intensity at different ellipticities different sequences of transitions all finally lead to a state with large director distortion as the intensity is increased. The nature of this largely distorted state, as well as intermediate regimes vary with ellipticity. Some of the regimes that appear at lower intensities were studied previously, both experimentally and theoretically, but a complete picture up to the largely distorted regime was missing. In the theoretical treatments developed in the Chapters above, as in all other treatments, the velocity field induced by the director motion (backflow) has been neglected. In Chapter 4 I have investigated the influence of backflow on the dynamical scenario described in Chapter 2 and have shown that the backflow leads to substantial quantitative changes. It turns out that the regime of nonuniform precession shifts to higher light intensities and exists in a larger interval. I have also found unanticipated spatial oscillations of the backflow across the layer for the state with large director distortion. This is a signature of the interference pattern of the light within the layer. Actually, in the theory presented, for the first time, a light-induced dynamical phenomenon has been derived from the full nematodynamic equations. Thus, for the first time, full quantitative comparison with experiments using a transversally extended laser light could be done. Also, in all previous theoretical treatments involving plane wave incident light, it was assumed that the director distortion does not depend on the coordinates in the plane of the layer, i.e. one dealt with a one dimensional situation. In Chapter 5 I have studied the instabilities induced by a linearly polarized ordinary light wave incident at a small oblique angle allowing for spatial variations of the director in the plane of the layer and including the case of a dye-doped nematic. It was previously known that for sufficiently small angles of incidence the homeotropic state looses stability in a stationary, homogeneous pitchfork bifurcation. I have shown that the resulting stationary distorted state looses stability via a secondary Hopf bifurcation to spatially inhomogeneous state (nonzero critical wavenumber) that leads to the formation of travelling waves in the plane of the layer. The wavelength of these waves depend on the angle of incidence and the ratios of the elastic constants. It is typically several times larger than the thickness of the layer.