Optically induced Freedericksz transition and bistability in a nematic liquid crystal

An Euler equation, consistent with Maxwell's equations, for describing the optically induced spatial reorientation of the director of a homeotropically oriented nematic liquid crystal is obtained for the case of normal incidence. The exact solution describing the orientation of the director is obtained. By examining the maximum deformation angle near the threshold, the threshold intensity and the criterion for the physical parameters that indicate whether the transition is first- or second-order at the threshold are obtained. The hysteresis accompanying the first-order Freedericksz transition is discussed. By choosing a compound (PAA, $p$-azoxyanisole) with suitable material parameters from known nematic liquid crystals, an experiment is proposed to observe, for the first time, a first-order Freedericksz transition in nematic liquid crystals. The Zel'dovich approach [Sov. Phys.-JETP 54, 32 (1981)] based on the geometrical-optics approximation is shown to be internally inconsistent and also inconsistent with the geometrical-optics approximation. The Euler equation using a self-consistent geometrical-optics approximation is also obtained, and turns out to be identical to our exact Euler equation, but different from the infinite-plane-wave approximation used by Durbin et al. [Phys. Rev. Lett. 47, 1411 (1981)]. Detailed comparisons between our approach and the Durbin approach are made. The dynamics of the transition are discussed and an approximate solution is given. The transient responses to the laser switch-on and switch-off are shown to have exponential time dependence. Finally, the effects of surface interactions on the transition are discussed and the exact solution is given. The procedure for determining the threshold, the saturation, and the parallel-state-maintenance intensities is given. We also discuss the first-order transition and propose experimental methods manifesting the effects of surface interaction. The criterion for the transition to be first order at any intensity is given.