Light-induced dynamics in nematic liquid crystals—a fascinating world of complex nonlinear phenomena

Intense laser light traversing a thin layer of nematic liquid crystal is an example of a simple, easy to realise physical system, that shows very complex behaviour. Light can turn the optical axis of this uniaxial medium while propagating through it, and the dynamical behaviour that results ranges from simple orientational instabilities, through low-dimensional chaotic behaviour, to spatiotemporal pattern formation. In this paper, we review recent advances in the theoretical description of the complex phenomena that light can induce in nematic liquid crystals. We discuss the various approximations made in the models, their range of applicability, and contrast their results with experimental observations. In particular, we discuss the achievements of the plane wave approximation in various geometries, and examine how the numerous bifurcation scenarios calculated from the models can be used to interpret observations. We treat with special emphasis the results achieved in the description of the strongly nonlinear regime, where experiments have revealed interesting bifurcations and chaotic behaviour. We also discuss the mostly open problems of transverse pattern formation and the effects that can be attributed to the finite cross-section of the laser beam.