Cholesteric helix: topological problem, photonics and electro-optics

Using numerical simulations and the results of our experiments we discuss the behaviour of a defect-free cholesteric liquid crystal in rather a strong electric field. The smooth helix unwinding predicted by de Gennes (Solid State Commun. 1968, 6, 163,) occurs under the thermodynamic equilibrium conditions and can easily proceed with the assistance of multiple defects. The defect-free helix in the field strictly perpendicular to the helical axis cannot be unwound for topological reasons. The field deforms the helix without a change of its period and induces higher harmonics of the helical structure. Due to the latter, the shape of the Bragg photonic stop-band changes and a second-order photonic band is observed in the optical transmission. Moreover, novel laser effects are predicted by modelling for the dye-doped, distorted cholesteric structure. The same field-induced anharmonicity results in a strong change of the polarisation state of the beam passing the helical structure along its axis. Due to fast relaxation of the higher harmonics, the switching time of the devices using the corresponding electro-optical effect (called in-plane switching) can be improved significantly. This is shown both experimentally and by numerical calculations.