Polarization grating based on liquid crystals doped with ferroelectric nanoparticles

We present a theoretical model in the framework of elastic continuum theory to describe the behaviour of a liquid crystalline host doped with ferroelectric nanoparticles acting as a liquid crystal polarization grating device. The effect of ferroelectric impurity dopants in liquid crystals and the Freedericksz transition is studied. We obtain the critical thickness and voltages of the system and find that, as in the case of pure liquid crystal devices, the critical voltages for weak anchoring conditions would be lower than those in a strong anchoring case. We also investigate the dynamic behaviour of the system and obtain the switching on and off times for the nano-doped cells with strong and weak anchoring conditions on the surfaces. The effects of the flow are excluded in our calculations. The findings show that the rise time of the suspension is lower than that of the pure liquid crystal, and switching times will be prolonged when the anchoring strength is reduced. Our results are consistent with existing experimental reports and may be useful for many applications in the industry. Obviously, electrically control is definitely fundamental in the operation of many liquid crystal devices such as displays, beam steering devices, and liquid crystal modulators.