Director-density coupling theory of the acousto-optic effect in nematic liquid crystals

Experiments with nematic liquid crystals have proved that an ultrasonic wave exerts a torque on the liquid-crystal molecules, causing a change in its optical properties (acousto-optic effect). In this work we report a theoretical study on the theory proposed by Selinger et al. [Phys. Rev. E 66, 051708 (2002).] and, independently, by Boneto et al. [Chem. Phys. Lett. 361, 237 (2002).] for this effect. We solved exactly the Euler-Lagrange equation, which determines the equilibrium configuration of the director profile. The liquid-crystal director is also calculated in powers of the acoustic intensity and a comparison of this expansion with the solution in a closed form is given. We show the existence of minimizers that does not satisfy the Euler-Lagrange equation and report the possibility of observing a Fréedericksz-type transition. Finally, a possibility of controlling light by ultrasonic wave is also discussed in the limit of low acoustic intensity.