Examination into the maximum rotational frequency for an in-plane switched active waveplate device

An examination of an active waveplate device using a one-dimensional model, giving numerical and analytical results, is presented. The model calculates the director and twist configuration by minimizing the free energy of the system with simple homeotropic boundary conditions. The effect of varying the in-plane electric field in both magnitude and direction is examined, and it is shown that the twist through the cell is constant in time as the field is rotated. As the electric field is rotated, the director field lags behind by an angle which increases as the frequency of the electric field rotation increases. When this angle reaches approximately π/4 the director field no longer follows the electric field in a uniform way. Using mathematical analysis it is shown that the conditions on which the director profile will fail to follow the rotating electric field depend on the frequency of electric field rotation, the magnitude of the electric field, the dielectric anisotropy and the viscosity of the liquid crystal.