Geometrical analysis of the electro-optical effect in nematic droplets

Using the boundary-layer approach, we study the radial-axial transition in a nematic sphere in the presence of an external field. We calculate analytically an asymptotic expression for the nematic configuration subject to an external low frequency field. Then, we consider an incident plane wave crossing a nematic droplet immersed in an isotropic matrix under the presence of a low frequency field. We calculate the ray trajectories within the optical limit for various values of the external field and find the ray deviation as a function of the incident position parametrized by the magnitude of the field.