Theoretical analyses of the electric field control of focal length in a gradient polymer stabilized liquid crystal lens

In this paper we study the process of network formation, director reorientation upon applied voltage and electro-optical properties of the gradient polymer stabilized liquid crystal (G-PSLC) lens. Using classical scheme of radical photopolymerization the profile of the polymer network concentration is obtained. Minimizing the total free energy functional we find the director profile in the cell subject to externally applied electric field. We suppose that polymer network creates additional torque onto LC director forcing it to preserve planar orientation competing with applied voltage. Thus, inhomogeneous director reorientation profile arises despite the use of uniform electrodes. As a result inhomogeneous refractive index is obtained, which generates the lens with focal length dependant from applied voltage. Obtained results can be applied to develop G-PSLC lenses that have no moving parts and allow the electro-optical zooming.