Numerical Modeling of Tunable Liquid-Crystal-Polymer-Network Lens

Abstract

A gradient polymer stabilized liquid crystal (G-PSLC) structure has recently been proposed for a tunable-focus lens application. A homogeneously-oriented nematic liquid crystal (NLC) cell, doped by a few percent of photopolymerizable monomer, is initially illuminated by a laser beam with a Gaussian spatial intensity distribution. This induces a spatially inhomogeneous polymer network in the cell. The electro-optical response of this system to a uniform electric field exhibits an inhomogeneous circularly symmetric pattern. The radial distribution of the effective refractive index possesses a maximum in the center of the beam. This cell acts as a positive focal length lens on the extraordinary polarized light component passing through it. The profile of the refractive index in the plane of the cell can be changed by varying the voltage across the cell. Thus the focal length of the lens changes with voltage. Here we present a numerical approach to our earlier theoretical model. The model describes the dependence of the focal length of the G-PSLC lens on applied voltage. The new feature of the model is that we have used several trial functions for the form of the polymer profile. The director profile in the cell was determined as a function of voltage. The model qualitatively agrees with the experimental data. The results can be applied to develop G-PSLC lenses with no moving parts and permit electro-optical zooming.