Relationship between lens properties and director orientation in a liquid crystal lens

Lenses with a homogeneously aligned liquid crystal having a Fresnel structure have been prepared by using a nematic with a positive dielectric anisotropy. Their focal length can be varied continuously from the value f_e for an extraordinary ray to f _o for an ordinary ray by applying an electric field across the lens cell. The effective refractive index of the lens where the director is aligned perpendicular to the grooves of the Fresnel structure becomes smaller than when the director is aligned parallel to the grooves. Then the liquid crystal lens has a characteristic aberration which could not be observed in a conventional glass lens; that is, the focal length of the lens becomes different according to the incidence of rays on the different parts of the lens. The properties of the liquid crystal lens can be improved by making the director orientation axially symmetric, in the form of a concentric circle, but the polarization component rotated 90° from the incident extraordinary ray appears when the voltage is applied across the lens cell. This phenomenon is discussed in relation to the optical properties and the director orientation in a liquid crystal prism cell.