A variable optical device for controlling the propagation of light has a liquid crystal layer (1), electrodes (4) arranged to generate an electric field acting on the liquid crystal layer, and an electric field modulation layer (3,71) arranged between the electrodes and adjacent the liquid crystal layer for spatially modulating said electric field in a manner to control the propagation of light passing through said optical device. The electric field modulation layer has either an optical index of refraction that is essentially spatially uniform, or a polar liquid or gel, or a very high low frequency dielectric constant material having a dielectric constant greater than 20, and preferably greater than 1000. The modulation layer can have a solid body having a first low frequency dielectric constant with a shape selected to impart a desired modulation of the electric field, and a second low frequency dielectric constant material surrounding or adjacent to the solid body such that the solid body and the second material form a layer geometry.