Over the past few years, different techniques have been developed to realize flat optical components. This makes it possible to replace traditional lenses or prisms with much thinner alternatives. One novel approach is to vary the optical axis in a thin film. Such a film can be realized with liquid crystal that is oriented by the illumination with ultra-violet light and may then be polymerized. In case of optical components for visible light, such a film is only 2 micrometers thick which is much less than the millimeter thicknesses in conventional optics. By now, high quality components have been demonstrated by different research groups and several components are used in commercial applications. One of the limitations of the technology is that the variation of the optical axis over the surface cannot be realized within one micrometer. However, rapid variations (within one micrometer) are very interesting to obtain new functionalities of the flat optical components. In my research proposal, I will use chiral liquid crystal, which is a material that spontaneously forms a helical structure with period below one micrometer. By combining this material with a fast orientation scheme, it should be possible to overcome the resolution limitation. The aim in my PhD is to have lateral variations of the optical axis with a period in the order of 400 nm. This result can lead to a whole new set of optical components, such as microscope lenses or light couplers for waveguides.