Planar liquid crystal optics for simultaneously surface displaying and diffraction-limited focusing

Planar optical elements have attracted widespread attentions because of their precise light modulation. Liquid crystals (LCs) are well known for their applications in the current displaying field, and show great potential in planar optical elements with the development and innovation of LC micro-operation technology. However, previous researches on LC elements mainly involved only one type of optical manipulation, which inevitably limited the functional diversity. In this work, we propose a multifunctional LC element which integrates the surface display into a binary-phase focusing lens by controlling the complex amplitude of the incident light. The light modulation of the anisotropic LC molecule satisfies a sinusoidal variation, which can be regarded as the combination of a continuous amplitude modulation and a binary phase modulation. The element with millimeter size is then fabricated, and the experimental measurements agree well with our design with a high-definition surface pattern and high-quality optical focusing/imaging performance. Furthermore, as the complex amplitude modulation changes from sine to cosine function after rotating the sample by 45°, a bifocal lens with two different focal lengths is also demonstrated. We expect the proposed multifunctional LC elements can find applications in information multiplexing, image displaying, etc.