Liquid crystal
Liquid crystal lenses converge or diverge the incident light by adjusting the refractive index of liquid crystal layer with applied voltage or temperature. Generally, the liquid crystal lenses generate a parabolic refractive index distribution by arranging molecular orientations. Therefore, a plane wave is reshaped into a parabolic wavefront by a liquid crystal lens. The focal length of liquid crystal lenses could be continuously tunable when the external electric field can be properly tuned. Liquid crystal lenses are a kind of adaptive optics. Imaging system can be benefited with focusing correction, image plane adjustment, or changing the range of depth-of-field or depth of focus. Liquid crystal lens is one of the candidates to develop vision correction device for myopia and presbyopia eyes (e.g., tunable eyeglass and smart contact lenses). Being an optical phase modulator, a liquid crystal lens feature space-variant optical path length (i.e., optical path length as the function of its pupil coordinate). In different imaging system, the required function of optical path length varies from one to another. For example, to converge a plane wave into a diffraction limited spot, for a physically-planar liquid crystal structure, the refractive index of liquid crystal layer should be spherical or paraboloidal under paraxial approximation. As for projecting images or sensing objects, it may be expected to have the liquid crystal lens with aspheric distribution of optical path length across its aperture of interest. Liquid crystal lenses with electrically tunable refractive index (by addressing the different magnitude of electric field on liquid crystal layer) have potentials to achieve arbitrary function of optical path length for modulating incoming wavefront; current liquid crystal freeform optical elements were extended from liquid crystal lens with same optical mechanisms. The applications of liquid crystals lenses includes pico-projectors, prescriptions lenses (eyeglasses or contact lenses), smart phone camera, augmented reality, virtual reality etc.