Cascaded chiral birefringent media enabled planar lens with programable chromatic aberration

Wavefront control is the fundamental requirement in optical informatics. Planar optics have drawn intensive attention due to the merits of compactness and light weight. However, it remains a challenge to freely manipulate the dispersion, hindering practical applications, especially in imaging. Here, we propose the concept of frequency-synthesized phase engineering to solve this problem. A phasefront-frequency matrix is properly designed to encode different spatial phases to separate frequencies, thus makes arbitrary dispersion tailoring and even frequency-separated functionalization possible. The periodically rotated director endows cholesteric liquid crystal with a spin and frequency selective reflection. Moreover, via presetting the local initial orientation of liquid crystal, geometric phase is encoded to the reflected light. We verify the proposed strategy by cascading the chiral anisotropic optical media of specifically designed helical pitches and initial director orientations. By this means, planar lenses with RGB achromatic, enhanced chromatic aberration and color routing properties are demonstrated. Inch-sized and high-efficient lenses are fabricated with low crosstalk among colors. It releases the freedom of dispersion control of planar optics, and even enables frequency decoupled phase modulations. This work brings new insights to functional planar optics and may upgrade the performance of existing optical apparatuses.