Achieving parabolic phase profiles in liquid crystal lenses using an analytical spiral electrode

We propose an analytical spiral electrode design for achieving a parabolic voltage distribution in liquid crystal (LC) lenses. Unlike conventional spiral designs, such as the Archimedean and Fermat spirals, the specially designed spiral electrode is derived through rigorous equation solving, enabling the precise generation of the parabolic voltage distribution. By incorporating concentric ring electrodes that extend the parabolic voltage profile across the active area, while ensuring the driving voltage stays within the material’s linear response region, we successfully realize an accurate parabolic phase profile. Experimental testing on a 50-μm-thick LC lens with a 4 mm aperture demonstrated a well-defined parabolic phase distribution, with the experimental results aligning closely with theoretical predictions, thereby confirming the design’s accuracy and effectiveness.