A liquid crystal geometric phase hyperbolic lens with a positive focal length for arbitrary circularly polarized incidence

This paper presents the design and experimental validation of a liquid crystal geometric phase hyperbolic lens (LCHL) with positive focal lengths for arbitrary circularly polarized light. Utilizing Pancharatnam-Berry phase modulation, the lens enables isotropic focusing for both left- and right-handed circular polarization. We fabricated and characterized two lenses with different focal lengths, and their diffraction patterns were analyzed experimentally. The results exhibit strong agreement with theoretical simulations, highlighting the lens's capability for precise optical field modulation. The proposed LCHL demonstrates significant potential for detecting weak polarization states, making it a promising tool for advanced applications in biomedical imaging, optical vortex generation, and multifocal optical systems.