On‐Demand Longitudinal Transformations of Light Beams via an Amplitude‐Phase‐Decoupled Pancharatnam‐Berry Phase Element

ABSTRACT To overcome the inherent phase‐only modulation limitation of conventional Pancharatnam‐Berry (PB) phase elements, we propose a checkerboard‐encoded design that enables simultaneous amplitude and phase modulation through PB phase engineering. This single‐element platform directly generates polarization‐rotating beams with continuously varying polarization angles along the propagation axis, eliminating traditional dynamic phase requirements. By strategically combining the proposed element with a liquid crystal q ‐plate and waveplates, we demonstrate on‐demand longitudinal transformations of polarization states and higher‐order Poincaré sphere beams. Significantly, we achieve, for the first time to our knowledge, the controllable propagation‐transformed optical skyrmions over multiple cycles, whose topological textures periodically evolve with propagation distance. This amplitude‐phase decoupling mechanism and the compatible solution for various longitudinal transformations significantly advance the development of a universal theoretical framework for longitudinal manipulation of light beams.