Misaligning Cascaded Liquid Crystal Elements for Continuously Tunable Axial Spin-Dependent Splitting

Achieving continuous tunability and spin-multiplexed functionality is essential for depth-resolved imaging, yet existing approaches suffer from fixed focal lengths, transverse-plane splitting, or inability to acquire two depth planes simultaneously. Here, we propose and experimentally demonstrate a cascaded liquid crystal Pancharatnam-Berry phase system. It comprises two phase elements and a classic convex lens, which enables continuously tunable axial spin-dependent splitting via controlled lateral misalignment. A relative in-plane displacement generates a spin-dependent quadratic phase, yielding equivalent focal powers linear with displacement and opposite signs for orthogonal spins. This mechanism continuously tunes the focal lengths of left and right circularly polarized light, producing two separate foci at distinct axial positions for parallel depth acquisition. Reversing the displacement sign dynamically interchanges the two foci. Leveraging this capability, we demonstrate multiplane imaging in a single exposure, eliminating mechanical axial scanning required in traditional microscopes. An analytical model is established to quantitatively link the lateral misalignment to the two focal positions. This work establishes misalignment-enabled axial spin splitting as a compact and efficient platform for depth-resolved and spin-dependent optical systems.