Multi-depth switching by triple wavefront modulation of quarter-waveplate geometric phase lenses for vergence-accommodation-matching extended reality.

We present a novel approach to resolving the vergence-accommodation conflict (VAC) in extended reality (XR) optics by introducing a quarter-waveplate (QWP) geometric phase lens (GPL) capable of triple wavefront modulation-focusing, defocusing, and non-modulating at infinity. This polarization-driven behavior is interpreted using contour trajectories on the Poincaré sphere and compared against conventional half-waveplate (HWP) GPLs. Leveraging this property, we propose a bi-stacked QWP GPL module that enables nine distinct varifocal states through polarization-controlled input selection and output filtering. In contrast, HWP-based modules under equivalent stacking conditions are limited to four focal states. The QWP GPL module supports a compact varifocal system spanning a continuous depth range from 24.27 cm to infinity, with a 0.3-diopter interval aligned with the human visual comfort zone. Importantly, the number of representable focal depths scales as 3n for n stacked layers, offering a (1.5)n-fold improvement over the 2n scaling of HWP systems. This enables finer depth transitions using fewer lens units while retaining both compactness and optical modularity, establishing a depth-switchable imaging platform that enhances visual comfort and depth fidelity in next-generation XR display systems.