Virtual Polarization Elements for Spatially Varying Jones Matrix Transformations on a Free-Space Plane

Precise control over the spatial and polarization properties of light is foundational for advanced photonic systems, yet most conventional approaches are constrained to local, contact-based manipulation at physical interfaces. To overcome these constraints, here we introduce a fundamentally new framework for action-at-a-distance polarization control using virtual polarization elements (VPEs). VPEs apply prescribed local Jones matrix transformations between an input field at the modulation plane and an output field at a remote, contactless free-space plane, enabling polarization transformations without physical interaction at the target. We demonstrate VPEs, in metasurface platform, realizing diverse polarization functionalities, including single-function VPEs for circular polarizer, linear polarizer, half-wave plate, and quarter-wave plate operations; a multifunction VPE simultaneously implementing distinct polarization functions with arbitrary phase difference across spatial regions; and vortex waveplate configurations generating structured vector vortex beams. By decoupling the modulation and target planes, VPEs open new opportunities for remote polarization shaping, non-invasive beam engineering, and contactless polarization manipulation in challenging optical environments.