Engineering wavefronts with machine learned structured polarization

Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping the polarization introduces a novel framework that permits the spatial modulation of polarization to control wavefront propagation and resulting amplitude distributions. We develop two distinct computational phase retrieval approaches for calculating the required polarization transformations and experimentally validate these. The first method extends the established Gerchberg-Saxton algorithm, while the second employs machine learning optimization to determine optimal polarization patterns. By implementing both amplitude and polarization control simultaneously using a single polarization mask, our approach significantly reduces system complexity compared to traditional methods. Our experimental results demonstrate the potential of polarization-based wavefront shaping as an efficient alternative to conventional techniques, paving the way for applications in optical manipulation and imaging.