Noninterferometric Measurement of the Optical Polarization Knots and Links

Three-dimensional (3D) topological structures of optical singularities offer robust, multidimensional degrees of freedom, making them highly promising for high-capacity optical information encoding and robust data storage. However, accurately and efficiently characterizing these complex fields remains a challenge due to the stringent stability requirements of interferometry and the dynamic errors associated with mechanical polarimetry. Here, we propose and experimentally demonstrate a noninterferometric approach for the 3D topological structure reconstruction of both phase and polarization singularities. By integrating a beam displacer into a compact, common-path framework and employing an iterative phase retrieval algorithm, our method physically separates orthogonal polarization components for simultaneous data acquisition and computationally decodes the full vector field without requiring any moving parts or reference beams. We experimentally validate this approach by successfully visualizing complex 3D topological structures, including Hopf links and trefoil knots, achieving high polarimetric fidelity (Stokes parameter RMSE ∼0.03). This robust and efficient method establishes a novel solution for characterizing complex optical fields, with potential implications for optical micromanipulation, polarimetric imaging, high-capacity communications, and optical data storage.