Fast reconstruction of scalar and vector polymorphic beams through strong scattering media

The retrieval of structured light fields with tailorable shapes and multiple degrees of freedom through strongly scattering media (SSM) is inherently hindered by multiple scattering effects. Here, we demonstrate the efficient reconstruction of both scalar and vector polymorphic beams (SPBs and VPBs) after propagating through SSM via discrete convolution-based vector point-spread-function (DC-VPSF) engineering. In our method, the required input field is calculated by performing digital optical phase conjugation on a vector transmission matrix (VTM)-based operator, which is derived from the convolution between the measured VTM and the conjugate of a discrete VPSF sampled from the Fourier field of a predefined polymorphic beam. Using this approach, SPBs and VPBs with tunable phase distributions (uniform and non-uniform), controllable topological charges, and adjustable polarization states are successfully generated through SSM. Additionally, focused VPBs with linear polarization tangential to the tailored curves are demonstrated through the SSM. Experimental results are in good agreement with the simulation results. Compared with VTM-based VPSF engineering, our method achieves higher intensity uniformity along the tailored curves and significantly reduces the computational time required for input field calculation. This work enables efficient customized SPBs and VPBs in disordered environments, with promising applications in optical micromanipulation and deep-tissue imaging.