Construction of double-ring perfect vortex beams through strongly scattering media with full vector transmission matrix-based vector point spread function engineering.

Double-ring perfect vortex beams (DR-PVBs), characterized by their unique double-ring radii that are independent of topological charges, have significant potential for applications in optical manipulation and communication. However, their wavefronts experience significant distortion when transmitted through strongly scattering media (SSM). In this study, we propose a method to reconstruct DR-PVBs through SSM using full vector transmission matrix-based vector point spread function (VTM-VPSF) engineering. Our approach involves computing a VTM-based operator by performing spatial filtering on each component of the full VTM using a carefully designed vector filtering mask in the Fourier domain. Next, two orthogonal input wavefronts are generated using digital optical phase conjugation (DOPC) on the VTM-based operator. The DR-PVBs with independently controllable topological charge, radius, amplitude, and polarization states for each ring are then reconstructed through the SSM. Additionally, petal-like intensity patterns can be formed when the inner and outer rings with different topological charges are adjusted to the same size. This work provides a promising approach for enhancing optical manipulation and communication of DR-PVBs in scattering environments.