Fast generation of perfect vortex and vector beams through highly scattering media via discrete convolution-based vector point-spread-function engineering

Recent advancements in optics have demonstrated that it is possible to take advantage of the feasibility of leveraging wavefront shaping to focus and image through highly scattering media (HSM). Herein, we report a method to rapidly focus perfect vortex beams (PVBs) and perfect vector vortex beams (PVVBs) through the HSM via discrete convolution-based vector point-spread-function (DC-VPSF) engineering. In our method, a vector transmission matrix (VTM)-based operator can be calculated by executing a convolution operation between the measured full VTM and the conjugate of a discrete VPSF sampled from a pre-defined spatial domain mask. The input field can be obtained by performing digital optical phase conjugation on the VTM-based operator. Then the desired output field (that is the discrete VPSF) can be generated through the HSM. Experimentally, the PVBs with different topological charges and identical optical ring sizes are generated through the HSM based on our method. Further, PVBs with controllable polarization states and a high peak-to-background ratio (PBR) are also generated after the HSM by introducing polarizers and wave plates before the recording plane. In addition, our method has advantages in fast calculating the required input field and improving the PBR of the focused light through the HSM compared with the general point-spread-function engineering. Finally, the experimentally generated PVVBs demonstrate the ability to tailor the focused light with more complex polarization distribution through the HSM. Our results may contribute to generalizing the convolution concepts for multiple degrees of freedom wavefront control and provide an effective idea for optical micromanipulation and imaging through scattering media.