Cylindrical vector (CV) beams have attracted increasing interest due to their particular properties and their applications in optical imaging, optical manipulation, and light–matter interactions. However, it is challenging to construct CV beams through highly anisotropic scattering media (HASM), such as thick biological tissue, posing a barrier to the applications of CV beams that involve HASM. Here, we present a scheme to construct CV beams beyond high scattering that only requires a single scalar transmission matrix (TM) calibration and manipulation of the spatial degrees of freedom of the scalar input field. Assisted by a radial polarization converter (S-waveplate) and a polarizer, the scheme enables one to obtain the correct incident wavefront for the creation of CV beams through HASM with only one single scalar TM calibration. Compared to the existing method, this user-friendly approach is fast and simple in terms of the optical implements and computations. Both radially and azimuthally polarized beams are experimentally constructed through a ZnO scattering layer to demonstrate the viability of the method. Arbitrarily generalized CV beams and arrays of CV beams are also created through the HASM to further prove the flexibility of the method. We believe this work may pave the way for applications of CV beams that involve a highly anisotropic scattering environment.

An algorithm is proposed for the fast reconstruction of off-axis digital holograms based on a combination of complex encoding (CE) and spatial multiplexing (SM). In this algorithm, every two off-axis holograms recorded in sequence are first assembled into a CE hologram using the CE method, and then four of the CE holograms are again encoded into one complex spatial multiplexing (CSM) hologram based on the SM algorithm. It is demonstrated that the eight holograms encoded into such one CSM hologram can be quickly reconstructed by performing a two-dimensional (2D) Fourier transform (FT) on the CSM hologram. Using this method, the eight 2D FTs required for the reconstruction of the eight holograms in the conventional spatial filtering methods can be simplified to a process with only one 2D FT, which can largely improve the computation efficiency with the resolution of the reconstructed images nearly unchanged.

A setup for the generation of arbitrary vector beams is proposed. The setup mainly consists of a spatial light modulator (SLM), an angle-adjustable polarization beam splitter modulator, and a spatial filtering imaging system. Compared with the system using a birefringent beam splitter with a non-adjustable splitting angle, the polarization splitting angle of the improved setup can be adjusted by slightly rotating the related mirrors, which will bring more convenience when different wavelengths and different pixel sizes of SLMs are involved. The experimental results also demonstrate that the setup possesses a good polarization-selective imaging ability, which reveals that the setup may also be useful in polarization-selective spatial filtering imaging and polarization-encoded encryption.