Shaping vector fields in three dimensions by random Fourier phase-only encoding

Simultaneously controlling the spatial distribution of multiple parameters of a light field in a three-dimensional (3D) space is highly desirable because of its prominent applications in the areas of optical imaging, microscopy, and manipulation. Phase-only encoding techniques that use a phase-only computer-generated hologram (CGH) to reshape and efficiently reconstruct target fields have fostered substantial interests. In this paper, we propose a convenient encoding method to construct vector fields with spatially structured multiple parameters in a 3D space by integrating the Fourier phase-only encoding technique into a modified Sagnac polarization conversion system. Without spatial filtering, various vector fields are constructed instantly at the image plane. Furthermore, utilizing a macro-pixel encoding approach, we demonstrate the possibility of a simultaneous and an independent construction of multiple vector fields in a 3D space. This method can also benefit the design of a metasurface to implement a polarization hologram.