Shaping fractional orbital angular momentum beams through highly scattering media

Fractional orbital angular momentum (FOAM) beams possessing radially notched intensity distributions play a unique role in fields such as optical manipulation and optical communication. Due to multiple scattering, the direct transmission of FOAM beams through highly scattering media, such as thick biological tissues and fog, remains challenging, inhibiting the applications of FOAM beams behind these media. To address this issue, we propose an approach to overcome high scattering and establish FOAM beams through highly scattering media. By employing the Fourier field of the desired FOAM beam as a filtered mask in the transmission matrix-based point spread function method, the target FOAM beam is constructed through highly scattering media. Apart from shaping a series of conventional FOAM beams, various perfect FOAM beams are also generated behind highly scattering media. The notch width and topological charge of the generated FOAM beams can be continuously engineered. As expected, the size of the generated conventional FOAM beams is larger when the magnitude of the topological charge increases. In contrast, the size of the reconstructed perfect FOAM beams is independent of the topological charge. All of the experimental results and simulation results agree well with the theoretical distributions. The proposed method is expected to promote the applications of FOAM beams in highly scattering environments.