Vortex Beam Applications: Control, Detection, and Fractional Topological Charge

The English text matches the meaning of the Chinese text. The text discusses 'vortex beams', which are beams with 'orbital angular momentum' (OAM). These beams can be regulated by 'wandering perturbations' in the environment, which opens up new possibilities for optical communication. The 'topological charge' (TC) is an important factor when using vortex beams, and accurate detection of TC is required for expanding the application of these beams in non-ideal settings. The paper covers three main topics: (1) a theoretical model for controlling the OAM of vortex beams using complex 'wandering perturbations', (2) a novel method for detecting the TC of vortex beams with 'wandering perturbations' and obstacles, and (3) a method for detecting the 'fractional topological charge' (FTC) of vortex beams using a holographic phase plate. The paper provides useful information for transforming destructive 'wandering perturbations' into constructive ones in turbulent environments and has significant applications for optical communication and optical encryption based on vortex beams.