Generation of perfect optical vortex arrays by an optical pen

Recently, perfect optical vortexes (POVs) have attracted substantial attention, because they have an orbital angular momentum (OAM) and the beam diameter is independent of the topological charges. There are numerous innovative results that have been found by modulating the POV optical field. However, methods for controlling the arbitrary parameters of POV are lacking. In this paper, we use the optical pen to overcome this problem. The optical pen is a high-precision optical field modulation method construction based on the relationship between the optical path difference and phase. Based on this method, we have achieved POV arrays with controllable arbitrary parameters in free space, including the spatial position, numbers, topological charges, beam diameter, and amplitude. This work can be applied not only in the fields of optical tweezers, particle manipulation, and super-resolution microscopic imaging, but also will promote the development of optical communication, quantum information coding, and so on.