Analysis on characteristic of Laguerre-Gaussian beams with topological charges of arithmetic progression

With the development of vortex beams with spiral phase front, the composite vortex beams, which can provide a variety of information and phase structure, have attracted considerable attention in the fields of free-space optical (FSO) communication and particle manipulation. In this research, the theoretical formula for the superposition of vortex beams with topological charges of arithmetic progression (the tolerance is Delta) is presented. The distribution characteristics of phase singularities of composite vortex beams generated by coaxial superposition are analyzed, and the number and position of angular solutions are solved. By changing the topological charges of vortex beams, it can be found that the intensity distribution of the composite vortex beam changes regularly. The number of outside bright spots is equal to Delta, and the number of dark spots is equal to Delta x (n-1). According to the rule of the number and location characteristics of bright and dark spots, it can also be used to detect the topological charge number of the composite vortex beam. When the composite vortex beam is used for information transmission, multiple channels of information can be transmitted simultaneously to increase channel capacity. This study provides a favorable basis for the superposition of vortex beams and a new method for the detection of vortex beams.