Propagation Properties of Optical Beams with Multi-OAM Modes: Effect of the Off-Axis Vortex

As one of the promising techniques to improve the spectral efficiency of the network in the Internet of Things (IoT), the orbital-angular-momentum (OAM) multiplexing optical wireless communication has been studied a lot. In the optical beams with multi-OAM modes, the vortices deviating from the beam center sometimes cannot be avoidable, and they will strongly influence the transverse patterns during the beam propagation. In this article, the expressions of optical beams with off-axis vortices are derived in a commonly used focusing system, and the effect of the vortices deviating from the beam center on the propagation properties of the optical beam is discussed. We find that the number of the bright spots in the transverse patterns of the superposition of two OAM modes with off-axis vortices is not always equal to the absolute value of the mode difference which is observed in the field with only on-axis vortices. The bright spot can also be found to rotate during the beam propagating, and as the number of the modes increases in the overlapping, the superposition patterns become more complicated and these patterns can be adjusted by the off-axis distance and the topological charge of the vortices. Our result will be helpful in developing the network of the IoT.