Restriction on orbital angular momentum distribution: a role of media in vortex beams propagation

The vortex beam carrying single orbital angular momentum (OAM) propagating through a medium with a certain transmission function is investigated. We show that the OAM mode weights in the output OAM spectrum involve two factors: the radial distribution of output beam power and the proposed restriction-characterized function. Based on the restriction-characterized function, we show that the OAM mode weights can only vary in a limited range. We analyze the relationship between the radial distribution of the output beam power and the OAM mode weights in the output OAM spectrum. Finally, our theoretical analysis is illustrated numerically with the cases of eccentric circular aperture and atmospheric turbulence in a weak fluctuation regime. These results provide new insights into the characterization of the OAM spectrum and may find applications for fields involving OAM, such as an OAM-based optical communication link and object detection.