Divergence of optical vortex beams

We show, both theoretically and experimentally, that the propagation of optical vortices in free space can be analysed by using the width ($w(z)$) of the host Gaussian beam and the inner and outer radii of the vortex beam at the source plane ($z=0$) as defined in \textit{Optics Letters \textbf{39,} 4364-4367 (2014)}. We also studied the divergence of vortex beams, considered as the rate of change of inner or outer radius with the propagation distance, and found that it varies with the order in the same way as that of the inner and outer radii at zero propagation distance. These results may be useful in designing optical fibers for orbital angular momentum modes that play a crucial role in quantum communication.