Dimensional properties of Laguerre-Gaussian vortex beams.

We derive and analyze the dimensional properties of Laguerre-Gaussian vortex beams theoretically and numerically. The analytical expressions of inner and outer radii are given out and proved to be proportional to the transverse beam size, when the topological charge remains. The ratio of the outer and inner radius only depends on the topological charge, having nothing to do with the waist radius and the propagation distance, and the ratio decreases as the topological charge increases. Using a spatial light modulator loaded with computer-generated holograms, we generate vortex beams. The experimental results are in good agreement with our numerical simulations. This research may provide useful insights into the study of the optical vortex beam and its further applications.