Completely revealing the amplitude properties of Laguerre-Gaussian vortex beams

In this paper, the amplitude properties of the Laguerre-Gaussian (LG) vortex beams are analyzed theoretically and demonstrated experimentally. Firstly, the ring width of the LG vortex beam is almost a constant, which can be considered to be independent of the topological charge (l) and only determined by the waist radius ω(z), and its general expression is derived via investigating Lambert W function. On this basis, concise expressions for inner and outer ring radii, ratio of inner and outer ring radius, ring area and beam divergence are also given out. Moreover, modification functions are added to obtain more accurate expressions. In the experiment, a spatial light modulator is employed to generate the LG vortex beams with l = 1∼20 at ω₀= 0.3mm and ω₀=0.4mm, and the LG vortex beams with l=10 at different propagation distances. The experimental results are in good agreement with the theoretical values. This work may help researchers to better understand the LG vortex beam and provide a useful guideline for its further applications.