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.

In this Letter, a simple optical vortex convolution generator is proposed where a microlens array (MLA) is utilized as an optical convolution device, and a focusing lens (FL) is employed to obtain the far field, which can convert a single optical vortex into a vortex array. Further, the optical field distribution on the focal plane of the FL is theoretically analyzed and experimentally verified using three MLAs of different sizes. Moreover, in the experiments, behind the FL, the self-imaging Talbot effect of the vortex array is also observed. Meanwhile, the generation of the high-order vortex array is also investigated. This method, with a simple structure and high optical power efficiency, can generate high spatial frequency vortex arrays using devices with low spatial frequency and has excellent application prospects in the field of optical tweezers, optical communication, optical processing, etc.