Propagation properties of a partially coherent Laguerre–Gaussian beam with multiple off-axis vortex phases

In this paper, a new theoretical model of a partially coherent Laguerre–Gaussian (LG) beam carrying multiple off-axis vortex phases was established. The evolution properties of the focused intensity of the beam after passing through a thin lens were theoretically studied, and then the modulation effect of multiple off-axis vortex phases on the beam with multiring structured intensity was explored. The results indicate that the multiple off-axis vortex phases can reconstruct the multiring structured intensity within the LG beam, thus generating a structured intensity with multilobe and multiring patterns. What is more, the intensity distribution of the lobes between two adjacent rings is complementary, and its number is related to the number and topological charge of off-axis vortex phases. However, with a decrease in the coherence, such a multilobe and multiring structured intensity distribution disappears, gradually evolves into a polygonal flat-topped distribution, and finally degenerates into a quasi-Gaussian distribution. This work demonstrates the effective regulation of multiple off-axis vortex phases on a beam with a multiring structured intensity and indicates that regulating the multiple off-axis vortices provides an additional degree of freedom for optical field modulation, which will have potential applications in the fields of optical micromanipulation and optical information storage.