Analytical study of the self-reconstruction of a Hermite non-uniformly correlated beams by an obstacle

In this study, we derived a theoretical formula to analyze the self-constructing properties of Hermite non-uniformly correlated (HNUC) beams when encountering an obstacle, focusing on intensity and coherence. Our results reveal that, despite an obstacle, the beam’s intensity distribution continues to display a significant self-focusing phenomenon. Within the focal length range, the lateral intensity distribution remains consistent with unobstructed propagation, regardless of the obstacle’s size. However, outside the self-focusing range, increasing the obstacle size leads to a decrease in the self-reconstructive capability of the intensity distribution, necessitating a longer propagation distance for recovery. Additionally, the presence of obstacles considerably impacts the coherence properties of the beams. When the obstacle is small, the degree of coherence (DOC) experiences a significant reconstructing effect. Our results have potential applications in optical tweezers, microscopy, and optical communication.